在将钢结构锚固到混凝土时，施工项目中通常使用锚栓或化学锚栓以确保结构稳定性和承载能力。该模型在 IDEA StatiCa Detail 软件中进行分析。
Widget #NaN: widget_content_image_collapse_item
Name: IDEA StatiCa Detail
ID: b3110a59-a173-4dde-81ac-e4d2ed554ff5
Show Raw Data
{
"title": {
"name": "Title",
"type": "text",
"value": "IDEA StatiCa Detail"
},
"description": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Description",
"type": "rich_text",
"value": "<p>最适用于含 D 区、开洞和加腋的构件，以及一般形状的二维构件 </p>\n<ul>\n <li>非线性 CSFM（协调应力场法）方法 </li>\n <li>混凝土及所有钢筋的应力和应变</li>\n <li>裂缝宽度校核</li>\n <li>应力限值校核</li>\n <li>非线性挠度</li>\n <li>从 Beam 软件导入数据</li>\n</ul>"
},
"link_text": {
"name": "Link text",
"type": "text",
"value": "了解更多关于计算的内容"
},
"link_url": {
"name": "Link URL",
"type": "text",
"value": ""
},
"content_item_link": {
"name": "Content item link",
"type": "modular_content",
"value": [
"detail_theoretical_background"
],
"linkedItems": [
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "IDEA StatiCa Detail – 混凝土不连续区的结构设计"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Structural design of concrete members in IDEA StatiCa Detail.png",
"description": null,
"type": "image/png",
"size": 163091,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7885cdc1-8e4a-4744-834e-72ea84ebbaf4/Structural%20design%20of%20concrete%20members%20in%20IDEA%20StatiCa%20Detail.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [],
"linkedItemCodenames": [
"n02b04ae1_9ac2_0186_8a2e_afbfaac3c39e",
"theoretical_background_detail___general",
"fd74de0b_9b01_01f9_b7d3_91842b4e64f4",
"theoretical_background_detail___main_assumptions_a",
"n1b6b2998_a82a_0102_1bb4_e052b35ff829",
"theoretical_background_detail___general___reinforc",
"n33af2c10_291e_0187_4660_55b94dbc3824",
"theoretical_background_detail___general___finite_e",
"n2d4304a1_f345_0104_32bf_85315c48d5cd",
"theoretical_background_detail___supports_and_load_",
"b6ecb5e3_7093_01ba_9dde_25d8369a02f7",
"theoretical_background_detail___load_transfer_at_t",
"n46b4e3db_3dd5_0178_937b_4e69c5404313",
"theoretical_background_detail___geometric_modifica",
"e2bcc72e_78c5_0163_a169_dc9ed613e170",
"theoretical_background_detail___finite_element_typ",
"n8a7103fc_e2a4_016b_6e78_a6c6e6a4807f",
"theoretical_background_detail___meshing",
"n7295ffdb_585b_01c8_eeea_cbfc7526af76",
"theoretical_background_detail___solution_method_an",
"d4d41655_a8d9_018a_7277_dad106e33f39",
"theoretical_background_detail___presentation_of_re",
"n805f2d39_5e1d_0196_07ec_d526e6056d4c",
"theoretical_background_detail___general___verifica",
"n34484ce7_0966_01b0_4e4e_ced1381a2b83",
"theoretical_background_detail___material_models__e",
"n87402a88_f6a7_01e2_3c54_6a74bb42f492",
"theoretical_background_detail___safety_factors",
"fc5356e8_ad66_019d_500e_56112b2c54e1",
"theoretical_background_detail___ultimate_limit_sta",
"n4ffa73af_7903_018b_f050_5cb47586f489",
"theoretical_background_detail___partially_loaded_a",
"c0faeafd_fe53_0187_955b_d143d9265810",
"theoretical_background_detail___serviceability_lim",
"e023fb1d_6a30_01c3_526e_d8c8d1a6b0e5",
"theoretical_background_detail___material_models__a",
"fc85da82_0693_016a_b193_f8a961ac8919",
"theoretical_background_detail___factors___aci",
"f654617f_d523_0106_0e28_6bbb16cb93f5",
"theoretical_background_detail___strength_analysis_",
"df2d07b6_cabe_0102_4254_6e44efaefb9b",
"theoretical_background_detail___bearing_and_anchor",
"ca9b6d78_562b_01cd_b7c1_e9e14bcade98",
"theoretical_background_detail___serviceability_ver",
"n718b61d6_ca9a_01c4_c411_608ecc9bfe42",
"theoretical_background_detail___material_models__a_0b99d24",
"n1e0b8118_0346_01fc_5843_6a60b409c862",
"theoretical_background_detail___resistance_and_loa",
"n835a26bd_d5f1_0140_4fe1_9ae73d901010",
"theoretical_background_detail___strength_limit_sta",
"a29abd54_d307_013b_44ed_56d973e7aacc",
"theoretical_background_detail___bearing_and_anchor_69cbe39",
"d19c5c7a_4da5_01be_7a24_1918c7d60c76",
"theoretical_background_detail___service_limit_stat",
"n83eff71e_cb6d_0152_d7f9_4621fe4095f0",
"theoretical_background_detail___material_models__a_b7035a6",
"n3541764a_859d_01a8_0078_115c1a96acda",
"theoretical_background_detail___stress_reduction_a",
"n10a5f687_325c_014e_ea85_7f516e5dd6e4",
"theoretical_background_detail___strength_analysis__8bc3bfe",
"ec38c193_dd6d_018f_8d40_071dc9fd107a",
"theoretical_background_detail___serviceability_ver_77b5f2c",
"n6aab19fe_22df_01fc_a1c7_3d0f7ddd9aab",
"theoretical_background_detail___material_models__c",
"n3131c97b_f469_015c_eb8e_4ec8df85f4fb",
"theoretical_background_detail___resistance_and_loa_3be42f4",
"cd09877f_7f1a_014d_d93d_f401610d7808",
"theoretical_background_detail___strength_limit_sta_fde100c",
"e26de44a_0888_0142_95ac_ff57c9eb6c2d",
"theoretical_background_detail___bearing_and_anchor_bfd09ef",
"n5c09040b_e0fb_01f6_3ab5_39d6d1e375b0",
"theoretical_background_detail___service_limit_stat_00c850c",
"n1ecc3d2d_b87a_01f1_a493_9161e2eae77d",
"prestressing_in_detail___model_description__body_",
"aec1d9ba_c119_0122_d551_4e09e764c5f9"
],
"linkedItems": [
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "1.1 General introduction"
},
"id": {
"name": "ID",
"type": "text",
"value": "general-introduction"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n02b04ae1_9ac2_0186_8a2e_afbfaac3c39e",
"collection": "default",
"id": "02b04ae1-9ac2-0186-8a2e-afbfaac3c39e",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "02b04ae1-9ac2-0186-8a2e-afbfaac3c39e",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "1.1 混凝土细部结构设计概述"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "General introduction for the structural design of concrete details.png",
"description": null,
"type": "image/png",
"size": 151821,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/918cd80e-191a-437a-8d6a-d2f8c7f688c2/General%20introduction%20for%20the%20structural%20design%20of%20concrete%20details.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "874c8092-fb41-44c6-804d-52727044d470",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc96c2fd-25aa-43fd-b6d5-556b5242b9cf/Discontinuity%20regions.png",
"height": 939,
"width": 1394
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>混凝土构件的设计与评估通常在截面（一维单元）或点（二维单元）层面进行。该方法在所有结构设计标准中均有描述，例如（EN 1992-1-1 或 ACI 318-19），并广泛应用于日常结构工程实践。然而，人们并不总是了解或遵守这样一点：该方法仅适用于满足平截面应变分布的 Bernoulli-Navier 假设的区域（称为 B 区）。不满足该假设的位置称为不连续区或扰动区（D 区）。一维单元的 B 区和 D 区示例见（图 1）。这些区域包括支承区、集中荷载作用部位、截面突变处、洞口等。在进行混凝土结构设计时，我们还会遇到许多其他 D 区，例如墙、桥梁横隔板、牛腿等。 </p>\n<figure data-asset-id=\"874c8092-fb41-44c6-804d-52727044d470\" data-image-id=\"874c8092-fb41-44c6-804d-52727044d470\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc96c2fd-25aa-43fd-b6d5-556b5242b9cf/Discontinuity%20regions.png\" data-asset-id=\"874c8092-fb41-44c6-804d-52727044d470\" data-image-id=\"874c8092-fb41-44c6-804d-52727044d470\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 1\\qquad Discontinuity regions (Navrátil et al. 2017)}}}\\]</em></p>\n<p>过去，不连续区的设计采用半经验设计规则。幸运的是，在过去几十年中，这些规则已在很大程度上被拉压杆模型（Schlaich 等，1987）和应力场（Marti 1985）所取代，二者已纳入现行设计规范，并被设计人员广泛使用。这些模型在力学上是自洽的，是功能强大的工具。需要注意的是，应力场通常可以是连续的或不连续的，而拉压杆模型是不连续应力场的一种特例。</p>\n<p>尽管过去几十年来计算工具不断发展，拉压杆模型本质上仍以手算为主。由于需要迭代，并且需要考虑多个荷载工况，将其应用于实际结构既繁琐又耗时。此外，该方法不适用于验证正常使用准则（变形、裂缝宽度等）。</p>\n<p>结构工程师对可靠、快速的 D 区设计工具的需求，促成了新的协调应力场法的开发。这是一种计算机辅助应力场设计方法，可对承受面内荷载的结构混凝土构件进行自动设计与评估。</p>\n<p>协调应力场法（CSFM）是一种基于有限元的连续应力场分析方法，在经典应力场解的基础上补充了运动学考虑，即对整个结构的应变状态进行评估。因此，可以根据横向应变状态自动计算混凝土的有效抗压强度，其方式与考虑压力软化的压力场分析 （Vecchio 和 Collins 1986；Kaufmann 和 Marti 1998）以及 EPSF 方法（Fernández Ruiz 和 Muttoni 2007）类似。此外，CSFM 考虑了拉力刚化，为单元提供真实的刚度，并涵盖了以往方法未能一致处理的所有设计规范规定（包括正常使用和变形能力方面）。CSFM 采用设计标准中给出的混凝土和钢筋的常用单轴本构关系。这些关系在设计阶段是已知的，因此可以使用分项系数法。因此，设计人员无需提供非线性有限元分析通常所需的、往往带有任意性的额外材料特性，使该方法非常适用于工程实践。</p>\n<p>为了促进结构工程师使用计算机辅助应力场，这些方法应在用户友好的软件环境中实现。为此，CSFM 已在 <em>IDEA StatiCa Detail</em> 中实现；这是一款新的用户友好型商业软件，由苏黎世联邦理工学院（ETH Zurich）与软件公司 IDEA StatiCa 在 DR-Design Eurostars-10571 项目框架内共同开发。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"detail_theoretical_background",
"theoretical_background_detail___general___reinforc",
"dimenzovani_zb_konstrukci_podle_csfm",
"prestressed_i_section"
],
"linkedItems": [
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "1.3 钢筋设计工具"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Reinforcement structural design.png",
"description": null,
"type": "image/png",
"size": 61765,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8d4e1ab7-8d44-491e-873f-8ea42d620992/Reinforcement%20structural%20design.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9b0c4840-5a55-46f3-95ba-86a9baabbf0c/Model%20used%20to%20illustrate%20the%20use%20of%20the%20reinforcement%20design%20tools.png",
"height": 603,
"width": 864
},
{
"description": null,
"imageId": "f6c14a09-4d2b-40e6-ac82-5ff08c10439a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ea7896d1-8276-4d08-b811-066cca73b455/Results%20from%20the%20linear%20analysis%20tool.jpg",
"height": 315,
"width": 1177
},
{
"description": null,
"imageId": "f4f47d5e-3196-4a88-96ca-7162b0c8c271",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f4d37064-76c7-4413-b1aa-87455a32852c/Results%20from%20the%20topology%20optimization%201.jpg",
"height": 320,
"width": 1179
},
{
"description": null,
"imageId": "7ddd1329-64ea-4a47-be5d-64994439e729",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d81f2841-8274-414a-8f30-b55427216169/Results%20from%20the%20topology%20optimization%202.png",
"height": 315,
"width": 1179
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "csfm_concrete_verification",
"linkId": "42ce7f6b-6491-4224-a01e-c4c0072ed1cd",
"urlSlug": "design-your-structural-concrete-details-with-confidence",
"type": "blog_post"
},
{
"codename": "topology_optimization_for_reinforced_concrete",
"linkId": "decdf07d-a46b-5894-9a22-793436e318c7",
"urlSlug": "topology-optimization-for-reinforced-concrete",
"type": "blog_post"
}
],
"name": "Content",
"type": "rich_text",
"value": "<h3>工作流程与目标</h3>\n<p><a data-item-id=\"42ce7f6b-6491-4224-a01e-c4c0072ed1cd\" href=\"\">CSFM（协调应力场法）</a>中钢筋设计工具的目标是帮助设计人员高效确定钢筋的位置和所需用量。以下工具可在此过程中为用户提供辅助和指导：线性计算和<a data-item-id=\"decdf07d-a46b-5894-9a22-793436e318c7\" href=\"\">拓扑优化</a>。</p>\n<p>钢筋设计工具采用的本构模型比结构最终验算所用的模型更为简化。因此，此步骤中的钢筋定义应视为预设计，需在最终验算步骤中确认或调整。图 3 所示模型为一根变截面简支梁的一端，承受均布荷载，下文将以该模型说明各种钢筋设计工具的使用。</p>\n<figure data-asset-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\" data-image-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9b0c4840-5a55-46f3-95ba-86a9baabbf0c/Model%20used%20to%20illustrate%20the%20use%20of%20the%20reinforcement%20design%20tools.png\" data-asset-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\" data-image-id=\"eee2b9e4-83cd-4b9c-98e7-f575b2ff9cff\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 3\\qquad Model used to illustrate the use of the reinforcement design tools.}}}\\]</em></p>\n<h3>线性分析</h3>\n<p>线性分析采用线弹性材料特性，并忽略混凝土区域内的钢筋。因此，该计算速度非常快，可初步判断拉力区和压力区的位置。此类计算的示例见图 4。</p>\n<figure data-asset-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\" data-image-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ea7896d1-8276-4d08-b811-066cca73b455/Results%20from%20the%20linear%20analysis%20tool.jpg\" data-asset-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\" data-image-id=\"f6c14a09-4d2b-40e6-ac82-5ff08c10439a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 4\\qquad Results from the linear analysis tool for defining reinforcement layout}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(red: areas in compression, blue: areas in tension).}}}\\]</em></p>\n<h3>拓扑优化</h3>\n<p>拓扑优化是一种方法，旨在针对特定荷载工况，在给定体积内寻找材料的最优分布。<em>Idea StatiCa Detail</em> 中实现的拓扑优化采用线性有限元模型。每个有限单元的相对密度可在 0 至 100 % 之间取值，表示所用材料的相对数量。这些单元密度即为优化问题中的优化参数。如果材料分布使系统的总应变能最小，则认为该分布对于给定荷载组合是最优的。根据定义，最优分布同时也是在给定荷载下刚度最大的几何形状。</p>\n<p>迭代优化过程从均匀的密度分布开始。<em> </em>计算针对多个总体积分数（20%、40%、60% 和 80%）进行，用户可据此选择最实用的结果。所得形状由包含压杆和拉杆的桁架组成，代表给定荷载工况下的最优形状（图 5）。</p>\n<figure data-asset-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\" data-image-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f4d37064-76c7-4413-b1aa-87455a32852c/Results%20from%20the%20topology%20optimization%201.jpg\" data-asset-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\" data-image-id=\"f4f47d5e-3196-4a88-96ca-7162b0c8c271\" alt=\"\"></figure>\n<figure data-asset-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\" data-image-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d81f2841-8274-414a-8f30-b55427216169/Results%20from%20the%20topology%20optimization%202.png\" data-asset-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\" data-image-id=\"7ddd1329-64ea-4a47-be5d-64994439e729\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 5\\qquad Results from the topology optimization design tool with 20\\% and 40\\% effective volume}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(red: areas in compression, blue: areas in tension).}}}\\]</em></p>\n<p><br></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general",
"theoretical_background_detail___general___finite_e",
"dimenzovani_zb_konstrukci_podle_csfm"
],
"linkedItems": [
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.1 有限元实现简介"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Finite element implementation in IDEA StatiCa Detail.png",
"description": null,
"type": "image/png",
"size": 481046,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/0388381a-906d-48f1-a5b2-ce00188fded9/Finite%20element%20implementation%20in%20IDEA%20StatiCa%20Detail.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "9e86fe68-36a5-433d-9451-40d2b5078b86",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png",
"height": 562,
"width": 847
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "untitled_content_item_a11adc2",
"linkId": "a11adc2d-9c84-4667-8061-600660e1ad87",
"urlSlug": "concrete-walls-challenge-or-routine",
"type": "blog_post"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>CSFM 考虑混凝土中的连续应力场（二维有限单元），并辅以代表钢筋的离散“杆”单元（一维有限单元）。因此，钢筋并非弥散嵌入混凝土二维有限单元中，而是被显式建模并与其连接。计算模型中采用平面应力状态。</p>\n<figure data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3f70008c-0c34-4dbe-8219-4d8aa7079bb5/Visualization%20of%20the%20calculation%20model.png\" data-asset-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" data-image-id=\"9e86fe68-36a5-433d-9451-40d2b5078b86\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 6\\qquad Visualization of the calculation model of a structural element (trimmed beam) in Idea StatiCa Detail.}}}\\]</em></p>\n<p>既可以对整片<a data-item-id=\"a11adc2d-9c84-4667-8061-600660e1ad87\" href=\"\">墙</a>和整根梁进行建模，也可以对梁的局部细部（孤立的不连续区，也称为截断端）进行建模。对于墙和整根梁，必须以使结构（外部）静定（静定结构）或超静定（静不定结构）的方式定义支座。梁截断端处的荷载传递通过特殊的圣维南传递区引入，从而确保在所分析的细部区域内获得符合实际的应力分布。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "3.1 极限状态和裂缝宽度计算"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Structural element verification in IDEA StatiCa Detail.png",
"description": null,
"type": "image/png",
"size": 174643,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3ab2c71e-930c-4975-88fe-72502fad03d5/Structural%20element%20verification%20in%20IDEA%20StatiCa%20Detail.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "8c27dc0f-1cfe-4026-bbf5-4b51604c3558",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG",
"height": 55,
"width": 421
}
],
"linkedItemCodenames": [
"theoretical_background_detail___crack_width_calcul"
],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>使用 CSFM 对结构进行评估时,需进行两种不同的分析:一种针对正常使用极限状态荷载组合,另一种针对承载能力极限状态荷载组合。正常使用分析假定构件的极限性能满足要求,且在正常使用荷载水平下材料不会达到屈服条件。这种方法允许在正常使用分析中采用简化的本构模型(混凝土应力-应变曲线采用线性段),以提高数值稳定性和计算速度。因此,建议采用下文所述的工作流程,即首先进行承载能力极限状态分析。</p>\n<h3>承载能力极限状态分析</h3>\n<p>各设计规范要求的不同验算,均基于模型提供的直接结果进行评估。承载能力极限状态验算包括混凝土强度、钢筋强度和锚固(粘结剪应力)验算。</p>\n<p>为确保结构构件的设计高效合理,强烈建议先进行初步分析,并考虑以下步骤:</p>\n<ul>\n <li>选取若干最不利的荷载组合。</li>\n <li>仅计算承载能力极限状态(ULS)荷载组合。</li>\n <li>使用粗网格(在 Setup 中增大默认网格尺寸的倍数(图 19))。</li>\n</ul>\n<figure data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aabe4d74-d599-4c9d-a62d-8e448a66360a/Mesh%20multiplier.PNG\" data-asset-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" data-image-id=\"8c27dc0f-1cfe-4026-bbf5-4b51604c3558\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 19\\qquad Mesh multiplier.}}}\\]</em></p>\n<p>此类模型计算速度很快,设计人员可以高效地检查结构构件的构造细节,并重新运行分析,直至最不利荷载组合下的所有验算要求均得到满足。一旦该初步分析的所有验算要求均得到满足,建议纳入完整的承载能力极限状态荷载组合,并采用精细网格尺寸(即程序推荐的网格尺寸)。用户可通过倍数调整网格尺寸,倍数取值范围为 0.5 至 5(图 19)。</p>\n<p>基本结果和验算(应力、应变和承载比(即计算值/规范限值),以及混凝土构件的主应力方向)通过不同的图形显示,其中压力通常以红色表示,拉力以蓝色表示。可以突出显示整个结构的全局最小值和最大值,以及每个用户自定义部分的最小值和最大值。在程序的单独选项卡中,可以显示高级结果,例如张量值、结构变形,以及用于计算钢筋拉力刚化的配筋率(有效配筋率和几何配筋率)。此外,还可以显示所选组合或荷载工况的荷载和反力。</p>\n<h3>正常使用极限状态分析</h3>\n<p>正常使用极限状态评估包括应力限值、裂缝宽度和挠度限值验算。混凝土和钢筋中的应力按照适用规范进行校核,方式与承载能力极限状态类似。</p>\n<p>正常使用分析对承载能力极限状态分析所用的本构模型作了一定简化。分析假定为完全粘结,即在正常使用状态下不验算锚固长度。此外,混凝土受压应力-应变曲线的塑性段被忽略,而弹性段为线性且无限延伸。这些简化提高了数值稳定性和计算速度,并且只要正常使用状态下材料的合成应力限值明显低于其屈服点(如标准所要求),就不会降低解的通用性。因此,正常使用分析所采用的简化模型仅在所有验算要求均得到满足时才有效。</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___crack_width_calcul\"></object>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___finite_e",
"theoretical_background_detail___finite_element_typ",
"general_description_of_sls_results_in_detail_appli"
],
"linkedItems": [
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.5 有限单元类型"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "finite elements.png",
"description": null,
"type": "image/png",
"size": 219517,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/48fa7d1e-4cae-4946-924d-ec19029fa362/finite%20elements.png",
"width": 1230,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "03fd72f4-b362-492a-8885-349785eaa70a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png",
"height": 449,
"width": 1177
},
{
"description": null,
"imageId": "a031a0ff-a5a7-4a37-b59f-cb1c408f080b",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG",
"height": 707,
"width": 1773
},
{
"description": null,
"imageId": "6e05f6d3-2d4c-4c6c-90f0-89e34117415c",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG",
"height": 702,
"width": 1792
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>非线性（非弹性）有限单元分析模型由多种有限单元类型构成，分别用于模拟混凝土、钢筋以及二者之间的粘结。混凝土单元和钢筋单元首先独立划分网格，然后通过多点约束（MPC 单元）相互连接。这使钢筋可以相对于混凝土处于任意位置。如需计算锚固长度验算，则在钢筋与 MPC 单元之间插入粘结单元和锚固端弹簧单元。</p>\n<figure data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/511cc4d5-618a-4542-ac53-52a29549070f/Finite%20element%20model.png\" data-asset-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" data-image-id=\"03fd72f4-b362-492a-8885-349785eaa70a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 13\\qquad Finite element model: reinforcement elements mapped to concrete mesh using MPC elements and bond elements.}}}\\]</em></p>\n<h3>混凝土</h3>\n<p>混凝土采用四边形和三角形壳单元 CQUAD4 和 CTRIA3 进行模拟，分别由四个或三个节点定义。这些单元仅假定存在平面应力，即不考虑 z 方向的应力或应变。</p>\n<p>每个单元有四个或三个积分点，位于约 1/4 单元尺寸处。在每个单元的每个积分点处，计算主应变方向 α<sub>1</sub>、α<sub>2</sub>。在这两个方向上，根据所指定的混凝土应力-应变图（见图 2）评估主应力 σ<em><sub>c</sub></em><sub>1</sub>、σ<em><sub>c</sub></em><sub>2</sub> 以及刚度 <em>E</em><sub>1</sub>、<em>E</em><sub>2</sub>。需要注意的是，压力软化效应会使主压应力方向的性能与另一主方向的实际状态相互耦合。</p>\n<h3>钢筋</h3>\n<p>钢筋采用仅具有轴向刚度的两节点一维“杆”单元（CROD）进行模拟。这些单元与专门开发的“粘结”单元相连，用于模拟钢筋与周围混凝土之间的滑移行为。这些粘结单元随后通过 MPC（多点约束）单元与代表混凝土的网格相连。这种方法允许钢筋和混凝土独立划分网格，同时在后续保证二者之间的连接。</p>\n<h3>粘结单元</h3>\n<p>锚固长度通过在有限单元模型中引入混凝土单元（二维）与钢筋单元（一维）之间的粘结剪应力来验算。为此，开发了“粘结”有限单元类型。</p>\n<p>粘结单元的定义与壳单元（CQUAD4）类似。它同样由 4 个节点定义，但与壳单元不同的是，它仅在上部两个节点与下部两个节点之间具有非零的剪切刚度。在模型中，上部节点与代表钢筋的单元相连，下部节点与代表混凝土的单元相连。该单元的性能由粘结应力 τ<em><sub>b</sub></em> 描述，它是上、下节点之间滑移 δ<em><sub>u</sub></em> 的双线性函数，见图 14。</p>\n<figure data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1cc20fd2-92d7-42dc-ac17-24f318cbd45c/Bond.PNG\" data-asset-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" data-image-id=\"a031a0ff-a5a7-4a37-b59f-cb1c408f080b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 14\\qquad (a) conceptual illustration of the deformation of a bond element; (b) a stress-deformation function.}}}\\]</em></p>\n<p><br></p>\n<p>粘结-滑移关系的弹性刚度模量 <em>G</em><em><sub>b</sub></em> 定义如下：</p>\n<p>\\[G_b = k_g \\cdot \\frac{E_c}{Ø}\\]</p>\n<p>其中：</p>\n<p><em>k</em><em><sub>g</sub></em> 取决于钢筋表面的系数（默认 <em>k</em><em><sub>g</sub></em><sub> </sub>= 0.2）</p>\n<p><em>E</em><em><sub>c</sub></em> 混凝土弹性模量（按 EN 取 <em>E</em><em><sub>cm</sub></em>）</p>\n<p>Ø 钢筋直径</p>\n<p>锚固长度验算采用所选设计规范 EN 1992-1-1 或 ACI 318-19 中给出的极限粘结剪应力设计值（系数化取值）<em>f</em><em><sub>bd</sub></em>。塑性段的强化默认按 <em>G</em><em><sub>b</sub></em>/10<sup>5</sup> 计算。</p>\n<h3>锚固弹簧</h3>\n<p>按照设计规范的规定为钢筋设置锚固端（即弯折、弯钩、环圈等），可使钢筋的基本锚固长度（<em>l</em><em><sub>b,net</sub></em>）按一定系数 β 折减（下文称为“锚固系数”）。锚固长度设计值（<em>l</em><em><sub>b</sub></em>）按下式计算：</p>\n<p>\\[l_b = \\left(1 - \\beta\\right)l_{b,net}\\]</p>\n<p><em>l</em><em><sub>b,net</sub></em> 的预期折减相当于钢筋端部按锚固折减系数所给定的最大承载力百分比被激活，如图 15a 所示。</p>\n<figure data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/748b5346-4251-4154-b923-919c94d0c6d0/Model%20for%20the%20reduction%20of%20the%20anchorage%20length.PNG\" data-asset-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" data-image-id=\"6e05f6d3-2d4c-4c6c-90f0-89e34117415c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 15\\qquad Model for the reduction of the anchorage length:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) anchorage force along the anchorage length of the reinforcing bar; (b) slip-anchorage force constitutive relationship.}}}\\]</em></p>\n<p>锚固长度的折减通过在钢筋端部设置弹簧单元（图 15）纳入有限单元模型，该弹簧单元由图 15b 所示的本构模型定义。该弹簧传递的最大力（<em>F</em><em><sub>au</sub></em>）为：</p>\n<p>\\[F_{au} = \\beta \\cdot A_s \\cdot f_{yd}\\]</p>\n<p>其中：</p>\n<p><em>β</em> 基于锚固类型的锚固系数，</p>\n<p><em>A</em><em><sub>s</sub></em> 钢筋的截面面积，</p>\n<p><em>f</em><em><sub>yd</sub></em><em> </em> 钢筋屈服强度的设计值（系数化取值）。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-5-finite-element-types"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"finite-element-types\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:29</li>\n <li>de-DE: Translated on 27.10.2026 14:08</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:04</li>\n <li>fr-FR: Translated on 27.10.2026 14:50</li>\n <li>hu-HU: Translated on 27.10.2026 18:08</li>\n <li>it-IT: Translated on 27.10.2026 15:28</li>\n <li>ja-JP: Translated on 26.10.2026 11:12</li>\n <li>ko-KR: Translated on 26.10.2026 11:11</li>\n <li>nl-NL: Translated on 27.10.2026 16:42</li>\n <li>pl-PL: Translated on 27.10.2026 19:35</li>\n <li>pt-PT: Translated on 27.10.2026 17:28</li>\n <li>ro-RO: Translated on 27.10.2026 18:52</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:10</li>\n <li>tr-TR: Translated on 26.10.2026 11:11</li>\n <li>vi-VN: Translated on 26.10.2026 11:11</li>\n <li>zh-CN: Translated on 27.10.2026 20:18</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___finite_element_typ",
"collection": "default",
"id": "85424e98-41cd-4bdd-a978-e4b540a10be5",
"language": "zh-CN",
"lastModified": "2026-10-27T19:18:13.2360986Z",
"name": "Theoretical background Detail - Finite element types",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7000
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "3-1-limit-states-and-crack-width-calculation"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"3-1-limit-states-and-crack-width-calculation\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "IDEA StatiCa Detail 中的结构构件验算"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "使用 CSFM 对结构进行评估时,需进行两种不同的分析:一种针对正常使用极限状态荷载组合,另一种针对承载能力极限状态荷载组合。IDEA StatiCa Detail - 一款结构工程设计软件。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:30</li>\n <li>de-DE: Translated on 27.10.2026 14:10</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:06</li>\n <li>fr-FR: Translated on 27.10.2026 14:52</li>\n <li>hu-HU: Translated on 27.10.2026 18:10</li>\n <li>it-IT: Translated on 27.10.2026 15:29</li>\n <li>ja-JP: Translated on 26.10.2026 11:24</li>\n <li>ko-KR: Translated on 26.10.2026 11:23</li>\n <li>nl-NL: Translated on 27.10.2026 16:44</li>\n <li>pl-PL: Translated on 27.10.2026 19:37</li>\n <li>pt-PT: Translated on 27.10.2026 17:29</li>\n <li>ro-RO: Translated on 27.10.2026 18:54</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:23</li>\n <li>tr-TR: Translated on 26.10.2026 11:24</li>\n <li>vi-VN: Translated on 26.10.2026 11:23</li>\n <li>zh-CN: Translated on 27.10.2026 20:19</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___general___verifica",
"collection": "default",
"id": "b42f7f51-b2ee-464e-bfeb-5170776cbd10",
"language": "zh-CN",
"lastModified": "2026-10-27T19:19:22.5205658Z",
"name": "Theoretical background Detail - General - Verification of the structural element",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "finite-element-implementation"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"finite-element-implementation\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "IDEA StatiCa Detail 中的有限元实现"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "IDEA StatiCa Detail 中有限元实现的详细说明。IDEA StatiCa Detail——一款混凝土设计软件。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:27</li>\n <li>de-DE: Translated on 27.10.2026 14:07</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:03</li>\n <li>fr-FR: Translated on 27.10.2026 14:49</li>\n <li>hu-HU: Translated on 27.10.2026 18:06</li>\n <li>it-IT: Translated on 27.10.2026 15:26</li>\n <li>ja-JP: Translated on 26.10.2026 10:57</li>\n <li>ko-KR: Translated on 26.10.2026 10:56</li>\n <li>nl-NL: Translated on 27.10.2026 16:41</li>\n <li>pl-PL: Translated on 27.10.2026 19:33</li>\n <li>pt-PT: Translated on 27.10.2026 17:26</li>\n <li>ro-RO: Translated on 27.10.2026 18:50</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 10:56</li>\n <li>tr-TR: Translated on 26.10.2026 10:57</li>\n <li>vi-VN: Translated on 26.10.2026 10:57</li>\n <li>zh-CN: Translated on 27.10.2026 20:16</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___general___finite_e",
"collection": "default",
"id": "1638f9e0-9e47-421b-9191-15d040e77c8a",
"language": "zh-CN",
"lastModified": "2026-10-27T19:16:51.217186Z",
"name": "Theoretical background Detail - General - Finite element implementation",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7200
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-reinforcement-design"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"2-reinforcement-design\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "结构钢筋设计"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "IDEA StatiCa Detail 混凝土钢筋结构设计的理论背景。IDEA StatiCa Detail - 混凝土设计软件。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:27</li>\n <li>de-DE: Translated on 27.10.2026 14:06</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:03</li>\n <li>fr-FR: Translated on 27.10.2026 14:48</li>\n <li>hu-HU: Translated on 27.10.2026 18:06</li>\n <li>it-IT: Translated on 27.10.2026 15:26</li>\n <li>ja-JP: Translated on 26.10.2026 10:53</li>\n <li>ko-KR: Translated on 26.10.2026 10:53</li>\n <li>nl-NL: Translated on 27.10.2026 16:40</li>\n <li>pl-PL: Translated on 27.10.2026 19:33</li>\n <li>pt-PT: Translated on 27.10.2026 17:26</li>\n <li>ro-RO: Translated on 27.10.2026 18:50</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 10:52</li>\n <li>tr-TR: Translated on 26.10.2026 10:53</li>\n <li>vi-VN: Translated on 26.10.2026 10:53</li>\n <li>zh-CN: Translated on 27.10.2026 20:16</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___general___reinforc",
"collection": "default",
"id": "0e906322-2262-4075-a13c-2f864a41b7ee",
"language": "zh-CN",
"lastModified": "2026-10-27T19:16:32.1251309Z",
"name": "Theoretical background Detail - General - Reinforcement design",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "CSFM",
"codename": "csfm"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7300
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "1-1-general-introduction-for-the-structural-design-of-concrete-details"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"general-introduction-for-the-structural-design-of-concrete-details\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "混凝土细部结构设计概述"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "IDEA StatiCa Detail 高级混凝土细部结构设计理论背景。采用 CSFM（协调应力场法）的混凝土构件结构设计。IDEA StatiCa Detail——混凝土设计软件。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:26</li>\n <li>de-DE: Translated on 27.10.2026 14:05</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:01</li>\n <li>fr-FR: Translated on 27.10.2026 14:47</li>\n <li>hu-HU: Translated on 27.10.2026 18:05</li>\n <li>it-IT: Translated on 27.10.2026 15:25</li>\n <li>ja-JP: Translated on 26.10.2026 10:44</li>\n <li>ko-KR: Language translation error (when inserting into Kontent.ai)</li>\n <li>nl-NL: Translated on 27.10.2026 16:39</li>\n <li>pl-PL: Translated on 27.10.2026 19:32</li>\n <li>pt-PT: Translated on 27.10.2026 17:25</li>\n <li>ro-RO: Translated on 27.10.2026 18:49</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Language translation error (when inserting into Kontent.ai)</li>\n <li>tr-TR: Language translation error (when inserting into Kontent.ai)</li>\n <li>vi-VN: Language translation error (when inserting into Kontent.ai)</li>\n <li>zh-CN: Translated on 27.10.2026 20:15</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___general",
"collection": "default",
"id": "2b523983-1e01-41c9-bad0-5807b5485059",
"language": "zh-CN",
"lastModified": "2026-10-27T19:15:23.157032Z",
"name": "Theoretical background Detail - General - Introduction",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "1.2 Main assumptions and limitations"
},
"id": {
"name": "ID",
"type": "text",
"value": "main-assumptions-and-limitations"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "fd74de0b_9b01_01f9_b7d3_91842b4e64f4",
"collection": "default",
"id": "fd74de0b-9b01-01f9-b7d3-91842b4e64f4",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "fd74de0b-9b01-01f9-b7d3-91842b4e64f4",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "1.2 CSFM（协调应力场法）在二维分析中的主要假定与限制"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Fig. 2 - Basic assumptions of CSFM.png",
"description": null,
"type": "image/png",
"size": 187222,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/70d687dc-a209-4d67-aeb9-c0bdabacd5c1/Fig.%202%20-%20Basic%20assumptions%20of%20CSFM.png",
"width": 1343,
"height": 824,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "a5b4f7ac-3fc1-4050-9269-afdb9901a92e",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/70d687dc-a209-4d67-aeb9-c0bdabacd5c1/Fig.%202%20-%20Basic%20assumptions%20of%20CSFM.png",
"height": 824,
"width": 1343
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "concrete",
"linkId": "b4790cf9-a605-45b3-b41b-e36909ad4291",
"urlSlug": "concrete",
"type": "landing_page"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p><strong>CSFM（协调应力场法） 考虑裂缝处混凝土的最大主压应力（σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>2</sub></strong><em><strong><sub>r</sub></strong></em><strong>）和钢筋应力（σ</strong><em><strong><sub>sr</sub></strong></em><strong>），同时忽略混凝土的抗拉强度（σ</strong><em><strong><sub>c</sub></strong></em><strong><sub>1</sub></strong><em><strong><sub>r</sub></strong></em><strong> = 0），但其对钢筋的刚化效应除外。</strong>考虑拉力刚化后，可以模拟钢筋的平均应变（ε<em><sub>m</sub></em>）。该方法假定存在无滑移张开的、虚拟的、可旋转的无应力裂缝（图 2a），并同时考虑裂缝处的平衡条件和钢筋的平均应变。 </p>\n<figure data-asset-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\" data-image-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/70d687dc-a209-4d67-aeb9-c0bdabacd5c1/Fig.%202%20-%20Basic%20assumptions%20of%20CSFM.png\" data-asset-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\" data-image-id=\"a5b4f7ac-3fc1-4050-9269-afdb9901a92e\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 2\\qquad Basic assumptions of the CSFM: (a) principal stresses in concrete; (b) stresses in the reinforcement direction;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(c) stress-strain diagram of concrete in terms of maximum stresses with consideration of compression softening;}}}\\) \\( \\textsf{\\textit{\\footnotesize{(d) stress-strain diagram of reinforcement in terms of stresses at cracks and average strains; (e) compression softening}}}\\) \\( \\textsf{\\textit{\\footnotesize{law; (f) bond shear stress-slip relationship for anchorage length verifications.}}}\\)</em></p>\n<p><br></p>\n<p>尽管这些假定较为简单，但已有研究表明，只要所配置的钢筋能够避免开裂时发生脆性破坏，类似假定即可对承受面内荷载的钢筋混凝土构件给出准确的预测（Kaufmann 1998；Kaufmann and Marti 1998）。此外，不考虑混凝土抗拉强度对极限荷载的任何贡献，也符合现代设计规范的原则，这些规范大多基于塑性理论。</p>\n<p>然而，<strong>CSFM（协调应力场法）不适用于细长构件</strong>（无横向钢筋时），因为对于此类构件起作用的机制，如骨料咬合、裂缝尖端的残余拉应力和销栓作用（它们都直接或间接依赖于混凝土的抗拉强度），均被忽略。虽然部分设计标准允许基于半经验规定来设计此类构件，但 CSFM（协调应力场法）并不适用于这类可能发生脆性破坏的结构。</p>\n<h4>混凝土</h4>\n<p>CSFM（协调应力场法）中采用的混凝土模型基于设计规范为截面设计规定的单轴受压本构关系，该关系仅取决于抗压强度。CSFM（协调应力场法）默认采用抛物线-矩形图（图 2c），但设计人员也可以选择更简化的理想弹塑性关系。按照 ACI 规范进行校核时，只能使用抛物线-矩形应力-应变图。如前所述，与经典钢筋混凝土设计一样，混凝土的抗拉强度被忽略。</p>\n<p>有效抗压强度根据主拉应变（ε<sub>1</sub>），通过折减系数 <em>k</em><em><sub>c</sub></em><sub>2</sub> 对开裂混凝土自动计算，如图 2c 和 2e 所示。所采用的折减关系（图 2e）是对 <em>fib</em> Model Code 2010 中抗剪验算建议的推广。该建议规定混凝土有效强度与混凝土抗压强度之比的上限值为 0.65，而此限值不适用于其他荷载工况。</p>\n<p><a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\"><em>IDEA StatiCa Detail</em></a> 中的 CSFM（协调应力场法）未针对受压混凝土考虑以应变表示的明确破坏准则（即在达到峰值应力后，假定存在无限延伸的塑性段）。这一简化不允许验算以受压方式破坏的结构的变形能力。然而，除了图 2e 中定义的开裂混凝土系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>）外，如果再通过 <em>fib</em> Model Code 2010 中定义的折减系数 <em>\\( \\eta_{fc} \\)</em> 考虑混凝土强度提高时脆性的增加，则可以正确预测其极限承载力，如下所示：</p>\n<p>\\[f_{c,red} = k_c \\cdot f_{c} = \\eta _{fc} \\cdot k_{c2} \\cdot f_{c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>k</em><em><sub>c </sub></em>为抗压强度的整体折减系数</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为因存在横向裂缝而产生的折减系数</p>\n<p><em>f</em><em><sub>c</sub></em> 为混凝土圆柱体特征强度（计算 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<p>出于计算稳定性的考虑，<em>k</em><em><sub>c</sub></em><sub>2</sub> 系数还会有一定折减。该折减不影响构件的总承载力。假定 <em>f</em><em><sub>cd</sub></em> 为混凝土的折算强度（设计值），则 <em>k</em><em><sub>c</sub></em><sub>2</sub> 值按以下规则折减。</p>\n<p>σ<em><sub>c</sub></em><sub>2</sub><em><sub>r</sub></em><em> < 0.11f</em><em><sub>cd</sub></em><em> k</em><em><sub>c</sub></em><sub>2</sub><em>=1.0<br>0.11f</em><em><sub>cd</sub></em><em> < </em>σ<em><sub>c</sub></em><sub>2</sub><em><sub>r</sub></em><em> < 0.37f</em><em><sub>cd</sub></em><em> k</em><em><sub>c</sub></em><sub>2</sub><em> </em>为 1.0 与从<br> 图 2f 所示曲线中取得的值之间的线性插值<em><br></em>σ<em><sub>c</sub></em><sub>2</sub><em><sub>r</sub></em><em> > 0.37f</em><em><sub>cd</sub></em><em> k</em><em><sub>c</sub></em><sub>2</sub><em> </em>直接取自图 2f 中的曲线</p>\n<h4>钢筋</h4>\n<p>采用设计规范通常规定的裸钢筋理想化双线性应力-应变图（图 2d）。该图的定义只需在设计阶段已知钢筋的基本特性（强度和延性等级）。也可以自定义应力-应变关系。</p>\n<p>通过修正裸钢筋的输入应力-应变关系来考虑拉力刚化，以反映埋置于混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<h4>粘结模型</h4>\n<p>钢筋与混凝土之间的粘结滑移通过图 2f 所示的简化刚性-理想塑性本构关系引入有限元模型，其中 <em>f</em><em><sub>bd</sub></em> 为设计规范针对具体粘结条件规定的极限粘结应力设计值（折算值）。</p>\n<p>这是一个简化模型，其唯一目的是按照设计规范验算粘结规定（即钢筋的锚固）。采用弯钩、环形及类似钢筋形式时锚固长度的折减，可通过在钢筋端部定义一定的承载力来考虑，后文将对此进行说明。 </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"detail_theoretical_background",
"theoretical_background_detail___general___reinforc",
"dimenzovani_zb_konstrukci_podle_csfm",
"prestressed_i_section"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "CSFM",
"codename": "csfm"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7300
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "main-assumptions-and-limitations-for-csfm"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"main-assumptions-and-limitations-for-csfm\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:27</li>\n <li>de-DE: Translated on 27.10.2026 14:06</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:02</li>\n <li>fr-FR: Translated on 27.10.2026 14:48</li>\n <li>hu-HU: Translated on 27.10.2026 18:06</li>\n <li>it-IT: Translated on 27.10.2026 15:26</li>\n <li>ja-JP: Translated on 26.10.2026 10:57</li>\n <li>ko-KR: Translated on 26.10.2026 10:55</li>\n <li>nl-NL: Translated on 27.10.2026 16:40</li>\n <li>pl-PL: Translated on 27.10.2026 19:32</li>\n <li>pt-PT: Translated on 27.10.2026 17:26</li>\n <li>ro-RO: Translated on 27.10.2026 18:50</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 10:55</li>\n <li>tr-TR: Translated on 26.10.2026 10:57</li>\n <li>vi-VN: Translated on 26.10.2026 10:56</li>\n <li>zh-CN: Translated on 27.10.2026 20:16</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___main_assumptions_a",
"collection": "default",
"id": "2ebdaf9c-827f-4fd6-9f82-28bc96970a64",
"language": "zh-CN",
"lastModified": "2026-10-27T19:16:04.8400834Z",
"name": "Theoretical background Detail - Main assumptions and limitations",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "1.3 Design tools for reinforcement"
},
"id": {
"name": "ID",
"type": "text",
"value": "design-tools-for-reinforcement"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n1b6b2998_a82a_0102_1bb4_e052b35ff829",
"collection": "default",
"id": "1b6b2998-a82a-0102-1bb4-e052b35ff829",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "1b6b2998-a82a-0102-1bb4-e052b35ff829",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.1 Introduction to finite element implementation"
},
"id": {
"name": "ID",
"type": "text",
"value": "introduction-to-finite-element-implementation"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n33af2c10_291e_0187_4660_55b94dbc3824",
"collection": "default",
"id": "33af2c10-291e-0187-4660-55b94dbc3824",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "33af2c10-291e-0187-4660-55b94dbc3824",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.2 Supports and load transmitting components"
},
"id": {
"name": "ID",
"type": "text",
"value": "supports-and-load-transmitting-components"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n2d4304a1_f345_0104_32bf_85315c48d5cd",
"collection": "default",
"id": "2d4304a1-f345-0104-32bf-85315c48d5cd",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "2d4304a1-f345-0104-32bf-85315c48d5cd",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.2 支座与传力构件"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "supports and load transmitting components.png",
"description": null,
"type": "image/png",
"size": 61630,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5a3640a9-3cfd-49bc-a306-ef899e97e9a7/supports%20and%20load%20transmitting%20components.png",
"width": 1230,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "168a03f0-9bf7-4893-87d9-9744163d0453",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e51c52f3-be54-4b55-bb4d-c4089b8239a5/Supports.png",
"height": 119,
"width": 606
},
{
"description": null,
"imageId": "d0cdeffe-373f-419a-8e49-d714b8494a68",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/069fe6fe-74e0-41a9-90ba-1aeeede8a0fb/Load%20transmitting%20devices.png",
"height": 129,
"width": 557
},
{
"description": null,
"imageId": "04324fc6-7d2d-43a7-9248-3056e9bcc513",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/38d4656d-6c90-445a-858b-cd97d4b29730/Patch%20support.png",
"height": 434,
"width": 1311
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "types_of_supports_in_idea_statica_detail__csfm_",
"linkId": "5a121972-f384-4f14-8788-9da298e1aae1",
"urlSlug": "types-of-supports-in-idea-statica-detail",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>为模拟施工过程中的大多数情况，CSFM 提供了多种支座类型（图 7）和用于传递荷载的构件（图 8）。</p>\n<h3>支座</h3>\n<p>点支座可以通过多种方式建模，以确保应力不会集中在一个点上，而是分布在更大的区域内。第一种方式是分布式点支座（图 7a），它将荷载沿构件边缘在指定宽度范围内均匀分布。</p>\n<figure data-asset-id=\"168a03f0-9bf7-4893-87d9-9744163d0453\" data-image-id=\"168a03f0-9bf7-4893-87d9-9744163d0453\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e51c52f3-be54-4b55-bb4d-c4089b8239a5/Supports.png\" data-asset-id=\"168a03f0-9bf7-4893-87d9-9744163d0453\" data-image-id=\"168a03f0-9bf7-4893-87d9-9744163d0453\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 7\\qquad Various types of supports:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) point distributed; (b) bearing plate; (c) line support; (d) patch support; (e) hanging.}}}\\]</em></p>\n<p>另一方面，局部支座（图 7d）只能布置在具有指定有效半径的混凝土体内。该支座通过刚性单元与此半径范围内的钢筋网格节点相连。因此，需要在局部支座周围定义钢筋笼。</p>\n<p>为了更精确地模拟某些实际情况，点支座还有另外两种选项。第一种是带有指定宽度和厚度承压板的点支座（图 7b）。可以指定承压板的材料，整个承压板独立划分网格。第二种是悬挂支座（图 7e），可用于模拟吊装锚栓或吊装栓钉。</p>\n<p>线支座（图 7c）可以定义在边缘上（通过指定其长度），也可以定义在单元内部（通过折线）。还可以指定其刚度和/或非线性行为（仅受压或受拉/受压支座）。</p>\n<ul>\n <li>详细说明请参阅<strong> </strong><a data-item-id=\"5a121972-f384-4f14-8788-9da298e1aae1\" href=\"\"><strong>IDEA StatiCa Detail 中的支座类型</strong></a></li>\n</ul>\n<h3>传力构件</h3>\n<p>向结构引入荷载同样可以通过多种方式建模。对于点荷载，可以采用与点支座类似的承压板（图 8a），借助具有指定宽度和厚度的钢板将集中荷载分散到更大的面积上。 </p>\n<figure data-asset-id=\"d0cdeffe-373f-419a-8e49-d714b8494a68\" data-image-id=\"d0cdeffe-373f-419a-8e49-d714b8494a68\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/069fe6fe-74e0-41a9-90ba-1aeeede8a0fb/Load%20transmitting%20devices.png\" data-asset-id=\"d0cdeffe-373f-419a-8e49-d714b8494a68\" data-image-id=\"d0cdeffe-373f-419a-8e49-d714b8494a68\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 8\\qquad Various types of load transfer components:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) bearing plate; (b) patch load; (c) hanging; (d) partially loaded area.}}}\\]</em></p>\n<p>点荷载既可以直接作用于结构表面并指定作用半径（荷载施加于混凝土单元），也可以通过称为局部荷载的特殊传力装置施加（图 8b 和图 9）。局部荷载可将荷载直接传递至有效半径范围内指定的钢筋。为确保局部荷载正常发挥作用，需要（在钢筋属性中）定义一组与荷载相互连接的钢筋。如果未定义相互连接的钢筋，则荷载传递机制与作用于构件表面的点荷载相同，荷载通过约束传递至混凝土单元，而不是直接传递至钢筋。 </p>\n<figure data-asset-id=\"04324fc6-7d2d-43a7-9248-3056e9bcc513\" data-image-id=\"04324fc6-7d2d-43a7-9248-3056e9bcc513\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/38d4656d-6c90-445a-858b-cd97d4b29730/Patch%20support.png\" data-asset-id=\"04324fc6-7d2d-43a7-9248-3056e9bcc513\" data-image-id=\"04324fc6-7d2d-43a7-9248-3056e9bcc513\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 9\\qquad Patch load: (a) load application; (b) load transferred through rebars (a group of bars for the load transfer is defined);}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(c) load transferred through concrete (a group of bars for the load transfer is not defined).}}}\\]</em></p>\n<p>吊装锚栓或吊装栓钉可以通过悬挂荷载建模（图 8c）。用户可以使用部分受荷面积（图 8d），根据 Eurocode 可提高混凝土的受压承载力（设置为 ACI 时，无法使用这种传力构件）。结构还可以承受边缘上的线荷载、一般折线荷载或面荷载。Detail 软件能够在分析中自动考虑自重。</p>\n<p><br></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-2-supports-and-load-transmitting-components"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"supports-and-load-transmitting-components\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:28</li>\n <li>de-DE: Translated on 27.10.2026 14:07</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:03</li>\n <li>fr-FR: Translated on 27.10.2026 14:49</li>\n <li>hu-HU: Translated on 27.10.2026 18:07</li>\n <li>it-IT: Translated on 27.10.2026 15:27</li>\n <li>ja-JP: Translated on 26.10.2026 11:04</li>\n <li>ko-KR: Translated on 26.10.2026 11:03</li>\n <li>nl-NL: Translated on 27.10.2026 16:41</li>\n <li>pl-PL: Translated on 27.10.2026 19:34</li>\n <li>pt-PT: Translated on 27.10.2026 17:27</li>\n <li>ro-RO: Translated on 27.10.2026 18:51</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:03</li>\n <li>tr-TR: Translated on 26.10.2026 11:04</li>\n <li>vi-VN: Translated on 26.10.2026 11:04</li>\n <li>zh-CN: Translated on 27.10.2026 20:17</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___supports_and_load_",
"collection": "default",
"id": "50ed723b-9b87-4870-a69f-e05b5a8a8150",
"language": "zh-CN",
"lastModified": "2026-10-27T19:17:11.3258424Z",
"name": "Theoretical background Detail - Supports and load transmitting components",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.3 Load transfer at trimmed ends of beams"
},
"id": {
"name": "ID",
"type": "text",
"value": "load-transfer-at-trimmed-ends-of-beams"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "b6ecb5e3_7093_01ba_9dde_25d8369a02f7",
"collection": "default",
"id": "b6ecb5e3-7093-01ba-9dde-25d8369a02f7",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "b6ecb5e3-7093-01ba-9dde-25d8369a02f7",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.3 梁端切割处的荷载传递"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "trimmed end.png",
"description": null,
"type": "image/png",
"size": 103606,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4af393d0-87fd-40a9-b70f-c259c02b14aa/trimmed%20end.png",
"width": 1230,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "aa4c7293-3a3e-4c89-b88b-f6a84b0c457f",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a2eb228a-7276-410a-a213-edf91bcfb6e9/Saint-Venant%20zone.PNG",
"height": 640,
"width": 1778
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>在许多情况下,我们只需对结构构件的某一局部(部分)建模,例如梁支座、梁中部的开洞等。这种做法可能产生在 <em>IDEA StatiCa Detail</em> 中不稳定但允许的支承配置(包括无支座的情况)。但是,在这类情况下,还需要建立表示与相邻 B 区连接的截面模型,并在该截面上施加满足平衡条件的内力。在某些情况下(例如对梁支座建模时),这些内力可由程序自动确定。</p>\n<p>在 B 区与所分析的不连续区之间,程序会自动创建圣维南传递区,以保证被分析区域内的应力分布符合实际。传递区的宽度取为截面高度的一半。由于圣维南区的唯一作用是使模型其余部分获得合理的应力分布,因此校核中不显示该区域的结果,此处也不考虑停止准则。</p>\n<p>圣维南区中代表梁切割端的边界被模拟为刚性,即该边界可以转动,但必须保持平面。具体做法是使用刚体单元<em> </em>(RBE2)将该边界上的所有有限元节点与位于截面惯性中心的一个独立节点相连。随后可在该节点上施加该单元的内力,如图 10 所示。</p>\n<figure data-asset-id=\"aa4c7293-3a3e-4c89-b88b-f6a84b0c457f\" data-image-id=\"aa4c7293-3a3e-4c89-b88b-f6a84b0c457f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a2eb228a-7276-410a-a213-edf91bcfb6e9/Saint-Venant%20zone.PNG\" data-asset-id=\"aa4c7293-3a3e-4c89-b88b-f6a84b0c457f\" data-image-id=\"aa4c7293-3a3e-4c89-b88b-f6a84b0c457f\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 10\\qquad Transfer of internal forces at a trimmed end.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-3-load-transfer-at-trimmed-ends-of-beams"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"2-3-load-transfer-at-trimmed-ends-of-beams\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:28</li>\n <li>de-DE: Translated on 27.10.2026 14:07</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:04</li>\n <li>fr-FR: Translated on 27.10.2026 14:49</li>\n <li>hu-HU: Translated on 27.10.2026 18:07</li>\n <li>it-IT: Translated on 27.10.2026 15:27</li>\n <li>ja-JP: Translated on 26.10.2026 11:03</li>\n <li>ko-KR: Translated on 26.10.2026 11:02</li>\n <li>nl-NL: Translated on 27.10.2026 16:41</li>\n <li>pl-PL: Translated on 27.10.2026 19:34</li>\n <li>pt-PT: Translated on 27.10.2026 17:27</li>\n <li>ro-RO: Translated on 27.10.2026 18:51</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:02</li>\n <li>tr-TR: Translated on 26.10.2026 11:03</li>\n <li>vi-VN: Translated on 26.10.2026 11:02</li>\n <li>zh-CN: Translated on 27.10.2026 20:17</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___load_transfer_at_t",
"collection": "default",
"id": "aa1a5fc8-a069-4196-9c2e-cde472068193",
"language": "zh-CN",
"lastModified": "2026-10-27T19:17:28.9893106Z",
"name": "Theoretical background Detail - Load transfer at trimmed ends of beams",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.4 Geometric modification of cross-sections"
},
"id": {
"name": "ID",
"type": "text",
"value": "geometric-modification-of-cross-sections"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n46b4e3db_3dd5_0178_937b_4e69c5404313",
"collection": "default",
"id": "46b4e3db-3dd5-0178-937b-4e69c5404313",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "46b4e3db-3dd5-0178-937b-4e69c5404313",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.4 横截面的几何修改"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "cross section.png",
"description": null,
"type": "image/png",
"size": 4944,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f7db528e-c5cc-4a96-b054-b9db8dc23939/cross%20section.png",
"width": 1230,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "ce95f78c-b3c0-4954-9fb1-7a5435c91008",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4e366c46-e62a-448b-8a80-26ed25dda17d/Cross-section%20reduction.png",
"height": 441,
"width": 1200
},
{
"description": null,
"imageId": "1068a23c-e975-4022-afc5-3143ddacfdd2",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/0baf2a09-9999-4a25-b83b-8433d9fae04d/Horizontal%20haunch.png",
"height": 605,
"width": 1384
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>对于定义为梁或框架节点的结构(由 x 轴和横截面定义),系统会自动对横截面进行折减。该修改会自动应用于翼缘很宽的横截面(图 11),其依据的假设是:压力应力场将从墙体以 45° 角扩展,因此上述折减后的宽度即为能够传递荷载的最大宽度</p>\n<p>请注意,CSFM 中采用的有效翼缘宽度确定方法不同于 EN 1992-1-1 (2015) 第 5.3.2.1 条或 ACI 318-19 第 9.2.4.4 条中规定的方法。除几何形状外,基于 Eurocode 的有效翼缘宽度还明确受结构的跨度和边界条件影响。</p>\n<figure data-asset-id=\"ce95f78c-b3c0-4954-9fb1-7a5435c91008\" data-image-id=\"ce95f78c-b3c0-4954-9fb1-7a5435c91008\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4e366c46-e62a-448b-8a80-26ed25dda17d/Cross-section%20reduction.png\" data-asset-id=\"ce95f78c-b3c0-4954-9fb1-7a5435c91008\" data-image-id=\"ce95f78c-b3c0-4954-9fb1-7a5435c91008\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 11\\qquad Width reduction of a cross-section: (a) user input; (b) FE model – automatically determined reduced flange width.}}}\\]</em></p>\n<p>对于位于水平面内的加腋(图 12),每个加腋沿其长度方向划分为五段。然后将每一段按等厚度墙体进行建模,其厚度等于该段中部的实际厚度。</p>\n<figure data-asset-id=\"1068a23c-e975-4022-afc5-3143ddacfdd2\" data-image-id=\"1068a23c-e975-4022-afc5-3143ddacfdd2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/0baf2a09-9999-4a25-b83b-8433d9fae04d/Horizontal%20haunch.png\" data-asset-id=\"1068a23c-e975-4022-afc5-3143ddacfdd2\" data-image-id=\"1068a23c-e975-4022-afc5-3143ddacfdd2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 12\\qquad Horizontal haunch: (a) user input; (b) FE model – a haunch automatically divided into five sections.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-4-geometric-modification-of-cross-sections"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"2-4-geometric-modification-of-cross-sections\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:28</li>\n <li>de-DE: Translated on 27.10.2026 14:08</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:04</li>\n <li>fr-FR: Translated on 27.10.2026 14:50</li>\n <li>hu-HU: Translated on 27.10.2026 18:08</li>\n <li>it-IT: Translated on 27.10.2026 15:27</li>\n <li>ja-JP: Translated on 26.10.2026 11:07</li>\n <li>ko-KR: Translated on 26.10.2026 11:07</li>\n <li>nl-NL: Translated on 27.10.2026 16:42</li>\n <li>pl-PL: Translated on 27.10.2026 19:34</li>\n <li>pt-PT: Translated on 27.10.2026 17:27</li>\n <li>ro-RO: Translated on 27.10.2026 18:52</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:07</li>\n <li>tr-TR: Translated on 26.10.2026 11:07</li>\n <li>vi-VN: Translated on 26.10.2026 11:07</li>\n <li>zh-CN: Translated on 27.10.2026 20:17</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___geometric_modifica",
"collection": "default",
"id": "5cff133b-460c-4bf2-94c2-3957a7b88e47",
"language": "zh-CN",
"lastModified": "2026-10-27T19:17:47.57107Z",
"name": "Theoretical background Detail - Geometric modification of cross-sections",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.5 Finite element types"
},
"id": {
"name": "ID",
"type": "text",
"value": "finite-element-types"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "e2bcc72e_78c5_0163_a169_dc9ed613e170",
"collection": "default",
"id": "e2bcc72e-78c5-0163-a169-dc9ed613e170",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "e2bcc72e-78c5-0163-a169-dc9ed613e170",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.6 Meshing"
},
"id": {
"name": "ID",
"type": "text",
"value": "meshing"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n8a7103fc_e2a4_016b_6e78_a6c6e6a4807f",
"collection": "default",
"id": "8a7103fc-e2a4-016b-6e78-a6c6e6a4807f",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "8a7103fc-e2a4-016b-6e78-a6c6e6a4807f",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.6 网格划分"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "meshing.png",
"description": null,
"type": "image/png",
"size": 97183,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5d7b4b67-07f2-43de-aeb0-425cd2860402/meshing.png",
"width": 1230,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "fdb308bd-ea8c-424d-84fd-7203d42e3a8d",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/addaaf72-0c44-4147-8ec2-03986c3fa271/Patch%20load%20mapping.png",
"height": 435,
"width": 1400
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "general_description_of_load_impulses_in_detail_app",
"linkId": "38cbe005-0e1e-4d75-ae8a-2ef9dcee4c2b",
"urlSlug": "general-description-of-load-impulses-in-detail-application",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>有限单元在内部实现，分析模型自动生成，无需用户具备专业的操作经验。该过程的重要环节是网格划分。</p>\n<h3>混凝土</h3>\n<p>所有混凝土构件一并划分网格。软件根据结构的尺寸和形状，并考虑最大钢筋直径，自动计算推荐的单元尺寸。此外，推荐的单元尺寸可保证在结构的薄弱部位（如细长柱或薄板）至少生成 4 个单元，以确保这些区域的结果可靠。混凝土单元的最大数量限制为 5000 个，但该数值足以满足大多数结构的推荐单元尺寸要求。设计人员始终可以通过修改默认网格尺寸的倍数来选择用户自定义的混凝土单元尺寸。</p>\n<h3>钢筋</h3>\n<p>钢筋被划分为长度与混凝土单元尺寸大致相同的单元。钢筋网格和混凝土网格生成后，通过粘结单元将二者相互连接，如图 13 所示。</p>\n<h3>承压板</h3>\n<p>辅助结构部件（如承压板）单独划分网格。这些单元的尺寸取为节点区域内混凝土单元尺寸的 2/3。然后，使用插值约束单元（RBE3）将承压板网格的节点与混凝土网格的边缘节点相连。</p>\n<h3>荷载和支座</h3>\n<p>局部荷载和局部支座仅与钢筋连接，如图 16 所示。因此，必须在其周围定义钢筋。通过等权重的 RBE3 单元，实现与有效半径范围内所有钢筋节点的连接。</p>\n<figure data-asset-id=\"fdb308bd-ea8c-424d-84fd-7203d42e3a8d\" data-image-id=\"fdb308bd-ea8c-424d-84fd-7203d42e3a8d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/addaaf72-0c44-4147-8ec2-03986c3fa271/Patch%20load%20mapping.png\" data-asset-id=\"fdb308bd-ea8c-424d-84fd-7203d42e3a8d\" data-image-id=\"fdb308bd-ea8c-424d-84fd-7203d42e3a8d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 16\\qquad Patch load mapping to reinforcement mesh.}}}\\]</em></p>\n<p>线支座和线荷载根据指定的宽度或有效半径，通过 RBE3 单元与混凝土网格的节点连接。连接的权重与到支座或荷载作用点的距离成反比。</p>\n<ul>\n <li>有关各荷载与网格之间连接关系的更多信息，请参阅<a data-item-id=\"38cbe005-0e1e-4d75-ae8a-2ef9dcee4c2b\" href=\"\"><strong>Detail 软件中荷载脉冲的一般说明</strong></a></li>\n</ul>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-6-meshing"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"2-6-meshing\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:29</li>\n <li>de-DE: Translated on 27.10.2026 14:09</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:05</li>\n <li>fr-FR: Translated on 27.10.2026 14:51</li>\n <li>hu-HU: Translated on 27.10.2026 18:08</li>\n <li>it-IT: Translated on 27.10.2026 15:28</li>\n <li>ja-JP: Translated on 26.10.2026 11:13</li>\n <li>ko-KR: Translated on 26.10.2026 11:12</li>\n <li>nl-NL: Translated on 27.10.2026 16:42</li>\n <li>pl-PL: Translated on 27.10.2026 19:35</li>\n <li>pt-PT: Translated on 27.10.2026 17:28</li>\n <li>ro-RO: Translated on 27.10.2026 18:53</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:12</li>\n <li>tr-TR: Translated on 26.10.2026 11:13</li>\n <li>vi-VN: Translated on 26.10.2026 11:12</li>\n <li>zh-CN: Translated on 27.10.2026 20:18</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___meshing",
"collection": "default",
"id": "5ac4303b-fbe3-4ca1-b1a4-850fd7a9657f",
"language": "zh-CN",
"lastModified": "2026-10-27T19:18:28.764934Z",
"name": "Theoretical background Detail - Meshing",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.7 Solution method and load control algorithm"
},
"id": {
"name": "ID",
"type": "text",
"value": "solution-method-and-load-control-algorithm"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n7295ffdb_585b_01c8_eeea_cbfc7526af76",
"collection": "default",
"id": "7295ffdb-585b-01c8-eeea-cbfc7526af76",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "7295ffdb-585b-01c8-eeea-cbfc7526af76",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.7 求解方法和荷载控制算法"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "solution method.png",
"description": null,
"type": "image/png",
"size": 17501,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/30d885ad-5360-4a31-bafe-34519ace3c53/solution%20method.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "883637b4-6077-43ff-b6e8-ac1e86785345",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c1026dcf-91ed-47ab-af2e-705ca886a9ed/Constitutive%20relationship%20of%20bond%20and%20anchorage.PNG",
"height": 603,
"width": 1788
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>采用标准的完整牛顿-拉夫森（Newton-Raphson，NR）算法求解非线性有限元问题。 </p>\n<p>一般情况下，若将全部荷载一次施加，NR 算法往往难以收敛。常用的做法（此处亦采用）是分多个增量依次施加荷载，并以上一个荷载增量的结果作为下一个增量牛顿求解的起点。为此，在牛顿-拉夫森算法的基础上实现了荷载控制算法。如果 NR 迭代不收敛，则将当前荷载增量减半，并重新进行 NR 迭代。</p>\n<p>荷载控制算法的第二个目的，是找出对应于特定“终止准则”的临界荷载，这些准则包括混凝土的最大应变、粘结单元的最大滑移、锚固单元的最大位移以及钢筋的最大应变。临界荷载采用二分法求得。如果模型中任何位置超出终止准则，则舍弃最后一个荷载增量的结果，并计算大小为前一增量一半的新增量。重复此过程，直至在一定的误差容限内求得临界荷载。</p>\n<p>对于混凝土，在壳单元的积分点处，终止准则设定为压力下 5% 的应变（即比混凝土的实际破坏应变大约高出一个数量级），拉力下为 7%。在拉力下，该值的设定是为了让钢筋先达到其极限应变（不考虑拉力刚化时通常约为 5%）。在压力下，该值是从若干备选值中选定的：它足够大，能使压碎的影响在结果中显现出来，同时又足够小，不会引起过多的数值稳定性问题。</p>\n<figure data-asset-id=\"883637b4-6077-43ff-b6e8-ac1e86785345\" data-image-id=\"883637b4-6077-43ff-b6e8-ac1e86785345\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c1026dcf-91ed-47ab-af2e-705ca886a9ed/Constitutive%20relationship%20of%20bond%20and%20anchorage.PNG\" data-asset-id=\"883637b4-6077-43ff-b6e8-ac1e86785345\" data-image-id=\"883637b4-6077-43ff-b6e8-ac1e86785345\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 17\\qquad Constitutive relationship of bond and anchorage elements used for anchorage length verification:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) bond shear stress slip response of a bond element; (b) force-displacement response of an anchorage element.}}}\\]</em></p>\n<p>对于钢筋，终止准则以应力来定义。由于对裂缝处的应力进行了建模，拉力下的准则对应于考虑安全系数后的钢筋抗拉强度。压力下的准则采用相同的值。</p>\n<p>粘结单元和锚固弹簧的终止准则为 α·δ<em>u</em><em><sub>max</sub></em>，其中 δ<em>u</em><em><sub>max</sub></em> 为规范校核中采用的最大滑移，α = 10。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-7-solution-method-and-load-control-algorithm"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"2-7-solution-method-and-load-control-algorithm\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:29</li>\n <li>de-DE: Translated on 27.10.2026 14:09</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:05</li>\n <li>fr-FR: Translated on 27.10.2026 14:51</li>\n <li>hu-HU: Translated on 27.10.2026 18:09</li>\n <li>it-IT: Translated on 27.10.2026 15:29</li>\n <li>ja-JP: Translated on 26.10.2026 11:17</li>\n <li>ko-KR: Translated on 26.10.2026 11:17</li>\n <li>nl-NL: Translated on 27.10.2026 16:43</li>\n <li>pl-PL: Translated on 27.10.2026 19:36</li>\n <li>pt-PT: Translated on 27.10.2026 17:29</li>\n <li>ro-RO: Translated on 27.10.2026 18:53</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:16</li>\n <li>tr-TR: Translated on 26.10.2026 11:17</li>\n <li>vi-VN: Translated on 26.10.2026 11:17</li>\n <li>zh-CN: Translated on 27.10.2026 20:18</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___solution_method_an",
"collection": "default",
"id": "b1a7fc51-513b-4798-bbdb-4f9488d24004",
"language": "zh-CN",
"lastModified": "2026-10-27T19:18:48.8773595Z",
"name": "Theoretical background Detail - Solution method and load-control algorithm",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "2.8 Presentation of results"
},
"id": {
"name": "ID",
"type": "text",
"value": "presentation-of-results"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "d4d41655_a8d9_018a_7277_dad106e33f39",
"collection": "default",
"id": "d4d41655-a8d9-018a-7277-dad106e33f39",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "d4d41655-a8d9-018a-7277-dad106e33f39",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "2.8 结果展示"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "presentation_results_preview2.png",
"description": null,
"type": "image/png",
"size": 258008,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b8b2eaf9-d685-410f-bf37-89ac34e16a40/presentation_results_preview2.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "5633d094-25c8-46e3-a481-843b6082214b",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9dac87f5-fd94-41db-bcb2-c56897b22a45/Result%20presentation.PNG",
"height": 801,
"width": 2000
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>结果分别针对混凝土和钢筋单元给出。混凝土中的应力和应变值在壳单元的积分点处计算。然而,由于以这种方式展示数据并不实用,因此默认在节点处展示结果,即取相连单元中相邻高斯积分点的压应力最大值(图 18)。需要注意的是,当有限单元尺寸与受压区高度相近时,这种展示方式可能会在构件受压边缘处局部低估结果。</p>\n<figure data-asset-id=\"5633d094-25c8-46e3-a481-843b6082214b\" data-image-id=\"5633d094-25c8-46e3-a481-843b6082214b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9dac87f5-fd94-41db-bcb2-c56897b22a45/Result%20presentation.PNG\" data-asset-id=\"5633d094-25c8-46e3-a481-843b6082214b\" data-image-id=\"5633d094-25c8-46e3-a481-843b6082214b\" alt=\"\"></figure>\n<p><em>图 18 - 带积分点和节点的混凝土有限单元:混凝土结果在节点和有限单元中的展示。</em></p>\n<p>钢筋有限单元的结果要么在每个单元内为常数(一个值,例如钢材应力),要么为线性分布(两个值,用于粘结结果)。对于辅助单元,例如承压板单元,仅给出变形结果。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___reinforc",
"theoretical_background_detail___general___verifica",
"n2017_solution_for_walls_and_details_of_concrete_st",
"fire_resistance_check_of_concrete_structures"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 7100
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "2-8-presentation-of-results"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"2-8-presentation-of-results\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:30</li>\n <li>de-DE: Translated on 27.10.2026 14:09</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:05</li>\n <li>fr-FR: Translated on 27.10.2026 14:51</li>\n <li>hu-HU: Translated on 27.10.2026 18:09</li>\n <li>it-IT: Translated on 27.10.2026 15:29</li>\n <li>ja-JP: Translated on 26.10.2026 11:17</li>\n <li>ko-KR: Translated on 26.10.2026 11:16</li>\n <li>nl-NL: Translated on 27.10.2026 16:43</li>\n <li>pl-PL: Translated on 27.10.2026 19:36</li>\n <li>pt-PT: Translated on 27.10.2026 17:29</li>\n <li>ro-RO: Translated on 27.10.2026 18:53</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:16</li>\n <li>tr-TR: Translated on 26.10.2026 11:17</li>\n <li>vi-VN: Translated on 26.10.2026 11:17</li>\n <li>zh-CN: Translated on 27.10.2026 20:19</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___presentation_of_re",
"collection": "default",
"id": "8b9399db-b927-491a-a50f-c66ad97560af",
"language": "zh-CN",
"lastModified": "2026-10-27T19:19:03.1480173Z",
"name": "Theoretical background Detail - Presentation of results",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "3.1 Limit states and crack width calculation"
},
"id": {
"name": "ID",
"type": "text",
"value": "limit-states-and-crack-width-calculation"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n805f2d39_5e1d_0196_07ec_d526e6056d4c",
"collection": "default",
"id": "805f2d39-5e1d-0196-07ec-d526e6056d4c",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "805f2d39-5e1d-0196-07ec-d526e6056d4c",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
"[Circular Reference]",
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "4.1 Material models EN"
},
"id": {
"name": "ID",
"type": "text",
"value": "material-models-en"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n34484ce7_0966_01b0_4e4e_ced1381a2b83",
"collection": "default",
"id": "34484ce7-0966-01b0-4e4e-ced1381a2b83",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "34484ce7-0966-01b0-4e4e-ced1381a2b83",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "4.1 材料模型（EN）"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Verification of the structural concrete elements (EN).png",
"description": null,
"type": "image/png",
"size": 69784,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5787011f-bbfb-47f8-8496-0401101a4bd0/Verification%20of%20the%20structural%20concrete%20elements%20%28EN%29.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "d99ce820-6afd-4050-a438-c0bd6d3e5e29",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e72b03ac-c1db-4c39-bbc2-f4d87b7522f2/Concrete%20stress-strain%20diagram%20CSFM.PNG",
"height": 571,
"width": 1739
},
{
"description": null,
"imageId": "b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG",
"height": 574,
"width": 1500
},
{
"description": null,
"imageId": "78f0e024-ae44-4ec0-b939-6ac74688ae23",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bca48b51-2839-4b96-8dac-078574e47c12/Fig.%2011%20-%20Concrete%20stress-strain%20for%20serviceability%20.png",
"height": 908,
"width": 1750
},
{
"description": null,
"imageId": "ba3b27c3-ad63-46d8-b734-279c1a98639f",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/47fb26f0-9509-403c-ac42-7d68821d59d1/Steel%20stress-strain%20diagram%20CSFM.PNG",
"height": 719,
"width": 1822
},
{
"description": null,
"imageId": "4a23c310-98c5-488d-a3a0-2ec9064a2f61",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/111ff130-8480-486a-adca-4c0068bcf66e/Tension%20stiffening%20CSFM.PNG",
"height": 569,
"width": 1761
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<h3>混凝土 - ULS</h3>\n<p>CSFM 中采用的混凝土模型基于 EN 1992-1-1 规定的用于截面设计的单轴受压本构关系，该关系仅取决于抗压强度。CSFM 默认采用 EN 1992-1-1 第 3.1.7 (1) 条（图 24a）规定的抛物线-矩形应力图，设计人员也可以根据 EN 1992-1-1 第 3.1.7 (2) 条（图 24b）选择更为简化的理想弹塑性关系。与经典钢筋混凝土设计一样，不考虑混凝土的抗拉强度。</p>\n<figure data-asset-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\" data-image-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e72b03ac-c1db-4c39-bbc2-f4d87b7522f2/Concrete%20stress-strain%20diagram%20CSFM.PNG\" data-asset-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\" data-image-id=\"d99ce820-6afd-4050-a438-c0bd6d3e5e29\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 24\\qquad The stress-strain diagrams of concrete for ULS: a) parabola-rectangle diagram; b) bilinear diagram.}}}\\]</em></p>\n<p><em>IDEA StatiCa Detail</em> 中的 CSFM 实现未针对受压混凝土考虑以应变表示的显式破坏准则（即达到峰值应力后，采用 ε<em><sub>cu</sub></em><sub>2</sub>（ε<em><sub>cu</sub></em><sub>3</sub>）取值为 5% 的塑性分支，而 EN 1992-1-1 假定极限应变小于 0.35%）。这一简化不允许对受压破坏结构的变形能力进行验证。但是，当除了考虑开裂混凝土系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，见（图 25））之外，还通过 <em>fib</em> Model Code 2010 中定义的折减系数 <em>\\(\\eta_{fc}\\)</em> 来考虑混凝土强度提高时脆性的增大，就可以准确预测其按 EN 1992-1-1 第 3.1.3 条确定的极限承载力 <em>f</em><em><sub>cd</sub></em>，公式如下：</p>\n<p>\\[f_{cd}={\\alpha_{cc}} \\cdot \\frac{f_{ck,red}}{γ_c} = {\\alpha_{cc}} \\cdot \\frac{k_c \\cdot f_{ck}}{γ_c} = {\\alpha_{cc}} \\cdot \\frac{\\eta _{fc} \\cdot k_{c2} \\cdot f_{ck}}{γ_c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f_{ck}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p>α<em><sub>cc</sub></em> 为考虑长期效应对抗压强度的影响以及荷载施加方式产生的不利影响的系数，按 EN 1992-1-1 第 3.1.6 (1) 条取值。默认值为 1,0。</p>\n<p><em>k</em><em><sub>c </sub></em>为抗压强度的整体折减系数</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为考虑横向裂缝影响的折减系数</p>\n<p><em>f</em><em><sub>ck</sub></em> 为混凝土圆柱体抗压强度特征值（在定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 25\\qquad The compression softening law.}}}\\]</em></p>\n<h3>混凝土 - SLS</h3>\n<p>正常使用状态分析对承载能力极限状态分析所用的本构模型做了某些简化。不考虑受压混凝土应力-应变曲线的塑性分支，弹性分支为线性且无限延伸，也不考虑压力软化规律。只要正常使用状态下材料的合成应力限值明显低于其屈服点（如欧洲规范所要求），这些简化就能提高数值稳定性和计算速度，并且不会降低解的通用性。因此，用于正常使用状态的简化模型仅在满足所有验算要求时才有效。</p>\n<figure data-asset-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\" data-image-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bca48b51-2839-4b96-8dac-078574e47c12/Fig.%2011%20-%20Concrete%20stress-strain%20for%20serviceability%20.png\" data-asset-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\" data-image-id=\"78f0e024-ae44-4ec0-b939-6ac74688ae23\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 26\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>在正常使用状态分析中，混凝土的长期效应通过有效无限徐变系数（\\(\\varphi\\)，默认取值 2.5）来考虑，该系数按 EN 1992-1-1 第 3.1.4 (3) 条及第 7.4.3 (5) 条对混凝土的割线弹性模量（<em>E</em><em><sub>cm</sub></em>）进行修正，公式如下：</p>\n<p>\\[E_{c,eff} = \\frac{E_{cm}}{1+\\varphi}\\]</p>\n<p>考虑长期效应时，首先计算包含全部永久荷载的荷载步，并考虑徐变系数（即采用混凝土有效弹性模量 <em>E</em><em><sub>c,eff</sub></em>），然后计算附加荷载，此时不考虑徐变系数（即采用 <em>E</em><em><sub>cm</sub></em>）。此外，为进行短期验算，还需另行进行一次计算，其中所有荷载均不考虑徐变系数。长期和短期验算的两次计算均如图 26 所示。</p>\n<p>徐变系数由用户在材料属性中定义，并应按 EN 1992-1-1 图 3.1 计算。</p>\n<h3>钢筋</h3>\n<p>默认采用 EN 1992-1-1 第 3.2.7 条（图 27）中定义的裸钢筋理想化双线性应力-应变图。该图的定义只需在设计阶段已知钢筋的基本特性（强度和延性等级）。如已知钢筋的实际应力-应变关系（热轧、冷加工、淬火自回火等），也可以采用该关系。钢筋应力-应变图可由用户自行定义，但在这种情况下无法考虑拉力刚化效应（也就无法计算裂缝宽度）。采用顶部为水平分支的应力-应变图，则无法验证结构的耐久性。因此，需要对标准延性要求进行手动验算。</p>\n<figure data-asset-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" data-image-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/47fb26f0-9509-403c-ac42-7d68821d59d1/Steel%20stress-strain%20diagram%20CSFM.PNG\" data-asset-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" data-image-id=\"ba3b27c3-ad63-46d8-b734-279c1a98639f\" alt=\"\"></figure>\n<p><em>\\( \\textsf{\\textit{\\footnotesize{Fig. 27 \\qquad Stress-strain diagram of reinforcement: a) bilinear diagram with an inclined top branch; b) bilinear diagram}}}\\) \\( \\textsf{\\textit{\\footnotesize{with a horizontal top branch.}}}\\)</em></p>\n<p><br></p>\n<p>拉力刚化（图 28） 通过修正裸钢筋的输入应力-应变关系自动考虑，以反映埋置于混凝土中的钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" data-image-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/111ff130-8480-486a-adca-4c0068bcf66e/Tension%20stiffening%20CSFM.PNG\" data-asset-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" data-image-id=\"4a23c310-98c5-488d-a3a0-2ec9064a2f61\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 28\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "4-1-material-models-en"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"4-1-material-models-en\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:31</li>\n <li>de-DE: Translated on 27.10.2026 14:11</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:06</li>\n <li>fr-FR: Translated on 27.10.2026 14:52</li>\n <li>hu-HU: Translated on 27.10.2026 18:10</li>\n <li>it-IT: Translated on 27.10.2026 15:30</li>\n <li>ja-JP: Translated on 26.10.2026 11:26</li>\n <li>ko-KR: Translated on 26.10.2026 11:25</li>\n <li>nl-NL: Translated on 27.10.2026 16:44</li>\n <li>pl-PL: Translated on 27.10.2026 19:37</li>\n <li>pt-PT: Translated on 27.10.2026 17:30</li>\n <li>ro-RO: Translated on 27.10.2026 18:54</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:25</li>\n <li>tr-TR: Translated on 26.10.2026 11:26</li>\n <li>vi-VN: Translated on 26.10.2026 11:25</li>\n <li>zh-CN: Translated on 27.10.2026 20:19</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___material_models__e",
"collection": "default",
"id": "1838439f-0398-4754-b0c9-6f627127a407",
"language": "zh-CN",
"lastModified": "2026-10-27T19:19:48.5819343Z",
"name": "Theoretical background Detail - Material models (EN)",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "4.2 Safety factors"
},
"id": {
"name": "ID",
"type": "text",
"value": "safety-factors"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n87402a88_f6a7_01e2_3c54_6a74bb42f492",
"collection": "default",
"id": "87402a88-f6a7-01e2-3c54-6a74bb42f492",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "87402a88-f6a7-01e2-3c54-6a74bb42f492",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "4.2 安全系数"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "safety factors.png",
"description": null,
"type": "image/png",
"size": 163446,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/776e0780-6d49-4fbc-9056-8923de185410/safety%20factors.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "7b26aa26-7ec4-4296-9296-645d3d6041b5",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4cadae4a-9a8a-4f9b-935c-51395116ed4e/Material%20factors.png",
"height": 124,
"width": 417
},
{
"description": null,
"imageId": "99632028-f378-4338-b74b-bef12aec3f6a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2d2607d1-29e9-4dfd-80ef-db2ba7d172bf/Combination%20factors.png",
"height": 164,
"width": 522
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "concrete",
"linkId": "b4790cf9-a605-45b3-b41b-e36909ad4291",
"urlSlug": "concrete",
"type": "landing_page"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>协调应力场法符合现代设计规范。由于计算模型仅使用标准材料特性，设计规范中规定的分项安全系数格式无需任何调整即可直接应用。这样，输入荷载乘以相应系数，材料特性标准值则按设计规范规定的相应安全系数折减，与常规混凝土分析完全一致。默认采用 EN 1992-1-1 第 2.4.2.4 节规定的材料安全系数值，但用户可以在规范与计算设置中修改安全系数（图 29）。</p>\n<figure data-asset-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" data-image-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4cadae4a-9a8a-4f9b-935c-51395116ed4e/Material%20factors.png\" data-asset-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" data-image-id=\"7b26aa26-7ec4-4296-9296-645d3d6041b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 29\\qquad The setting of material safety factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>荷载安全系数需要由用户在组合规则中为每个荷载工况的非线性组合进行定义（图 30）。对于 <a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\">Idea StatiCa Detail</a> 中实现的所有模板，分项安全系数均已预先定义。</p>\n<figure data-asset-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" data-image-id=\"99632028-f378-4338-b74b-bef12aec3f6a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2d2607d1-29e9-4dfd-80ef-db2ba7d172bf/Combination%20factors.png\" data-asset-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" data-image-id=\"99632028-f378-4338-b74b-bef12aec3f6a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 30\\qquad The setting of load partial factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>通过使用适当的用户自定义分项安全系数组合，用户也可以采用整体抗力系数法（Navrátil, et al. 2017）进行 CSFM（协调应力场法）计算，但这种方法在设计实践中很少使用。一些指南建议在非线性分析中采用整体抗力系数法。然而，在简化的非线性分析（如 CSFM（协调应力场法））中，只需要常规手算所使用的那些材料特性，因此仍然更适合采用分项安全系数格式。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "4-2-safety-factors"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"4-2-safety-factors\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:31</li>\n <li>de-DE: Translated on 27.10.2026 14:11</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:06</li>\n <li>fr-FR: Translated on 27.10.2026 14:53</li>\n <li>hu-HU: Translated on 27.10.2026 18:11</li>\n <li>it-IT: Translated on 27.10.2026 15:30</li>\n <li>ja-JP: Translated on 26.10.2026 11:28</li>\n <li>ko-KR: Translated on 26.10.2026 11:27</li>\n <li>nl-NL: Translated on 27.10.2026 16:45</li>\n <li>pl-PL: Translated on 27.10.2026 19:38</li>\n <li>pt-PT: Translated on 27.10.2026 17:30</li>\n <li>ro-RO: Translated on 27.10.2026 18:55</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:27</li>\n <li>tr-TR: Translated on 26.10.2026 11:27</li>\n <li>vi-VN: Translated on 26.10.2026 11:27</li>\n <li>zh-CN: Translated on 27.10.2026 20:20</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___safety_factors",
"collection": "default",
"id": "3cbd210f-4490-4b0e-9de8-c84044452bc1",
"language": "zh-CN",
"lastModified": "2026-10-27T19:20:08.2519957Z",
"name": "Theoretical background Detail - Safety factors",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "4.3 Ultimate limit state analysis"
},
"id": {
"name": "ID",
"type": "text",
"value": "ultimate-limit-state-analysis"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "fc5356e8_ad66_019d_500e_56112b2c54e1",
"collection": "default",
"id": "fc5356e8-ad66-019d-500e-56112b2c54e1",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "fc5356e8-ad66-019d-500e-56112b2c54e1",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "4.3 承载能力极限状态分析"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "eurocodes.png",
"description": null,
"type": "image/png",
"size": 295317,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/44f1ebbb-483c-4c24-bf68-64ec39607c70/eurocodes.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "c6ca9e31-4172-4034-a8b0-cdb2ad98d82a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7aa307dc-3cd6-4d42-8dd8-d0ff97994677/Bond%20conditions.PNG",
"height": 701,
"width": 1116
},
{
"description": null,
"imageId": "8a2ed21c-590e-4061-8c46-c5cc4c60ade1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png",
"height": 442,
"width": 1011
},
{
"description": null,
"imageId": "d3675eaf-0adb-4512-9366-58e4bdf171b1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png",
"height": 520,
"width": 1463
},
{
"description": null,
"imageId": "a4b32213-4a43-4c1d-a3c3-21d42d5dfbad",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b16975dc-aeea-4e7e-bfc7-23a8f8b28c7e/Available%20anchorage%20types%20for%20longitudinal%20rebars.png",
"height": 141,
"width": 1200
},
{
"description": null,
"imageId": "ec5159ea-3a7f-43fa-a807-a217b79d6cc9",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86ffb525-5912-4a7f-9576-fff17481b7a1/Available%20anchorage%20types%20for%20stirrups.png",
"height": 230,
"width": 1200
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "rn_25_1__smooth_rebars_in_detail",
"linkId": "182f8ba8-899b-44fc-a1c7-59d562ef8c6c",
"urlSlug": "smooth-rebars-in-detail",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>EN 1992-1-1 要求的各项验算，均基于模型给出的直接结果进行评估。承载能力极限状态验算包括混凝土强度、钢筋强度和锚固（粘结剪应力）。</p>\n<p>受压<strong>混凝土强度</strong>按有限元分析得到的最大主压应力 σ<em><sub>c </sub></em>= σ<em><sub>c</sub></em><sub>2</sub> 与极限值 σ<em><sub>c,lim</sub></em> = <em>f</em><em><sub>cd</sub></em> 之比进行评估。 </p>\n<p><strong>钢筋强度</strong>在受拉和受压两种情况下，均按裂缝处钢筋应力 σ<em><sub>sr</sub></em> 与规定极限值 σ<em><sub>s,lim</sub></em> 之比进行评估：</p>\n<p>\\(σ_{s,lim} = \\frac{k \\cdot f_{yk}}{γ_s}\\qquad\\qquad\\textsf{\\small{for bilinear diagram with inclined top branch}}\\)</p>\n<p>\\(σ_{s,lim} = \\frac{f_{yk}}{γ_s}\\qquad\\qquad\\,\\,\\,\\,\\textsf{\\small{for bilinear diagram with horizontal top branch}}\\)</p>\n<p>其中：</p>\n<p><em>f</em><em><sub>yk</sub></em> 钢筋的屈服强度，依据 EN 1992-1-1 第 3.2.3 条，</p>\n<p><em>k</em> 抗拉强度 <em>f</em><em><sub>tk</sub></em> 与屈服应力之比，<br> \\(k = \\frac{f_{tk}}{f_{yk}}\\)</p>\n<p><em>γ</em><em><sub>s </sub></em><sub> </sub>为钢筋的分项安全系数</p>\n<p><strong>粘结剪应力</strong>单独评估，按有限元分析计算得到的粘结应力 τ<em><sub>b</sub></em> 与极限粘结强度 <em>f</em><em><sub>bd</sub></em><sub>,</sub> 之比确定，依据 EN 1992-1-1 第 8.4.2 节：</p>\n<p>\\[\\frac{τ_{b}}{f_{bd}}\\]</p>\n<p>\\[f_{bd} = 2.25 \\cdot η_1\\cdot η_2\\cdot f_{ctd}\\]</p>\n<p>其中：</p>\n<p><em>f</em><em><sub>ctd</sub></em><sub> </sub> 为混凝土抗拉强度的设计值，依据 EN 1992-1-1 第 3.1.6 (2) 条。由于较高强度混凝土的脆性增大，<em>f</em><em><sub>ctk,0.05</sub></em><sub> </sub>依据 EN 1992-1-1 第 8.4.2 (2) 条限制为 C60/75 的取值</p>\n<p>η<sub>1</sub> 为与粘结条件质量及浇筑混凝土时钢筋位置相关的系数（图 31）。</p>\n<p>当获得“良好”条件时，η<sub>1</sub> = 1.0；</p>\n<p>其他所有情况，以及采用滑模施工的结构构件中的钢筋，η<sub>1</sub> = 0.7，除非能够证明存在“良好”的粘结条件</p>\n<p>η<sub>2</sub> 与钢筋直径相关：</p>\n<p> 当 Ø ≤ 32 mm 时，η<sub>2</sub> = 1.0</p>\n<p> 当 Ø > 32 mm 时，η<sub>2</sub> = (132 - Ø)/100</p>\n<figure data-asset-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" data-image-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7aa307dc-3cd6-4d42-8dd8-d0ff97994677/Bond%20conditions.PNG\" data-asset-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" data-image-id=\"c6ca9e31-4172-4034-a8b0-cdb2ad98d82a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 31\\qquad EN 1992-1-1 Figure 8.2 - Description of bond conditions.}}}\\]</em></p>\n<p>在 IDEA StatiCa Detail 中，粘结条件按图 31 c) 和 d) 考虑。浇筑混凝土的方向可在软件中针对每个项目条目按如下方式设置。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p>这些验算针对结构各相应部分的适当极限值进行（即，尽管混凝土和钢筋材料各只有一个强度等级，但由于拉力刚化和压力软化效应，结构各部分最终的应力-应变曲线仍会有所不同）。</p>\n<p>此外，还可以选择对<strong>光圆钢筋</strong>进行建模。更多信息请见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 是有限元分析的结果，可以通过两种方式定义。</p>\n<p>\\[F_{tot}=A_{s}\\cdot \\sigma_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面面积，<em>σ</em><em><sub>s</sub></em> 为钢筋应力。</p>\n<p>或者定义为 锚固力 <em>F</em><em><sub>a </sub></em>与 粘结力 <em>F</em><em><sub>bond</sub></em><em> </em>之和。</p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分得到。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋的周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是钢筋单元中的最大力，同时考虑钢筋的<strong>极限强度</strong>和<strong>锚固条件</strong>（混凝土与钢筋之间的粘结，以及锚固弯钩、环形锚固等）。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=k\\cdot f_{yd}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot k\\cdot f_{yd}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bd}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋的周长，<em>l</em> 为从钢筋起点到所考察点的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 32\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元之间的夹角大小计算得到的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括直钢筋（即不考虑锚固端折减）、弯折、弯钩、环形、焊接横向钢筋、完全粘结和连续钢筋。所有这些类型及其对应的锚固系数 β，纵向钢筋见图 32，箍筋见图 33。所采用的锚固系数取值符合 EN 1992-1-1 第 8.4.4 节表 8.2。需要注意的是，尽管有多种可选类型，CSFM（协调应力场法）实际上区分三种锚固端类型：(i) 锚固长度不折减，(ii) 标准锚固时锚固长度折减 30 %，以及 (iii) 完全粘结。</p>\n<figure data-asset-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" data-image-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b16975dc-aeea-4e7e-bfc7-23a8f8b28c7e/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" data-image-id=\"a4b32213-4a43-4c1d-a3c3-21d42d5dfbad\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 33\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in the CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) bend; (c) hook; (d) loop; (e) welded transverse bar; (f) perfect bond; (g) continuous bar.}}}\\]</em></p>\n<p><br></p>\n<figure data-asset-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" data-image-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86ffb525-5912-4a7f-9576-fff17481b7a1/Available%20anchorage%20types%20for%20stirrups.png\" data-asset-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" data-image-id=\"ec5159ea-3a7f-43fa-a807-a217b79d6cc9\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 33\\qquad Available anchorage types and respective anchorage coefficients for stirrups.}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Closed stirrups: (a) hook; (b) bend; (c) overlap. Open stirrups: (d) hook; (e) continuous bar.}}}\\]</em></p>\n<p>为符合 EN 1992-1-1，计算中应使用锚固弹簧，且锚固弹簧由 β 系数修正，因此用户在定义钢筋的起始和终止条件时，必须选用其中一种可用的锚固类型。 </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "4-3-ultimate-limit-state-analysis"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"ultimate-limit-state-analysis\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:32</li>\n <li>de-DE: Language translation error (when inserting into Kontent.ai)</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Language translation error (when inserting into Kontent.ai)</li>\n <li>fr-FR: Translated on 27.10.2026 14:53</li>\n <li>hu-HU: Translated on 27.10.2026 18:12</li>\n <li>it-IT: Translated on 27.10.2026 15:31</li>\n <li>ja-JP: Translated on 26.10.2026 11:36</li>\n <li>ko-KR: Translated on 26.10.2026 11:34</li>\n <li>nl-NL: Translated on 27.10.2026 16:45</li>\n <li>pl-PL: Translated on 27.10.2026 19:38</li>\n <li>pt-PT: Translated on 27.10.2026 17:31</li>\n <li>ro-RO: Translated on 27.10.2026 18:56</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:34</li>\n <li>tr-TR: Translated on 26.10.2026 11:35</li>\n <li>vi-VN: Translated on 26.10.2026 11:35</li>\n <li>zh-CN: Translated on 27.10.2026 20:20</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___ultimate_limit_sta",
"collection": "default",
"id": "49596809-9b1e-4b70-8cf6-27aa7f840b83",
"language": "zh-CN",
"lastModified": "2026-10-27T19:20:49.0723171Z",
"name": "Theoretical background Detail - Ultimate limit state analysis",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "4.4 Partially loaded areas (PLA)"
},
"id": {
"name": "ID",
"type": "text",
"value": "partially-loaded-areas"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n4ffa73af_7903_018b_f050_5cb47586f489",
"collection": "default",
"id": "4ffa73af-7903-018b-f050-5cb47586f489",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "4ffa73af-7903-018b-f050-5cb47586f489",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "4.4 局部受压区域 (PLA)"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Partially loaded areas.png",
"description": null,
"type": "image/png",
"size": 105195,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3a60077b-3642-4e6c-b93e-e264a9f4609e/Partially%20loaded%20areas.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/94ecb791-703a-44b7-8665-2f1526a20c1e/Partially%20loaded%20areas%20EC.PNG",
"height": 480,
"width": 1191
},
{
"description": null,
"imageId": "77fdebe4-afac-4ee7-aee5-716984d4e6d3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG",
"height": 420,
"width": 1633
},
{
"description": null,
"imageId": "05c2e193-bc14-42b5-bc07-da8610febda8",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png",
"height": 406,
"width": 1857
},
{
"description": null,
"imageId": "47a5fe4b-0b51-4d87-a9cd-8e59e61835e4",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c4ff37a9-9d49-493b-946e-f048713b05cf/Partially%20loaded%20areas.PNG",
"height": 474,
"width": 1791
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>在设计混凝土结构时，我们会遇到两大类局部受压区域 (PLA)：第一类包括支座，第二类包括锚固区。根据现行钢筋混凝土结构设计标准 EN 1992-1-1 第 6.7 章（<em>图 34</em>），对于局部受压区域，应考虑混凝土的局部压碎和横向拉力。对于作用在面积 <em>A</em><em><sub>c0</sub></em> 上的均布荷载，混凝土的受压承载力可根据设计分布面积 <em>A</em><em><sub>c1.</sub></em> 提高至多三倍。</p>\n<figure data-asset-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\" data-image-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/94ecb791-703a-44b7-8665-2f1526a20c1e/Partially%20loaded%20areas%20EC.PNG\" data-asset-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\" data-image-id=\"d2ebd9b3-ebcd-4cb6-a090-4b0a9a1d2566\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 34\\qquad Partially loaded areas according to EN 1992-1-1.}}}\\]</em></p>\n<p>局部受压区域必须配置足够的横向钢筋，其设计应能传递该区域内产生的劈裂力。对于局部受压区域横向钢筋的设计，按照 Eurocode 采用拉压杆法。如果没有所需的横向钢筋，则不能考虑提高混凝土的受压承载力。</p>\n<p><br></p>\n<p><strong>CSFM 中的局部受压区域</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 35\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>利用 CSFM，可以在考虑局部受压区域内混凝土抗压承载力提高影响的情况下，对钢筋混凝土结构进行设计和评估。由于 CSFM 是墙（2D）模型，而局部受压区域属于空间（3D）问题，因此需要找到一种能够将这两种不同类型问题结合起来的解决方案（<em>图 35</em>）。如果启用“局部受压区域”功能，将按照 Eurocode 生成允许锥体几何形状（<em>图 34</em>）。对于指定的混凝土构件几何形状和每个 PLA 的尺寸，所有几何冲突均在 3D 中完全求解。随后，创建局部受压区域的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 36\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>事实证明，修改材料模型并不是合适的方法，主要原因是将属性映射到有限元网格存在问题。经确定，与有限元网格无关的方法是更合适的解决方案。针对已知的压力锥体几何形状，创建完全协调的虚拟压杆（<em>图 35</em> <em>和图 37</em>）。这些压杆具有与模型中所用混凝土相同的材料属性，包括应力-应变图。锥体的形状决定了压杆的方向，压杆将荷载沿 PLA 逐步分散到设计分布面积上。虚拟压杆的面积密度在锥体的每个部位都是变化的，并在荷载方向上增加了虚拟混凝土面积。在受荷面积 (<em>A</em><em><sub>c0</sub></em>) 处，按照比值 \\(\\sqrt{A_{c0} \\cdot A_{c1}} - A_{real}\\) 增加虚拟混凝土面积（其中 <em>A</em><em><sub>real</sub></em> 为 2D 计算模型中假定的支座面积），该面积朝设计分布面积 (<em>A</em><em><sub>c1</sub></em>) 方向线性减小至零。该方案可确保整个锥体体积内混凝土的压应力保持恒定。</p>\n<figure data-asset-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\" data-image-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c4ff37a9-9d49-493b-946e-f048713b05cf/Partially%20loaded%20areas.PNG\" data-asset-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\" data-image-id=\"47a5fe4b-0b51-4d87-a9cd-8e59e61835e4\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{c1}}{A_{c0}}} - \\frac{A_{real}}{A_{c0}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 37\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部受压区域的承载力按照设计分布面积与受荷面积之比提高，该比值见 EN 1992-1-1 (6.7)。 需要注意的是，这是一种设计模型，无法精确描述局部受压区域的应力状态，其实际应力流要复杂得多。不过，该方案能够将荷载正确分布到整个模型，同时兼顾局部受压区域提高后的承载能力。此外，它还能正确引入该区域的横向应力。</p>\n<p>在使用局部受压区域功能来模拟混凝土受压承载力提高时，需要根据 EN 1992-1-1 第 6.7 (2) 节单独进行规范校核。由钢筋承担的横向拉力（劈裂力）将自动校核。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "4-4-partially-loaded-areas-pla"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"partially-loaded-areas-pla\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:32</li>\n <li>de-DE: Translated on 27.10.2026 14:12</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:08</li>\n <li>fr-FR: Translated on 27.10.2026 14:54</li>\n <li>hu-HU: Translated on 27.10.2026 18:12</li>\n <li>it-IT: Translated on 27.10.2026 15:31</li>\n <li>ja-JP: Translated on 26.10.2026 11:35</li>\n <li>ko-KR: Translated on 26.10.2026 11:34</li>\n <li>nl-NL: Translated on 27.10.2026 16:46</li>\n <li>pl-PL: Translated on 27.10.2026 19:39</li>\n <li>pt-PT: Translated on 27.10.2026 17:31</li>\n <li>ro-RO: Translated on 27.10.2026 18:56</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:34</li>\n <li>tr-TR: Translated on 26.10.2026 11:35</li>\n <li>vi-VN: Translated on 26.10.2026 11:34</li>\n <li>zh-CN: Translated on 27.10.2026 20:21</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___partially_loaded_a",
"collection": "default",
"id": "9fd288fa-b420-4063-981c-e44e8a4daf55",
"language": "zh-CN",
"lastModified": "2026-10-27T19:21:10.721686Z",
"name": "Theoretical background Detail - Partially loaded areas",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "4.5 Serviceability limit state analysis"
},
"id": {
"name": "ID",
"type": "text",
"value": "serviceability-limit-state-analysis"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "c0faeafd_fe53_0187_955b_d143d9265810",
"collection": "default",
"id": "c0faeafd-fe53-0187-955b-d143d9265810",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "c0faeafd-fe53-0187-955b-d143d9265810",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "4.5 正常使用极限状态分析"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "eurocodes.png",
"description": null,
"type": "image/png",
"size": 295317,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/44f1ebbb-483c-4c24-bf68-64ec39607c70/eurocodes.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>正常使用极限状态评估包括应力限值、裂缝宽度和挠度限值。根据 EN 1992-1-1 对混凝土和钢筋单元进行应力校核，方式与承载能力极限状态类似。</p>\n<h3>应力限制</h3>\n<p>应限制混凝土中的压应力，以避免出现纵向裂缝。根据 EN 1992-1-1 第 7.2 (2) 条，如果特征荷载组合下的应力水平超过 <em>k</em><sub>1</sub><em>f</em><em><sub>ck</sub></em>，则可能出现纵向裂缝。混凝土压应力以有限元分析在正常使用极限状态下得到的最大主压应力 σ<em><sub>c</sub></em> <em>= σ</em><em><sub>c</sub></em><sub>2</sub><em><sub> </sub></em>与限值 σ<em><sub>c,lim</sub></em> 之比进行评估。即：</p>\n<p>\\[\\frac{σ_{c}}{σ_{c,lim}}\\]</p>\n<p>\\[σ_{c,lim} = k_1\\cdot f_{ck}\\]</p>\n<p>式中：</p>\n<p><em>f</em><em><sub>ck</sub></em> 混凝土特征圆柱体抗压强度，</p>\n<p><em>k</em><sub>1</sub> =0.6。</p>\n<p>根据 EN 1992-1-1 第 7.2(3) 条，如果准永久荷载下混凝土中的应力小于 <em>k</em><sub>2</sub><em>f</em><em><sub>ck</sub></em>，则可假定为线性徐变。如果混凝土中的应力超过 <em>k</em><sub>2</sub><em>f</em><em><sub>ck</sub></em>，则应考虑非线性徐变（参见 EN 1992-1-1 第 3.1.4 条）。在 IDEA StatiCa Detail 中，仅可假定为符合 EN 1992-1-1 第 3.1.4 (3) 条的线性徐变（参见材料模型 (EN)）。</p>\n<p>如果在特征荷载组合下，钢筋中的拉应力不超过 <em>k</em><sub>3</sub><em>f</em><em><sub>yk</sub></em>，则可认为避免了不可接受的开裂或变形（EN 1992-1-1 第 7.2 (5) 条）。钢筋强度以裂缝处钢筋中的应力 σ<em><sub>s</sub></em> <em>= </em>σ<em><sub>sr</sub></em> 与规定限值 σ<em><sub>s,lim</sub></em> 之比进行评估：</p>\n<p>\\[\\frac{σ_{s}}{σ_{s,lim}}\\]</p>\n<p>\\[σ_{s,lim} = k_3\\cdot f_{yk}\\]</p>\n<p>式中：</p>\n<p><em>f</em><em><sub>yk</sub></em> 钢筋屈服强度，</p>\n<p><em>k</em><sub>3</sub> =0.8。</p>\n<h3>挠度</h3>\n<p>挠度仅可针对墙或静定（静力确定）梁、超静定（静力不确定）梁进行评估。在这些情况下，考虑的是挠度的绝对值（与加载前的初始状态相比），且挠度的最大允许值必须由用户设定。截断端处的挠度无法校核，因为这类结构本质上是不稳定的，其平衡是通过附加端部力来满足的，因此挠度并不真实。可计算短期挠度 <em>u</em><em><sub>z,st</sub></em> 或长期挠度 <em>u</em><em><sub>z,lt</sub></em>，并与用户定义的限值进行校核：</p>\n<p>\\[\\frac{u_ z}{u_{z,lim}}\\]</p>\n<p>式中：</p>\n<p><em>u</em><em><sub>z</sub></em> 由有限元分析计算得到的短期或长期挠度，</p>\n<p><em>u</em><em><sub>z,lim</sub></em> 用户定义的挠度限值。</p>\n<h3>裂缝宽度</h3>\n<p>裂缝宽度和方向仅针对启用了裂缝宽度评估的组合，按长期效应（使用 <em>E</em><em><sub>c,eff</sub></em>）进行计算。根据 Eurocode 基于用户指定限值的验算表示如下：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>式中：</p>\n<p><em>w</em> 由有限元分析计算得到的裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 用户定义的裂缝宽度限值。</p>\n<p><br></p>\n<p>裂缝宽度有两种计算方式（稳定裂缝和非稳定裂缝）。在一般情况下（稳定裂缝），裂缝宽度通过对钢筋一维单元上的应变进行积分来计算。然后，根据二维混凝土单元中最接近的三个积分点（距给定钢筋一维有限单元中心最近）计算裂缝方向。虽然这种计算裂缝方向的方法与裂缝的真实位置并不对应，但它仍能给出具有代表性的数值，由此得到的裂缝宽度结果可与规范要求的钢筋位置处的裂缝宽度值进行比较。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "4-5-serviceability-limit-state-analysis"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"serviceability-limit-state-analysis\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:33</li>\n <li>de-DE: Translated on 27.10.2026 14:13</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:08</li>\n <li>fr-FR: Translated on 27.10.2026 14:54</li>\n <li>hu-HU: Translated on 27.10.2026 18:13</li>\n <li>it-IT: Translated on 27.10.2026 15:32</li>\n <li>ja-JP: Translated on 26.10.2026 11:40</li>\n <li>ko-KR: Translated on 26.10.2026 11:39</li>\n <li>nl-NL: Translated on 27.10.2026 16:46</li>\n <li>pl-PL: Translated on 27.10.2026 19:39</li>\n <li>pt-PT: Translated on 27.10.2026 17:32</li>\n <li>ro-RO: Translated on 27.10.2026 18:57</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:39</li>\n <li>tr-TR: Translated on 26.10.2026 11:40</li>\n <li>vi-VN: Translated on 26.10.2026 11:39</li>\n <li>zh-CN: Translated on 27.10.2026 20:21</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___serviceability_lim",
"collection": "default",
"id": "70b033ed-8364-4692-a84d-8eda80f00dce",
"language": "zh-CN",
"lastModified": "2026-10-27T19:21:41.1915439Z",
"name": "Theoretical background Detail - Serviceability limit state analysis",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "5.1 Material models (ACI)"
},
"id": {
"name": "ID",
"type": "text",
"value": "material-models-aci"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "e023fb1d_6a30_01c3_526e_d8c8d1a6b0e5",
"collection": "default",
"id": "e023fb1d-6a30-01c3-526e-d8c8d1a6b0e5",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "e023fb1d-6a30-01c3-526e-d8c8d1a6b0e5",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "5.1 材料模型（ACI）"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Material models (ACI)_00.png",
"description": null,
"type": "image/png",
"size": 62814,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d34cdf5e-0275-4137-8744-a69bc4303153/Material%20models%20%28ACI%29_00.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "a84d11ec-b1f2-431e-afad-b6e1b7e8a83c",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f578dd02-9167-45e0-b80f-4a1331dfe20a/Concrete%20stress-strain%20diagram%20CSFM%20-%20ACI.png",
"height": 571,
"width": 859
},
{
"description": null,
"imageId": "b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG",
"height": 574,
"width": 1500
},
{
"description": null,
"imageId": "0d015331-6ce6-4a70-b087-58766f33e248",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/07b977ad-1511-48d6-b96e-12b3c67bb3b9/Concrete%20stress-strain%20for%20serviceability%20-%20ACI.png",
"height": 858,
"width": 1235
},
{
"description": null,
"imageId": "f5a1e9f7-76c9-4bdf-9d6b-a28ade763397",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1bb4b6d8-065d-4c52-a7e0-66ed3c01281f/Sustained%20load%20duration%20-%20ACI.png",
"height": 220,
"width": 690
},
{
"description": null,
"imageId": "2d9c6401-28af-4bfe-bc92-1d6f830f7c93",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png",
"height": 719,
"width": 938
},
{
"description": null,
"imageId": "c9add949-2ad5-4922-8e6c-0d75fb47cb70",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png",
"height": 569,
"width": 883
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<h3>混凝土 - 承载力</h3>\n<p>CSFM 中用于承载力计算的混凝土模型，基于混凝土的抛物线-塑性应力-应变曲线，该曲线源自波特兰水泥协会（Portland Cement Association）的抛物线应力-应变曲线，见 PCA 的 Notes on ACI 318-99 Building Code Requirements for Structural Concrete 图 6-8。与经典钢筋混凝土设计一样，忽略混凝土的抗拉强度。</p>\n<figure data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f578dd02-9167-45e0-b80f-4a1331dfe20a/Concrete%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 38\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p><em>IDEA StatiCa Detail</em> 中 CSFM 的实现未考虑受压混凝土以应变表示的显式破坏准则（即达到峰值应力后，采用塑性分支，其中 ε<em><sub>c</sub></em><sub>0</sub> 的最大值为 5%，而 ACI 318-19 第 22.2.2.1 条假定极限应变小于 0.3%）。这一简化使得无法验证受压破坏结构的变形能力。然而，除了考虑开裂混凝土的系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，定义见（图 39））之外，如果再通过 <em>fib</em> Model Code 2010 中定义的折减系数 <em>\\(\\eta_{fc}\\)</em> 来考虑混凝土强度提高时脆性增大的影响，则可以正确预测承载力，如下所示：</p>\n<p>\\[f'_{c,lim}=\\alpha_{1}\\cdot\\phi_{c}\\cdot k_{c}\\cdot f'_{c}\\]</p>\n<p>\\[k_{c}=\\eta_{fc}\\cdot k_{c2}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em><sub>1</sub> 为 ACI 318-19 第 22.2.2.4.1 条定义的混凝土抗压强度折减系数。采用抛物线-矩形应力-应变图时，需要用该系数折减最大压应力。这样可使受压区的应力分布取平均值，使所得抗压强度小于或等于采用带下降塑性分支的应力-应变图所计算的 抗压强度 <em>。</em></p>\n<p><em>Φ</em><em><sub>c </sub></em>为混凝土的强度折减系数。默认值按 ACI 318-19 表 24.2.1 (b)(f) 设定。</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为考虑横向裂缝影响的折减系数。</p>\n<p><em>f'</em><em><sub>c</sub></em> 为混凝土圆柱体抗压强度（定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 39\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 是一个折减系数，其假定与 ACI 318-19 表 23.9.2 中给出的节点区系数 <em>β</em><em><sub>n</sub></em> 相同，不同之处在于，CSFM 对每个有限单元都校核是否存在垂直于主压应力的主拉应力（而不仅仅是拉压杆模型的节点）。</p>\n<h3>混凝土 – 正常使用</h3>\n<p>正常使用分析对承载力分析所用的本构模型做了一定简化。受压混凝土应力-应变曲线的塑性分支被忽略，而弹性分支为线性且无限延伸。不考虑压力软化规律。这些简化提高了数值稳定性和计算速度，并且只要正常使用状态下材料的最终应力限值明显低于其屈服点（如 ACI 所要求），就不会降低解的通用性。因此，正常使用分析所采用的简化模型仅在满足所有验算要求时才有效。</p>\n<figure data-asset-id=\"0d015331-6ce6-4a70-b087-58766f33e248\" data-image-id=\"0d015331-6ce6-4a70-b087-58766f33e248\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/07b977ad-1511-48d6-b96e-12b3c67bb3b9/Concrete%20stress-strain%20for%20serviceability%20-%20ACI.png\" data-asset-id=\"0d015331-6ce6-4a70-b087-58766f33e248\" data-image-id=\"0d015331-6ce6-4a70-b087-58766f33e248\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 40\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>结构的长期性能，例如长期挠度或持续荷载引起的裂缝宽度计算，会受到混凝土徐变的影响。ACI 318-19 第 24.2.4.1.3 条定义了持续荷载的时间相关系数 ξ，用以表示在指定持续荷载作用时间下的徐变效应。</p>\n<p>在 Detail 软件中，通过系数 ξ 调整弹性模量 <em>E</em><em><sub>c</sub></em>，以确定结构的长期性能。调整后的弹性模量称为 <em>E</em><em><sub>c,eff</sub></em>，见图 40。</p>\n<p>假定单元的变形以应变表示，则可写为：</p>\n<p>\\[\\epsilon_{tot} = \\epsilon_{0} + \\epsilon_{creep} = \\epsilon_{0} \\cdot (1+\\xi)\\]</p>\n<p>其中：</p>\n<p><em>ε</em><em><sub>0</sub></em> 为短期应变（不含徐变影响），<em>ε</em><em><sub>creep</sub></em> 为徐变引起的应变。</p>\n<p>根据胡克定律，可写出：</p>\n<p>\\[E_{c,eff} = \\frac{f_{c}}{\\epsilon_{tot}}\\]</p>\n<p>代入 \\(\\epsilon_{tot} = \\epsilon_{0} \\cdot (1+\\xi)\\) 和 \\(\\epsilon_{0} = f_{c} / E_{c}\\)，得到：</p>\n<p>\\[E_{c,eff} = \\frac{E_{c}}{1+\\xi}\\]</p>\n<p>用于确定系数 ξ 的持续荷载作用时间，可针对每个正常使用长期组合单独设定。</p>\n<figure data-asset-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\" data-image-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1bb4b6d8-065d-4c52-a7e0-66ed3c01281f/Sustained%20load%20duration%20-%20ACI.png\" data-asset-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\" data-image-id=\"f5a1e9f7-76c9-4bdf-9d6b-a28ade763397\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 41\\qquad Sustained load duration}}}\\]</em></p>\n<p>随后采用修正后的材料模型计算随时间变化的挠度、应力和裂缝宽度，其中受压细化效应由有限元分析的特性自动考虑。因此，无需再将其乘以第 24.2.4.1.1 条中定义的系数。</p>\n<p><strong>短期效应</strong></p>\n<p>进行短期验算时，需另行进行一次计算，其中所有荷载均不乘以持续荷载的时间相关系数。长期和短期验算的两次计算均如图 40 所示。</p>\n<h3>钢筋</h3>\n<p>对于非预应力钢筋，采用具有明确屈服点的理想弹塑性应力-应变图，见 ACI 319-19 第 20.2.1 条。定义该图仅需已知钢筋的基本性能，即强度和弹性模量。</p>\n<p>钢筋的应力-应变图也可由用户自行定义，但在这种情况下，无法考虑拉力刚化效应（无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 42 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s </sub></em>为钢筋的强度折减系数。默认值按 ACI 318-19 表 24.2.1 设定。</p>\n<p><em>f</em><em><sub>y</sub></em> 为钢筋的屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 为钢筋的弹性模量</p>\n<p>选取 10% 作为终止计算的极限应变。根据 ASTM A955/A955M-20c 第 7 条，这一取值被认为是安全的。</p>\n<p>拉力刚化（图 43） 通过修正裸钢筋的输入应力-应变关系自动考虑，以反映埋置于混凝土中的钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png\" data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 43\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "5-1-material-models-aci"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"5-1-material-models-aci\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:33</li>\n <li>de-DE: Translated on 27.10.2026 14:14</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:09</li>\n <li>fr-FR: Translated on 27.10.2026 14:55</li>\n <li>hu-HU: Translated on 27.10.2026 18:14</li>\n <li>it-IT: Translated on 27.10.2026 15:32</li>\n <li>ja-JP: Translated on 26.10.2026 11:46</li>\n <li>ko-KR: Translated on 26.10.2026 11:44</li>\n <li>nl-NL: Translated on 27.10.2026 16:47</li>\n <li>pl-PL: Translated on 27.10.2026 19:40</li>\n <li>pt-PT: Translated on 27.10.2026 17:33</li>\n <li>ro-RO: Translated on 27.10.2026 18:57</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Language translation error (when inserting into Kontent.ai)</li>\n <li>tr-TR: Translated on 26.10.2026 11:45</li>\n <li>vi-VN: Translated on 26.10.2026 11:45</li>\n <li>zh-CN: Translated on 27.10.2026 20:22</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___material_models__a",
"collection": "default",
"id": "068aeaae-4e4d-4b95-904a-fe6148f87287",
"language": "zh-CN",
"lastModified": "2026-10-27T19:22:15.9088463Z",
"name": "Theoretical background Detail - Material models (ACI)",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "5.2 Strength reduction and load factors"
},
"id": {
"name": "ID",
"type": "text",
"value": "strength-reduction-and-load-factors"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "fc85da82_0693_016a_b193_f8a961ac8919",
"collection": "default",
"id": "fc85da82-0693-016a-b193-f8a961ac8919",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "fc85da82-0693-016a-b193-f8a961ac8919",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "5.2 强度折减系数和荷载系数"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png",
"height": 496,
"width": 879
},
{
"description": null,
"imageId": "fe8369c9-e929-4d00-b389-fa2c8d9c0cca",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png",
"height": 339,
"width": 678
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>协调应力场法符合现代设计规范。由于计算模型仅使用标准材料特性，设计规范中规定的分项安全系数格式无需任何调整即可直接应用。这样，输入荷载乘以荷载系数，材料特征值则使用相应的强度折减系数进行折减，与常规混凝土分析完全一致。</p>\n<p><strong>强度折减系数</strong>的取值见 ACI 318-19 第 21.2 条。混凝土和钢筋的默认值是按软件中求解的典型算例为剪力控制来选取的（依据表 21.2.1 (b)、(f)、(g)）。不过，软件可以对任意类型的构件建模。因此，若校核的是压力控制或拉力控制的构件，用户可以在首选项中修改强度折减系数的取值。</p>\n<figure data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7f5c8c73-4050-4623-9f74-04bee16498f2/Strength%20reduction%20factors%20-%20ACI.png\" data-asset-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" data-image-id=\"1fa1394b-aa7d-4e35-ba1b-74d51ffa7f89\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 44\\qquad The setting of strength reduction factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>强度组合的<strong>荷载系数</strong>应按照 ACI 318-19 表 5.3.1 定义。</p>\n<p>除第 34 章另有规定外，ACI 318-19 未定义正常使用级荷载组合。建议采用基于 ASCE/SEI 7-16 附录 C 的组合规则。所有模板均已预定义荷载系数。</p>\n<figure data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/db9f1517-72eb-45bd-9f0c-6c748d7c9146/Load%20factors%20-%20ACI.png\" data-asset-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" data-image-id=\"fe8369c9-e929-4d00-b389-fa2c8d9c0cca\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 45\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "5-2-strength-reduction-and-load-factors"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"5-2-strength-reduction-and-load-factors\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:34</li>\n <li>de-DE: Translated on 27.10.2026 14:14</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:09</li>\n <li>fr-FR: Translated on 27.10.2026 14:56</li>\n <li>hu-HU: Translated on 27.10.2026 18:14</li>\n <li>it-IT: Translated on 27.10.2026 15:33</li>\n <li>ja-JP: Translated on 26.10.2026 11:43</li>\n <li>ko-KR: Translated on 26.10.2026 11:42</li>\n <li>nl-NL: Translated on 27.10.2026 16:47</li>\n <li>pl-PL: Translated on 27.10.2026 19:40</li>\n <li>pt-PT: Translated on 27.10.2026 17:33</li>\n <li>ro-RO: Translated on 27.10.2026 18:58</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:42</li>\n <li>tr-TR: Translated on 26.10.2026 11:42</li>\n <li>vi-VN: Translated on 26.10.2026 11:42</li>\n <li>zh-CN: Translated on 27.10.2026 20:22</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___factors___aci",
"collection": "default",
"id": "bc990646-f698-490d-851e-4ab70850a3bc",
"language": "zh-CN",
"lastModified": "2026-10-27T19:22:34.0519292Z",
"name": "Theoretical background Detail - Strength reduction and load factors - ACI",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "5.3 Strength verifications"
},
"id": {
"name": "ID",
"type": "text",
"value": "strength-verifications"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "f654617f_d523_0106_0e28_6bbb16cb93f5",
"collection": "default",
"id": "f654617f-d523-0106-0e28-6bbb16cb93f5",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "f654617f-d523-0106-0e28-6bbb16cb93f5",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "5.3 强度验算"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "8a2ed21c-590e-4061-8c46-c5cc4c60ade1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png",
"height": 442,
"width": 1011
},
{
"description": null,
"imageId": "d3675eaf-0adb-4512-9366-58e4bdf171b1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png",
"height": 520,
"width": 1463
},
{
"description": null,
"imageId": "85c164c0-d864-4723-8c34-a84a426100b2",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png",
"height": 140,
"width": 951
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "rn_25_1__smooth_rebars_in_detail",
"linkId": "182f8ba8-899b-44fc-a1c7-59d562ef8c6c",
"urlSlug": "smooth-rebars-in-detail",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>ACI 318-19 要求的各项验算均基于模型给出的直接结果进行评估。验算内容包括混凝土强度、钢筋强度和锚固（粘结剪应力）。</p>\n<p>受压<strong>混凝土强度</strong>按有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em>（即辅助结果中的 σ<sub>2</sub>）与限值 <em>f'</em><em><sub>c,lim</sub></em> 之比进行评估。</p>\n<p><strong>钢筋强度</strong>同时按拉力和压力进行评估，取裂缝处钢筋应力 <em>f</em><em><sub>s</sub></em> 与规定限值 <em>f</em><em><sub>y,lim</sub></em> 之比。</p>\n<p><strong>粘结剪应力</strong>单独评估，取有限元分析计算得到的粘结应力 τ<em><sub>b</sub></em> 与粘结强度 <em>f</em><em><sub>bu</sub></em> 之比。</p>\n<p>然而，ACI 标准并未明确给出粘结强度，而是通过所谓锚固长度的计算来处理，相关内容见第 25.4.2 节。由于粘结强度是确定锚固长度的基本输入参数（见 R25.4.1.1 和 ACI Committee 408 1966），粘结强度可按如下方法计算：</p>\n<p>假设将钢筋锚固到混凝土块中，锚固长度为 <em>l</em><em><sub>d</sub></em> 或更大，则拔出钢筋时将导致钢筋断裂，而不是从混凝土中被拔出。这可以用下式表示。</p>\n<p>\\[\\pi\\cdot d_{b} \\cdot l_{d} \\cdot f_{bu}=f_{y}\\cdot A_{s}\\]</p>\n<p>其中：</p>\n<p><em>d</em><em><sub>b</sub></em> 为钢筋直径，<em>l</em><em><sub>d</sub></em> 为锚固长度，<em>f</em><em><sub>bu</sub></em> 为粘结强度，<em>f</em><em><sub>y</sub></em> 为钢筋屈服强度，<em>A</em><em><sub>s</sub></em> 为钢筋截面面积。</p>\n<p>由上式可以很容易地推导出粘结强度的计算公式：</p>\n<p>\\[f_{bu}=\\frac{f_{y}\\cdot A_{s}}{\\pi\\cdot d_{b} \\cdot l_{d} }\\]</p>\n<p>锚固长度 <em>l</em><em><sub>d</sub></em> 随后按 ACI 318-19 表 25.4.2.3 确定如下：</p>\n<p>\\[l_{d}=\\left( \\frac{f_{y}\\cdot\\psi_{t}\\cdot\\psi_{e}\\cdot\\psi_{g}}{C\\cdot\\lambda\\sqrt{f'_{c}}} \\right)\\cdot d_{b}\\]</p>\n<p>其中：</p>\n<p>对于 6 号及以下钢筋和变形钢丝，<em>C = 25</em>（公制为 2.1）；对于 7 号及以上钢筋，<em>C = 20</em>（公制为 1.7）；对于普通重量混凝土，λ = 1.0；<em>ψ</em><em><sub>t</sub></em>、<em>ψ</em><em><sub>e</sub></em><sub>,</sub> <em>ψ</em><em><sub>g</sub></em> 按 ACI 318-19 表 25.4.2.3 确定。 </p>\n<p>仅支持无涂层或镀锌钢筋，因此 <em>ψ</em><em><sub>e</sub></em><em> = 1.0</em>。<em>ψ</em><em><sub>g</sub></em> 根据钢筋等级自动确定，<em>ψ</em><em><sub>t</sub></em> 则根据钢筋在模型中的位置以及混凝土浇筑方向自动得出，浇筑方向可在软件中为每个项目构件按如下方式设置。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 46\\qquad Direction of concreting}}}\\]</em></p>\n<p>这些验算针对结构各部分相应的限值进行（即，尽管混凝土和钢筋材料各只有一个强度等级，但由于拉力刚化和压力软化效应，结构各部分最终的应力-应变图仍会有所不同）。</p>\n<p>还可以对<strong>光圆钢筋</strong>进行建模。更多信息请见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 和极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 是有限元分析的结果，可以通过两种方式定义。</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面面积，<em>f</em><em><sub>s</sub></em> 为钢筋应力。</p>\n<p>或者定义为 锚固力 <em>F</em><em><sub>a </sub></em>与 粘结力 <em>F</em><em><sub>bond</sub></em><em> </em>之和。</p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分得到。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是考虑钢筋<strong>强度</strong>以及<strong>锚固条件</strong>（混凝土与钢筋之间的粘结，以及锚固弯钩、环形钢筋等）后，钢筋单元中的最大力。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋周长，<em>l</em> 为从钢筋起点到所考察点的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 47\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元之间的夹角大小计算得到的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM 中可用的<strong>锚固类型</strong>包括直钢筋（即不折减锚固端）、90 度弯钩、180 度弯钩、完全粘结和连续钢筋。图 48 给出了纵向钢筋的所有这些类型及相应的锚固系数 β。所采用的锚固系数值，是通过比较 ACI 318-19 第 25.4.3.1 节的公式与 ACI 318-19 第 25.4.2.3 节的公式推导得出的。需要指出的是，尽管有多种可选项，CSFM 仅区分三种锚固端类型：(i) 锚固长度不折减；(ii) 标准化锚固情况下锚固长度折减 30%；(iii) 完全粘结。</p>\n<figure data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 48\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) 90-degree hook; (c) 180-degree hook; (d) perfect bond; (e) continuous bar}}}\\]</em></p>\n<p>箍筋的锚固系数始终为 β = 1.0。</p>\n<p>为符合 ACI 的要求，计算中应使用锚固弹簧。锚固弹簧由 β 系数修正，因此用户在定义钢筋的起点和终点条件时，必须选择其中一种可用的锚固类型。 </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "5-3-strength-verifications"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"5-3-strength-verifications\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:34</li>\n <li>de-DE: Translated on 27.10.2026 14:15</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:10</li>\n <li>fr-FR: Translated on 27.10.2026 14:56</li>\n <li>hu-HU: Translated on 27.10.2026 18:15</li>\n <li>it-IT: Translated on 27.10.2026 15:33</li>\n <li>ja-JP: Translated on 26.10.2026 11:52</li>\n <li>ko-KR: Translated on 26.10.2026 11:51</li>\n <li>nl-NL: Translated on 27.10.2026 16:48</li>\n <li>pl-PL: Translated on 27.10.2026 19:41</li>\n <li>pt-PT: Translated on 27.10.2026 17:34</li>\n <li>ro-RO: Translated on 27.10.2026 18:58</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:51</li>\n <li>tr-TR: Translated on 26.10.2026 11:52</li>\n <li>vi-VN: Translated on 26.10.2026 11:51</li>\n <li>zh-CN: Translated on 27.10.2026 20:23</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___strength_analysis_",
"collection": "default",
"id": "6364de3b-5531-4046-a57b-f8150ac0e9f6",
"language": "zh-CN",
"lastModified": "2026-10-27T19:23:11.0793712Z",
"name": "Theoretical background Detail - Strength analysis - ACI",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "5.4 Bearing and anchorage zones - Partially loaded areas"
},
"id": {
"name": "ID",
"type": "text",
"value": "bearing-and-anchorage-zones-partially-loaded-areas"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "df2d07b6_cabe_0102_4254_6e44efaefb9b",
"collection": "default",
"id": "df2d07b6-cabe-0102-4254-6e44efaefb9b",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "df2d07b6-cabe-0102-4254-6e44efaefb9b",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "5.4 支承区与锚固区 – 局部受压面积"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2d1db553-b91c-4327-8c20-396cc2144140/Partially%20loaded%20areas%20Bearings.png",
"height": 659,
"width": 1059
},
{
"description": null,
"imageId": "77fdebe4-afac-4ee7-aee5-716984d4e6d3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG",
"height": 420,
"width": 1633
},
{
"description": null,
"imageId": "05c2e193-bc14-42b5-bc07-da8610febda8",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png",
"height": 406,
"width": 1857
},
{
"description": null,
"imageId": "aff079fa-74f7-4575-a46b-8e589950238a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png",
"height": 474,
"width": 1791
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>在混凝土结构设计中，我们会遇到两大类局部受压面积（PLA）：第一类是<strong>支承</strong>，第二类是<strong>锚固区</strong>。 </p>\n<p>根据现行钢筋混凝土结构设计标准 ACI 318-19 第 22.8 节，<strong>支承</strong>应考虑混凝土局部压碎和横向拉力。对于作用在面积 <em>A</em><em><sub>c1</sub></em> 上的均布荷载，混凝土的抗压承载力可根据设计分布面积 <em>A</em><em><sub>c2</sub></em> 提高至最多 2 倍。见 ACI 318-19 表 22.8.3.2。</p>\n<figure data-asset-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\" data-image-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2d1db553-b91c-4327-8c20-396cc2144140/Partially%20loaded%20areas%20Bearings.png\" data-asset-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\" data-image-id=\"0d1d9eab-8cca-488d-a1fc-a0e55a22ba6e\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 49\\qquad Partially loaded areas for bearings according to ACI 318-19}}}\\]</em></p>\n<p>对于后张<strong>锚固区</strong>，应遵循 ACI 318-19 第 25.9 节。</p>\n<p>局部受压面积必须配置足够的横向钢筋，其设计应能传递该区域内产生的劈裂力。如果没有所需的横向钢筋，则不能考虑混凝土抗压承载力的提高。</p>\n<p><br></p>\n<p><strong>CSFM（协调应力场法）中的局部受压面积</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 50\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>采用 CSFM（协调应力场法），可以在设计和评估钢筋混凝土结构时考虑局部受压面积中混凝土抗压承载力的提高。由于 CSFM（协调应力场法）是墙（2D）模型，而局部受压面积属于空间（3D）问题，因此需要找到一种方法将这两类不同的问题结合起来（<em>Fig. 50</em>）。启用“局部受压面积”功能后，将按照 ACI 创建允许的锥体几何形状（<em>Fig. 49</em>）。针对指定的混凝土构件几何形状和各 PLA 的尺寸，所有几何冲突均在 3D 中完整求解。随后，创建局部受压面积的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 51\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>事实证明，修改材料模型并不是合适的方法，主要原因是将属性映射到有限元网格存在问题。研究确定，与有限元网格无关的方法是更合适的解决方案。针对已知的受压锥体几何形状，创建完全协调的虚拟压杆（<em>Fig. 51</em> <em>and Fig. 52</em>）。这些压杆的材料属性与模型中所用混凝土相同，包括应力-应变图。锥体的形状决定了压杆的方向，压杆将荷载经由 PLA 逐步分布到设计分布面积上。虚拟压杆的面积密度在锥体的每个部位都是变化的，它在荷载方向上增加了虚拟的混凝土面积。在受荷面积（<em>A</em><em><sub>c1</sub></em>）处，按照比值 \\(\\sqrt{A_{c1} \\cdot A_{c2}} - A_{real}\\) 增加虚拟混凝土面积（其中 <em>A</em><em><sub>real</sub></em> 为 2D 计算模型中假定的支座面积），该面积向设计分布面积（<em>A</em><em><sub>c2</sub></em>）方向线性减小至零。这种方法可确保整个锥体体积内混凝土的压应力保持恒定。</p>\n<figure data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png\" data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{c2}}{A_{c1}}} - \\frac{A_{real}}{A_{c1}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 52\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部受压面积的承载力按照 ACI 318-19 第 22.8 节规定的设计分布面积与受荷面积之比提高。需要注意的是，这是一种设计模型，无法精确描述局部受压面积上的应力状态，其实际传力路径要复杂得多。然而，这种方法能够将荷载正确分布到整个模型，同时考虑局部受压面积承载力的提高。此外，它还能正确引入该区域的横向应力，从而针对劈裂力正确设计钢筋。</p>\n<p>表 22.8.3.2 给出了<strong>承压</strong>应力的允许值 <em>0.85f</em><em><sub>c</sub></em><em>'</em>。密度受到限制，以确保不超过表 22.8.3.2(b) 公式给出的最大 2 倍承载力。 </p>\n<p>对于<strong>锚固区</strong>，软件中 PLA 的使用方式与支承相同。因此，ACI 318-19 第 25.9 节定义的局部区域必须按照 ACI 318-19 第 25.9.3 条手动校核。因此，PLA 仅用于避免在局部区域内超过应变准则而导致计算提前终止。另一方面，根据 ACI 318-19 第 25.9.4.3.1 (b) 条，抵抗面内崩裂和剥落应力的钢筋可以直接在软件中方便地验证。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "5-4-bearing-and-anchorage-zones-partially-loaded-areas"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"bearing-and-anchorage-zones-partially-loaded-areas\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:35</li>\n <li>de-DE: Translated on 27.10.2026 14:15</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:10</li>\n <li>fr-FR: Translated on 27.10.2026 14:57</li>\n <li>hu-HU: Translated on 27.10.2026 18:15</li>\n <li>it-IT: Translated on 27.10.2026 15:34</li>\n <li>ja-JP: Translated on 26.10.2026 11:53</li>\n <li>ko-KR: Translated on 26.10.2026 11:52</li>\n <li>nl-NL: Translated on 27.10.2026 16:48</li>\n <li>pl-PL: Translated on 27.10.2026 19:41</li>\n <li>pt-PT: Translated on 27.10.2026 17:34</li>\n <li>ro-RO: Translated on 27.10.2026 18:59</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:52</li>\n <li>tr-TR: Translated on 26.10.2026 11:53</li>\n <li>vi-VN: Translated on 26.10.2026 11:53</li>\n <li>zh-CN: Translated on 27.10.2026 20:23</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___bearing_and_anchor",
"collection": "default",
"id": "e1ddec17-9dd8-4216-bef1-8157fd1a576d",
"language": "zh-CN",
"lastModified": "2026-10-27T19:23:40.7718641Z",
"name": "Theoretical background Detail – Bearing and anchorage zones – Partially loaded areas - ACI",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "5.5 Serviceability verifications"
},
"id": {
"name": "ID",
"type": "text",
"value": "serviceability-verifications"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "ca9b6d78_562b_01cd_b7c1_e9e14bcade98",
"collection": "default",
"id": "ca9b6d78-562b-01cd-b7c1-e9e14bcade98",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "ca9b6d78-562b-01cd-b7c1-e9e14bcade98",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "5.5 正常使用验算"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "aebd4701-afaa-4f1f-b7f6-e531c65ed403",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5dff4f86-fd02-432a-812c-cf520aabe92b/Prestressed%20member%20class.png",
"height": 445,
"width": 856
},
{
"description": null,
"imageId": "5f5abc59-7c83-43de-9aa6-045ba160e215",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/26aa9ff8-a409-41a2-b69b-b28fc2841ec0/Concrete%20compressive%20stress%20limits%20at%20service%20loads%20-%20ACI.png",
"height": 156,
"width": 455
},
{
"description": null,
"imageId": "977137a7-f1f0-4e67-8f44-06634328b1a4",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/35ae9de1-6a34-4952-a6e7-ffc528e1e5aa/Deflection%20limit%20value%20selection.png",
"height": 94,
"width": 588
},
{
"description": null,
"imageId": "00675749-f338-4b86-80b7-14648ef6e0b5",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4af498a4-6b3b-4043-be8f-f10522f5b188/Reasonable%20crack%20widths%20-%20ACI.png",
"height": 414,
"width": 1150
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>正常使用评估包括应力限值、裂缝宽度和挠度限值。混凝土和钢筋单元的应力按照 ACI 318-19 进行校核，方式与承载力验算中的规定类似。</p>\n<h3>应力限值</h3>\n<p>对于 U 类和 T 类预应力构件，应验算正常使用荷载下混凝土的容许压应力。根据表 R24.5.2.1，对于假定已开裂的混凝土，无需进行应力限值校核。用户需要在设计构件设置中设定预应力构件的类别。</p>\n<figure data-asset-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\" data-image-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5dff4f86-fd02-432a-812c-cf520aabe92b/Prestressed%20member%20class.png\" data-asset-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\" data-image-id=\"aebd4701-afaa-4f1f-b7f6-e531c65ed403\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 53\\qquad Prestressed flexural member class selection}}}\\]</em></p>\n<p>ACI 318-19 第 24.5.4.1 条规定，承受瞬时荷载的构件，其容许压应力为 <em>0.6f</em><em><sub>c</sub></em><em>'. </em>设定压应力限值 <em>0.45f</em><em><sub>c</sub></em><em>'</em> 是为了降低预应力混凝土构件在重复荷载作用下发生破坏的概率。该限值也有助于避免过大的徐变变形。应力水平较高时，徐变应变会随着外加应力的增加而更快增长。</p>\n<p>混凝土压应力以正常使用极限状态有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em> <em>= σ</em><em><sub>c</sub></em><sub>2</sub><em><sub> </sub></em>与限值之比来评估，该限值根据表 24.5.4.1 确定。</p>\n<figure data-asset-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\" data-image-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/26aa9ff8-a409-41a2-b69b-b28fc2841ec0/Concrete%20compressive%20stress%20limits%20at%20service%20loads%20-%20ACI.png\" data-asset-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\" data-image-id=\"5f5abc59-7c83-43de-9aa6-045ba160e215\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 54\\qquad Concrete compressive stress limits at service loads}}}\\]</em></p>\n<p>在软件中，<em>预应力加持续荷载</em>按长期组合处理，<em>预应力加总荷载</em>按短期组合处理。</p>\n<h3>挠度</h3>\n<p>根据所选的组合类型（长期或短期），分别评估长期挠度或短期挠度。最大容许挠度值由用户确定，并应按照 ACI 138-19 第 24.2 条考虑。 </p>\n<figure data-asset-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\" data-image-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/35ae9de1-6a34-4952-a6e7-ffc528e1e5aa/Deflection%20limit%20value%20selection.png\" data-asset-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\" data-image-id=\"977137a7-f1f0-4e67-8f44-06634328b1a4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 55\\qquad Maximum allowable deflection value}}}\\]</em></p>\n<p>在软件中，可以在显示变形形状的同时，分别显示恒荷载挠度 <em>Δ</em><em><sub>DL</sub></em>、活荷载挠度 <em>Δ</em><em><sub>LL</sub></em> 以及总挠度 <em>Δ</em><em><sub>Tot</sub></em><sub> </sub>（恒荷载+活荷载）。</p>\n<p>截断端处的挠度无法校核。</p>\n<h3>裂缝宽度</h3>\n<p><br></p>\n<p>裂缝宽度和裂缝方向按正常使用的短期或长期组合计算。由于 ACI 没有直接规定裂缝宽度限值，用户必须指定裂缝宽度限值 <em>w</em><em><sub>lim</sub></em>。</p>\n<p>验算结果按如下形式给出：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>式中：</p>\n<p><em>w</em> 由有限元分析计算得到的短期或长期裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 用户定义的裂缝宽度限值。</p>\n<p>软件中采用的裂缝宽度计算方法符合 ACI 224R-01，本文档中也对其作了更详细的说明。因此，可以使用 ACI 224R-01 表 4.1 来确定裂缝宽度限值。</p>\n<figure data-asset-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\" data-image-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4af498a4-6b3b-4043-be8f-f10522f5b188/Reasonable%20crack%20widths%20-%20ACI.png\" data-asset-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\" data-image-id=\"00675749-f338-4b86-80b7-14648ef6e0b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 56\\qquad Reasonable crack widths for reinforced concrete under service load}}}\\]</em></p>\n<p>裂缝宽度有两种计算方式（稳定裂缝和非稳定裂缝）。在一般情况下（稳定裂缝），裂缝宽度通过对钢筋一维单元上的应变积分来计算。然后，根据二维混凝土单元中距离（从给定钢筋一维有限单元的中心起算）最近的三个积分点计算裂缝方向。虽然这种计算裂缝方向的方法与裂缝的实际位置并不一致，但它仍能给出具有代表性的数值，由此得到的裂缝宽度结果可以与规范要求的钢筋位置处的裂缝宽度限值进行比较。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "5-5-serviceability-verifications"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"serviceability-verifications\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:36</li>\n <li>de-DE: Translated on 27.10.2026 14:16</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:11</li>\n <li>fr-FR: Translated on 27.10.2026 14:57</li>\n <li>hu-HU: Translated on 27.10.2026 18:16</li>\n <li>it-IT: Translated on 27.10.2026 15:34</li>\n <li>ja-JP: Translated on 26.10.2026 11:55</li>\n <li>ko-KR: Translated on 26.10.2026 11:54</li>\n <li>nl-NL: Translated on 27.10.2026 16:49</li>\n <li>pl-PL: Translated on 27.10.2026 19:42</li>\n <li>pt-PT: Translated on 27.10.2026 17:34</li>\n <li>ro-RO: Translated on 27.10.2026 19:00</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:53</li>\n <li>tr-TR: Translated on 26.10.2026 11:54</li>\n <li>vi-VN: Translated on 26.10.2026 11:54</li>\n <li>zh-CN: Translated on 27.10.2026 20:24</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___serviceability_ver",
"collection": "default",
"id": "6a23f6dd-ff47-4acc-8fab-37165f10b585",
"language": "zh-CN",
"lastModified": "2026-10-27T19:24:06.8470041Z",
"name": "Theoretical background Detail – Serviceability verifications – ACI",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "6.1 Material models (AASHTO)"
},
"id": {
"name": "ID",
"type": "text",
"value": "material-models-aahsto"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n718b61d6_ca9a_01c4_c411_608ecc9bfe42",
"collection": "default",
"id": "718b61d6-ca9a-01c4-c411-608ecc9bfe42",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "718b61d6-ca9a-01c4-c411-608ecc9bfe42",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "6.1 材料模型（AASHTO）"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Material models (ACI)_00.png",
"description": null,
"type": "image/png",
"size": 62814,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d34cdf5e-0275-4137-8744-a69bc4303153/Material%20models%20%28ACI%29_00.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "a84d11ec-b1f2-431e-afad-b6e1b7e8a83c",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f578dd02-9167-45e0-b80f-4a1331dfe20a/Concrete%20stress-strain%20diagram%20CSFM%20-%20ACI.png",
"height": 571,
"width": 859
},
{
"description": null,
"imageId": "b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG",
"height": 574,
"width": 1500
},
{
"description": null,
"imageId": "fdcc5f99-090b-4af6-af2f-efa12840c367",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/be2c4149-9e8e-4595-b5a5-7e9fa87c20f3/Concrete%20stress-strain%20for%20serviceability%20-%20AASHTO.png",
"height": 1241,
"width": 2349
},
{
"description": null,
"imageId": "2d9c6401-28af-4bfe-bc92-1d6f830f7c93",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png",
"height": 719,
"width": 938
},
{
"description": null,
"imageId": "c9add949-2ad5-4922-8e6c-0d75fb47cb70",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png",
"height": 569,
"width": 883
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<h3>混凝土 - 强度</h3>\n<p>CSFM 中用于强度计算的混凝土模型基于 AASHTO LRFD 强度设计中的平衡和应变协调假定。根据 AASHTO LRFD (2024) 第 5.6.2.1 条，忽略混凝土的抗拉强度。</p>\n<figure data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f578dd02-9167-45e0-b80f-4a1331dfe20a/Concrete%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" data-image-id=\"a84d11ec-b1f2-431e-afad-b6e1b7e8a83c\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 57\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p><em>IDEA StatiCa Detail</em> 中的 CSFM 实现没有对承受压力的混凝土考虑以应变表示的显式破坏准则（即达到峰值应力后，采用塑性分支，其中 ε<em><sub>c</sub></em><sub>0</sub> 的最大值为 5%，而 AASHTO LRFD (2024) 第 5.6.2.1 条假定极限应变小于 0.3%）。这一简化无法验证发生受压破坏的结构的变形能力。然而，除开裂混凝土系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，定义见 (Fig. 57)）外，若再通过 <em>fib</em> Model Code 2010 中定义的折减系数 <em>\\(\\eta_{fc}\\)</em> 考虑混凝土强度提高时脆性的增加，则可以正确预测强度，如下所示：</p>\n<p>\\[f'_{c,lim}=\\alpha_{1}\\cdot\\phi_{c}\\cdot k_{c}\\cdot f'_{c}\\]</p>\n<p>\\[k_{c}=\\eta_{fc}\\cdot k_{c2}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em><sub>1</sub> 为 AASHTO LRFD (2024) 第 5.6.2.2 条定义的混凝土抗压强度折减系数。采用抛物线-矩形 应力-应变图时，需要用该系数折减最大压应力。这样可使压区的应力分布取平均，使得到的抗压强度小于或等于采用带下降塑性分支的应力-应变图 计算得到的抗压强度<em>。</em></p>\n<p><em>Φ</em><em><sub>c </sub></em>为混凝土的抗力系数。默认值按 AASHTO LRFD (2024) 第 5.5.4.2 条设置。</p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 为考虑横向裂缝影响的折减系数。</p>\n<p><em>f'</em><em><sub>c</sub></em> 为混凝土圆柱体强度（在定义 <em>\\( \\eta_{fc} \\)</em> 时单位为 MPa）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 58\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>k</em><em><sub>c</sub></em><sub>2</sub> 是一个折减系数，其假定与 AASHTO LRFD (2024) 第 5.8.2.5.3a 条及表 5.8.2.5.3a-1 中给出的混凝土效率系数 <em>ν</em> 相同，区别在于 CSFM 对每个有限单元（而不仅仅是拉压杆模型的节点）都检查是否存在垂直于主压应力的主拉应力。</p>\n<h3>混凝土 – 正常使用</h3>\n<p>正常使用分析对强度分析所用的本构模型做了一些简化。忽略承受压力的混凝土应力-应变曲线的塑性分支，而弹性分支为线性且无限延伸。不考虑压力软化规律。只要正常使用状态下材料的合成应力限值明显低于其屈服点（与 AASHTO LRFD 正常使用极限状态的方法一致），这些简化就能提高数值稳定性和计算速度，并且不会降低解的通用性。因此，只有满足所有验算要求时，正常使用分析所用的简化模型才有效。</p>\n<figure data-asset-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\" data-image-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/be2c4149-9e8e-4595-b5a5-7e9fa87c20f3/Concrete%20stress-strain%20for%20serviceability%20-%20AASHTO.png\" data-asset-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\" data-image-id=\"fdcc5f99-090b-4af6-af2f-efa12840c367\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 59\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>在顶部功能区选择长期效应时，长期本构规律（Fig. 59 中的红色曲线）用于裂缝宽度计算、总挠度计算以及预应力构件的应力限值验算。在 IDEA StatiCa Detail 软件中，如 AASHTO LRFD (2024) C5.12.5.3.6-1 所述，长期效应验算采用有效弹性模量。</p>\n<p>\\[E_{eff} = \\frac{E_{c}}{1+\\psi}\\]</p>\n<p>其中：<br><em>E</em><em><sub>c</sub></em> 为 AASHTO LRFD (2024) 第 5.4.2.4 条定义的弹性模量<br><em>ψ</em> 为 AASHTO LRFD (2024) 第 5.4.2.3.2 条定义的徐变系数</p>\n<p>徐变系数由用户在材料属性中定义。</p>\n<p><strong>短期效应</strong></p>\n<p>进行短期验算时，需另行计算，所有荷载均不考虑徐变系数。长期和短期验算的两种计算结果见 Fig. 59。</p>\n<h3>钢筋</h3>\n<p>对非预应力钢筋采用具有明确屈服点的理想弹塑性应力-应变图，见 AASHTO LRFD (2024) 第 5.4.3 条。定义该图只需已知钢筋的基本性能，即强度和弹性模量。</p>\n<p>钢筋的应力-应变图也可由用户定义，但在这种情况下，无法考虑拉力刚化效应（无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 60 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s </sub></em>为钢筋的抗力系数。默认值按 AASHTO LRFD (2024) 第 5.5.4.2 条设置。</p>\n<p><em>f</em><em><sub>y</sub></em> 为钢筋的屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 为钢筋的弹性模量</p>\n<p>选取 10% 作为终止计算的极限应变。根据 ASTM A955/A955M-20c 第 7 条，这一取值被认为是安全的。</p>\n<p>拉力刚化 (Fig. 61) 通过修正裸钢筋的输入应力-应变关系自动考虑，以反映埋置于混凝土中的钢筋的平均刚度 (ε<em><sub>m</sub></em>)。</p>\n<figure data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png\" data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 61\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "6-1-material-models-aashto"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-1-material-models-aashto\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:36</li>\n <li>de-DE: Translated on 27.10.2026 14:16</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:11</li>\n <li>fr-FR: Translated on 27.10.2026 14:58</li>\n <li>hu-HU: Translated on 27.10.2026 18:17</li>\n <li>it-IT: Translated on 27.10.2026 15:35</li>\n <li>ja-JP: Translated on 26.10.2026 12:02</li>\n <li>ko-KR: Translated on 26.10.2026 12:01</li>\n <li>nl-NL: Translated on 27.10.2026 16:50</li>\n <li>pl-PL: Translated on 27.10.2026 19:43</li>\n <li>pt-PT: Translated on 27.10.2026 17:35</li>\n <li>ro-RO: Translated on 27.10.2026 19:00</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:00</li>\n <li>tr-TR: Translated on 26.10.2026 12:02</li>\n <li>vi-VN: Translated on 26.10.2026 12:01</li>\n <li>zh-CN: Translated on 27.10.2026 20:24</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___material_models__a_0b99d24",
"collection": "default",
"id": "0b99d249-5c32-434f-8f94-5df6cabb8f16",
"language": "zh-CN",
"lastModified": "2026-10-27T19:24:40.0709841Z",
"name": "Theoretical background Detail - Material models (AASHTO)",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "6.2 Resistance and load factors"
},
"id": {
"name": "ID",
"type": "text",
"value": "resistance-and-load-factors"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n1e0b8118_0346_01fc_5843_6a60b409c862",
"collection": "default",
"id": "1e0b8118-0346-01fc-5843-6a60b409c862",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "1e0b8118-0346-01fc-5843-6a60b409c862",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "6.2 抗力系数与荷载系数"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/22c831e5-30cb-49da-9661-edf4748ca6aa/Resistance%20factors%20-%20AASHTO.png",
"height": 494,
"width": 796
},
{
"description": null,
"imageId": "d3234a33-200e-46f1-99bd-ef3eb153e6ee",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b3a557f2-2e6a-4b2c-8ba8-bfd210e04c3f/Load%20factors%20AASHTO.png",
"height": 291,
"width": 717
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>协调应力场法符合现代设计规范。由于计算模型仅使用标准材料特性，设计规范规定的分项安全系数格式无需任何调整即可直接应用。这样，输入荷载乘以系数，材料特征值则按相应的抗力系数折减，与常规混凝土分析完全一致。</p>\n<p><strong>抗力系数</strong>的取值见 AASHTO LRFD (2024) 第 5.5.4 条。混凝土和钢筋的默认值取值偏保守，其假设是典型的求解示例为 D 区，这也是 SaT 方法的典型应用场景。不过，该方法可以对任意类型的构件进行建模。因此，若评估的是压力控制或拉力控制的构件，用户可以在首选项中修改强度折减系数的取值。</p>\n<figure data-asset-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\" data-image-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/22c831e5-30cb-49da-9661-edf4748ca6aa/Resistance%20factors%20-%20AASHTO.png\" data-asset-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\" data-image-id=\"4d2e1aae-3ec0-4e09-9461-ce5d5cb329b4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 62\\qquad The setting of resistance factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>荷载系数和荷载组合应按照 AASHTO LRFD Bridge Design Specifications (2024) 第 3.4.1 条及表 3.4.1-1 至表 3.4.1-6 确定。AASHTO LRFD 明确规定了强度极限状态荷载组合（强度 I 至强度 V）以及正常使用极限状态荷载组合（正常使用 I 至正常使用 IV），并给出了各工况对应的荷载系数。</p>\n<p>对于每个模板，程序均包含预定义的基本组合，需根据所处理的构件进一步补充完善。</p>\n<figure data-asset-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\" data-image-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b3a557f2-2e6a-4b2c-8ba8-bfd210e04c3f/Load%20factors%20AASHTO.png\" data-asset-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\" data-image-id=\"d3234a33-200e-46f1-99bd-ef3eb153e6ee\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 63\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "6-2-resistance-and-load-factors"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-2-resistance-and-load-factors\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:37</li>\n <li>de-DE: Translated on 27.10.2026 14:17</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:11</li>\n <li>fr-FR: Translated on 27.10.2026 14:58</li>\n <li>hu-HU: Language translation error (when inserting into Kontent.ai)</li>\n <li>it-IT: Translated on 27.10.2026 15:35</li>\n <li>ja-JP: Translated on 26.10.2026 11:59</li>\n <li>ko-KR: Translated on 26.10.2026 11:58</li>\n <li>nl-NL: Translated on 27.10.2026 16:50</li>\n <li>pl-PL: Translated on 27.10.2026 19:43</li>\n <li>pt-PT: Translated on 27.10.2026 17:35</li>\n <li>ro-RO: Translated on 27.10.2026 19:01</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 11:58</li>\n <li>tr-TR: Translated on 26.10.2026 11:58</li>\n <li>vi-VN: Translated on 26.10.2026 11:58</li>\n <li>zh-CN: Translated on 27.10.2026 20:24</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___resistance_and_loa",
"collection": "default",
"id": "1d3ee7ff-bce3-4aa5-b98c-7b3461b77650",
"language": "zh-CN",
"lastModified": "2026-10-27T19:24:59.7394236Z",
"name": "Theoretical background Detail - Resistance and load factors - AASHTO",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "6.3 Strength limit state"
},
"id": {
"name": "ID",
"type": "text",
"value": "strength-limit-state"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n835a26bd_d5f1_0140_4fe1_9ae73d901010",
"collection": "default",
"id": "835a26bd-d5f1-0140-4fe1-9ae73d901010",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "835a26bd-d5f1-0140-4fe1-9ae73d901010",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "6.3 强度极限状态"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "bdffaabf-ad2b-43bf-b943-deeafb3d57b3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9daaedd3-8368-4677-b72f-1dbc0933690e/Bond%20conditions%20-%20AASHTO.png",
"height": 286,
"width": 587
},
{
"description": null,
"imageId": "8a2ed21c-590e-4061-8c46-c5cc4c60ade1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png",
"height": 442,
"width": 1011
},
{
"description": null,
"imageId": "d3675eaf-0adb-4512-9366-58e4bdf171b1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png",
"height": 520,
"width": 1463
},
{
"description": null,
"imageId": "85c164c0-d864-4723-8c34-a84a426100b2",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png",
"height": 140,
"width": 951
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "rn_25_1__smooth_rebars_in_detail",
"linkId": "182f8ba8-899b-44fc-a1c7-59d562ef8c6c",
"urlSlug": "smooth-rebars-in-detail",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>AASHTO 要求的各项验算均基于模型给出的直接结果进行评估。验算内容包括混凝土强度、钢筋强度和锚固（粘结剪应力）。</p>\n<p>受压<strong>混凝土强度</strong>按有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em>（即辅助结果中的 σ<sub>2</sub>）与限值 <em>f'</em><em><sub>c,lim</sub></em> 之比进行评估。</p>\n<p><strong>钢筋强度</strong>在拉力和压力两种情况下均按裂缝处钢筋应力 <em>f</em><em><sub>s</sub></em> 与规定限值 <em>f</em><em><sub>y,lim</sub></em> 之比进行评估。</p>\n<p><strong>粘结剪应力</strong>单独评估，按有限元分析计算得到的粘结应力 τ<em><sub>b</sub></em> 与粘结强度 <em>f</em><em><sub>bu</sub></em> 之比进行评估。</p>\n<p>然而，AASHTO 并未明确定义粘结强度，因此其数值必须通过定义锚固长度的公式来确定。事实上，粘结强度是确定锚固长度的主要输入量，例如参见 AASHTO LRFD (2024) 第 C5.10.8.2 条或 NCHRP Report 733 附件 E 第 E-9 页。</p>\n<p>AASHTO LRFD (2024) 第 5.10.8.2.1 条和第 5.10.8.2.2 条所述的计算，需要已知 <em>l</em><em><sub>d</sub></em> 范围内横向钢筋的最大中心间距、沿劈裂面锚固的钢筋或钢丝数量、全部横向钢筋的总截面积以及其他几何量。这些量无法在 Detail 软件的通用输入模型中可靠确定，因此采用了 AASHTO LRFD (2014) 第 5.11.2.1.1 条的方法，具体如下：</p>\n<p>假设将钢筋锚固在混凝土块中，锚固长度达到或超过锚固长度 <em>l</em><em><sub>d</sub></em>，则拔出钢筋时将导致钢筋断裂，而不是从混凝土中被拔出。这可以用以下公式表示。</p>\n<p>\\[\\pi\\cdot d_{b} \\cdot l_{d} \\cdot f_{bu}=f_{y}\\cdot A_{b}\\]</p>\n<p>其中：</p>\n<ul>\n <li><em>d</em><em><sub>b</sub></em> 为钢筋直径</li>\n <li><em>l</em><em><sub>d</sub></em> 为锚固长度</li>\n <li><em>f</em><em><sub>bu</sub></em> 为粘结强度</li>\n <li><em>f</em><em><sub>y</sub></em> 为钢筋屈服强度</li>\n <li><em>A</em><em><sub>b</sub></em> 为钢筋面积</li>\n</ul>\n<p>由上式可以很容易地推导出粘结强度的计算公式。</p>\n<p> \\[f_{bu}=\\frac{f_{y}\\cdot A_{b}}{\\pi\\cdot d_{b} \\cdot l_{d} }\\]</p>\n<p><br></p>\n<p>基本受拉锚固长度 <em>l</em><em><sub>db</sub></em> 按 AASHTO LRFD (2014) 第 5.11.2.1.1 条确定如下：</p>\n<p>对于 No. 11 及以下钢筋： \\(l_{bd}=\\max\\left(1.25\\cdot\\dfrac{A_{b}\\cdot f_{y}}{\\sqrt{f'_{c}}},\\ 0.4\\cdot d_{b}\\cdot f_{y}\\right)\\)</p>\n<p>对于 No. 14 钢筋： \\(l_{bd}=\\dfrac{2.70\\cdot f_{y}}{\\sqrt{f'_{c}}}\\)</p>\n<p>对于 No. 18 钢筋： \\(l_{bd}=\\dfrac{3.5\\cdot f_{y}}{\\sqrt{f'_{c}}}\\)</p>\n<p>其中：</p>\n<ul>\n <li><em>A</em><em><sub>b</sub></em> 为钢筋面积 (in<sup>2</sup>)</li>\n <li><em>f</em><em><sub>y</sub></em> 为钢筋规定屈服强度 (ksi)</li>\n <li><em>f'</em><em><sub>c</sub></em> 为混凝土 28 天规定抗压强度，除非另行规定其他龄期 (ksi)</li>\n <li><em>d</em><em><sub>b</sub></em> 为钢筋直径 (in)</li>\n</ul>\n<p>然后，将基本锚固长度 <em>l</em><em><sub>db</sub></em> 乘以 AASHTO LRFD (2014) 第 5.11.2.1.2 条和第 5.11.2.1.3 条所述的系数，即可确定作为输入的锚固长度 <em>l</em><em><sub>d</sub></em>。</p>\n<p>在软件中，第 5.11.2.1.3 条中减小锚固长度的修正系数始终取 1.0。对于顶部水平或接近水平的钢筋，当粘结条件为“不良”时，修正系数取 1.4，具体见下图：</p>\n<figure data-asset-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\" data-image-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9daaedd3-8368-4677-b72f-1dbc0933690e/Bond%20conditions%20-%20AASHTO.png\" data-asset-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\" data-image-id=\"bdffaabf-ad2b-43bf-b943-deeafb3d57b3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 64\\qquad Description of bond conditions; a) b) ‘good’ bond conditions for all bars; c) d) unhatched zone – ‘good’ bond conditions, hatched zone – ‘poor’ bond conditions}}}\\]</em></p>\n<p>混凝土浇筑方向可在软件中设置。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 65\\qquad Direction of concreting}}}\\]</em></p>\n<p>第 5.11.2.1.2 条中确定的所有其他系数均取 1.0，因为软件仅支持普通重量混凝土和无涂层钢筋。</p>\n<p>受压钢筋的粘结剪应力和粘结强度的计算方式与受拉钢筋类似，但采用 AASHTO LRFD (2014) 第 5.11.2.2 条中的公式。</p>\n<p>还可以对<strong>光圆钢筋</strong>进行建模。更多信息请参见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><br></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 和极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 是有限元分析的结果，可以通过两种方式定义。</p>\n<p>\\[F_{tot}=A_{b} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>b</sub></em> 为钢筋面积，<em>f</em><em><sub>s</sub></em> 为钢筋应力。</p>\n<p>或者定义为 锚固力 <em>F</em><em><sub>a </sub></em>与 粘结力 <em>F</em><em><sub>bond</sub></em><em> 之和。</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可沿钢筋长度 <em>l.</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分得到。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是钢筋单元中的最大力，同时考虑钢筋的<strong>强度</strong>和<strong>锚固条件 </strong>（混凝土与钢筋之间的粘结以及锚固弯钩、环形钢筋等）。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{b}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{b}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋周长，<em>l</em> 为从钢筋起点到所关注点的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 66\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元之间的夹角大小计算得到的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括直钢筋（即不考虑锚固端折减）、90 度弯钩、180 度弯钩、完全粘结和连续钢筋。所有这些类型及相应的锚固系数 β 如图 67 所示（适用于纵向钢筋）。所采用的锚固系数值由 AASHTO LRFD (2014) 第 5.11.2.1 条的公式与第 5.11.2.4.1 条的公式对比推导得出。需要注意的是，尽管有多种可选类型，CSFM（协调应力场法）仅区分三种锚固端类型：(i) 锚固长度不折减，(ii) 标准锚固时锚固长度折减 30%，(iii) 完全粘结。</p>\n<figure data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 67\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) 90-degree hook; (c) 180-degree hook; (d) perfect bond; (e) continuous bar}}}\\]</em></p>\n<p>箍筋（适用于梁单元）的锚固系数始终为 β = 1.0。</p>\n<p>为符合 AASHTO 要求，计算中应使用锚固弹簧。锚固弹簧由 β 系数修正，因此用户在定义钢筋的起始和端部条件时，必须选用其中一种可用的锚固类型。 </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "6-3-strength-limit-state"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-3-strength-limit-state\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:37</li>\n <li>de-DE: Translated on 27.10.2026 14:17</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:12</li>\n <li>fr-FR: Translated on 27.10.2026 14:59</li>\n <li>hu-HU: Translated on 27.10.2026 18:18</li>\n <li>it-IT: Translated on 27.10.2026 15:36</li>\n <li>ja-JP: Translated on 26.10.2026 12:09</li>\n <li>ko-KR: Translated on 26.10.2026 12:07</li>\n <li>nl-NL: Translated on 27.10.2026 16:51</li>\n <li>pl-PL: Translated on 27.10.2026 19:44</li>\n <li>pt-PT: Translated on 27.10.2026 17:36</li>\n <li>ro-RO: Translated on 27.10.2026 19:01</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:07</li>\n <li>tr-TR: Translated on 26.10.2026 12:09</li>\n <li>vi-VN: Translated on 26.10.2026 12:08</li>\n <li>zh-CN: Translated on 27.10.2026 20:25</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___strength_limit_sta",
"collection": "default",
"id": "a3ff905f-f430-4f50-9411-e44b10d46e90",
"language": "zh-CN",
"lastModified": "2026-10-27T19:25:40.0059044Z",
"name": "Theoretical background Detail - Strength limit state - AASHTO",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "6.4 Bearing and anchorage zones resistance partially loaded areas"
},
"id": {
"name": "ID",
"type": "text",
"value": "bearing-and-anchorage-zones-resistance-partially-loaded-areas"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "a29abd54_d307_013b_44ed_56d973e7aacc",
"collection": "default",
"id": "a29abd54-d307-013b-44ed-56d973e7aacc",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "a29abd54-d307-013b-44ed-56d973e7aacc",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "6.4 局部受压区与锚固区承载力 – 局部承压面积"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "635e6258-ee56-41b1-8137-b791039b6b3b",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e777285d-ac56-4c61-801e-d2edd9ae0318/PLA%20AASHTO.png",
"height": 725,
"width": 1006
},
{
"description": null,
"imageId": "77fdebe4-afac-4ee7-aee5-716984d4e6d3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG",
"height": 420,
"width": 1633
},
{
"description": null,
"imageId": "05c2e193-bc14-42b5-bc07-da8610febda8",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png",
"height": 406,
"width": 1857
},
{
"description": null,
"imageId": "aff079fa-74f7-4575-a46b-8e589950238a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png",
"height": 474,
"width": 1791
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>在混凝土结构设计中，局部承压区（PLA）主要有两大类：第一类是<strong>支座</strong>，第二类是<strong>锚固区</strong>。 </p>\n<p>根据现行钢筋混凝土结构设计标准，<strong>支座</strong>应考虑混凝土的局部压碎以及横向拉力。对于作用在面积 <em>A</em><em><sub>1</sub></em> 上的均布荷载，混凝土的抗压承载力可根据设计分布面积 <em>A</em><em><sub>2</sub></em> 提高至多两倍。参见 AASHTO LRFD (2024) 第 5.6.5 条。<br></p>\n<figure data-asset-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\" data-image-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e777285d-ac56-4c61-801e-d2edd9ae0318/PLA%20AASHTO.png\" data-asset-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\" data-image-id=\"635e6258-ee56-41b1-8137-b791039b6b3b\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 68\\qquad Partially loaded areas for bearings according to AASHTO LRFD (2024) Article 5.6.5}}}\\]</em></p>\n<p>对于后张<strong>锚固区</strong>，应遵循 AASHTO LRFD (2024) 第 5.8.4.4 条。</p>\n<p>局部承压区必须配置足够的横向钢筋，用以传递该区域产生的劈裂力。若没有所需的横向钢筋，则不能考虑提高混凝土的抗压承载力。</p>\n<p><br></p>\n<p><strong>CSFM（协调应力场法）中的局部承压区</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 69\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>采用 CSFM（协调应力场法），可以在设计和评估钢筋混凝土结构时考虑局部承压区内混凝土抗压承载力提高的影响。由于 CSFM（协调应力场法）是墙体（2D）模型，而局部承压区属于空间（3D）问题，因此需要找到一种能够将这两类不同问题结合起来的解决方案（<em>图 69</em>）。如果启用“局部承压区”功能，则按照 ACI 生成允许的锥体几何（<em>图 68</em>）。针对指定的混凝土构件几何和各 PLA 的尺寸，所有几何冲突均在 3D 中完整求解。随后，建立局部承压区的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 70\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>事实证明，修改材料模型并不是合适的方法，主要原因是将属性映射到有限元网格上存在困难。经研究确定，与有限元网格无关的方法是更合适的解决方案。针对已知的受压锥体几何，建立完全协调的虚拟压杆（<em>图 70</em> <em>和图 71</em>）。这些压杆具有与模型中所用混凝土相同的材料属性，包括应力-应变图。锥体的形状决定压杆的方向，压杆将荷载沿 PLA 逐步分布到设计分布面积上。虚拟压杆的面密度在锥体各部位是变化的，并在荷载方向上增加虚拟的混凝土面积。在受荷面积 (<em>A</em><em><sub>1</sub></em>) 的位置，按比值 \\(\\sqrt{A_{1} \\cdot A_{2}} - A_{real}\\) 增加一块虚拟混凝土面积（其中 <em>A</em><em><sub>real</sub></em> 为 2D 计算模型中假定的支承面积），该面积向设计分布面积 (<em>A</em><em><sub>2</sub></em>) 方向线性减小至零。该方案可确保整个锥体体积内混凝土的压应力保持恒定。</p>\n<figure data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png\" data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{2}}{A_{1}}} - \\frac{A_{real}}{A_{1}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 71\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部承压区的承载力按照 AASHTO LRFD (2024) 第 5.6.5 条中规定的设计分布面积与受荷面积之比提高。需要注意的是，这是一个设计模型，无法精确描述局部承压区上的应力状态，其实际传力路径要复杂得多。不过，该方案能够在考虑局部承压区承载力提高的同时，将荷载正确地分布到整个模型。此外，它还能在该区域正确引入横向应力，从而针对劈裂力正确地设计钢筋。</p>\n<p>AASHTO LRFD (2024) 第 5.8.4.4 条给出了<strong>承压</strong>应力的允许值 <em>0.85f</em><em><sub>c</sub></em><em>'</em>。密度受到限制，以确保不超过公式 5.6.5-3 中给出的最大两倍承载力。 </p>\n<p>对于<strong>锚固区</strong>，软件中 PLA 的使用方式与支座相同。因此，第 5.8.4.4 条和第 5.8.4.5 条所定义的局部区和整体区的压应力必须手动校核。所以，PLA 仅用于避免在局部区超出应变准则而导致计算过早中止。另一方面，用于抵抗一般区（第 5.8.4.5 条定义）中爆裂应力、平面内剥落应力和边缘拉应力的钢筋，可以直接在软件中方便地验算。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "6-4-bearing-and-anchorage-zones-resistance-partially-loaded-areas"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-4-bearing-and-anchorage-zones-resistance-partially-loaded-areas\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:38</li>\n <li>de-DE: Translated on 27.10.2026 14:18</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:13</li>\n <li>fr-FR: Translated on 27.10.2026 14:59</li>\n <li>hu-HU: Translated on 27.10.2026 18:18</li>\n <li>it-IT: Translated on 27.10.2026 15:36</li>\n <li>ja-JP: Translated on 26.10.2026 12:06</li>\n <li>ko-KR: Translated on 26.10.2026 12:05</li>\n <li>nl-NL: Translated on 27.10.2026 16:51</li>\n <li>pl-PL: Translated on 27.10.2026 19:44</li>\n <li>pt-PT: Translated on 27.10.2026 17:37</li>\n <li>ro-RO: Translated on 27.10.2026 19:02</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:05</li>\n <li>tr-TR: Translated on 26.10.2026 12:06</li>\n <li>vi-VN: Translated on 26.10.2026 12:05</li>\n <li>zh-CN: Translated on 27.10.2026 20:26</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___bearing_and_anchor_69cbe39",
"collection": "default",
"id": "69cbe393-59e2-4587-a72e-45cf2c2b0e45",
"language": "zh-CN",
"lastModified": "2026-10-27T19:26:09.8240964Z",
"name": "Theoretical background Detail – Bearing and anchorage zones – Partially loaded areas - AASHTO",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "6.5 Service limit state"
},
"id": {
"name": "ID",
"type": "text",
"value": "service-limit-state"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "d19c5c7a_4da5_01be_7a24_1918c7d60c76",
"collection": "default",
"id": "d19c5c7a-4da5-01be-7a24-1918c7d60c76",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "d19c5c7a-4da5-01be-7a24-1918c7d60c76",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "6.5 正常使用极限状态"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "0946a8a5-4fdf-4626-ad28-c49499d4d6eb",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aacf656a-eb2c-4aae-a8b2-6b1c16cdc864/Compressive%20Stress%20Limits%20in%20Prestressed%20Concrete%20at%20Service%20Limit%20State%20-%20AASHTO.png",
"height": 141,
"width": 1110
},
{
"description": null,
"imageId": "ac528856-0620-4e95-9877-ea4415ba38b5",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bf637c0b-a972-4836-a119-45f59df9ed58/Combination%20types%20-%20AASHTO.png",
"height": 208,
"width": 972
},
{
"description": null,
"imageId": "ceefbba0-847a-4d2d-8c6c-5430e5e9c43d",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/74bf96e4-46c2-4bb5-9b9f-2ab9ebf8f58b/Stress%20limitation%20model%20type%20-%20AASHTO.png",
"height": 415,
"width": 2559
},
{
"description": null,
"imageId": "ddf1f284-82ac-44ca-a815-6e64b4471afe",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b95113f5-c76d-4a13-8962-99fd504ce2f2/Deflection%20check%20AASHTO.png",
"height": 97,
"width": 674
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>正常使用极限状态验算包括应力限值、裂缝宽度和挠度限值。混凝土和钢筋单元的应力按照 AASHTO LRFD 进行校核，方式与承载能力极限状态（Strength）的规定类似。</p>\n<h3>应力限值</h3>\n<p>混凝土压应力仅对预应力构件（模型中存在预应力荷载工况时）进行评估。评估方法是计算正常使用状态下有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em> <em>= σ</em><em><sub>c</sub></em><sub>2</sub><em><sub> </sub></em>与限值之比，限值依据 AASHTO LRFD 表 5.9.2.3.2a-1 确定。</p>\n<figure data-asset-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\" data-image-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aacf656a-eb2c-4aae-a8b2-6b1c16cdc864/Compressive%20Stress%20Limits%20in%20Prestressed%20Concrete%20at%20Service%20Limit%20State%20-%20AASHTO.png\" data-asset-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\" data-image-id=\"0946a8a5-4fdf-4626-ad28-c49499d4d6eb\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 72\\qquad Concrete compressive stress limits at service loads}}}\\]</em></p>\n<p>在软件中，<em>预应力加永久荷载</em>按持续荷载（Sustain load）处理，<em>预应力、永久荷载和可变荷载</em>按总荷载（Total load）处理。</p>\n<figure data-asset-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" data-image-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bf637c0b-a972-4836-a119-45f59df9ed58/Combination%20types%20-%20AASHTO.png\" data-asset-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" data-image-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 73\\qquad Serviceability combination types}}}\\]</em></p>\n<p>此外，用户始终可以对短期效应和长期效应进行分析，所用材料模型可考虑或不考虑徐变系数，详见\"材料模型（AASHTO）\"一节。</p>\n<figure data-asset-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\" data-image-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/74bf96e4-46c2-4bb5-9b9f-2ab9ebf8f58b/Stress%20limitation%20model%20type%20-%20AASHTO.png\" data-asset-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\" data-image-id=\"ceefbba0-847a-4d2d-8c6c-5430e5e9c43d\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 74\\qquad Serviceability material models}}}\\]</em></p>\n<h3>挠度</h3>\n<p>对于每个启用了挠度评估的组合，均会计算瞬时挠度和总挠度。 </p>\n<ul>\n <li>计算瞬时挠度时，采用 AASHTO LRFD（2024）第 5.4.2.4 条规定的弹性模量 <em>E</em><em><sub>c</sub></em>。 </li>\n <li>计算总挠度时，采用 AASHTO LRFD（2024）第 C5.12.5.3.6 条规定的有效弹性模量 <em>E</em><em><sub>c,eff</sub></em>。 </li>\n</ul>\n<p>请参阅本文档中的章节\"<em>材料模型（AASHTO）- 混凝土 – 正常使用</em>\"。</p>\n<p>挠度校核需在顶部功能区中启用。用户根据所分析单元的类型，按照 AASHTO LRFD（2024）第 2.5.2.6.2 条设定挠度限值。</p>\n<figure data-asset-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\" data-image-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b95113f5-c76d-4a13-8962-99fd504ce2f2/Deflection%20check%20AASHTO.png\" data-asset-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\" data-image-id=\"ddf1f284-82ac-44ca-a815-6e64b4471afe\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 75\\qquad Maximum allowable deflection value}}}\\]</em></p>\n<p>无法校核裁切端处的挠度。</p>\n<h3>裂缝宽度</h3>\n<p>裂缝宽度和裂缝方向仅针对长期效应计算（采用 AASHTO LRFD（2024）第 C5.12.5.3.6 条规定的 <em>E</em><em><sub>c,eff</sub></em>），且仅针对启用了裂缝宽度评估的组合。基于用户指定限值的验算如下：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中：</p>\n<p><em>w</em> 由有限元分析计算得到的裂缝宽度，</p>\n<p><em>w</em><em><sub>lim</sub></em> 用户定义的裂缝宽度限值。</p>\n<p>限值 <em>w</em><em><sub>lim</sub></em> 应根据单元类型和暴露等级，按照 AASHTO LRFD（2024）第 5.6.7 条及其条文说明确定。 </p>\n<p>裂缝宽度有两种计算方式（稳定裂缝和非稳定裂缝）。一般情况下（稳定裂缝），裂缝宽度通过对钢筋一维单元上的应变进行积分得到。裂缝方向则根据最靠近的三个积分点计算，这些积分点位于二维混凝土单元上，距给定钢筋一维有限单元的中心最近。这种计算裂缝方向的方法与裂缝的实际位置并不一致，但仍能给出具有代表性的数值，由此得到的裂缝宽度结果可与规范要求的钢筋位置处的裂缝宽度限值进行比较。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "6-5-service-limit-state"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-5-service-limit-state\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:38</li>\n <li>de-DE: Translated on 27.10.2026 14:18</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:13</li>\n <li>fr-FR: Translated on 27.10.2026 15:00</li>\n <li>hu-HU: Translated on 27.10.2026 18:19</li>\n <li>it-IT: Translated on 27.10.2026 15:37</li>\n <li>ja-JP: Translated on 26.10.2026 12:09</li>\n <li>ko-KR: Translated on 26.10.2026 12:09</li>\n <li>nl-NL: Translated on 27.10.2026 16:52</li>\n <li>pl-PL: Translated on 27.10.2026 19:45</li>\n <li>pt-PT: Translated on 27.10.2026 17:37</li>\n <li>ro-RO: Translated on 27.10.2026 19:03</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:08</li>\n <li>tr-TR: Translated on 26.10.2026 12:09</li>\n <li>vi-VN: Translated on 26.10.2026 12:09</li>\n <li>zh-CN: Translated on 27.10.2026 20:26</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___service_limit_stat",
"collection": "default",
"id": "740b1c37-551b-4c6b-9841-f493f718cd47",
"language": "zh-CN",
"lastModified": "2026-10-27T19:26:38.9926401Z",
"name": "Theoretical background Detail – Service limit state – AASHTO",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "7.1 Material models (AUS)"
},
"id": {
"name": "ID",
"type": "text",
"value": "material-models-aus"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n83eff71e_cb6d_0152_d7f9_4621fe4095f0",
"collection": "default",
"id": "83eff71e-cb6d-0152-d7f9-4621fe4095f0",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "83eff71e-cb6d-0152-d7f9-4621fe4095f0",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "7.1 材料模型（AS 3600）"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc47139c-3c53-4397-bfa6-71fe09d5c24b/Concrete%20stress-strain%20diagram%20CSFM%20-%20AUS.png",
"height": 571,
"width": 859
},
{
"description": null,
"imageId": "b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG",
"height": 574,
"width": 1500
},
{
"description": null,
"imageId": "1a187098-8984-42f2-b203-d261cab0f727",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5b3dc17b-2a5b-4258-8495-b5d436e4885b/Concrete%20stress-strain%20for%20serviceability%20-%20AUS.png",
"height": 628,
"width": 1181
},
{
"description": null,
"imageId": "7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f9c75c70-4a16-4077-963e-7ccbed22202a/Desgn%20creep%20factor%20-%20AUS.png",
"height": 649,
"width": 1916
},
{
"description": null,
"imageId": "b5b99d46-a4ed-4625-853e-cdc4c4ede122",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4e33b934-9d0f-4ba7-9764-4f31801c752b/Steel%20stress-strain%20diagram%20CSFM%20-%20AUS.png",
"height": 719,
"width": 938
},
{
"description": null,
"imageId": "c9465d3e-05e3-4514-a218-3a96876ed503",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b27b5ab6-24ea-410b-901a-fccbd7e4005f/Tension%20stiffening%20CSFM%20-%20AUS.png",
"height": 569,
"width": 883
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<h3>混凝土 - 强度</h3>\n<p>CSFM（协调应力场法）中用于强度计算的混凝土模型基于抛物线-塑性应力-应变曲线。与经典钢筋混凝土设计一样，该模型忽略混凝土的抗拉强度。</p>\n<figure data-asset-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\" data-image-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc47139c-3c53-4397-bfa6-71fe09d5c24b/Concrete%20stress-strain%20diagram%20CSFM%20-%20AUS.png\" data-asset-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\" data-image-id=\"1ce5c049-0015-4d84-8bd2-9bacc8e4b5b4\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 76\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p><em>IDEA StatiCa Detail</em> 中的 CSFM（协调应力场法）实现没有针对受压混凝土考虑以应变表示的显式破坏准则（即达到峰值应力后，采用塑性分支，其 ε<em><sub>c</sub></em><sub>0</sub> 最大值为 5%，而 AS 3600 第 8.3.1 条假定极限应变小于 0.3%）。这一简化无法验算发生受压破坏的结构的变形能力。但是，除了考虑开裂混凝土的系数（<em>k</em><em><sub>c</sub></em><sub>2</sub>，见图 77）之外，如果还通过 <em>fib</em> Model Code 2010 中定义的折减系数 <em>\\(\\eta_{fc}\\)</em> 来考虑混凝土强度提高时脆性增大的影响，则可以正确预测强度，该折减系数如下：</p>\n<p>\\[f'_{c,lim}=\\alpha_{2}\\cdot\\phi_{s}\\cdot \\beta \\cdot \\eta_{fc}\\cdot f'_{c}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em><sub>2</sub> 为 AS 3600 第 8.3.1 条定义的混凝土抗压强度折减系数<br>采用抛物线-矩形应力-应变图时，需要用该系数折减最大压应力。这样可使受压区的应力分布取平均值，使得到的抗压强度小于或等于采用带下降塑性分支的应力-应变图计算得到的 抗压强度<em>。</em>矩形应力块的处理方法与此类似，见第 8.1.3 章。</p>\n<p><em>Φ</em><em><sub>s </sub></em>为混凝土的应力折减系数。默认值按 AS 3600 表 2.2.3 设定。</p>\n<p><em>β</em> 为考虑横向裂缝影响的折减系数（本文中也称为 <em>k</em><em><sub>c</sub></em><sub>2</sub>）</p>\n<p><em>f'</em><em><sub>c</sub></em> 为混凝土圆柱体强度（在定义 <em>\\( \\eta_{fc} \\)</em> 时以 MPa 为单位）。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 77\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>β</em> 是与第 2.2.3 章定义的有效抗压强度系数基于相同原理的折减系数。确定该系数所依据的文献（包括 AS3600 标准的相关背景）可参见 AS3600:2018 Sup 1:2022 第 C2.2.3 条。</p>\n<h3>混凝土 – 正常使用</h3>\n<p>正常使用分析对用于强度分析的本构模型作了一些简化。混凝土受压应力-应变曲线的塑性分支被忽略，弹性分支为线性且无限延伸。不考虑压力软化规律。这些简化提高了数值稳定性和计算速度，并且只要正常使用状态下材料的应力结果明显低于其屈服点（如 AS3600 所要求），就不会降低解的通用性。因此，用于正常使用分析的简化模型仅在满足所有验算要求时才有效。</p>\n<figure data-asset-id=\"1a187098-8984-42f2-b203-d261cab0f727\" data-image-id=\"1a187098-8984-42f2-b203-d261cab0f727\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5b3dc17b-2a5b-4258-8495-b5d436e4885b/Concrete%20stress-strain%20for%20serviceability%20-%20AUS.png\" data-asset-id=\"1a187098-8984-42f2-b203-d261cab0f727\" data-image-id=\"1a187098-8984-42f2-b203-d261cab0f727\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 78\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><br></p>\n<p><strong>长期效应</strong></p>\n<p>在正常使用分析中，混凝土的长期效应通过 AS 3600 第 3.1.8 条的设计徐变系数（<em>φ</em><em><sub>cc</sub></em>，默认取 2.5）来考虑，该系数用于修正混凝土的割线弹性模量（<em>E</em><em><sub>c</sub></em>）， 如下所示：</p>\n<p>\\[E_{c,eff} = \\frac{E_{c}}{1+\\varphi_{cc}}\\]</p>\n<p>荷载增量按以下顺序依次计算：预应力 - 永久荷载 - 可变荷载，每个增量采用相应的有效弹性模量，如图 78 所示。徐变系数由用户在材料属性中定义，并应按 AS 3600 第 3.1.8.3 条计算。</p>\n<figure data-asset-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\" data-image-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f9c75c70-4a16-4077-963e-7ccbed22202a/Desgn%20creep%20factor%20-%20AUS.png\" data-asset-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\" data-image-id=\"7c1e2af1-4d0f-46da-8cf0-d5bee4931cf3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 79\\qquad Definition of the design creep factor}}}\\]</em></p>\n<p><strong>短期效应</strong></p>\n<p>为进行短期验算，需另行计算一次，其中所有荷载均不考虑持续荷载的时间相关系数。长期和短期验算的两次计算均见图 78。</p>\n<h3>钢筋</h3>\n<p>对于非预应力钢筋，采用具有确定屈服点的理想弹塑性应力-应变图，见 AS 3600 第 3.2 节。定义该图只需已知钢筋的基本属性，即强度和弹性模量。</p>\n<p>钢筋的应力-应变图也可由用户自行定义，但在这种情况下无法考虑拉力刚化效应（无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" data-image-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4e33b934-9d0f-4ba7-9764-4f31801c752b/Steel%20stress-strain%20diagram%20CSFM%20-%20AUS.png\" data-asset-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" data-image-id=\"b5b99d46-a4ed-4625-853e-cdc4c4ede122\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 80 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s </sub></em>为钢筋的强度折减系数。默认值按 AS 3600 表 2.2.3 设定。</p>\n<p><em>f</em><em><sub>y</sub></em> 为钢筋的屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 为钢筋的弹性模量</p>\n<p>拉力刚化（图 81） 通过修正裸钢筋的输入应力-应变关系自动考虑，以反映埋入混凝土中的钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" data-image-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b27b5ab6-24ea-410b-901a-fccbd7e4005f/Tension%20stiffening%20CSFM%20-%20AUS.png\" data-asset-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" data-image-id=\"c9465d3e-05e3-4514-a218-3a96876ed503\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 81\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "7-1-material-models-as-3600"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"material-models-aci\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": []
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:39</li>\n <li>de-DE: Translated on 27.10.2026 14:19</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:14</li>\n <li>fr-FR: Translated on 27.10.2026 15:00</li>\n <li>hu-HU: Translated on 27.10.2026 18:19</li>\n <li>it-IT: Translated on 27.10.2026 15:37</li>\n <li>ja-JP: Translated on 26.10.2026 12:14</li>\n <li>ko-KR: Translated on 26.10.2026 12:13</li>\n <li>nl-NL: Translated on 27.10.2026 16:53</li>\n <li>pl-PL: Translated on 27.10.2026 19:46</li>\n <li>pt-PT: Translated on 27.10.2026 17:38</li>\n <li>ro-RO: Translated on 27.10.2026 19:03</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:13</li>\n <li>tr-TR: Translated on 26.10.2026 12:14</li>\n <li>vi-VN: Translated on 26.10.2026 12:14</li>\n <li>zh-CN: Translated on 27.10.2026 20:27</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___material_models__a_b7035a6",
"collection": "default",
"id": "b7035a6c-2e63-49b0-9f5a-4924322cc969",
"language": "zh-CN",
"lastModified": "2026-10-27T19:27:09.7304679Z",
"name": "Theoretical background Detail - Material models (AS 3600)",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "7.2 Stress reduction and load factors"
},
"id": {
"name": "ID",
"type": "text",
"value": "stress-reduction-and-load-factors"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n3541764a_859d_01a8_0078_115c1a96acda",
"collection": "default",
"id": "3541764a-859d-01a8-0078-115c1a96acda",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "3541764a-859d-01a8-0078-115c1a96acda",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "7.2 应力折减和荷载系数"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "61735d28-361b-4275-b2d7-9ca00e01ebcf",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1d32796c-ae70-42fb-a3d3-4542e785f5b1/Stress%20reduction%20factors_AUS.png",
"height": 496,
"width": 876
},
{
"description": null,
"imageId": "c986c0fc-2e9a-42e1-95b4-1055d3ae76e2",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/887ee546-c598-41fd-b494-c43ccbc55194/Load%20factors%20AUS.png",
"height": 217,
"width": 609
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>协调应力场法符合现代设计规范。由于计算模型仅使用标准材料特性，规范中规定的分项安全系数格式无需任何调整即可直接应用。这样，输入荷载将乘以相应系数，而材料特征值则通过相应的应力折减系数进行折减，与常规混凝土分析完全一致。</p>\n<p><strong>应力折减系数</strong>的取值在 AUS 3600 Cl. 2.2.3 中有规定。混凝土和钢筋的默认值按照表 2.2.3 设置</p>\n<figure data-asset-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\" data-image-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1d32796c-ae70-42fb-a3d3-4542e785f5b1/Stress%20reduction%20factors_AUS.png\" data-asset-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\" data-image-id=\"61735d28-361b-4275-b2d7-9ca00e01ebcf\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 82\\qquad The setting of stress reduction factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p><br></p>\n<p>强度组合的<strong>荷载系数</strong>应按照 AS 3600 Cl. 4.2.2 确定。正常使用组合的荷载系数应按照表 4.1 确定。所有模板中的荷载系数均已预先定义。</p>\n<figure data-asset-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\" data-image-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/887ee546-c598-41fd-b494-c43ccbc55194/Load%20factors%20AUS.png\" data-asset-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\" data-image-id=\"c986c0fc-2e9a-42e1-95b4-1055d3ae76e2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 83\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "7-2-stress-reduction-and-load-factors"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"stress-reduction-and-load-factors\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:39</li>\n <li>de-DE: Translated on 27.10.2026 14:19</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:14</li>\n <li>fr-FR: Translated on 27.10.2026 15:01</li>\n <li>hu-HU: Translated on 27.10.2026 18:20</li>\n <li>it-IT: Translated on 27.10.2026 15:38</li>\n <li>ja-JP: Translated on 26.10.2026 12:12</li>\n <li>ko-KR: Translated on 26.10.2026 12:12</li>\n <li>nl-NL: Translated on 27.10.2026 16:53</li>\n <li>pl-PL: Translated on 27.10.2026 19:46</li>\n <li>pt-PT: Translated on 27.10.2026 17:38</li>\n <li>ro-RO: Translated on 27.10.2026 19:04</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:11</li>\n <li>tr-TR: Translated on 26.10.2026 12:12</li>\n <li>vi-VN: Translated on 26.10.2026 12:12</li>\n <li>zh-CN: Translated on 27.10.2026 20:27</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___stress_reduction_a",
"collection": "default",
"id": "86837551-3791-4e0a-bdac-5523ce25f882",
"language": "zh-CN",
"lastModified": "2026-10-27T19:27:24.218931Z",
"name": "Theoretical background Detail - Stress reduction and load factors - AUS",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "7.3 Strength and anchorage verifications"
},
"id": {
"name": "ID",
"type": "text",
"value": "strength-and-anchorage-verifications"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n10a5f687_325c_014e_ea85_7f516e5dd6e4",
"collection": "default",
"id": "10a5f687-325c-014e-ea85-7f516e5dd6e4",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "10a5f687-325c-014e-ea85-7f516e5dd6e4",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "7.3 强度与锚固验算"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "8a2ed21c-590e-4061-8c46-c5cc4c60ade1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png",
"height": 442,
"width": 1011
},
{
"description": null,
"imageId": "d3675eaf-0adb-4512-9366-58e4bdf171b1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png",
"height": 520,
"width": 1463
},
{
"description": null,
"imageId": "ea687a47-41cc-487f-b7b9-2ed97bfb2932",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/021688e6-24c8-441b-8210-9f0bb4377e75/Available%20anchorage%20types%20for%20longitudinal%20rebars_AUS.png",
"height": 140,
"width": 951
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "rn_25_1__smooth_rebars_in_detail",
"linkId": "182f8ba8-899b-44fc-a1c7-59d562ef8c6c",
"urlSlug": "smooth-rebars-in-detail",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>AS 3600 要求的各项验算均基于模型给出的直接结果进行评估。验算内容包括混凝土强度、钢筋强度和锚固（粘结剪应力）。</p>\n<p>受压<strong>混凝土强度</strong>按有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em>（即辅助结果中的 σ<sub>2</sub>）与限值 <em>f'</em><em><sub>c,lim</sub></em> 之比进行评估。</p>\n<p><strong>钢筋强度</strong>在受拉和受压两种情况下，均按裂缝处钢筋应力 <em>f</em><em><sub>s</sub></em> 与规定限值 <em>f</em><em><sub>sy,lim</sub></em> 之比进行评估。</p>\n<p><strong>粘结剪应力</strong>单独评估，按有限元分析计算得到的粘结应力 τ<em><sub>b</sub></em> 与设计极限粘结应力 <em>f</em><em><sub>bu</sub></em> 之比确定。</p>\n<p>软件在确定设计极限粘结应力 <em>f</em><em><sub>bu</sub></em> 时，采用 AS3600:2018 Sup 1:2022 中定义的公式 C13.1.2.2。</p>\n<p>\\[f_{bu}=\\frac{k_{2}}{k_{1} \\cdot k_{3}} \\cdot (0.5 \\cdot \\sqrt{f'_{c}})\\]</p>\n<p>其中 <em>f'</em><em><sub>c</sub></em><em> ≤ 65 MPa</em>（公式中以 MPa 为单位），<em>k</em> 系数按 AS 3600 Cl. 13.1.2.2 确定如下：</p>\n<p><em>k</em><em><sub>3</sub></em><em> = 0.7</em> （适用于所有钢筋的保守取值）<br><em>k</em><em><sub>2</sub></em><em> = (132 - d</em><em><sub>b</sub></em><em>) / 100</em> （<em>d</em><em><sub>b</sub></em> 为钢筋直径，单位为毫米）<br>= 1.3，适用于水平钢筋且钢筋下方浇筑的混凝土厚度大于 300 mm 的情况；其他情况取 1.0</p>\n<p><em>k</em><em><sub>1</sub></em> 由软件根据钢筋在模型中的位置以及浇筑方向自动确定，浇筑方向可在软件中为每个项目分别设置，如下所示。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 84\\qquad Direction of concreting}}}\\]</em></p>\n<p>基本锚固长度 <em>L</em><em><sub>sy,tb</sub></em> 按 AS 3600 中的公式 13.1.2.2 计算如下：</p>\n<p>\\[L_{sy,tb}=\\frac{0.5\\cdot k_{1}\\cdot k_{3}\\cdot f_{sy}\\cdot d_{b}}{k_{2}\\cdot \\sqrt{f'_{c}}}\\ge 29 \\cdot k_{1}\\cdot d_{b}\\]</p>\n<p>由公式可见，基本锚固长度 <em>L</em><em><sub>sy,tb</sub></em> 有下限值，因此软件中的设计极限粘结应力 <em>f</em><em><sub>bu</sub></em> 也必须以同样的方式加以限制，即应满足：</p>\n<p>\\[f_{bu}\\le \\frac{f_{sy}}{116 \\cdot k_{1}} \\]</p>\n<p>其中 <em>f</em><em><sub>sy</sub></em> 的单位为 MPa。</p>\n<p><em>f</em><em><sub>bu</sub></em> 限值的推导如下：</p>\n<p>\\[f_{bu}= \\frac{f_{sy}\\cdot A_{s}}{ \\pi \\cdot d_{b} \\cdot L_{sy,tb}}=\\frac{f_{sy}\\cdot \\pi \\cdot d_{b}^{2}}{4 \\cdot \\pi \\cdot d_{b} \\cdot 29 \\cdot k{1} \\cdot d_{b}} =\\frac{f_{sy}}{116 \\cdot k_{1}} \\]</p>\n<p>软件还提供<strong>光圆钢筋</strong>的建模选项。更多信息请参见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><br></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 是有限元分析的结果，可通过两种方式定义。</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面面积，<em>f</em><em><sub>s</sub></em> 为钢筋应力。</p>\n<p>或者定义为 锚固力 <em>F</em><em><sub>a </sub></em>与 粘结力 <em>F</em><em><sub>bond</sub></em><em> </em>之和。</p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分得到。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋的周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是钢筋单元中的最大力，同时考虑钢筋的<strong>强度</strong>以及<strong>锚固条件 </strong>（混凝土与钢筋之间的粘结，以及锚固弯钩、环形锚固等）。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋的周长，<em>l</em> 为从钢筋起点到所关注位置的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 85\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元之间的夹角大小计算得到的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>CSFM（协调应力场法）中可用的<strong>锚固类型</strong>包括：直钢筋（即无锚固端折减）、标准直角弯钩、标准弯钩、完全粘结和连续钢筋。图 86 给出了纵向钢筋的所有这些类型及相应的锚固系数 β。所采用的锚固系数取值源自 AS 3600 Cl. 13.1.2。需要说明的是，CSFM（协调应力场法）区分三种锚固端类型：(i) 锚固长度不折减；(ii) 标准化锚固时，锚固长度折减 50%；(iii) 完全粘结。</p>\n<figure data-asset-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" data-image-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/021688e6-24c8-441b-8210-9f0bb4377e75/Available%20anchorage%20types%20for%20longitudinal%20rebars_AUS.png\" data-asset-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" data-image-id=\"ea687a47-41cc-487f-b7b9-2ed97bfb2932\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 86\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) Standard cog; (c) Standard hook; (d) perfect bond; (e) continuous bar}}}\\]</em></p>\n<p>箍筋的锚固系数始终为 β = 1.0。</p>\n<p>为符合 AS 3600 的要求，计算中应使用锚固弹簧，且锚固弹簧由 β 系数修正，因此用户在定义钢筋的起点和终点条件时，必须选用其中一种可用的锚固类型。 </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "7-3-strength-and-anchorage-verifications"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"7-3-strength-and-anchorage-verifications\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:40</li>\n <li>de-DE: Translated on 27.10.2026 14:20</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:14</li>\n <li>fr-FR: Translated on 27.10.2026 15:01</li>\n <li>hu-HU: Translated on 27.10.2026 18:20</li>\n <li>it-IT: Translated on 27.10.2026 15:38</li>\n <li>ja-JP: Translated on 26.10.2026 12:22</li>\n <li>ko-KR: Translated on 26.10.2026 12:21</li>\n <li>nl-NL: Translated on 27.10.2026 16:54</li>\n <li>pl-PL: Translated on 27.10.2026 19:47</li>\n <li>pt-PT: Translated on 27.10.2026 17:39</li>\n <li>ro-RO: Translated on 27.10.2026 19:04</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:20</li>\n <li>tr-TR: Translated on 26.10.2026 12:22</li>\n <li>vi-VN: Translated on 26.10.2026 12:21</li>\n <li>zh-CN: Translated on 27.10.2026 20:28</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": "{\"version\":1,\"requestId\":\"9aaf5d4e-e299-45be-b8ee-1e69bcaf2f23\",\"selections\":[{\"kind\":\"element\",\"path\":{\"rootElementId\":\"8c772882-d641-44d1-8dd1-be528f66940b\",\"componentIds\":[],\"elementId\":\"8c772882-d641-44d1-8dd1-be528f66940b\"}},{\"kind\":\"element\",\"path\":{\"rootElementId\":\"1dc89cef-ec7f-4a81-81ac-25c92f5d92e1\",\"componentIds\":[],\"elementId\":\"1dc89cef-ec7f-4a81-81ac-25c92f5d92e1\"}},{\"kind\":\"element\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[],\"elementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\"}}]}"
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___strength_analysis__8bc3bfe",
"collection": "default",
"id": "8bc3bfea-3de7-4f48-bc7e-4b5c199c56ba",
"language": "zh-CN",
"lastModified": "2026-10-27T19:28:00.8670437Z",
"name": "Theoretical background Detail - Strength analysis - AUS",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "7.4 Serviceability checks"
},
"id": {
"name": "ID",
"type": "text",
"value": "serviceability-checks"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "ec38c193_dd6d_018f_8d40_071dc9fd107a",
"collection": "default",
"id": "ec38c193-dd6d-018f-8d40-071dc9fd107a",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "ec38c193-dd6d-018f-8d40-071dc9fd107a",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "7.4 正常使用极限状态校核"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "c0d94b19-9672-487a-ac1b-41ee34a7f969",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b1e12226-ebe6-4ecf-be42-0f9857c02cf9/Maximum%20allowable%20deflections.png",
"height": 96,
"width": 587
},
{
"description": null,
"imageId": "58beec32-b322-44cc-8a6f-af552cb75f67",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/34472a7f-e0a5-4d30-b990-361d7cd59f2b/REcommended%20final%20design%20crack%20widths%20-%20AUS.png",
"height": 619,
"width": 1035
},
{
"description": null,
"imageId": "709c3d3e-e2bf-4160-9dc7-8edfba902ee0",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e16caacd-4f7b-4ba4-a7d1-48dd71a47890/Reccomended%20max%20cracks%20widths%20values%20for%20long-term%20loads.png",
"height": 310,
"width": 1130
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>正常使用极限状态验算包括裂缝宽度和挠度限值的校核。 </p>\n<h3>挠度</h3>\n<p>根据所选组合类型(长期或短期),分别计算长期挠度或短期挠度。最大允许挠度值应由用户确定,并应符合 AS 3600 Cl. 2.3.2 的规定。 </p>\n<figure data-asset-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\" data-image-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b1e12226-ebe6-4ecf-be42-0f9857c02cf9/Maximum%20allowable%20deflections.png\" data-asset-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\" data-image-id=\"c0d94b19-9672-487a-ac1b-41ee34a7f969\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 87\\qquad Maximum allowable deflection values}}}\\]</em></p>\n<p>在软件中,可以分别显示永久荷载引起的挠度 <em>Δ</em><em><sub>PL</sub></em>、可变荷载引起的挠度 <em>Δ</em><em><sub>IL</sub></em>,以及总挠度 <em>Δ</em><em><sub>Tot</sub></em><sub> </sub>(永久荷载 + 可变荷载),同时显示变形形状。</p>\n<p>无法校核修剪端部的挠度。</p>\n<h3>裂缝宽度</h3>\n<p>裂缝宽度和裂缝方向针对正常使用极限状态的短期 或长期组合进行计算。软件中直接计算裂缝宽度的方法符合(基于)AS 3600 8.6.2.3 给出的方法。 </p>\n<p>验算结果表示如下:</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中:</p>\n<p><em>w</em> 由有限元分析计算得到的短期或长期裂缝宽度,</p>\n<p><em>w</em><em><sub>lim</sub></em> 由用户定义的裂缝宽度限值。</p>\n<p>推荐的最大裂缝宽度可参见 AS3600:2018 Sup 1:2022 Table C2.3.3.1。</p>\n<figure data-asset-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\" data-image-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/34472a7f-e0a5-4d30-b990-361d7cd59f2b/REcommended%20final%20design%20crack%20widths%20-%20AUS.png\" data-asset-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\" data-image-id=\"58beec32-b322-44cc-8a6f-af552cb75f67\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 88\\qquad Recommended final design crack widths}}}\\]</em></p>\n<p>此外,根据 AS3600:2018 Sup 1:2022 Cl. C8.6.1,对于承受长期使用荷载的结构,<em>w</em><em><sub>lim</sub></em> 的推荐值如下:</p>\n<figure data-asset-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\" data-image-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e16caacd-4f7b-4ba4-a7d1-48dd71a47890/Reccomended%20max%20cracks%20widths%20values%20for%20long-term%20loads.png\" data-asset-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\" data-image-id=\"709c3d3e-e2bf-4160-9dc7-8edfba902ee0\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 89\\qquad Recommended values for the limit value of the crack width for beams based on exposure classes}}}\\]</em></p>\n<p>裂缝宽度有两种计算方式(稳定裂缝和非稳定裂缝)。一般情况下(稳定裂缝),裂缝宽度通过对钢筋一维单元上的应变进行积分来计算。随后,裂缝方向由二维混凝土单元中距给定钢筋一维有限单元中心最近的三个积分点计算得出。虽然这种计算裂缝方向的方法与裂缝的实际位置并不对应,但它仍能给出具有代表性的数值,所得裂缝宽度结果可与规范要求的钢筋位置处的裂缝宽度值进行比较。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "7-4-serviceability-checks"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"7-4-serviceability-checks\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:40</li>\n <li>de-DE: Translated on 27.10.2026 14:20</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:15</li>\n <li>fr-FR: Translated on 27.10.2026 15:02</li>\n <li>hu-HU: Translated on 27.10.2026 18:21</li>\n <li>it-IT: Translated on 27.10.2026 15:39</li>\n <li>ja-JP: Translated on 26.10.2026 12:19</li>\n <li>ko-KR: Translated on 26.10.2026 12:19</li>\n <li>nl-NL: Language translation error (when inserting into Kontent.ai)</li>\n <li>pl-PL: Translated on 27.10.2026 19:47</li>\n <li>pt-PT: Translated on 27.10.2026 17:39</li>\n <li>ro-RO: Translated on 27.10.2026 19:05</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:19</li>\n <li>tr-TR: Translated on 26.10.2026 12:19</li>\n <li>vi-VN: Translated on 26.10.2026 12:19</li>\n <li>zh-CN: Translated on 27.10.2026 20:28</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___serviceability_ver_77b5f2c",
"collection": "default",
"id": "77b5f2cf-4383-4009-baad-662643d8f2ad",
"language": "zh-CN",
"lastModified": "2026-10-27T19:28:19.6488347Z",
"name": "Theoretical background Detail – Serviceability verifications – AUS",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "8.1 Material models (CSA)"
},
"id": {
"name": "ID",
"type": "text",
"value": "material-models-csa"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n6aab19fe_22df_01fc_a1c7_3d0f7ddd9aab",
"collection": "default",
"id": "6aab19fe-22df-01fc-a1c7-3d0f7ddd9aab",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "6aab19fe-22df-01fc-a1c7-3d0f7ddd9aab",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "8.1 材料模型（CSA）"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Material models (ACI)_00.png",
"description": null,
"type": "image/png",
"size": 62814,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d34cdf5e-0275-4137-8744-a69bc4303153/Material%20models%20%28ACI%29_00.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "75c1ac5f-22d1-4eee-8e6b-136e3d35e377",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/0e30004f-06ce-46e3-a200-775a2e5e0e5a/fig_8-01_concrete_stress_strain_strength.png",
"height": 571,
"width": 859
},
{
"description": null,
"imageId": "b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG",
"height": 574,
"width": 1500
},
{
"description": null,
"imageId": "a8a59d43-d248-4fda-8c1c-139fe673e512",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9385417d-7ed8-49b6-8fdc-8bb1eab30e5e/Concrete%20stress-strain%20for%20serviceability%20-%20CSA.png",
"height": 960,
"width": 1858
},
{
"description": null,
"imageId": "2d9c6401-28af-4bfe-bc92-1d6f830f7c93",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png",
"height": 719,
"width": 938
},
{
"description": null,
"imageId": "c9add949-2ad5-4922-8e6c-0d75fb47cb70",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png",
"height": 569,
"width": 883
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<h3>混凝土 - 强度</h3>\n<p>CSFM 中用于强度计算的混凝土模型基于抛物线-塑性应力-应变曲线。与经典钢筋混凝土设计一样，该模型忽略抗拉强度。CSA 设计规范仅支持混凝土的抛物线-矩形图。</p>\n<figure data-asset-id=\"75c1ac5f-22d1-4eee-8e6b-136e3d35e377\" data-image-id=\"75c1ac5f-22d1-4eee-8e6b-136e3d35e377\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/0e30004f-06ce-46e3-a200-775a2e5e0e5a/fig_8-01_concrete_stress_strain_strength.png\" data-asset-id=\"75c1ac5f-22d1-4eee-8e6b-136e3d35e377\" data-image-id=\"75c1ac5f-22d1-4eee-8e6b-136e3d35e377\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 90\\qquad The stress-strain diagram of concrete for Strength analysis}}}\\]</em></p>\n<p>IDEA StatiCa Detail 中的 CSFM 实现并未考虑受压混凝土以应变表示的显式破坏准则（即达到峰值应力后，采用塑性分支，其 ε<sub>c</sub> 最大值取 5%，而 CSA A23.3:24 第 10.1.3 条假定混凝土最大压应变为 0.0035）。这一简化无法验证受压破坏结构的变形能力。不过，除了开裂混凝土系数（k<sub>c2</sub> ，见图 90）之外，如果再通过 fib Model Code 2010 中定义的折减系数 η<sub>fc</sub> 来考虑混凝土强度提高时脆性的增加，则可以正确预测强度，其定义如下：</p>\n<p>\\[f'_{c,lim}=\\alpha\\cdot\\phi_{c}\\cdot k_{c}\\cdot f'_{c}\\]</p>\n<p>\\[k_{c}=\\eta_{fc}\\cdot k_{c2}\\]</p>\n<p>\\[{\\eta _{fc}} = {\\left( {\\frac{{30}}{{{f'_{c}}}}} \\right)^{\\frac{1}{3}}} \\le 1\\]</p>\n<p>其中：</p>\n<p><em>α</em> 是考虑现场强度与标准圆柱体强度之间差异的系数，依据 CSA A23.3:24 第 10.1.6 条。该条的注释要求应力块基于峰值应力不大于 0.9 f'<sub>c</sub> 的应力-应变曲线。该系数还与第 11.4.2.3 条中限制压杆压应力的要求一致。默认值为 0.85，可在项目设置中修改。<br>注：α 是应用于抛物线-矩形应力-应变图的单一用户自定义值。不应将其与等效矩形混凝土应力分布的系数 α<sub>1</sub> 混淆，CSA A23.3:24 第 10.1.7 条将后者定义为与强度相关的系数（α<sub>1</sub> = 0.85 − 0.0015 f'<sub>c</sub> ≥ 0.67，公式 10.1）。</p>\n<p><em>Φ</em><em><sub>c</sub></em> 是混凝土的抗力系数，依据 CSA A23.3:24 第 8.4.2 条。 </p>\n<p><em>k</em><em><sub>c2</sub></em> 是由于存在横向裂缝而引入的折减系数（压力软化）。</p>\n<p><em>f'</em><em><sub>c</sub></em> 是混凝土规定的抗压强度（在定义 <em>η</em><em><sub>fc</sub></em> 时以 MPa 为单位）。</p>\n<p>使用抛物线-矩形应力-应变图时，需要通过系数 α 折减最大压应力。这样可使受压区的应力分布取平均，从而使所得抗压强度小于或等于采用带下降塑性分支的应力-应变图计算出的抗压强度。CSA A23.3:24 第 10.1.7 条对等效矩形混凝土应力分布规定了类似的方法，其中假定折算后的混凝土应力 <em>α</em><em><sub>1</sub></em><em> Φ</em><em><sub>c</sub></em><em> f'</em><em><sub>c</sub></em> 在等效受压区内均匀分布。</p>\n<figure data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/085222c7-055a-4870-9bcb-8f18bd65620f/Compression%20softening%20CSFM.PNG\" data-asset-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" data-image-id=\"b9d5ff6a-d0b5-43f3-a686-dddbe6675ac1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 91\\qquad The compression softening law.}}}\\]</em></p>\n<p><em>k</em><em><sub>c2</sub></em> 是一个折减系数，其假定与 CSA A23.3:24 第 11.4.2.3 条中对压杆压应力的限制相同，区别在于 CSFM 对每个有限单元都检查垂直于主压应力方向是否存在主拉应变（而不仅仅针对拉压杆模型的压杆和节点区）。</p>\n<h3>混凝土 – 正常使用</h3>\n<p>正常使用分析对强度分析所用的本构模型进行了一些简化。受压混凝土应力-应变曲线的塑性分支被忽略，而弹性分支为线性且无限延伸。不考虑压力软化规律。这些简化提高了数值稳定性和计算速度，并且只要正常使用状态下材料的合成应力限值明显低于其屈服点（符合 CSA A23.3:24 第 9.8 条以及预应力构件第 18.3 条的正常使用要求），就不会降低解的普遍性。因此，用于正常使用的简化模型仅在所有验证要求均得到满足时才有效。</p>\n<p><strong>长期效应</strong></p>\n<p>当在顶部功能区中选择长期效应时，长期本构规律用于裂缝宽度计算、总挠度计算以及预应力构件的应力限制。 </p>\n<p>在 IDEA StatiCa Detail 软件中，通过与时间相关的系数 <em>s</em> 调整弹性模量 <em>E</em><em><sub>c</sub></em> ，以确定结构的长期性能。调整后的弹性模量记为 <em>E</em><em><sub>c,eff</sub></em> – 见图 92。</p>\n<p>假设单元的变形以应变表示，则可写为：</p>\n<p>\\[\\epsilon_{tot} = \\epsilon_{0} + \\epsilon_{creep} = \\epsilon_{0} \\cdot (1+s)\\]</p>\n<p>其中：</p>\n<p><em>ε</em><em><sub>0</sub></em> 是短期应变（不含徐变影响），<em>ε</em><em><sub>creep</sub></em> 是由徐变引起的应变。</p>\n<p>利用胡克定律，可以写出：</p>\n<p>\\[E_{c,eff} = \\frac{f_{c}}{\\epsilon_{tot}}\\]</p>\n<p>代入 \\(\\epsilon_{tot} = \\epsilon_{0} \\cdot (1+\\xi)\\) 和 \\(\\epsilon_{0} = f_{c} / E_{c}\\)，得到：</p>\n<p>\\[E_{c,eff} = \\frac{E_{c}}{1+s}\\]</p>\n<p>其中：<br><em>E</em><em><sub>c</sub></em> 是混凝土的弹性模量，定义见 CSA A23.3:24 第 8.6.2.2 条<br><em>s</em> 是与时间相关的系数。用户可在“材料”选项卡中定义三个系数，并应依据 CSA A23.3:24 第 9.8.2.5 条（预应力构件为第 9.8.4.4 条）中给出的持续荷载下挠度系数 ζ<sub>s</sub> 确定：</p>\n<figure data-asset-id=\"a8a59d43-d248-4fda-8c1c-139fe673e512\" data-image-id=\"a8a59d43-d248-4fda-8c1c-139fe673e512\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9385417d-7ed8-49b6-8fdc-8bb1eab30e5e/Concrete%20stress-strain%20for%20serviceability%20-%20CSA.png\" data-asset-id=\"a8a59d43-d248-4fda-8c1c-139fe673e512\" data-image-id=\"a8a59d43-d248-4fda-8c1c-139fe673e512\" alt=\"\"></figure>\n<p><br><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 92\\qquad Concrete stress-strain diagrams implemented for serviceability analysis: short- and long-term verifications.}}}\\]</em></p>\n<p><strong>短期效应</strong></p>\n<p>为进行短期验证，需另行计算，其中所有荷载均不乘以与时间相关的系数。长期和短期验证的两种计算均如图 92 所示。</p>\n<h3>钢筋</h3>\n<p>对于非预应力钢筋，采用具有确定屈服点的理想弹塑性应力-应变图。钢筋材料依据 CSA G30.18:21 定义。定义该图仅需已知钢筋的基本性能——强度和弹性模量。</p>\n<p>用户也可以自定义钢筋应力-应变图，但在这种情况下，无法考虑拉力刚化效应（无法计算裂缝宽度）。 </p>\n<figure data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/77dadff9-85d4-402e-94e5-a3725f908933/Steel%20stress-strain%20diagram%20CSFM%20-%20ACI.png\" data-asset-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" data-image-id=\"2d9c6401-28af-4bfe-bc92-1d6f830f7c93\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 93 \\qquad Stress-strain diagram of reinforcement}}}\\]</em></p>\n<p>其中：</p>\n<p><em>Φ</em><em><sub>s</sub></em><em> </em>是钢筋的抗力系数，依据 CSA A23.3:24 第 8.4.3 条。</p>\n<p><em>f</em><em><sub>sy</sub></em> 是钢筋的屈服强度</p>\n<p><em>E</em><em><sub>s</sub></em> 是钢筋的弹性模量</p>\n<p>选取 10% 作为终止计算的极限应变。根据 ASTM A955/A955M-20c 第 7 条，这被认为是安全的。</p>\n<p>拉力刚化（图 94） 通过修改裸钢筋的输入应力-应变关系自动考虑，以反映埋入混凝土中钢筋的平均刚度（ε<em><sub>m</sub></em>）。</p>\n<figure data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/c045fcb6-32c6-4a92-aa15-24530fb11484/Tension%20stiffening%20CSFM%20-%20ACI.png\" data-asset-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" data-image-id=\"c9add949-2ad5-4922-8e6c-0d75fb47cb70\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 94\\qquad Scheme of tension stiffening.}}}\\]</em></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "8-1-material-models-csa"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-1-material-models-aashto\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:41</li>\n <li>de-DE: Translated on 27.10.2026 14:21</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:16</li>\n <li>fr-FR: Translated on 27.10.2026 15:03</li>\n <li>hu-HU: Translated on 27.10.2026 18:22</li>\n <li>it-IT: Translated on 27.10.2026 15:39</li>\n <li>ja-JP: Translated on 26.10.2026 12:29</li>\n <li>ko-KR: Translated on 26.10.2026 12:27</li>\n <li>nl-NL: Translated on 27.10.2026 16:55</li>\n <li>pl-PL: Translated on 27.10.2026 19:48</li>\n <li>pt-PT: Translated on 27.10.2026 17:40</li>\n <li>ro-RO: Translated on 27.10.2026 19:05</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:27</li>\n <li>tr-TR: Translated on 26.10.2026 12:28</li>\n <li>vi-VN: Translated on 26.10.2026 12:28</li>\n <li>zh-CN: Translated on 27.10.2026 20:28</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___material_models__c",
"collection": "default",
"id": "ec897db0-a93b-4aaa-8f5c-803ee9e31c58",
"language": "zh-CN",
"lastModified": "2026-10-27T19:28:58.7850773Z",
"name": "Theoretical background Detail - Material models (CSA)",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "8.2 Resistance and load factors"
},
"id": {
"name": "ID",
"type": "text",
"value": "resistance-and-load-factors-csa"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n3131c97b_f469_015c_eb8e_4ec8df85f4fb",
"collection": "default",
"id": "3131c97b-f469-015c-eb8e-4ec8df85f4fb",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "3131c97b-f469-015c-eb8e-4ec8df85f4fb",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "8.2 抗力系数与荷载系数"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "27f1f3f8-4d11-4585-bd0b-70180ea21803",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ddf3d73b-8052-4900-87b7-38242fba4936/Rezistance%20factors%20CSA.png",
"height": 495,
"width": 875
},
{
"description": null,
"imageId": "6a37fbcf-6032-4f79-b377-4103af3bbe77",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/62863d25-8bd8-4cd1-b62c-2e29a7fd3382/Clause%2010%20factor%20alfa%20CSA.png",
"height": 497,
"width": 878
},
{
"description": null,
"imageId": "075cd332-27e0-42ce-9042-ab405cd4453a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2b56741b-83ac-4d27-bc28-cf744cf86d23/Load%20factors%20CSA.png",
"height": 305,
"width": 771
},
{
"description": null,
"imageId": "2adb3c90-7b6d-473e-a14b-42f116fff503",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/87f20241-0920-4ebc-be8a-8ce069ea59a4/Limit%20state%20definition%20CSA.png",
"height": 770,
"width": 1797
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>协调应力场法符合现代设计规范。由于计算模型仅采用标准材料特性，因此设计规范中规定的分项安全系数格式无需任何调整即可直接应用。这样，输入荷载乘以荷载系数，规定的材料特性则采用相应的抗力系数予以折减，与常规混凝土分析完全一致。</p>\n<p>材料抗力系数的取值见 CSA A23.3:24 第 8.4 条。折算后的混凝土强度在第 8.4.2 条中定义，折算后的钢筋和钢束力在第 8.4.3 条中定义。IDEA StatiCa Detail 中的默认值对应按第 8 条设计的结构在上述条款中给出的取值，即未针对按第 16.1.3 条认证的预制混凝土工厂所允许采用的降低材料系数进行调整。如需评估此类情况，用户可以在项目设置中修改抗力系数的取值。</p>\n<figure data-asset-id=\"27f1f3f8-4d11-4585-bd0b-70180ea21803\" data-image-id=\"27f1f3f8-4d11-4585-bd0b-70180ea21803\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ddf3d73b-8052-4900-87b7-38242fba4936/Rezistance%20factors%20CSA.png\" data-asset-id=\"27f1f3f8-4d11-4585-bd0b-70180ea21803\" data-image-id=\"27f1f3f8-4d11-4585-bd0b-70180ea21803\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 95\\qquad The setting of resistance factors in IDEA StatiCa Detail.}}}\\]</em></p>\n<p>其中：</p>\n<ul>\n <li>Φ<sub>c</sub> 为混凝土的抗力系数，依据 CSA A23.3:24 第 8.4.2 条。</li>\n <li>Φ<sub>s</sub> 为钢筋和预埋钢锚栓的抗力系数，依据 CSA A23.3:24 第 8.4.3 条 a)。</li>\n <li>Φ<sub>p</sub> 为预应力钢束的抗力系数，依据 CSA A23.3:24 第 8.4.3 条 b)。 </li>\n</ul>\n<p>除材料抗力系数外，用于考虑现场强度与标准圆柱体强度之间差异的系数 α 也在项目设置中定义。该系数在第 8.1 章中说明，其默认值 0.85 同时反映了 CSA A23.3:24 第 10.1.6 条的要求以及第 11.4.2.3 条对压杆中压应力的限制。</p>\n<figure data-asset-id=\"6a37fbcf-6032-4f79-b377-4103af3bbe77\" data-image-id=\"6a37fbcf-6032-4f79-b377-4103af3bbe77\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/62863d25-8bd8-4cd1-b62c-2e29a7fd3382/Clause%2010%20factor%20alfa%20CSA.png\" data-asset-id=\"6a37fbcf-6032-4f79-b377-4103af3bbe77\" data-image-id=\"6a37fbcf-6032-4f79-b377-4103af3bbe77\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 96\\qquad The setting of the factor α in IDEA StatiCa Detail}}}\\]</em></p>\n<p>荷载系数和荷载组合应按照适用的建筑规范确定，如 CSA A23.3:24 第 8.2.1 条和第 8.3.1 条所要求。CSA A23.3:24 本身依据加拿大国家建筑规范（第 1.1 条）规定了相关要求，其荷载组合条款的改编版本收录于 CSA A23.3:24 附录 C（资料性附录）。承载能力极限状态的荷载组合：不含吊车荷载的荷载工况见表 C.1 a)，含吊车荷载的荷载工况见表 C.1 b)，适用的组合取产生最不利效应的组合。依据第 C.1.2.4 条，侧向土压力 H、预应力约束效应 P 和强加变形 T 的荷载系数分别取 1.5、1.0 和 1.25。</p>\n<p>正常使用极限状态的荷载组合应取对所考虑的极限状态产生最不利效应的组合，如第 8.3.3 条所要求。</p>\n<p>由于 IDEA StatiCa Detail 也用于桥梁细部的设计——例如墩帽、横隔梁和桥台——需要注意的是，附录 C 中收录的加拿大国家建筑规范的荷载组合和荷载系数适用于建筑物。对于加拿大的公路桥梁，起主导作用的文件是《加拿大公路桥梁设计规范》CSA S6，该规范规定了自身的设计荷载、荷载组合和荷载系数。在这种情况下，荷载系数和荷载组合应改为按 CSA S6 确定。用户有责任定义与所评估结构以及相关主管部门所执行的规范版本相适用的荷载组合。</p>\n<figure data-asset-id=\"075cd332-27e0-42ce-9042-ab405cd4453a\" data-image-id=\"075cd332-27e0-42ce-9042-ab405cd4453a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2b56741b-83ac-4d27-bc28-cf744cf86d23/Load%20factors%20CSA.png\" data-asset-id=\"075cd332-27e0-42ce-9042-ab405cd4453a\" data-image-id=\"075cd332-27e0-42ce-9042-ab405cd4453a\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 97\\qquad The setting of load factors in Idea StatiCa Detail.}}}\\]</em></p>\n<p>软件中提供以下荷载工况类型：</p>\n<ul>\n <li>预应力</li>\n <li>恒载</li>\n <li>可变荷载</li>\n</ul>\n<p>每个组合都被指定一个极限状态，该极限状态决定分析中采用的材料模型以及所执行的规范校核：</p>\n<ul>\n <li><strong>ULS</strong> – 第 8.3 章中所述的强度校核采用混凝土抛物线-矩形材料模型进行。</li>\n <li><strong>SLS</strong> – 第 8.5 章中所述的正常使用校核采用混凝土线性材料模型进行。正常使用组合区分为两种子类型：\n <ul>\n <li><strong>持久荷载</strong> – 预应力加永久荷载，用于预应力构件在持久荷载下的应力限值校核。</li>\n <li><strong>总荷载</strong> – 预应力、永久荷载和短暂荷载，用于预应力构件在总荷载下的应力限值校核。</li>\n </ul>\n </li>\n</ul>\n<p>对于每个正常使用组合，用户还需决定该组合是否用于裂缝宽度校核和挠度校核。</p>\n<figure data-asset-id=\"2adb3c90-7b6d-473e-a14b-42f116fff503\" data-image-id=\"2adb3c90-7b6d-473e-a14b-42f116fff503\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/87f20241-0920-4ebc-be8a-8ce069ea59a4/Limit%20state%20definition%20CSA.png\" data-asset-id=\"2adb3c90-7b6d-473e-a14b-42f116fff503\" data-image-id=\"2adb3c90-7b6d-473e-a14b-42f116fff503\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 98\\qquad The setting of load cases and combinations in IDEA StatiCa Detail}}}\\]</em></p>\n<p>对于每个模板，程序包含预定义的基本组合，需根据所处理的单元进行补充完善。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "8-2-resistance-and-load-factors"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"8-2-resistance-and-load-factors\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:41</li>\n <li>de-DE: Translated on 27.10.2026 14:22</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:16</li>\n <li>fr-FR: Translated on 27.10.2026 15:03</li>\n <li>hu-HU: Translated on 27.10.2026 18:22</li>\n <li>it-IT: Translated on 27.10.2026 15:40</li>\n <li>ja-JP: Translated on 26.10.2026 12:28</li>\n <li>ko-KR: Translated on 26.10.2026 12:27</li>\n <li>nl-NL: Translated on 27.10.2026 16:55</li>\n <li>pl-PL: Translated on 27.10.2026 19:49</li>\n <li>pt-PT: Translated on 27.10.2026 17:40</li>\n <li>ro-RO: Translated on 27.10.2026 19:06</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:27</li>\n <li>tr-TR: Translated on 26.10.2026 12:28</li>\n <li>vi-VN: Translated on 26.10.2026 12:27</li>\n <li>zh-CN: Translated on 27.10.2026 20:29</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___resistance_and_loa_3be42f4",
"collection": "default",
"id": "3be42f44-a92d-4a5a-b15a-e266df922900",
"language": "zh-CN",
"lastModified": "2026-10-27T19:29:22.6723697Z",
"name": "Theoretical background Detail - Resistance and load factors - CSA",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "8.3 Ultimate limit state"
},
"id": {
"name": "ID",
"type": "text",
"value": "ultimate-limit-state-csa"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "cd09877f_7f1a_014d_d93d_f401610d7808",
"collection": "default",
"id": "cd09877f-7f1a-014d-d93d-f401610d7808",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "cd09877f-7f1a-014d-d93d-f401610d7808",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "8.3 承载能力极限状态"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "f34c70d7-218f-4c0b-b198-8ecc1d1dc177",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5caad6cb-d8bc-4fe6-a92a-35869c377ef5/bond%20modification%20factors%20CSA.png",
"height": 470,
"width": 1197
},
{
"description": null,
"imageId": "f0e69ed2-6640-446f-94b0-f06ed48a87d8",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bc7cd4e7-291d-4204-83f3-17e9d9cc7b3b/Bond%20conditions%20-%20CSA.png",
"height": 286,
"width": 587
},
{
"description": null,
"imageId": "8a2ed21c-590e-4061-8c46-c5cc4c60ade1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png",
"height": 442,
"width": 1011
},
{
"description": null,
"imageId": "d3675eaf-0adb-4512-9366-58e4bdf171b1",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png",
"height": 520,
"width": 1463
},
{
"description": null,
"imageId": "85c164c0-d864-4723-8c34-a84a426100b2",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png",
"height": 140,
"width": 951
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "rn_25_1__smooth_rebars_in_detail",
"linkId": "182f8ba8-899b-44fc-a1c7-59d562ef8c6c",
"urlSlug": "smooth-rebars-in-detail",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>CSA A23.3:24 要求的各项验算均基于模型给出的直接结果进行评估。验算内容包括混凝土强度、钢筋强度和锚固（粘结剪应力）。</p>\n<p>受压<strong>混凝土强度</strong>按有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em> （在辅助结果中也称为 <em>σ</em><em><sub>c2</sub></em><em> </em>）与极限值 <em>f'</em><em><sub>c,lim</sub></em> 之比进行评估。</p>\n<p><strong>钢筋强度</strong>在受拉和受压两种情况下均按裂缝处钢筋应力 <em>f</em><em><sub>s</sub></em> 与规定极限值 <em>f</em><em><sub>sy,lim</sub></em> 之比进行评估。</p>\n<p><strong>粘结剪应力</strong>单独评估，按有限元分析计算得到的粘结应力 τ<sub>b</sub> 与设计粘结强度 <em>f</em><em><sub>bu</sub></em> 之比确定。</p>\n<p>CSA A23.3:24 没有明确定义粘结强度。但第 12 条的锚固长度规定正是由该量推导而来，因此可以由这些规定反推得到。推导分几步进行。</p>\n<p>根据定义，锚固长度 <em>l</em><em><sub>d</sub></em> 是仅靠粘结就能将钢筋的全部屈服力传递给混凝土所需的埋置长度。若钢筋的埋置长度达到或超过 <em>l</em><em><sub>d</sub></em>，拔出钢筋时将导致钢筋屈服，而不是粘结破坏。令作用于钢筋周长上的均匀粘结应力 <em>f</em><em><sub>bu</sub></em> 所传递的力等于钢筋截面的屈服力：</p>\n<p>\\[\\pi\\cdot d_{b} \\cdot l_{d} \\cdot f_{bu}=f_{yg}\\cdot A_{b}\\]</p>\n<p>其中：</p>\n<ul>\n <li><em>d</em><em><sub>b</sub></em> 为钢筋公称直径，<em>π d</em><em><sub>b</sub></em><em> l</em><em><sub>d</sub></em> 为粘结表面积；</li>\n <li><em>A</em><em><sub>b</sub></em><em> = π d</em><em><sub>b</sub></em><em><sup>2</sup></em><em> / 4</em> 为钢筋截面积；</li>\n <li><em>f</em><em><sub>yg</sub></em> 为钢筋的规定屈服强度。</li>\n</ul>\n<p>可以写成：</p>\n<p>\\[f_{bu}=\\frac{f_{yg} \\cdot A_{b}}{\\pi \\cdot d_{b} \\cdot l_{d}}=\\frac{f_{yg} \\cdot \\frac{\\pi \\cdot d_{b}^{2}}{4}}{\\pi \\cdot d_{b} \\cdot l_{d}}=\\frac{f_{y} \\cdot d_{b}}{4 \\cdot l_{d}}\\]</p>\n<p>变形钢筋受拉锚固长度的简化公式见 CSA A23.3:24 表 12.1（第 12.2.3 条）。软件采用第二种更保守的情况，即<em>其他情况</em>。 </p>\n<p>在软件中，CSA A23.3:24 表 12.2（第 12.2.4 条）定义的修正系数取 k<sub>c</sub> = 1.0（因为仅支持无涂层钢筋）和 k<sub>a</sub> = 1.0（因为仅支持普通密度混凝土）。因此采用的表达式为</p>\n<p>\\[l_{d}=0{,}6 \\cdot k_{1} k_{s} k_{g} \\cdot \\frac{f_{y}}{\\sqrt{f'_{c}}} \\cdot d_{b}\\]</p>\n<p>将该表达式代入平衡条件，即可消去锚固长度：</p>\n<p>\\[f_{bu}=\\frac{f_{yg} \\cdot d_{b}}{4 \\cdot 0{,}6 \\cdot k_{1} k_{s} k_{g} \\cdot \\frac{f_{yg}}{\\sqrt{f'_{c}}} \\cdot d_{b}}\\]</p>\n<p><em>f</em><em><sub>yg</sub></em> 和 <em>d</em><em><sub>b</sub></em> 同时出现在分子和分母中，因此相互抵消：</p>\n<p>\\[f_{bu}=\\frac{\\sqrt{f'_{c}}}{4 \\cdot 0{,}6 \\cdot k_{1} k_{s} k_{g}}=\\frac{1}{2{,}4} \\cdot \\frac{\\sqrt{f'_{c}}}{k_{1} k_{s} k_{g}}\\]</p>\n<p>计算常数 1 / 2,4 = 0,4167，取整为 0,42，即得到软件中采用的设计粘结强度：</p>\n<p>\\[f_{bu}=0{,}42 \\cdot \\frac{\\sqrt{f'_{c}}}{k_{1} \\cdot k_{s} \\cdot k_{g}}\\]</p>\n<p>修正系数按 CSA A23.3:24 表 12.2（第 12.2.4 条）确定：</p>\n<figure data-asset-id=\"f34c70d7-218f-4c0b-b198-8ecc1d1dc177\" data-image-id=\"f34c70d7-218f-4c0b-b198-8ecc1d1dc177\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5caad6cb-d8bc-4fe6-a92a-35869c377ef5/bond%20modification%20factors%20CSA.png\" data-asset-id=\"f34c70d7-218f-4c0b-b198-8ecc1d1dc177\" data-image-id=\"f34c70d7-218f-4c0b-b198-8ecc1d1dc177\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 99\\qquad Modification factors}}}\\]</em></p>\n<p>根据 CSA A23.3:24 第 12.1.2 条，计算锚固长度时所用 <em>√f'</em><em><sub>c</sub></em> 的最大允许值为 8 MPa。</p>\n<p>系数 <em>k</em><em><sub>1</sub></em> 根据钢筋在模型中的位置按下图自动确定： </p>\n<figure data-asset-id=\"f0e69ed2-6640-446f-94b0-f06ed48a87d8\" data-image-id=\"f0e69ed2-6640-446f-94b0-f06ed48a87d8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bc7cd4e7-291d-4204-83f3-17e9d9cc7b3b/Bond%20conditions%20-%20CSA.png\" data-asset-id=\"f0e69ed2-6640-446f-94b0-f06ed48a87d8\" data-image-id=\"f0e69ed2-6640-446f-94b0-f06ed48a87d8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 100\\qquad Description of bond conditions; a) b) ‘good’ bond conditions for all bars; c) d) unhatched zone – ‘good’ bond conditions, hatched zone – ‘poor’ bond conditions}}}\\]</em></p>\n<p>对于不良粘结条件，<em>k</em><em><sub>1</sub></em><em>=1.3</em></p>\n<p>浇筑方向可以在软件中设置。</p>\n<figure data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e00845bc-3d60-4315-a8b3-67d4a52666a4/Direction%20of%20concreting.png\" data-asset-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" data-image-id=\"8a2ed21c-590e-4061-8c46-c5cc4c60ade1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 101\\qquad Direction of concreting}}}\\]</em></p>\n<p>受压钢筋的粘结剪应力和粘结强度的计算方法与受拉钢筋类似，但采用 CSA A23.3:24 第 12.3.2 条的受压锚固长度公式。</p>\n<p>软件还提供<strong>光圆钢筋</strong>建模选项。更多信息请见：<a data-item-id=\"182f8ba8-899b-44fc-a1c7-59d562ef8c6c\" href=\"\">Detail 中的光圆钢筋</a></p>\n<p><br></p>\n<p><strong>总力 </strong><em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em><strong> 与极限力 </strong><em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em></p>\n<p>总力 <em><strong>F</strong></em><em><strong><sub>tot</sub></strong></em> 是有限元分析的结果，可以通过两种方式定义。</p>\n<p>\\[F_{tot}=A_{s} \\cdot f_{s}\\]</p>\n<p>其中 <em>A</em><em><sub>s</sub></em> 为钢筋截面积，<em>f</em><em><sub>s</sub></em> 为钢筋应力。</p>\n<p>或者定义为 锚固力 <em>F</em><em><sub>a </sub></em>与 粘结力 <em>F</em><em><sub>bond</sub></em><em> 之和。</em></p>\n<p>\\[F_{tot}=F_{a}+F_{bond}\\]</p>\n<p>其中 <em>F</em><em><sub>a</sub></em> 为锚固弹簧中的实际力，<em>F</em><em><sub>bond</sub></em> 为粘结力，可通过沿钢筋长度 <em>l</em> 对粘结应力 <em>τ</em><em><sub>b</sub></em> 积分得到。</p>\n<p>\\[F_{bond}=C_{s} \\cdot \\int_{0}^{l}\\tau_{b}\\left( x \\right)dx\\]</p>\n<p>C<sub>s</sub> 为钢筋周长。</p>\n<p>极限力 <em><strong>F</strong></em><em><strong><sub>lim</sub></strong></em> 是钢筋单元中的最大力，同时考虑钢筋的<strong>强度</strong>和<strong>锚固条件 </strong>（混凝土与钢筋之间的粘结，以及锚固弯钩、环筋等）。</p>\n<p>\\[F_{lim}=min\\left( F_{lim,bond}+F_{au},F_{u} \\right)\\]</p>\n<p>\\[F_{u}=f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{au}=\\beta\\cdot f_{y,lim}\\cdot A_{s}\\]</p>\n<p>\\[F_{lim,bond}=C_{s}\\cdot l \\cdot f_{bu}\\]</p>\n<p>其中 C<sub>s</sub> 为钢筋周长，<em>l</em> 为从钢筋起点到所考察点的长度。</p>\n<figure data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1a6bbdca-e56b-47e1-a85f-00d4317689a8/Flim.png\" data-asset-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" data-image-id=\"d3675eaf-0adb-4512-9366-58e4bdf171b1\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 102\\qquad Definition of the limit force Flim}}}\\]</em></p>\n<p><br></p>\n<p>\\[F_{lim,2}=F_{lim,1}+F_{lim,add}\\]</p>\n<p>其中 <em>F</em><em><sub>lim,add</sub></em> 为根据相邻单元之间夹角大小计算得到的附加力。<em>F</em><em><sub>lim,2</sub></em> 必须始终小于 <em>F</em><em><sub>u</sub></em>。</p>\n<p><br></p>\n<p>纵向钢筋和横向钢筋可用的<strong>锚固类型</strong>遵循 CSA A23.1:19 第 6.6.2 条定义的弯钩和弯折。第 6.6.2.2 条将标准弯钩定义为半圆形（180 度）弯折，或在钢筋自由端带有规定延伸长度的 90 度弯折；对于箍筋和拉筋的锚固，则定义为 90 度或 135 度弯折。CSFM（协调应力场法）中纵向钢筋可用的锚固类型包括直钢筋（即不考虑锚固端折减）、90 度弯折、180 度弯折、完全粘结和连续钢筋。所有这些类型及相应的锚固系数 β 见图 103。</p>\n<figure data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b76bc446-995d-4d16-8ef9-4aa26671edda/Available%20anchorage%20types%20for%20longitudinal%20rebars.png\" data-asset-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" data-image-id=\"85c164c0-d864-4723-8c34-a84a426100b2\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 103\\qquad Available anchorage types and respective anchorage coefficients for longitudinal reinforcing bars in CSFM:}}}\\]</em></p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{(a) straight bar; (b) 90-degree hook; (c) 180-degree hook; (d) perfect bond; (e) continuous bar}}}\\]</em></p>\n<p>需要指出，尽管有多种可选项，CSFM（协调应力场法）仅区分三种锚固端类型：(i) 不折减锚固长度；(ii) 标准锚固时锚固长度折减 30%；(iii) 完全粘结。采用的锚固系数如下：</p>\n<p>箍筋（适用于梁单元）的锚固系数始终为 β = 1.0。</p>\n<p>为符合 CSA A23.3 的要求，计算中应使用锚固弹簧。锚固弹簧由 β 系数修正，因此用户在定义钢筋起点和终点条件时，必须选择其中一种可用的锚固类型。 </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "8-3-ultimate-limit-state"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-3-strength-limit-state\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:42</li>\n <li>de-DE: Translated on 27.10.2026 14:22</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:17</li>\n <li>fr-FR: Translated on 27.10.2026 15:04</li>\n <li>hu-HU: Translated on 27.10.2026 18:23</li>\n <li>it-IT: Language translation error (when inserting into Kontent.ai)</li>\n <li>ja-JP: Translated on 26.10.2026 12:36</li>\n <li>ko-KR: Translated on 26.10.2026 12:34</li>\n <li>nl-NL: Language translation error (when inserting into Kontent.ai)</li>\n <li>pl-PL: Translated on 27.10.2026 19:49</li>\n <li>pt-PT: Translated on 27.10.2026 17:41</li>\n <li>ro-RO: Translated on 27.10.2026 19:07</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:34</li>\n <li>tr-TR: Translated on 26.10.2026 12:36</li>\n <li>vi-VN: Translated on 26.10.2026 12:35</li>\n <li>zh-CN: Translated on 27.10.2026 20:30</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___strength_limit_sta_fde100c",
"collection": "default",
"id": "fde100cb-04df-47d4-a4f1-fe4973b79dc1",
"language": "zh-CN",
"lastModified": "2026-10-27T19:30:07.6098583Z",
"name": "Theoretical background Detail - Strength limit state - CSA",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "8.4 Bearing and anchorage zones resistance partially loaded areas"
},
"id": {
"name": "ID",
"type": "text",
"value": "bearing-and-anchorage-zones-resistance-partially-loaded-areas-csa"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "e26de44a_0888_0142_95ac_ff57c9eb6c2d",
"collection": "default",
"id": "e26de44a-0888-0142-95ac-ff57c9eb6c2d",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "e26de44a-0888-0142-95ac-ff57c9eb6c2d",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "8.4 承压区与锚固区承载力 – 局部受压区域"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "77fdebe4-afac-4ee7-aee5-716984d4e6d3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG",
"height": 420,
"width": 1633
},
{
"description": null,
"imageId": "05c2e193-bc14-42b5-bc07-da8610febda8",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png",
"height": 406,
"width": 1857
},
{
"description": null,
"imageId": "aff079fa-74f7-4575-a46b-8e589950238a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png",
"height": 474,
"width": 1791
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>在设计混凝土结构时，我们会遇到两大类局部受压区域（PLA）——第一类是<strong>支座</strong>，另一类是<strong>锚固区</strong>。</p>\n<p>根据现行钢筋混凝土结构设计标准，对于<strong>支座</strong>，应考虑混凝土的局部压碎和横向拉力。对于作用在面积 A<sub>1</sub> 上的均布荷载，混凝土的抗压承载力可根据设计分布面积 A<sub>2</sub> 提高至多两倍。参见 CSA A23.3:24 第 10.8.1 条。</p>\n<p>\\[B_{r}=0{,}85 \\cdot \\Phi_{c} \\cdot f'_{c} \\cdot A_{1}\\]</p>\n<p>除非支承面在各边均宽于受荷面积，此时受荷面积上的承压承载力可乘以</p>\n<p>\\[\\sqrt{\\frac{A_{2}}{A_{1}}} \\leq 2\\]</p>\n<p>其中：</p>\n<ul>\n <li>A<sub>1</sub> 为受荷面积；</li>\n <li>A<sub>2</sub> 为设计分布面积，在荷载允许扩散所确定的平面上量取；</li>\n <li>Φ<sub>c</sub> 为按第 8.4.2 条确定的混凝土抗力系数，其默认值为 0.65（见第 8.2 章）。</li>\n</ul>\n<p>对于后张锚固区，应遵循 CSA A23.3:24 第 18.13 条。第 18.13.1 条要求后张锚固区的设计须能抵抗钢束的规定抗拉强度；第 18.13.2 条允许采用下列方法之一进行设计：根据第 11.4 条、基于拉压杆模型的平衡法；采用有限单元法或等效方法的弹性应力分析；基于试验的方法；或适用时采用简化公式。第 18.13.4 条还要求，对因截面突变而产生应力集中的区域配置足够的钢筋。</p>\n<p>这些方法中的第二种即为 CSFM（协调应力场法）所代表的方法，因此 Detail 可直接用于 CSA A23.3:24 下钢束锚固区的设计。</p>\n<p>根据第 10.8.2 条的要求，局部受压区域必须配置足够的横向钢筋，用以传递该区域内产生的劈裂力；该条要求在支座区配置钢筋以抵抗爆裂力、劈裂力和剥落力。若没有所需的横向钢筋，则不能考虑提高混凝土的抗压承载力。</p>\n<p><br></p>\n<p><strong>CSFM（协调应力场法）中的局部受压区域</strong></p>\n<figure data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3dcea2b1-7700-46f3-a938-4c08204d52e8/Fictitious%20struts.PNG\" data-asset-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" data-image-id=\"77fdebe4-afac-4ee7-aee5-716984d4e6d3\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 104\\qquad Fictitious struts with concrete finite element mesh.}}}\\]</em></p>\n<p>利用 CSFM（协调应力场法），可以在设计和评估钢筋混凝土结构时考虑局部受压区域中混凝土抗压承载力提高的影响。由于 CSFM（协调应力场法）是墙（2D）模型，而局部受压区域是空间（3D）问题，因此需要找到一种能够结合这两种不同类型问题的解决方案（<em>图 105</em>）。如果激活“局部受压区域”功能，则会根据 CSA 创建允许的锥体几何形状（<em>图 104</em>）。针对指定的混凝土构件几何形状和各 PLA 的尺寸，所有几何冲突均在 3D 中完整求解。随后，创建局部受压区域的计算模型。</p>\n<figure data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6ae87bd2-682b-4b92-ab1f-4b12e9d3a0df/Cone%20geometry.png\" data-asset-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" data-image-id=\"05c2e193-bc14-42b5-bc07-da8610febda8\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 105\\qquad Allowable cone geometries.}}}\\]</em></p>\n<p>事实证明，修改材料模型并不是合适的方法，主要原因是将属性映射到有限元网格上存在问题。经确定，与有限元网格无关的方法是更合适的解决方案。针对已知的受压锥体几何形状，创建完全协调一致的虚拟压杆（<em>图 105</em> <em>和图 106</em>）。这些压杆具有与模型中所用混凝土相同的材料属性，包括应力-应变图。锥体的形状决定了压杆的方向，压杆将荷载经 PLA 逐步分布到设计分布面积上。虚拟压杆的面密度在锥体各部分是变化的，并沿荷载方向增加一块虚拟混凝土面积。在受荷面积（<em>A</em><em><sub>1</sub></em>）处，按比例 \\(\\sqrt{A_{1} \\cdot A_{2}} - A_{real}\\) （其中 <em>A</em><em><sub>real</sub></em> 为 2D 计算模型中假定的支承面积）增加一块虚拟混凝土面积，该面积向设计分布面积（<em>A</em><em><sub>2</sub></em>）方向线性减小至零。该方案可确保混凝土中的压应力在整个锥体体积内保持恒定。</p>\n<figure data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1dae350c-2f3a-445d-930f-f383e991dcca/Partially%20loaded%20areas%20-%20ACI.png\" data-asset-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" data-image-id=\"aff079fa-74f7-4575-a46b-8e589950238a\" alt=\"\"></figure>\n<p>\\[\\rho \\left( {\\beta ,z} \\right) = \\left( {\\sqrt {\\frac{A_{2}}{A_{1}}} - \\frac{A_{real}}{A_{1}}} \\right)\\,\\cdot\\,\\left( {1 - \\frac{z}{h}} \\right)\\,\\cdot\\,\\frac{1}{{\\cos \\beta }}\\]</p>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 106\\qquad Fictitious struts in the computational model}}}\\]</em></p>\n<p>局部受压区域的承载力按 CSA A23.3:24 第 10.8.1 条规定的设计分布面积与受荷面积之比提高。应当注意，这是一个设计模型，无法精确描述局部受压区域上的应力状态，其实际传力情况要复杂得多。不过，该方案能够在考虑局部受压区域承载力提高的同时，将荷载正确分布到整个模型。此外，它还能在该区域正确引入横向应力，从而正确设计抵抗劈裂力的钢筋。</p>\n<p>面密度受到限制，以确保不超过第 10.8.1 条中极限 √(A<sub>2</sub>/A<sub>1</sub>) ≤ 2 所给出的最大两倍承载力。</p>\n<p>对于锚固区，在软件中 PLA 的使用方式与支座相同。因此，锚固装置处的压应力必须按照第 18.13 条的要求手动校核。在这种情况下，使用 PLA 是为了避免局部区域的应变超过准则限值，从而导致计算过早终止。另一方面，第 10.8.2 条所要求的抵抗爆裂力、劈裂力和剥落力的钢筋，以及第 18.13.4 条所要求的应力集中区域的钢筋，均可直接在软件中方便地验算。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "8-4-bearing-and-anchorage-zones-resistance-partially-loaded-areas"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-4-bearing-and-anchorage-zones-resistance-partially-loaded-areas\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:43</li>\n <li>de-DE: Translated on 27.10.2026 14:23</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:17</li>\n <li>fr-FR: Translated on 27.10.2026 15:05</li>\n <li>hu-HU: Translated on 27.10.2026 18:24</li>\n <li>it-IT: Translated on 27.10.2026 15:41</li>\n <li>ja-JP: Translated on 26.10.2026 12:38</li>\n <li>ko-KR: Translated on 26.10.2026 12:36</li>\n <li>nl-NL: Translated on 27.10.2026 16:57</li>\n <li>pl-PL: Translated on 27.10.2026 19:50</li>\n <li>pt-PT: Translated on 27.10.2026 17:42</li>\n <li>ro-RO: Translated on 27.10.2026 19:07</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:36</li>\n <li>tr-TR: Translated on 26.10.2026 12:38</li>\n <li>vi-VN: Translated on 26.10.2026 12:37</li>\n <li>zh-CN: Translated on 27.10.2026 20:30</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___bearing_and_anchor_bfd09ef",
"collection": "default",
"id": "bfd09ef1-7ff6-4437-814d-03e5047851a8",
"language": "zh-CN",
"lastModified": "2026-10-27T19:30:50.0991026Z",
"name": "Theoretical background Detail – Bearing and anchorage zones – Partially loaded areas - CSA",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "8.5 Serviceability limit state"
},
"id": {
"name": "ID",
"type": "text",
"value": "serviceability-limit-state-csa"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n5c09040b_e0fb_01f6_3ab5_39d6d1e375b0",
"collection": "default",
"id": "5c09040b-e0fb-01f6-3ab5-39d6d1e375b0",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "5c09040b-e0fb-01f6-3ab5-39d6d1e375b0",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "8.5 正常使用极限状态"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": null
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "9b3ba577-076c-4f6b-a629-a45d9894c473",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/83423ed4-9e4e-4819-973b-fadb4306a55e/Compressive%20Stress%20Limits%20in%20Prestressed%20Concrete%20at%20Service%20Limit%20State%20-%20CSA.png",
"height": 186,
"width": 1327
},
{
"description": null,
"imageId": "ac528856-0620-4e95-9877-ea4415ba38b5",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bf637c0b-a972-4836-a119-45f59df9ed58/Combination%20types%20-%20AASHTO.png",
"height": 208,
"width": 972
},
{
"description": null,
"imageId": "fbc3aacf-e2f7-4cc0-b101-2f0fa684380e",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2c6c69d5-b379-4463-96e4-7552c71aea93/Stress%20limitation%20settings_CSA.png",
"height": 496,
"width": 876
},
{
"description": null,
"imageId": "b9ef304f-a055-4045-9ba8-6b74c494bddb",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/de69aea9-f032-4643-9b9b-dcd15607b9f5/Results%20of%20the%20stress%20limitation%20check_CSA.png",
"height": 772,
"width": 1795
},
{
"description": null,
"imageId": "94e2d55d-6acc-4677-9eba-71eb8230fd37",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8a3f43f8-bb03-4f34-a2a6-a40da697f9af/Deflection%20check%20CSA.png",
"height": 96,
"width": 660
},
{
"description": null,
"imageId": "6314246f-310c-4b09-97b2-62afb0553116",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/29ed7393-c339-4488-9451-9a3c3299a02c/Wlim%20recomendation%20CSA.png",
"height": 405,
"width": 1709
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>CSA A23.3:24 的正常使用极限状态在第 8.1.4 条 中定义：挠度按第 8.1.4.1 条，局部损伤和开裂按第 8.1.4.2 条，振动按第 8.1.4.3 条。Detail 中的正常使用验算包括应力限值、裂缝宽度和挠度限值。振动不作评估。</p>\n<p>所有正常使用验算均采用第 8.1 章所述的线性材料模型，并针对第 8.2 章所述的正常使用组合进行。可进行短期和长期计算，分别采用平均弹性模量 <em>E</em><em><sub>c</sub></em> 和有效模量 <em>E</em><em><sub>c,eff</sub></em><sub>,</sub> 。</p>\n<h3>应力限值</h3>\n<p>应力限值验算仅针对预应力构件进行，即仅当模型中存在预应力荷载工况时才执行，依据 第 18.3 条。</p>\n<p>CSA A23.3:24 要求同时验算混凝土应力和钢束应力。第 18.4 条规定的钢束容许应力适用于张拉力以及预应力传递后的即时状态，即需在张拉过程中进行验证；这超出了模型的范围，因此 Detail 不对其进行评估。</p>\n<p>混凝土受压应力以正常使用有限元分析得到的最大主压应力 <em>f</em><em><sub>c</sub></em><em> = σ</em><em><sub>c2</sub></em> 与限值之比来评估。限值取自 第 18.3.2 条，该条适用于在计入全部预应力损失后，规定荷载和预应力作用下的应力：</p>\n<figure data-asset-id=\"9b3ba577-076c-4f6b-a629-a45d9894c473\" data-image-id=\"9b3ba577-076c-4f6b-a629-a45d9894c473\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/83423ed4-9e4e-4819-973b-fadb4306a55e/Compressive%20Stress%20Limits%20in%20Prestressed%20Concrete%20at%20Service%20Limit%20State%20-%20CSA.png\" data-asset-id=\"9b3ba577-076c-4f6b-a629-a45d9894c473\" data-image-id=\"9b3ba577-076c-4f6b-a629-a45d9894c473\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 107\\qquad Concrete compressive stress limits at service loads}}}\\]</em></p>\n<p>在软件中，<em>预应力加永久荷载</em>按持续荷载处理，<em>预应力、永久荷载和可变荷载</em>按总荷载处理。</p>\n<figure data-asset-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" data-image-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/bf637c0b-a972-4836-a119-45f59df9ed58/Combination%20types%20-%20AASHTO.png\" data-asset-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" data-image-id=\"ac528856-0620-4e95-9877-ea4415ba38b5\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 108\\qquad Serviceability combination types}}}\\]</em></p>\n<p>这两个限值对应第 8.2 章所述正常使用组合的两个子类型：持续荷载组合按 0.45 f'<sub>c</sub> 验算，总荷载组合按 0.60 f'<sub>c</sub> 验算。两个数值均可在项目设置中修改，且两项验算可分别独立关闭。</p>\n<figure data-asset-id=\"fbc3aacf-e2f7-4cc0-b101-2f0fa684380e\" data-image-id=\"fbc3aacf-e2f7-4cc0-b101-2f0fa684380e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2c6c69d5-b379-4463-96e4-7552c71aea93/Stress%20limitation%20settings_CSA.png\" data-asset-id=\"fbc3aacf-e2f7-4cc0-b101-2f0fa684380e\" data-image-id=\"fbc3aacf-e2f7-4cc0-b101-2f0fa684380e\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 109\\qquad The setting of the stress limitation parameters}}}\\]</em></p>\n<p>混凝土中的应力采用线性应力-应变图计算。对于每个正常使用组合，进行两次计算：</p>\n<ul>\n <li><strong>短期</strong> – 采用混凝土的平均弹性模量 E<sub>c</sub> ；</li>\n <li><strong>长期</strong> – 在所有计算步骤中均采用包含徐变的有效弹性模量 E<sub>c,eff</sub>，即适用于预应力、永久荷载和可变荷载的施加。</li>\n</ul>\n<p>徐变系数按第 8.1 章所述作为材料属性定义。若显示的是混凝土实际应力 f<sub>c</sub> 的结果，则可使用调整色标限值的功能。</p>\n<figure data-asset-id=\"b9ef304f-a055-4045-9ba8-6b74c494bddb\" data-image-id=\"b9ef304f-a055-4045-9ba8-6b74c494bddb\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/de69aea9-f032-4643-9b9b-dcd15607b9f5/Results%20of%20the%20stress%20limitation%20check_CSA.png\" data-asset-id=\"b9ef304f-a055-4045-9ba8-6b74c494bddb\" data-image-id=\"b9ef304f-a055-4045-9ba8-6b74c494bddb\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 110\\qquad Results of the stress limitation check}}}\\]</em></p>\n<h3>消压</h3>\n<p>若模型中定义了钢束对象，Detail 还会对预应力钢筋进行消压验算。该验算校核钢束所在位置的混凝土是否保持受压，这是 第 18.3.2 条 c) 款中预压受拉区拉应力限值所依据的条件。</p>\n<h3>挠度</h3>\n<p>CSA A23.3:24 要求计算三种不同类型的挠度，非预应力构件依据 第 9.8.2 条，预应力构件依据 第 9.8.4 条：</p>\n<ul>\n <li><strong>瞬时</strong> – 由所定义荷载组合引起的挠度，依据第 9.8.2.2 条，采用混凝土的平均弹性模量 E<sub>c</sub>计算；</li>\n <li><strong>长期</strong> – 由徐变和收缩效应引起的附加挠度，依据第 9.8.2.5 条；</li>\n <li><strong>总挠度</strong> – 由所定义荷载组合引起的挠度，采用有效弹性模量 E<sub>c,eff</sub>计算。有效模量针对每个计算步骤——预应力、恒载和可变荷载——分别计算，采用第 8.1 章所述混凝土材料属性中定义的徐变系数。</li>\n</ul>\n<p>长期挠度为总挠度与瞬时挠度之差。</p>\n<p>计算针对所有对挠度验算有效的组合进行，混凝土采用线性应力-应变图及相应的弹性模量。</p>\n<p>结果显示在挠度验算中。用户可启用或停用总挠度和瞬时挠度的规范校核，并分别定义各自的限值。</p>\n<figure data-asset-id=\"94e2d55d-6acc-4677-9eba-71eb8230fd37\" data-image-id=\"94e2d55d-6acc-4677-9eba-71eb8230fd37\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8a3f43f8-bb03-4f34-a2a6-a40da697f9af/Deflection%20check%20CSA.png\" data-asset-id=\"94e2d55d-6acc-4677-9eba-71eb8230fd37\" data-image-id=\"94e2d55d-6acc-4677-9eba-71eb8230fd37\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 111\\qquad Maximum allowable deflection value}}}\\]</em></p>\n<p>数据视图以表格形式显示所选荷载组合的瞬时挠度、长期挠度和总挠度结果。</p>\n<p>计算挠度的最大容许值见 CSA A23.3:24 表 9.3，该表区分了构件类型和需考虑的挠度。</p>\n<p>限值应由用户根据所分析构件的类型确定。请注意，表 9.3 中第三和第四种构件类型的限值针对的是非结构构件安装后发生的那部分总挠度，而 Detail 报告的是自荷载历程开始以来的总挠度。表 9.3 的注释允许将长期挠度减去计算得出的在该安装之前已发生的部分；此折减由用户负责。</p>\n<h3>裂缝宽度</h3>\n<p>CSA A23.3:24 在第 10.6.1 条 中通过裂缝控制参数 z 间接控制开裂。第 8.1.4.2 条 的注释明确指出“本标准未对裂缝宽度作具体限制”，第 10.6.1 条的注释进一步指出，对于处于极强侵蚀环境或按防水要求设计的结构，该条的要求可能不够充分。</p>\n<p>参数 z 表示潜在的开裂程度，而非实际的裂缝宽度。其所依据的关系式未考虑裂缝间距，而裂缝间距无法可靠预测，因此 z 值不能换算为裂缝宽度并与之比较。</p>\n<p>由于 CSA A23.3:24 未给出裂缝宽度的计算方法，Detail 采用与设计规范无关的通用 CSFM 方法评估裂缝宽度：将沿钢筋计算得到的平均应变，在由拉力弦模型得到的裂缝间距上进行积分。裂缝宽度验算针对所有启用了“用于裂缝宽度验算”属性的正常使用组合进行。</p>\n<p>计算采用混凝土的线性应力-应变图。对于分配给裂缝宽度验算的每个正常使用组合，均进行上述短期和长期计算。</p>\n<p>验算表示如下：</p>\n<p>\\[\\frac{w}{w_{lim}}\\]</p>\n<p>其中：</p>\n<ul>\n <li>w 为有限元分析计算得到的短期或长期裂缝宽度；</li>\n <li>w<sub>lim</sub> 为用户定义的裂缝宽度限值。</li>\n</ul>\n<p>由于 CSA A23.3 未规定裂缝宽度限值，用户须根据环境条件和项目要求指定 w<sub>lim</sub> 。</p>\n<p>可参考 CSA S6:14《加拿大公路桥梁设计规范》第 8.12.3.1 条和表 8.6，其中规定了适用的结构构件类型和环境条件下正常使用极限状态的最大裂缝宽度：</p>\n<figure data-asset-id=\"6314246f-310c-4b09-97b2-62afb0553116\" data-image-id=\"6314246f-310c-4b09-97b2-62afb0553116\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/29ed7393-c339-4488-9451-9a3c3299a02c/Wlim%20recomendation%20CSA.png\" data-asset-id=\"6314246f-310c-4b09-97b2-62afb0553116\" data-image-id=\"6314246f-310c-4b09-97b2-62afb0553116\" alt=\"\"></figure>\n<p><em>\\[ \\textsf{\\textit{\\footnotesize{Fig. 112\\qquad Reasonable crack widths for reinforced concrete under service load}}}\\]</em></p>\n<p>这些数值是针对公路桥梁制定的。对于按 CSA A23.3 设计的建筑，它们并非强制性要求，但代表了加拿大设计实践针对相应环境条件所采用的限值。</p>\n<p>它们也与软件所评估的量一致。CSA S6:14 第 8.12.3.2 条将裂缝宽度计算为 w = k<sub>b</sub> β<sub>c</sub> s<sub>rm</sub> ε<sub>sm</sub></p>\n<p>即裂缝间距 <em>s</em><em><sub>rm</sub></em> 与钢筋平均应变 <em>ε</em><em><sub>sm</sub></em>，这与 CSFM（协调应力场法）将沿钢筋计算得到的应变在裂缝间距上积分所得的量相同。因此，表 8.6 的限值所针对的裂缝宽度，与软件所报告的裂缝宽度性质相同，这不同于由钢筋分布参数（如 <em>z</em>）导出的限值。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"theoretical_background_detail___general___verifica",
"detail_theoretical_background",
"reinforcement_template_in_idea_statica_detail",
"n2022_03_16_code_check_of_walls_and_deep_beams"
],
"linkedItems": [
"[Circular Reference]",
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "AMER",
"codename": "amer"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 6900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "8-5-serviceability-limit-state"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"6-5-service-limit-state\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:43</li>\n <li>de-DE: Translated on 27.10.2026 14:25</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:18</li>\n <li>fr-FR: Translated on 27.10.2026 15:05</li>\n <li>hu-HU: Translated on 27.10.2026 18:25</li>\n <li>it-IT: Translated on 27.10.2026 15:42</li>\n <li>ja-JP: Translated on 26.10.2026 12:41</li>\n <li>ko-KR: Translated on 26.10.2026 12:39</li>\n <li>nl-NL: Translated on 27.10.2026 16:58</li>\n <li>pl-PL: Translated on 27.10.2026 19:51</li>\n <li>pt-PT: Language translation error (when inserting into Kontent.ai)</li>\n <li>ro-RO: Translated on 27.10.2026 19:08</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:38</li>\n <li>tr-TR: Translated on 26.10.2026 12:41</li>\n <li>vi-VN: Translated on 26.10.2026 12:40</li>\n <li>zh-CN: Translated on 27.10.2026 20:31</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "theoretical_background_detail___service_limit_stat_00c850c",
"collection": "default",
"id": "00c850c6-e080-4a44-87ec-f4e1f192f2d3",
"language": "zh-CN",
"lastModified": "2026-10-27T19:31:33.719722Z",
"name": "Theoretical background Detail – Service limit state – CSA",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": "9 Prestressing in Detail - Model description"
},
"id": {
"name": "ID",
"type": "text",
"value": "prestressing-in-detail-model-description"
},
"printable_anchor": {
"name": "Printable anchor used in PDF content table",
"type": "multiple_choice",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n1ecc3d2d_b87a_01f1_a493_9161e2eae77d",
"collection": "default",
"id": "1ecc3d2d-b87a-01f1-a493-9161e2eae77d",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "1ecc3d2d-b87a-01f1-a493-9161e2eae77d",
"sitemapLocations": [],
"type": "widget_anchor_target",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "简介与材料模型"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": []
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": "Europe/Prague"
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "7d9fac4b-fa97-49d3-a624-ddfab1bf7dee",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aa25e678-c691-4887-9f8f-b5ae0c4a4fb2/prestressing%20model_Detail_01.png",
"height": 605,
"width": 2141
},
{
"description": null,
"imageId": "7b26f280-9951-4255-98c4-90f558de030f",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1c112ef0-c06a-4141-9d09-1e3cfa42d079/prestressing%20model_Detail__ACI.png",
"height": 605,
"width": 2141
},
{
"description": null,
"imageId": "cd6cee68-68e6-44b3-921a-4ccf8cd4df35",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/035bbeed-4b37-4477-b848-8ee98b174f72/prestressing%20model_Detail_02.png",
"height": 361,
"width": 1387
},
{
"description": null,
"imageId": "3b267c80-ee0e-457f-af00-f74c91a48d7d",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a028db63-b458-44e7-945b-bedabb1a6785/prestressing%20model_Detail_03.png",
"height": 309,
"width": 1011
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "theoretical_background_detail___finite_element_typ",
"linkId": "85424e98-41cd-4bdd-a978-e4b540a10be5",
"urlSlug": "2-5-finite-element-types",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>协调应力场法（CSFM）是一种基于二维平面应力的计算方法。该方法采用二维有限单元模拟混凝土，一维钢筋单元通过约束与其连接。模型中还可以添加用于表示有粘结预应力钢筋的特殊一维单元，这些单元可模拟为先张和后张两种形式。</p>\n<p>预应力钢筋的模拟方式与普通钢筋类似，均采用传递轴力的线单元。每个预应力钢筋单元由其面积和材料特性表征。这些特性由所用规范（EN 1992-1-1、ACI 318-19 等）规定的材料特征曲线给出。</p>\n<p><strong>欧洲规范</strong></p>\n<p>预应力钢筋的应力-应变图：a) EN 1992-1-1 定义的应力-应变图；b) 先张钢筋的初始应变</p>\n<figure data-asset-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\" data-image-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/aa25e678-c691-4887-9f8f-b5ae0c4a4fb2/prestressing%20model_Detail_01.png\" data-asset-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\" data-image-id=\"7d9fac4b-fa97-49d3-a624-ddfab1bf7dee\" alt=\"\"></figure>\n<p><strong>ACI</strong></p>\n<p>预应力钢筋的应力-应变图：a) 应力-应变图；b) 先张钢筋的初始应变</p>\n<figure data-asset-id=\"7b26f280-9951-4255-98c4-90f558de030f\" data-image-id=\"7b26f280-9951-4255-98c4-90f558de030f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1c112ef0-c06a-4141-9d09-1e3cfa42d079/prestressing%20model_Detail__ACI.png\" data-asset-id=\"7b26f280-9951-4255-98c4-90f558de030f\" data-image-id=\"7b26f280-9951-4255-98c4-90f558de030f\" alt=\"\"></figure>\n<p><br></p>\n<p>钢筋单元通过粘结模型与混凝土模型的二维单元相连，其方式与传统混凝土钢筋相同。 </p>\n<ul>\n <li>阅读 <a data-item-id=\"85424e98-41cd-4bdd-a978-e4b540a10be5\" href=\"\">有限单元类型</a></li>\n</ul>\n<p>粘结模型单元允许预应力钢筋与混凝土之间产生相对变形，并具有相应的非线性特性。这样既能正确模拟钢筋与混凝土之间的粘结作用，也能模拟先张钢筋的锚固模型。后张钢筋的端部构造（例如锚板）由一个单元模拟，其刚度与预应力钢筋端部的锚具相对应；端部预应力以面荷载的形式施加到混凝土模型上，作用面积与锚板尺寸相同。该模型无法准确描述锚下区域的局部三轴应力，该区域须单独考虑。 </p>\n<p>预应力钢筋不考虑混凝土相互作用引起的钢筋拉力刚化，因为预应力钢筋附近的混凝土被假定处于受压状态。</p>\n<h2>先张钢筋</h2>\n<p>先张钢筋在构件浇筑之前张拉。预应力钢筋几乎总是按直线布置，因此不会产生摩擦预应力损失。当混凝土达到所需强度后，钢筋从锚固台座上放松，预应力钢筋随之激活，并将力从钢筋传递给混凝土。这一效应在物理上等同于钢筋的冷缩，可通过类似于温度荷载的初始应变来模拟。由此得到预应力钢筋的应力-应变图，如上图 b) 所示。计算模型会自动计算结构对所施加预应力的变形响应，因此可直接确定由单元弹性应变引起的预应力损失。</p>\n<p>由于预应力是已知的，因此预应力应力 <em>σ</em><em><sub>pmo</sub></em> 也是已知的，应力对变形的依赖关系采用钢筋的材料图，可表示为：</p>\n<p><em>\\[{{σ}_{p}}=~{{f}}({{ε}}-{{ε}_{0}})\\]</em></p>\n<p>假定钢筋中的预应力低于屈服强度（即满足 EN 1992-1-1 第 5.10.3 条规定的条件），初始变形也可按下式计算：</p>\n<p><em>\\[{{ε}_{0}}=\\frac{{{σ}_{pm0}}}{{{E}_{p}}}\\]</em></p>\n<p><em>ε</em><em><sub>0</sub></em> - 预应力引起的初始应变<br><em>σ</em><em><sub>pm0</sub></em> - 放张前瞬间的应力<br><em>E</em><em><sub>p</sub></em> - 预应力钢筋的弹性模量</p>\n<p>先张钢筋的特殊之处在于，其端部锚固通过多种不同机制实现：钢筋与混凝土在分子层面的粘附作用、钢筋表面与混凝土界面产生的摩擦、螺旋钢筋对混凝土的机械咬合，以及预应力钢筋直径增大所形成的楔入机制（即 Hoyer 效应）。上述效应通过修改先张钢筋端部区域锚固模型的特性，纳入 CSFM（协调应力场法）计算模型中。</p>\n<p>先张钢筋与混凝土的相互作用：a) 螺旋钢筋咬入混凝土；b) Hoyer 效应</p>\n<figure data-asset-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\" data-image-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/035bbeed-4b37-4477-b848-8ee98b174f72/prestressing%20model_Detail_02.png\" data-asset-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\" data-image-id=\"cd6cee68-68e6-44b3-921a-4ccf8cd4df35\" alt=\"\"></figure>\n<h2>后张钢筋</h2>\n<p>后张钢筋在结构浇筑之后张拉。张拉设备直接支承在结构上，因此消除了预应力引起的结构弹性应变损失。达到预期预应力后，钢筋被锚固，随后对预应力孔道进行灌浆，从而使钢筋与结构形成粘结。因此，在模拟后张钢筋时，计算分为若干荷载步：预应力张拉、施加其他永久荷载以及施加可变荷载。</p>\n<p>附带一维预应力钢筋单元的混凝土有限元网格：</p>\n<figure data-asset-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\" data-image-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a028db63-b458-44e7-945b-bedabb1a6785/prestressing%20model_Detail_03.png\" data-asset-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\" data-image-id=\"3b267c80-ee0e-457f-af00-f74c91a48d7d\" alt=\"\"></figure>\n<h4>荷载步“预应力张拉”</h4>\n<p>在钢筋张拉时，钢筋的刚度并未计入结构刚度。在该荷载步中，模型不考虑线单元的刚度，钢筋单元由与预应力应力和钢筋面积相对应的等效荷载代替，如上图所示。当预应力产生的荷载全部施加完毕且该荷载步收敛后，读取各线单元的变形，并据此确定预应力钢筋各线单元的初始应变 <em>ε</em><em><sub>0</sub></em>。</p>\n<p>预应力应力可沿钢筋长度手动定义，也可根据钢筋几何形状自动计算。如果选择自动计算损失，则会考虑摩擦损失（依据 EN 1992-1-1 第 5.10.5.2 条或 ACI 318-19 第 20.3.2 条）以及锚固时的钢筋滑移（锚具楔片回缩）。由于所有预应力钢筋均在一步内施加，因此不考虑逐根张拉引起的损失。</p>\n<h4>预应力钢筋参与工作的后续荷载步</h4>\n<p>在后续荷载步（施加其他永久荷载和可变荷载）中，采用与先张钢筋相同的处理方式。此时考虑预应力钢筋的全部刚度以及钢筋与周围混凝土之间的粘结，并通过初始应变 <em>ε</em><em><sub>0</sub></em> 修正预应力钢筋的应力-应变图。该应变对每个单元各不相同，由前一荷载步“预应力张拉”得出。由于钢筋与混凝土之间存在粘结，模型能够正确考虑外荷载作用下结构弹性变形所引起的预应力变化。</p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [],
"linkedItems": []
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [
{
"name": "Beginner",
"codename": "beginner"
},
{
"name": "Intermediate",
"codename": "intermediate"
},
{
"name": "Expert",
"codename": "expert"
}
],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "CSFM",
"codename": "csfm"
},
{
"name": "Prestressed members",
"codename": "prestressed_members"
},
{
"name": "Prestressing losses",
"codename": "prestressing_losses"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "AISC (USA)",
"codename": "aisc"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": null
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "introduction-and-material-models"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"introduction-and-material-models\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": ""
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": ""
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:44</li>\n <li>de-DE: Translated on 27.10.2026 14:25</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:19</li>\n <li>fr-FR: Translated on 27.10.2026 15:06</li>\n <li>hu-HU: Translated on 27.10.2026 18:26</li>\n <li>it-IT: Translated on 27.10.2026 15:43</li>\n <li>ja-JP: Translated on 26.10.2026 12:42</li>\n <li>ko-KR: Translated on 26.10.2026 12:41</li>\n <li>nl-NL: Translated on 27.10.2026 16:59</li>\n <li>pl-PL: Translated on 27.10.2026 19:52</li>\n <li>pt-PT: Translated on 27.10.2026 17:43</li>\n <li>ro-RO: Translated on 27.10.2026 19:09</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 26.10.2026 12:40</li>\n <li>tr-TR: Translated on 26.10.2026 12:42</li>\n <li>vi-VN: Translated on 26.10.2026 12:41</li>\n <li>zh-CN: Translated on 27.10.2026 20:32</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "prestressing_in_detail___model_description__body_",
"collection": "default",
"id": "9e466f52-e5a6-4543-9d32-164897c5165e",
"language": "zh-CN",
"lastModified": "2026-10-27T19:32:07.6510475Z",
"name": "Prestressing in Detail - Model description (body)",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": ""
},
"event_id": {
"name": "Event ID",
"type": "text",
"value": ""
},
"description_top": {
"name": "Description before",
"type": "text",
"value": ""
},
"link_text": {
"name": "Link text",
"type": "text",
"value": "开始免费试用"
},
"link_url": {
"name": "Link URL",
"type": "text",
"value": ""
},
"content_item_link": {
"name": "Content Item Link",
"type": "modular_content",
"value": [
"landing_page_role_navigation"
],
"linkedItems": [
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "免费开始使用"
},
"subtitle": {
"name": "Subtitle",
"type": "text",
"value": ""
},
"breadcrumbs_page_title": {
"name": "Breadcrumbs page title",
"type": "text",
"value": ""
},
"breadcrumbs_parent": {
"name": "Breadcrumbs parent",
"type": "modular_content",
"value": [],
"linkedItems": []
},
"content": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p>请在下方选择您的角色，我们将为您发送适合您需求的免费 IDEA StatiCa 许可证。</p>"
},
"shared_content": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "portal_dashboard_landing_page",
"linkId": "2f0412c5-5b52-423c-a352-8af4da02be92",
"urlSlug": "dashboard",
"type": "portal_landing_page"
}
],
"name": "Shared content",
"type": "rich_text",
"value": "<h3>已有账户？<a data-item-id=\"2f0412c5-5b52-423c-a352-8af4da02be92\" href=\"\">登录</a></h3>"
},
"design": {
"name": "Design",
"type": "multiple_choice",
"value": []
},
"asset": {
"name": "Asset",
"type": "asset",
"value": []
},
"header_link": {
"name": "Header link",
"type": "text",
"value": ""
},
"header_content_item_link": {
"name": "Header Content Item Link",
"type": "modular_content",
"value": [],
"linkedItems": []
},
"header_cross_links": {
"name": "Header cross links",
"type": "modular_content",
"value": [],
"linkedItems": []
},
"header_content": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Header content",
"type": "rich_text",
"value": "<p><br></p>"
},
"header_title": {
"name": "Header title",
"type": "text",
"value": ""
},
"header_alignment": {
"name": "Header alignment",
"type": "multiple_choice",
"value": []
},
"header_button_text": {
"name": "Header button text",
"type": "text",
"value": ""
},
"is_breadcrumbs_hidden": {
"name": "Hide breadcrumbs",
"type": "multiple_choice",
"value": []
},
"header_background_image": {
"name": "Background image",
"type": "asset",
"value": []
},
"header_background_image_effects": {
"name": "Background image effect",
"type": "multiple_choice",
"value": []
},
"is_header_full_height": {
"name": "Small height header",
"type": "multiple_choice",
"value": []
},
"header_background_video": {
"name": "Background video",
"type": "asset",
"value": []
},
"url_slug": {
"name": "URL slug",
"type": "url_slug",
"value": "role-navigation"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"role-navigation\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": []
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "14 天免费试用"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "选择最适合您的免费许可证。我们为企业用户提供 14 天免费试用许可证，学生可享受 1 年教育许可证。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 30.9.2026 16:56</li>\n <li>de-DE: Translated on 30.9.2026 16:58</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 30.9.2026 17:03</li>\n <li>fr-FR: Translated on 30.9.2026 17:00</li>\n <li>hu-HU: Translated on 30.9.2026 17:07</li>\n <li>it-IT: Translated on 30.9.2026 17:01</li>\n <li>ja-JP: Translated on 11.8.2026 04:10</li>\n <li>ko-KR: Translated on 15.8.2026 01:59</li>\n <li>nl-NL: Translated on 30.9.2026 17:04</li>\n <li>pl-PL: Translated on 30.9.2026 17:11</li>\n <li>pt-PT: Translated on 30.9.2026 17:06</li>\n <li>ro-RO: Translated on 30.9.2026 17:09</li>\n <li>ru-RU: Translated on 12.6.2026 11:20</li>\n <li>th-TH: Translated on 15.8.2026 00:10</li>\n <li>tr-TR: Translated on 15.8.2026 04:36</li>\n <li>vi-VN: Translated on 15.8.2026 03:11</li>\n <li>zh-CN: Translated on 30.9.2026 17:12</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "landing_page_role_navigation",
"collection": "default",
"id": "0c872071-6a3f-4b99-8cd4-66440db9cc0d",
"language": "zh-CN",
"lastModified": "2026-09-30T15:12:56.4726769Z",
"name": "Free trial / EDU license request – Role-navigation",
"sitemapLocations": [],
"type": "landing_page",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"description_bottom": {
"name": "Description after",
"type": "text",
"value": ""
},
"button_styles": {
"name": "Button style",
"type": "multiple_choice",
"value": [
{
"name": "filled button",
"codename": "filled_button"
}
]
},
"button_position": {
"name": "Button position",
"type": "multiple_choice",
"value": [
{
"name": "center",
"codename": "center"
}
]
},
"visibleinregion": {
"name": "VisibleInRegion",
"type": "multiple_choice",
"value": []
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "region"
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "aec1d9ba_c119_0122_d551_4e09e764c5f9",
"collection": "default",
"id": "aec1d9ba-c119-0122-d551-4e09e764c5f9",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "aec1d9ba-c119-0122-d551-4e09e764c5f9",
"sitemapLocations": [],
"type": "widget_cta_button",
"workflowStep": null,
"workflow": null
}
}
],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<p><br></p>\n<p>理论基础源自 COMPATIBLE STRESS FIELD DESIGN OF STRUCTURAL CONCRETE<br>(Kaufmann et al., 2020)</p>\n<h2>IDEA StatiCa Detail 中混凝土不连续区的结构设计</h2>\n<h3>1 CSFM（协调应力场法）简介</h3>\n<p><a href=\"#general-introduction\">1.1 混凝土构造细节结构设计概述</a><br><a href=\"#main-assumptions-and-limitations\">1.2 主要假定与局限</a><br><a href=\"#design-tools-for-reinforcement\">1.3 钢筋设计工具</a></p>\n<h3>2 IDEA StatiCa Detail 的分析模型</h3>\n<p><a href=\"#introduction-to-finite-element-implementation\">2.1 有限单元实现简介</a><br><a href=\"#supports-and-load-transmitting-components\">2.2 支座与传力构件</a><br><a href=\"#load-transfer-at-trimmed-ends-of-beams\">2.3 梁截断端的荷载传递</a><br><a href=\"#geometric-modification-of-cross-sections\">2.4 截面几何修改</a><br><a href=\"#finite-element-types\">2.5 有限单元类型</a><br><a href=\"#meshing\">2.6 网格划分</a><br><a href=\"#solution-method-and-load-control-algorithm\">2.7 求解方法与荷载控制算法</a><br><a href=\"#presentation-of-results\">2.8 结果展示</a></p>\n<h3>3 模型验证</h3>\n<p><a href=\"#limit-states-and-crack-width-calculation\">3.1 极限状态、裂缝宽度计算与拉力刚化</a></p>\n<h3>4 依据欧洲规范的结构验算</h3>\n<p><a href=\"#material-models-en\">4.1 材料模型 (EN)</a><br><a href=\"#safety-factors\">4.2 安全系数</a><br><a href=\"#ultimate-limit-state-analysis\">4.3 承载能力极限状态分析</a><br><a href=\"#partially-loaded-areas\">4.4 局部受压区 (PLA)<br></a><a href=\"#serviceability-limit-state-analysis\">4.5 正常使用极限状态分析</a></p>\n<h3>5 依据 ACI 318-19 的结构验算</h3>\n<p><a href=\"#material-models-aci\">5.1 材料模型 (ACI)</a><br><a href=\"#strength-reduction-and-load-factors\">5.2 强度折减系数与荷载系数</a><br><a href=\"#strength-verifications\">5.3 承载力验算</a><br><a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\">5.4 承压与锚固区 - 局部受压区<br></a><a href=\"#serviceability-verifications\">5.5 正常使用验算</a></p>\n<h3>6 依据 AASHTO 的结构验算</h3>\n<p><a href=\"#material-models-aahsto\">6.1 材料模型 (AASHTO)</a><br><a href=\"#resistance-and-load-factors\">6.2 抗力系数与荷载系数</a><br><a href=\"#strength-limit-state\">6.3 强度极限状态</a><br><a href=\"#bearing-and-anchorage-zones-resistance-partially-loaded-areas\">6.4 承压与锚固区抗力 – 局部受压区</a><br><a href=\"#service-limit-state\">6.5 使用极限状态</a></p>\n<h3>7 依据 AS 3600 的结构验算</h3>\n<p><a href=\"#material-models-aus\">7.1 材料模型 (AUS)</a><br><a href=\"#stress-reduction-and-load-factors\">7.2 应力折减系数与荷载系数</a><br><a href=\"#strength-and-anchorage-verifications\">7.3 承载力与锚固验算</a><a href=\"#bearing-and-anchorage-zones-partially-loaded-areas\"><br></a><a href=\"#serviceability-checks\">7.4 正常使用验算</a></p>\n<h3>8 依据 CSA A23.3:24 的结构验算</h3>\n<p><a href=\"#material-models-csa\">8.1 材料模型 (CSA)</a><br><a href=\"#resistance-and-load-factors-csa\">8.2 抗力系数与荷载系数</a><br><a href=\"#ultimate-limit-state-csa\">8.3 承载能力极限状态</a><br><a href=\"#bearing-and-anchorage-zones-resistance-partially-loaded-areas-csa\">8.4 承压与锚固区抗力 – 局部受压区</a><br><a href=\"#serviceability-limit-state-csa\">8.5 正常使用极限状态</a></p>\n<p><br></p>\n<h3><a href=\"#prestressing-in-detail-model-description\">9 Detail 中的预应力 - 模型说明</a></h3>\n<p><br></p>\n<p><br></p>\n<h2>1 CSFM（协调应力场法）简介</h2>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n02b04ae1_9ac2_0186_8a2e_afbfaac3c39e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"fd74de0b_9b01_01f9_b7d3_91842b4e64f4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___main_assumptions_a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1b6b2998_a82a_0102_1bb4_e052b35ff829\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___reinforc\"></object>\n<h1><br></h1>\n<h2>2 IDEA StatiCa Detail 的分析模型</h2>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n33af2c10_291e_0187_4660_55b94dbc3824\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___finite_e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n2d4304a1_f345_0104_32bf_85315c48d5cd\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___supports_and_load_\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"b6ecb5e3_7093_01ba_9dde_25d8369a02f7\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___load_transfer_at_t\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n46b4e3db_3dd5_0178_937b_4e69c5404313\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___geometric_modifica\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e2bcc72e_78c5_0163_a169_dc9ed613e170\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___finite_element_typ\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n8a7103fc_e2a4_016b_6e78_a6c6e6a4807f\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___meshing\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n7295ffdb_585b_01c8_eeea_cbfc7526af76\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___solution_method_an\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d4d41655_a8d9_018a_7277_dad106e33f39\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___presentation_of_re\"></object>\n<h1><br></h1>\n<h2>3 模型验证</h2>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n805f2d39_5e1d_0196_07ec_d526e6056d4c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___general___verifica\"></object>\n<h1><br></h1>\n<h2>4 依据欧洲规范的结构验算</h2>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用极限状态，另一种针对承载能力极限状态荷载组合。正常使用分析假定构件的极限性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。这种方法允许在正常使用分析中采用简化的本构模型（混凝土应力-应变图采用线性段），以提高数值稳定性和计算速度。</p>\n<p><br></p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n34484ce7_0966_01b0_4e4e_ced1381a2b83\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__e\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n87402a88_f6a7_01e2_3c54_6a74bb42f492\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___safety_factors\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"fc5356e8_ad66_019d_500e_56112b2c54e1\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___ultimate_limit_sta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n4ffa73af_7903_018b_f050_5cb47586f489\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___partially_loaded_a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"c0faeafd_fe53_0187_955b_d143d9265810\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___serviceability_lim\"></object>\n<h1><br></h1>\n<h2>5 依据 ACI 318-19 的结构验算</h2>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用，另一种针对承载力荷载组合。正常使用分析假定设计荷载作用下的性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。这种方法允许在正常使用分析中采用简化的本构模型（混凝土应力-应变图采用线性段），以提高数值稳定性和计算速度。</p>\n<p>CSFM（协调应力场法）符合 ACI 318-19 第 6.8.1.1 条的规定。为使 CSFM（协调应力场法）满足 ACI 318-19 第 6.8.1.2 节的要求，多所大学开展了大量验证试验。汇总验证与确认结果的各篇文章可通过以下链接查找到。</p>\n<ul>\n <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">验证：Detail 2D</a></li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e023fb1d_6a30_01c3_526e_d8c8d1a6b0e5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"fc85da82_0693_016a_b193_f8a961ac8919\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___factors___aci\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"f654617f_d523_0106_0e28_6bbb16cb93f5\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___strength_analysis_\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"df2d07b6_cabe_0102_4254_6e44efaefb9b\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___bearing_and_anchor\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ca9b6d78_562b_01cd_b7c1_e9e14bcade98\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___serviceability_ver\"></object>\n<h1><br></h1>\n<h2>6 依据 AASHTO 的结构验算</h2>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n718b61d6_ca9a_01c4_c411_608ecc9bfe42\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__a_0b99d24\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1e0b8118_0346_01fc_5843_6a60b409c862\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___resistance_and_loa\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n835a26bd_d5f1_0140_4fe1_9ae73d901010\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___strength_limit_sta\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"a29abd54_d307_013b_44ed_56d973e7aacc\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___bearing_and_anchor_69cbe39\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"d19c5c7a_4da5_01be_7a24_1918c7d60c76\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___service_limit_stat\"></object>\n<h1><br></h1>\n<h2>7 依据澳大利亚标准 AS 3600 (2018) 的结构验算</h2>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用，另一种针对承载力荷载组合。正常使用分析假定设计荷载作用下的性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。这种方法允许在正常使用分析中采用简化的本构模型（混凝土应力-应变图采用线性段），以提高数值稳定性和计算速度。</p>\n<p>CSFM（协调应力场法）是一种满足第 6.1.1 条和第 6.1.2 条一般规则的结构分析方法，在第 6.1.3 条中被定义为 (f) 非线性应力分析，详见第 6.6 条。 </p>\n<p>CSFM（协调应力场法）分析考虑了第 6.6.3 条中定义的所有相关非线性和非弹性效应（收缩除外）。 </p>\n<p>为满足第 6.6.4 条和第 6.6.5 条的要求（更多内容见 AS3600:2018 Sup 1:2022 第 C6.6 节），多所大学对该方法进行了验证与确认。汇总验证与确认结果的各篇文章可通过以下链接查找。</p>\n<ul>\n <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">验证：Detail 2D</a></li>\n</ul>\n<p>由于 IDEA StatiCa Detail 是一款实用设计软件，计算中采用经折减的 28 天混凝土圆柱体抗压强度特征值 <em>f'</em><em><sub>c</sub></em>，详见下一章。</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n83eff71e_cb6d_0152_d7f9_4621fe4095f0\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__a_b7035a6\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n3541764a_859d_01a8_0078_115c1a96acda\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___stress_reduction_a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n10a5f687_325c_014e_ea85_7f516e5dd6e4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___strength_analysis__8bc3bfe\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"ec38c193_dd6d_018f_8d40_071dc9fd107a\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___serviceability_ver_77b5f2c\"></object>\n<h2><br></h2>\n<h2>8 依据 CSA A23.3:24 的结构验算</h2>\n<p>采用 CSFM（协调应力场法）对结构进行评估时，需进行两种不同的分析：一种针对正常使用，另一种针对承载力荷载组合。正常使用分析假定设计荷载作用下的性能满足要求，且在正常使用荷载水平下材料不会达到屈服条件。这种方法允许在正常使用分析中采用简化的本构模型（混凝土应力-应变图采用线性段），以提高数值稳定性和计算速度。</p>\n<p>CSFM（协调应力场法）是一种结构分析方法，满足 CSA A23.3:24 第 9.5 条对有限元分析的要求。开裂的影响直接体现在材料模型中（第 9.5.1 条），钢筋的锚固得到明确考虑（第 9.5.3 条），裂缝控制和挠度作为正常使用验算的一部分进行验证（第 9.5.5 条）。由于 CSFM（协调应力场法）是一种连续应力场方法，它也与第 9.4 条允许的拉压杆模型分析相一致，第 11.4.2.3 条规定的压杆中压应力限值已体现在混凝土的极限抗压强度中（见下文系数 α 和 k<sub>c2</sub> 的定义）。</p>\n<p>多所大学对该方法进行了验证与确认。汇总验证与确认结果的各篇文章可通过以下链接查找。</p>\n<ul>\n <li><a href=\"https://www.ideastatica.com/support-center-verifications?label=detail\">验证：Detail 2D</a></li>\n</ul>\n<p>由于 IDEA StatiCa Detail 是一款实用设计软件，计算中采用经折减的混凝土规定抗压强度 f'<sub>c</sub> ，详见下一章。</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n6aab19fe_22df_01fc_a1c7_3d0f7ddd9aab\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___material_models__c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n3131c97b_f469_015c_eb8e_4ec8df85f4fb\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___resistance_and_loa_3be42f4\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"cd09877f_7f1a_014d_d93d_f401610d7808\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___strength_limit_sta_fde100c\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"e26de44a_0888_0142_95ac_ff57c9eb6c2d\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___bearing_and_anchor_bfd09ef\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n5c09040b_e0fb_01f6_3ab5_39d6d1e375b0\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"theoretical_background_detail___service_limit_stat_00c850c\"></object>\n<h2>9 预应力 - 模型说明</h2>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1ecc3d2d_b87a_01f1_a493_9161e2eae77d\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"prestressing_in_detail___model_description__body_\"></object>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"aec1d9ba_c119_0122_d551_4e09e764c5f9\"></object>\n<h1><br></h1>\n<h2>参考文献</h2>\n<p>AASHTO. 2014. AASHTO LRFD Bridge Design Specifications. 7th ed. Washington, DC: American Association of State Highway and Transportation Officials.</p>\n<p><br></p>\n<p>AASHTO. 2024. AASHTO LRFD Bridge Design Specifications. 10th ed. Washington, DC: American Association of State Highway and Transportation Officials.</p>\n<p><br></p>\n<p>ACI Committee 318. 2019. Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary. Farmington Hills, MI: American Concrete Institute.</p>\n<p><br></p>\n<p>Alvarez, Manuel. 1998. Einfluss des Verbundverhaltens auf das Verformungsvermögen von Stahlbeton. IBK Bericht 236. Basel: Institut für Baustatik und Konstruktion, ETH Zurich, Birkhäuser Verlag.</p>\n<p><br></p>\n<p>Beeby, A. W. 1979. “The Prediction of Crack Widths in Hardened Concrete.” The Structural Engineer 57A (1): 9–17.</p>\n<p><br></p>\n<p>Broms, Bengt B. 1965. “Crack Width and Crack Spacing In Reinforced Concrete Members.” ACI Journal Proceedings 62 (10): 1237–56. https://doi.org/10.14359/7742.</p>\n<p><br></p>\n<p>Burns, C.. 2012. “Serviceability Analysis of Reinforced Concrete Members Based on the Tension Chord Model.” IBK Report Nr. 342, Zurich, Switzerland: ETH Zurich.</p>\n<p><br></p>\n<p>Crisfield, M. A. 1997. Non-Linear Finite Element Analysis of Solids and Structures. Wiley.</p>\n<p><br></p>\n<p>CSA Group. 2014. Canadian Highway Bridge Design Code (CSA S6-14). Toronto, ON: CSA Group.</p>\n<p><br></p>\n<p>CSA Group. 2024. Design of Concrete Structures (CSA A23.3:24). Toronto, ON: CSA Group.</p>\n<p><br></p>\n<p>European Committee for Standardization (CEN). 2015. 1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings. Brussels: CEN, 2005.</p>\n<p><br></p>\n<p>Fernández Ruiz, M., and A. Muttoni. 2007. “On Development of Suitable Stress Fields for Structural Concrete.” ACI Structural Journal 104 (4): 495–502.</p>\n<p><br></p>\n<p>Kaufmann, W., J. Mata-Falcón, M. Weber, T. Galkovski, D. Thong Tran, J. Kabelac, M. Konecny, J. Navratil, M. Cihal, and P. Komarkova. 2020. “Compatible Stress Field Design Of Structural Concrete. Berlin, Germany.”AZ Druck und Datentechnik GmbH, ISBN 978-3-906916-95-8.</p>\n<p><br></p>\n<p>Kaufmann, W., and P. Marti. 1998. “Structural Concrete: Cracked Membrane Model.” Journal of Structural Engineering 124 (12): 1467–75. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467).</p>\n<p><br></p>\n<p>Kaufmann, W.. 1998. “Strength and Deformations of Structural Concrete Subjected to In-Plane Shear and Normal Forces.” Doctoral dissertation, Basel: Institut für Baustatik und Konstruktion, ETH Zürich. https://doi.org/10.1007/978-3-0348-7612-4.</p>\n<p><br></p>\n<p>Konečný, M., J. Kabeláč, and J. Navrátil. 2017. Use of Topology Optimization in Concrete Reinforcement Design. 24. Czech Concrete Days (2017). ČBS ČSSI. https://resources.ideastatica.com/Content/06_Detail/Verification/Articles/Topology_optimization_US.pdf.</p>\n<p><br></p>\n<p>Marti, P. 1985. “Truss Models in Detailing.” Concrete International 7 (12): 66–73.</p>\n<p><br></p>\n<p>Marti, P. 2013. Theory of Structures: Fundamentals, Framed Structures, Plates and Shells. First edition. Berlin, Germany: Wiley Ernst & Sohn.</p>\n<p>http://sfx.ethz.ch/sfx_locater?sid=ALEPH:EBI01&genre=book&isbn=9783433029916.</p>\n<p><br></p>\n<p>Marti, P., M.Alvarez, W. Kaufmann, and V. Sigrist. 1998. “Tension Chord Model for Structural Concrete.” Structural Engineering International 8 (4): 287–298.</p>\n<p>https://doi.org/10.2749/101686698780488875.</p>\n<p><br></p>\n<p>Mata-Falcón, J. 2015. “Serviceability and Ultimate Behaviour of Dapped-End Beams (In Spanish: Estudio Del Comportamiento En Servicio y Rotura de Los Apoyos a Media Madera).” PhD thesis, Valencia: Universitat Politècnica de València.</p>\n<p><br></p>\n<p>Meier, H. 1983. “Berücksichtigung Des Wirklichkeitsnahen Werkstoffverhaltens Beim Standsicherheitsnachweis Turmartiger Stahlbetonbauwerke.” Institut für Massivbau, Universität Stuttgart.</p>\n<p><br></p>\n<p>Navrátil, J., P. Ševčík, L. Michalčík, P. Foltyn, and J. Kabeláč. 2017. A Solution for Walls and Details of Concrete Structures. 24. Czech Concrete Days.</p>\n<p><br></p>\n<p>Schlaich, J., K. Schäfer, and M. Jennewein. 1987a. “Toward a Consistent Design of Structural Concrete.” PCI Journal 32 (3): 74–150.</p>\n<p><br></p>\n<p>Standards Australia. 2018. Concrete Structures (AS 3600:2018). Sydney, NSW: Standards Australia.</p>\n<p><br></p>\n<p>Standards Australia. 2022. Concrete Structures – Commentary (Supplement 1 to AS 3600:2018). Sydney, NSW: Standards Australia.</p>\n<p><br></p>\n<p>Vecchio, F.J., and M.P. Collins. 1986. “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear.” ACI Journal 83 (2): 219–31. </p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"csfm___how_it_works__code_compliance__validation_a",
"n2026_02_25_webinar_concrete___bridge_detail",
"donaucitytower_2__vienna__austria",
"detail_verification__shear_tests_in_beams_with_low"
],
"linkedItems": [
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "CSFM（协调应力场法）详解"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Plain strain (4).png",
"description": null,
"type": "image/png",
"size": 373017,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/3b429490-28c0-4b4d-9dc3-9b36a136fbec/Plain%20strain%20%284%29.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": "Asia/Singapore"
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": "协调应力场法（CSFM）是对现有不连续区域求解方法的扩展。CSFM（协调应力场法）与拉压杆法有何区别？它能得出哪些结果？这些结果是否符合规范要求？请阅读下面的文章了解详情！"
},
"content": {
"images": [
{
"description": null,
"imageId": "a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7fd8d041-20d1-40a8-9a71-eb9cdce27155/7.png",
"height": 1200,
"width": 1862
},
{
"description": null,
"imageId": "59f28d4a-b793-4501-a11a-6ae6245cab70",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7aecb55f-dac0-47db-a25c-48082e5e70c4/Untitled%20design.png",
"height": 2000,
"width": 1414
},
{
"description": null,
"imageId": "6552ad81-c0fa-4071-9b95-00d09eb9fea4",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9e760312-8401-44c8-aae1-020b514876fb/2.png",
"height": 747,
"width": 1900
},
{
"description": null,
"imageId": "9739b6d6-2cbc-4745-a590-4a85f7e1862f",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc56c80f-67f3-481d-a2c8-26dacc258bb2/csfm%20explained%20%281%29.png",
"height": 789,
"width": 1476
},
{
"description": null,
"imageId": "c5bf3113-2223-4ddc-bbab-2131db37ac0c",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/40e41bf7-4a81-4245-bd1b-843963c104e8/3.png",
"height": 883,
"width": 1900
},
{
"description": null,
"imageId": "6c73faf0-64d4-41ce-b816-520ccadff05a",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/51628156-5014-4501-8f28-9f3b93783840/1.png",
"height": 918,
"width": 1900
},
{
"description": null,
"imageId": "6c090b06-f906-4e6e-9016-d73de172f321",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8fd3f66a-63b9-4aba-bb10-9e12889ed7d4/Finite%20element%20model.png",
"height": 449,
"width": 1177
},
{
"description": null,
"imageId": "9d541a10-b879-4d35-a6f8-4e85fa9843a6",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7bd9ebbf-5d30-448a-93e2-c89641d05677/4.png",
"height": 1900,
"width": 1232
}
],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [
{
"codename": "concrete",
"linkId": "b4790cf9-a605-45b3-b41b-e36909ad4291",
"urlSlug": "concrete",
"type": "landing_page"
},
{
"codename": "landing_page___verifications",
"linkId": "1e879886-9e36-49e1-acb1-e6001361531f",
"urlSlug": "support-center-verifications",
"type": "landing_page_support_center"
},
{
"codename": "detail_theoretical_background",
"linkId": "0000c94c-b603-48c4-8d31-bc56d7c95886",
"urlSlug": "theoretical-background-for-idea-statica-detail",
"type": "support_center_article"
},
{
"codename": "csfm_book___compatible_stress_field_design_of_stru",
"linkId": "0dd36e25-63b2-4d63-a33e-6043644fda4f",
"urlSlug": "csfm-book-compatible-stress-field-design-of-structural-concrete",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<p>在实际工程中，<strong>拉压杆（Strut-and-Tie，S&T）</strong>法和<strong>应力场法</strong>通常用于设计钢筋混凝土和预应力混凝土结构中的不连续区域。<strong>协调应力场法（CSFM）</strong>是在这些经典理论的基础上发展而来的，自动化程度高，并符合设计标准。该方法虽然简单，却能非常真实地描述混凝土结构在<strong>承载能力极限状态</strong>（ULS）和<strong>正常使用极限状态</strong>（SLS）下的响应。CSFM（协调应力场法）已在 <a data-item-id=\"b4790cf9-a605-45b3-b41b-e36909ad4291\" href=\"\">IDEA StatiCa Detail</a> 中实现。 </p>\n<figure data-asset-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" data-image-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7fd8d041-20d1-40a8-9a71-eb9cdce27155/7.png\" data-asset-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" data-image-id=\"a7b3dcf1-10ed-4b44-99e3-f59b4bd2a7fe\" alt=\"\"></figure>\n<p><em>图 1 a) 带洞口的墙 b) 剪力墙 c) 带企口端和洞口的梁 d) 桥墩 e) 桥梁横隔板 </em></p>\n<p>在符合伯努利-纳维平截面假定（即平面应变分布假定）的部位（B 区），可采用混凝土结构截面设计的标准方法。不符合该假定的部位称为<strong>不连续区域（D 区）</strong>。这些部位包括出现集中荷载或截面突变的结构部分，例如企口端（图 1c）、深梁、带洞口的墙（图 1a、1b），以及牛腿和桩承台。在桥梁工程领域，这类部位包括桥墩盖梁（图 1d）、横隔板（图 1e）、转向块等。</p>\n<h2>1. 拉压杆法</h2>\n<p>建立 S&T 模型的基本假定是忽略混凝土的抗拉强度。简单的桁架模型由受压和受拉的单元组成，用于表示承载能力极限状态下的行为。通常，这并不是一个复杂的问题，对于经验丰富的工程师来说，建立基本的 S&T 模型（图 2a）应当不成问题。然而，即使是这项基本工作，按照设计标准对模型进行正确评估，也可能是一个繁琐、手动且需反复迭代的过程。</p>\n<figure data-asset-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\" data-image-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7aecb55f-dac0-47db-a25c-48082e5e70c4/Untitled%20design.png\" data-asset-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\" data-image-id=\"59f28d4a-b793-4501-a11a-6ae6245cab70\" alt=\"\"></figure>\n<p><em>图 2 a) S&T 模型方案 1 b) S&T 模型方案 2 c) S&T 模型方案 3 </em></p>\n<p>必须对拉杆、节点区以及压杆中的横向拉应变进行验算。如果模型未通过校核，就必须调整 S&T 的几何形状，或选用其他 S&T 模型（图 2b、2c）。这往往导致结构工程师只选择一次 S&T 模型几何形状，并且只验算钢筋，从而可能造成很大的误差。模型的选择始终取决于经验。对于更复杂的结构细部，要选出与结构实际行为足够吻合的 S&T 模型，可能不像上述情况那样容易。此外，S&T 仅是一种用于极限状态承载能力设计的方法。它无法用于<strong>正常使用极限状态（变形、裂缝）</strong>的设计，而这些恰恰是关键的判据，对于重要结构尤其如此，因为它们直接影响结构的使用寿命。</p>\n<h2>2. 协调应力场法 - CSFM</h2>\n<p>CSFM（协调应力场法）是一种现代的<strong>非线性方法</strong>，用于分析 D 区以及其行为可简化为平面应力（即二维模型）的构件。 不过，它仍然基于标准中基本而安全的假定：<strong>混凝土不承受拉力</strong>，所有拉力都必须由钢筋承担。协调应力场法（CSFM）是 S&T 和应力场法的发展，消除了上述两种方法的主要缺点：模型选择的不确定性、难以实现自动化，以及无法验算正常使用极限状态。</p>\n<figure data-asset-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\" data-image-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/9e760312-8401-44c8-aae1-020b514876fb/2.png\" data-asset-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\" data-image-id=\"6552ad81-c0fa-4071-9b95-00d09eb9fea4\" alt=\"\"></figure>\n<p><em>图 3 a) 平面应变 b) 主应力 c) CSFM（协调应力场法）</em></p>\n<p>CSFM（协调应力场法）的原理可以通过钢筋混凝土结构中基本平面单元的<strong>平面应力</strong>来说明。图 3a 显示了处于平面应力状态的基本二维单元，这是所有弹性力学和材料力学教科书中都有的内容。这是结构中某一点的应力，例如可通过有限单元法（FEM）的线弹性分析得到。该单元承受水平正应力 σ<sub>x</sub>、竖向正应力 σ<sub>z</sub> 和剪应力 τ<sub>xz</sub>。由这些应力可以确定所谓的<strong>主应力</strong>及其方向（由角度 θ 定义）（图 3b）。此时，该单元承受主拉应力 σ<sub>1</sub> 和主压应力 σ<sub>2</sub>。</p>\n<p>用 CSFM（协调应力场法）分析同一单元，其应变会是什么样？应变如图 3c 所示。受压混凝土出现在主压应力 σ<sub>2</sub> 的方向上，并形成应力为 σ<sub>c2</sub> 的应力场。如上所述，基本假定是混凝土不承受拉力。因此，横向主拉应力 σ<sub>1</sub> 不会由混凝土传递，并将在垂直于该方向上形成裂缝。因此，应力 σ<sub>c1r</sub> 必须为零。为避免该二维单元破坏，所有拉应力都必须由钢筋承担（图 3c 中以蓝色表示），钢筋必须是计算模型的一部分。 </p>\n<p>如果使用 CSFM（协调应力场法）在待求解的<strong>整个二维区域内连续</strong>进行这种应力分析，其结果就是混凝土中连续的压力场，以及钢筋中的拉应力和压应力。图 4 给出了 CSFM（协调应力场法）应力场的简化图示。除混凝土和钢筋的承载比外，该图还显示了计算得到的应力 σ<sub>c2</sub> 沿各区域变化的方向。</p>\n<figure data-asset-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\" data-image-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/dc56c80f-67f3-481d-a2c8-26dacc258bb2/csfm%20explained%20%281%29.png\" data-asset-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\" data-image-id=\"9739b6d6-2cbc-4745-a590-4a85f7e1862f\" alt=\"\"></figure>\n<p><em>图 4 IDEA StatiCa Detail 的整体结果 </em></p>\n<p>使用 <strong>CSFM（协调应力场法）对细部或结构进行的分析基于有限单元法</strong>。混凝土采用二维墙单元模拟，钢筋采用一维构件单元模拟（图 7）。由于这是一个非线性问题，分析不是一步完成的。计算过程中分级施加荷载，并使用<strong>牛顿-拉夫森法</strong>求解非线性方程组。 </p>\n<p>虚拟的弥散裂缝（ε<sub>1</sub> 为平均值）\"形成\"于垂直于主应力的方向上。随着单元在每一级荷载作用下\"逐步开裂\"，该方向在非线性计算过程中可能发生变化。总之，这里考虑的是一种虚拟的无应力旋转裂缝。 </p>\n<p>采用 CSFM（协调应力场法）进行有限单元法求解，得到的是协调应力场（即模型中的混凝土不会分裂为各自独立作用的压杆）和应变状态，二者在整个求解的二维区域内都是连续的。与经典的 S&T 方法相比，这是一项重大优势，并使计算模型可以实现自动化和细化，详见以下各段。</p>\n<figure data-asset-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\" data-image-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/40e41bf7-4a81-4245-bd1b-843963c104e8/3.png\" data-asset-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\" data-image-id=\"c5bf3113-2223-4ddc-bbab-2131db37ac0c\" alt=\"\"></figure>\n<p><em>图 5 混凝土软化原理</em></p>\n<p>CSFM（协调应力场法）的表述简单，因此可以按照设计标准，对受压混凝土采用标准的单轴抛物线-矩形应力-应变图。众所周知，当混凝土因横向裂缝而受损时，其抗压强度会降低（图 5）。这种所谓的<strong>压力软化</strong>效应，通过自动考虑混凝土的有效抗压强度而纳入该方法中。 </p>\n<p>根据横向拉应变 ε<sub>1</sub> 的水平确定折减系数 k<sub>c</sub>，并据此调整混凝土的应力-应变图（图 5）。由于整个结构的应变场是已知的，因此可根据横向拉应变 ε<sub>1</sub> 的局部水平，在各个截面处自动计算混凝土的有效抗压强度。</p>\n<figure data-asset-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\" data-image-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/51628156-5014-4501-8f28-9f3b93783840/1.png\" data-asset-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\" data-image-id=\"6c73faf0-64d4-41ce-b816-520ccadff05a\" alt=\"\"></figure>\n<p><em>图 6 拉力刚化原理</em></p>\n<p>此外，CSFM（协调应力场法）还考虑了裂缝之间受拉混凝土对钢筋的<strong>刚化效应</strong>，即所谓的拉力刚化。计算模型中采用平均配筋应变 ε<sub>m</sub>，并据此修正钢筋的应力-应变图（图 6）。这样可以真实地反映因开裂而受损的钢筋混凝土结构的刚度。但混凝土的抗拉强度仍然不计入极限承载力。裂缝处钢筋的最大应力 σ<sub>sr</sub> 对设计起控制作用（图 6）。</p>\n<p>CSFM（协调应力场法）采用<strong>设计标准</strong>中定义的常用单轴材料模型（应力-应变图），并采用标准方法，即分项安全系数法，来验算承载能力极限状态。该方法简单，适用于工程实践，并且符合设计标准。 </p>\n<p>尽管这是一种非线性有限元分析，但结构工程师无需在计算中输入额外的材料特性和混凝土特征参数。这些参数在设计阶段可能根本无法获得，而基于断裂力学的非线性有限元分析等方法则必须用到它们。如前所述，除承载能力极限状态外，CSFM（协调应力场法）分析的另一大优势是能够验算<strong>正常使用极限状态：挠度、应力限值，尤其是裂缝宽度</strong>。</p>\n<figure data-asset-id=\"6c090b06-f906-4e6e-9016-d73de172f321\" data-image-id=\"6c090b06-f906-4e6e-9016-d73de172f321\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/8fd3f66a-63b9-4aba-bb10-9e12889ed7d4/Finite%20element%20model.png\" data-asset-id=\"6c090b06-f906-4e6e-9016-d73de172f321\" data-image-id=\"6c090b06-f906-4e6e-9016-d73de172f321\" alt=\"\"></figure>\n<p><em>图 7 IDEA StatiCa Detail 中有限元模型表示示例</em></p>\n<p>（图 7）CSFM（协调应力场法）中的有限元模型由多种类型的有限单元组成：</p>\n<ul>\n <li>用于钢筋的具有轴向刚度的一维单元</li>\n <li>用于混凝土的二维等参单元</li>\n <li>用于带端部处理的钢筋锚固模型的端部弹簧</li>\n <li>用于模拟钢筋与混凝土之间粘结的特殊二维单元</li>\n <li>粘结单元与混凝土之间的刚性和插值约束（多点约束，MPC）</li>\n</ul>\n<p>如果所设计的钢筋能够防止构件发生脆性破坏，那么尽管 CSFM（协调应力场法）的表述简单，实践已证明它能很好地预测结构的响应和极限承载力。换言之，该方法不适用于例如无横向抗剪钢筋的梁的设计，因为这类梁可能表现出脆性行为。该方法的<a data-item-id=\"1e879886-9e36-49e1-acb1-e6001361531f\" href=\"\">验证</a>（包括试验）见文献 [1]。对该方法更详细的描述超出了本文的范围，也可参见<a data-item-id=\"0000c94c-b603-48c4-8d31-bc56d7c95886\" href=\"\">理论背景</a>。</p>\n<p>显然，CSFM（协调应力场法）的原理具有普遍性，因此其应用不限于 D 区，也可用于对整个构件（例如预制梁）建模，只要该构件可以简化为平面二维模型。该方法及其软件实现（IDEA StatiCa Detail）也已得到扩展，可指定<strong>预应力和后张钢筋</strong>。</p>\n<h2>3. 桥墩盖梁设计示例</h2>\n<p>图 8 中的桥墩盖梁设计展示了 CSFM（协调应力场法）的实际应用。该桥墩是一座三跨连续桥梁的第二个桥墩，跨径分别为 30.0 m、42.0 m 和 30.0 m。钢筋混凝土桥墩的墩帽采用 C40/50 混凝土，其厚度（沿桥梁纵向）为 2.0 m。</p>\n<figure data-asset-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\" data-image-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/7bd9ebbf-5d30-448a-93e2-c89641d05677/4.png\" data-asset-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\" data-image-id=\"9d541a10-b879-4d35-a6f8-4e85fa9843a6\" alt=\"\"></figure>\n<p><em>图 8 桥墩盖梁：a) 设计汇总；b) 承载能力极限状态下混凝土中的压应力； c) 承载能力极限状态下钢筋中的拉应力；d) 正常使用极限状态下的裂缝宽度</em></p>\n<p>在桥墩盖梁顶部，首先设计了一道横梁，采用 B500 钢筋，配置 20xϕ28+20xϕ25（顶部四层）。图 8a 给出了承载能力极限状态下的设计汇总，显示了混凝土中的压应力、压应力方向以及钢筋中的应力。混凝土和钢筋中更详细的应力分布见图 8b 和图 8c。横向钢筋的应力刚好低于屈服强度，混凝土中的应力（及相应的应变）在承载能力极限状态下也满足要求。然而，裂缝宽度的计算结果（图 8d）表明，该设计在<strong>正常使用极限状态</strong>下不满足要求：w<sub>max</sub> = 0.36 mm > w<sub>lim</sub> = 0.3 mm。<strong>为满足裂缝宽度限值，必须增加</strong>横梁的<strong>钢筋</strong>，配置增至 20xϕ32+20xϕ28。如果 w<sub>lim</sub> = 0.2 mm（例如桥墩靠近会产生盐雾的道路，环境影响等级 XF2），则横梁的钢筋甚至需要增加到 24xϕ32+24xϕ28。</p>\n<h2>结论</h2>\n<p>CSFM（协调应力场法）适合工程实践，因为它采用设计标准中定义的<strong>简单材料模型</strong>。除承载能力极限状态外，它还可用于正常使用极限状态的设计，而此前采用 S&T 模型时，很难想象能对其进行验算。通过在 <strong>IDEA StatiCa Detail</strong> 中实现该方法，可以真实地反映结构的响应，并高效、安全地对不连续区域和较大的组合构件进行设计和验算。</p>\n<p>CSFM（协调应力场法）主要是通过苏黎世联邦理工学院（ETH Zurich）结构工程系主任 Walter Kaufmann 教授的工作发展起来的。他和他的团队还<a data-item-id=\"0dd36e25-63b2-4d63-a33e-6043644fda4f\" href=\"\">对该方法及其软件实现进行了验证</a>。</p>\n<h2>参考文献</h2>\n<p>[1] KAUFMANN, Walter, et al.: Compatible stress field design of structural concrete, ETH Zurich, 2020, ISBN 978-3-906916-95-8,</p>\n<p>[2] KAUFMANN, W., MARTI, P.: Structural Concrete: Cracked Membrane Model. Journal of Structural Engineering 124 (12): 1467-75, 1998 https://doi.org/10.1061/(ASCE)0733-9445(1998)124:12(1467)</p>\n<p>[3] KRAUS, M., M. WEBER, W. KAUFMANN, W, BOBEK, L.: Numerical analysis of experimentally tested frame corners with opening moments using the Compatible Stress Field Method (CSFM). In: Computational Modelling of Concrete and Concrete Structures, pp. 694-03. CRC Press, 2022 <a href=\"https://doi.org/10.1201/9781003316404\">https://doi.org/10.1201/9781003316404</a></p>\n<h2>作者</h2>\n<p>Ing. Pavel Kaláb, Ph.D.</p>\n<p>IDEA StatiCa s.r.o.</p>\n<p><br></p>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"csfm_book___compatible_stress_field_design_of_stru",
"design_of_reinforced_concrete_walls",
"detail_tutorial___prestressed_beam_with_openings_0a8c1ef",
"detail_theoretical_background"
],
"linkedItems": [
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Knowledge base",
"codename": "knowledgebase_article"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "Corbels/Brackets",
"codename": "corbels_brackets"
},
{
"name": "CSFM",
"codename": "csfm"
},
{
"name": "Coupling beams",
"codename": "coupling_beams"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Deflections",
"codename": "deflections"
},
{
"name": "Diaphragms",
"codename": "diaphragms"
},
{
"name": "Pier caps",
"codename": "pier_caps"
},
{
"name": "Openings",
"codename": "openings"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
},
{
"name": "SLS",
"codename": "sls"
},
{
"name": "Stress in reinforcement",
"codename": "stress_in_reinforcement"
},
{
"name": "ULS",
"codename": "uls"
},
{
"name": "Wall",
"codename": "wall"
},
{
"name": "Bridges",
"codename": "bridges"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 10000
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "csfm-explained"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"csfm-explained\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": []
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "协调应力场法（CSFM）"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "协调应力场法（CSFM）是对现有不连续区域求解方法的扩展。CSFM（协调应力场法）与拉压杆法有何区别？请阅读我们关于 CSFM（协调应力场法）的入门文章，了解更多信息。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:47</li>\n <li>de-DE: Translated on 27.10.2026 14:28</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:21</li>\n <li>fr-FR: Translated on 27.10.2026 15:08</li>\n <li>hu-HU: Translated on 27.10.2026 18:29</li>\n <li>it-IT: Translated on 27.10.2026 15:45</li>\n <li>ja-JP: Never translated</li>\n <li>ko-KR: Translated on 15.8.2026 02:17</li>\n <li>nl-NL: Translated on 27.10.2026 17:02</li>\n <li>pl-PL: Translated on 27.10.2026 19:55</li>\n <li>pt-PT: Translated on 27.10.2026 17:46</li>\n <li>ro-RO: Translated on 27.10.2026 19:11</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 15.8.2026 00:41</li>\n <li>tr-TR: Translated on 15.8.2026 04:58</li>\n <li>vi-VN: Translated on 15.8.2026 03:33</li>\n <li>zh-CN: Translated on 27.10.2026 20:34</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "csfm___how_it_works__code_compliance__validation_a",
"collection": "default",
"id": "eaab962d-ba44-4ee0-8fa7-45193c9f52b5",
"language": "zh-CN",
"lastModified": "2026-10-27T19:34:20.4640158Z",
"name": "CSFM explained",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "Donau City Tower 2"
},
"location": {
"name": "Location",
"type": "text",
"value": "维也纳"
},
"country_74e5565__countries": {
"name": "Country",
"type": "custom",
"value": "[\"AT\"]"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Donau City Tower 2.png",
"description": null,
"type": "image/png",
"size": 1057868,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2b173586-d786-4ebd-b1a0-759f6c38a9a2/Donau%20City%20Tower%202.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"header_image": {
"name": "Header image",
"type": "asset",
"value": []
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": "Donau City Tower 2 是维也纳第22区 Donau City 开发区内最后一座高层建筑。它与 Donau City Tower 1 共同构成一组建筑组合，该组合源自由 Dominique Perrault Architektur 事务所赢得的设计竞赛。ghp gmeiner haferl & partner zt GmbH 公司受委托负责 DC2 项目的计算工作。这一令人瞩目的项目的业主为 S+B Group，代表 Commerzreal 委托建设。"
},
"content": {
"images": [
{
"description": null,
"imageId": "2621fdfd-e4ce-40e8-9e9b-1f8c18a1a2de",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5e0bd81a-222c-4f60-9467-6055c255e066/DC1.png",
"height": 500,
"width": 640
},
{
"description": null,
"imageId": "04b8b13b-dc14-4f46-adce-ea93ba9b6fcc",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/44c5b18a-04c8-4973-a6be-afe42482a139/DC2.png",
"height": 500,
"width": 640
}
],
"linkedItemCodenames": [
"n1dd64f9f_1c80_01cb_0a8f_a0a557234189",
"n13105726_e502_01a6_4534_14bb5b7d376d",
"n54afc44a_118e_0176_2d32_bb73744b921f",
"untitled_content_item_1e33271"
],
"linkedItems": [
{
"elements": {
"url": {
"name": "Video URL",
"type": "text",
"value": "https://youtu.be/v9plCHSYS3U"
}
},
"system": {
"codename": "n1dd64f9f_1c80_01cb_0a8f_a0a557234189",
"collection": "default",
"id": "1dd64f9f-1c80-01cb-0a8f-a0a557234189",
"language": "zh-CN",
"lastModified": "2026-10-27T19:35:45.6052051Z",
"name": "1dd64f9f-1c80-01cb-0a8f-a0a557234189",
"sitemapLocations": [],
"type": "video",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"title": {
"name": "Title",
"type": "text",
"value": ""
},
"description": {
"name": "Description",
"type": "text",
"value": ""
},
"images": {
"name": "Images",
"type": "modular_content",
"value": [
"dc_2_2",
"dc_2_3",
"dc_2",
"dc_2_afe52ba"
],
"linkedItems": []
},
"cta_text": {
"name": "CTA text",
"type": "text",
"value": ""
},
"cta_link_url": {
"name": "CTA link URL",
"type": "text",
"value": ""
},
"cta_content_item_link": {
"name": "CTA content item link",
"type": "modular_content",
"value": [],
"linkedItems": []
},
"visibleinregion": {
"name": "VisibleInRegion",
"type": "multiple_choice",
"value": []
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "region"
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p><br></p>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": []
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
},
"system": {
"codename": "n13105726_e502_01a6_4534_14bb5b7d376d",
"collection": "default",
"id": "13105726-e502-01a6-4534-14bb5b7d376d",
"language": "zh-CN",
"lastModified": "2026-10-27T19:35:45.6052051Z",
"name": "13105726-e502-01a6-4534-14bb5b7d376d",
"sitemapLocations": [],
"type": "widget_grid_gallery",
"workflowStep": null,
"workflow": null
}
},
{
"elements": {
"testimonial": {
"name": "Testimonial",
"type": "modular_content",
"value": [
"untitled_content_item_8d5c39c"
],
"linkedItems": []
}
},
"system": {
"codename": "n54afc44a_118e_0176_2d32_bb73744b921f",
"collection": "default",
"id": "54afc44a-118e-0176-2d32-bb73744b921f",
"language": "zh-CN",
"lastModified": "2026-10-27T19:35:45.6052051Z",
"name": "54afc44a-118e-0176-2d32-bb73744b921f",
"sitemapLocations": [],
"type": "widget_single_testimonial",
"workflowStep": null,
"workflow": null
}
}
],
"links": [],
"name": "Content",
"type": "rich_text",
"value": "<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n1dd64f9f_1c80_01cb_0a8f_a0a557234189\"></object>\n<h1><br></h1>\n<h1>项目简介</h1>\n<p>Donau City Tower 2 拥有 52 层地上楼层和 6 层地下室，地面以上高度为 175 米，总建筑面积达 148,000 m²，令人印象深刻。该项目体现了现代建筑与卓越技术的结合。建成后，它将成为继 Millennium Tower 之后奥地利第三高的建筑。</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n13105726_e502_01a6_4534_14bb5b7d376d\"></object>\n<h1>工程挑战</h1>\n<p>该项目面临诸多挑战：</p>\n<ul>\n <li><strong>最优楼面面积比：</strong>最大限度提高可使用空间在总面积中所占的比例</li>\n <li><strong>最大限度减少障碍</strong>，便于建筑设备布置和使用</li>\n <li><strong>最大结构刚度：</strong> 以最少的资源消耗实现最佳稳定性</li>\n <li><strong>可持续性：</strong>承重结构应能够使用至少 500 年，因此可为未来的各种用途提供零排放的施工方案</li>\n</ul>\n<p>综合考虑这些方面，需要采用创新的方法和精确的技术规划。</p>\n<figure data-asset-id=\"2621fdfd-e4ce-40e8-9e9b-1f8c18a1a2de\" data-image-id=\"2621fdfd-e4ce-40e8-9e9b-1f8c18a1a2de\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/5e0bd81a-222c-4f60-9467-6055c255e066/DC1.png\" data-asset-id=\"2621fdfd-e4ce-40e8-9e9b-1f8c18a1a2de\" data-image-id=\"2621fdfd-e4ce-40e8-9e9b-1f8c18a1a2de\" alt=\"\"></figure>\n<p><br></p>\n<h1>IDEA StatiCa 的作用</h1>\n<p>IDEA StatiCa 是该项目中不可或缺的工具，大大方便了公司处理复杂的细部设计，尤其是在存在局部极端荷载的<a href=\"https://www.ideastatica.com/walls-and-details\" data-new-window=\"true\" target=\"_blank\" rel=\"noopener noreferrer\">Detail 混凝土模块</a>方面：</p>\n<ul>\n <li><strong>连梁：</strong>这些梁将四个核心筒部分连接成一个整体核心筒。它们需按极端荷载进行设计和校核，并需适应建筑设备规划中常常每天都在变化的要求。<br>如果没有 IDEA StatiCa，这些验算不可能在短时间内完成。</li>\n <li><strong>承重构件：</strong>一道墙式深梁将高层柱的荷载转移至车库车道上方，而在其他位置，一块墙板则将 190,000 kN 的集中支撑力传递给一根钢柱。</li>\n</ul>\n<figure data-asset-id=\"04b8b13b-dc14-4f46-adce-ea93ba9b6fcc\" data-image-id=\"04b8b13b-dc14-4f46-adce-ea93ba9b6fcc\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/44c5b18a-04c8-4973-a6be-afe42482a139/DC2.png\" data-asset-id=\"04b8b13b-dc14-4f46-adce-ea93ba9b6fcc\" data-image-id=\"04b8b13b-dc14-4f46-adce-ea93ba9b6fcc\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"component\" data-codename=\"n54afc44a_118e_0176_2d32_bb73744b921f\"></object>\n<h1>结语</h1>\n<p>Donau City Tower 2 象征着建筑愿景与技术精湛的结合。IDEA StatiCa 为确保该项目达到可持续性、稳定性和效率方面的最高标准作出了重要贡献。</p>\n<p>该公司使用混凝土结构模块已有两年，使用钢结构模块的时间则更长。事实证明 IDEA StatiCa 不可或缺，他们可以将这款工具推荐给每一位工程师。它简化了规划，节省了时间，是成功实施 Donau City Tower 2 等具有挑战性的项目的决定性因素。</p>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"untitled_content_item_1e33271\"></object>"
},
"associated_companies": {
"name": "Associated customer",
"type": "modular_content",
"value": [
"ghp_gmeiner_haferl___partner_zt_gmbh__austria_"
],
"linkedItems": []
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
}
],
"taxonomyGroup": "product_group"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "CSFM",
"codename": "csfm"
},
{
"name": "Coupling beams",
"codename": "coupling_beams"
}
],
"taxonomyGroup": "labels"
},
"image_gallery__files": {
"name": "Image gallery",
"type": "asset",
"value": []
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "donau-city-tower-2"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"donaucitytower-2\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": []
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "案例研究：Donau City Tower 2 是 Donau City 的最后一座高层建筑。"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "Donau City Tower 2 拥有 52 层地上楼层和 6 层地下室，地面以上高度为 175 米，总建筑面积达 148,000 m²，令人印象深刻。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:48</li>\n <li>de-DE: Translated on 27.10.2026 14:29</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:22</li>\n <li>fr-FR: Translated on 27.10.2026 15:09</li>\n <li>hu-HU: Translated on 27.10.2026 18:30</li>\n <li>it-IT: Translated on 27.10.2026 15:46</li>\n <li>ja-JP: Translated on 20.10.2026 17:30</li>\n <li>ko-KR: Translated on 15.8.2026 02:18</li>\n <li>nl-NL: Translated on 27.10.2026 17:03</li>\n <li>pl-PL: Translated on 27.10.2026 19:56</li>\n <li>pt-PT: Translated on 27.10.2026 17:47</li>\n <li>ro-RO: Translated on 27.10.2026 19:12</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 15.8.2026 00:43</li>\n <li>tr-TR: Translated on 15.8.2026 05:00</li>\n <li>vi-VN: Translated on 15.8.2026 03:35</li>\n <li>zh-CN: Translated on 27.10.2026 20:35</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "donaucitytower_2__vienna__austria",
"collection": "default",
"id": "329b1417-6be5-46ca-ba21-6e9394565ad2",
"language": "zh-CN",
"lastModified": "2026-10-27T19:35:45.6052051Z",
"name": "Donau City Tower 2",
"sitemapLocations": [],
"type": "case_study",
"workflowStep": "published",
"workflow": "default"
}
},
{
"elements": {
"title": {
"name": "Main headline (H1)",
"type": "text",
"value": "带少量箍筋的梁的剪力试验"
},
"preview_image": {
"name": "Preview image",
"type": "asset",
"value": [
{
"name": "Shear tests in beams with low amounts of stirrups preview.png",
"description": null,
"type": "image/png",
"size": 451885,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/33f4ed1e-7615-4b08-9378-34fc5d51a75d/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20preview.png",
"width": 1200,
"height": 630,
"renditions": {}
}
]
},
"post_date": {
"name": "Post date",
"type": "date_time",
"value": null,
"displayTimeZone": "Europe/Prague"
},
"perex_content": {
"name": "Lead paragraph",
"type": "text",
"value": ""
},
"content": {
"images": [
{
"description": null,
"imageId": "7a127e09-323a-47c2-bb68-f6d7305df916",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b04ab1b6-8164-42a4-8153-b0bca529109d/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.17.png",
"height": 766,
"width": 1331
},
{
"description": null,
"imageId": "ae1b1eb6-ac3f-45d5-908f-58e08887a726",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f016576c-b58f-4934-8a91-92a8f02ada8b/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%2010.png",
"height": 600,
"width": 1328
},
{
"description": null,
"imageId": "460dd1dc-d307-4f49-b7d8-f46b081238f6",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1c39493d-2611-4b20-8595-b15bd109181c/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%2010-2.png",
"height": 581,
"width": 1320
},
{
"description": null,
"imageId": "8493aef1-7d61-4eca-8e25-aeda94512c10",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d40a91ae-9e7a-4cbe-9980-8bc295693359/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11.png",
"height": 539,
"width": 1328
},
{
"description": null,
"imageId": "b38d80f8-07f0-4992-b707-36da923011d3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/037428f1-0d3f-4404-9321-db2a2a0f0c8c/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11-2.png",
"height": 308,
"width": 1323
},
{
"description": null,
"imageId": "78bf381f-664d-41ad-a30e-cb1dc0204a8e",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6388402c-7243-4c35-9936-241e9bbc86e5/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11-3.png",
"height": 652,
"width": 1329
},
{
"description": null,
"imageId": "be95afab-6efa-4ca2-af2d-187495214492",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ee8f6a35-2573-4491-a59a-c75249bae2ec/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.18.png",
"height": 326,
"width": 1324
},
{
"description": null,
"imageId": "f066bc6c-98fe-48c4-b90d-1eb356184726",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/654a5eaa-78a1-4ba4-aa24-c24a2bb360bd/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.12.png",
"height": 408,
"width": 1329
},
{
"description": null,
"imageId": "31352232-bbe5-4fb4-b54e-b0809010c318",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4c6d49ee-719b-4472-9a67-06b062b2df81/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13.png",
"height": 345,
"width": 1325
},
{
"description": null,
"imageId": "2fcb4c3b-de08-410f-93c2-989b65091df0",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f3c49504-d203-4f82-a25e-0ab44da27aaa/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13-2.png",
"height": 242,
"width": 1328
},
{
"description": null,
"imageId": "48a1d13e-083a-4eb5-927c-4812e5f4e37d",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6fcfdbf1-9666-447a-988f-40df2e112587/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13-3.png",
"height": 699,
"width": 1325
},
{
"description": null,
"imageId": "82f061b1-5fb4-4ea7-8342-375c6db59907",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/23242854-167d-40ac-8182-edd05e68f870/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19.png",
"height": 425,
"width": 1322
},
{
"description": null,
"imageId": "3ccbbd8a-d639-4133-be1c-6e4e9c0abade",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a1037f6e-2499-4ade-bb10-681d8ea41e54/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19-2.png",
"height": 411,
"width": 1324
},
{
"description": null,
"imageId": "52e40f52-8d8f-4d36-a4c6-7885d25979c3",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2391dda1-eba7-4458-8142-a7ff352da592/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19-3.png",
"height": 600,
"width": 1318
},
{
"description": null,
"imageId": "72d9b512-35a8-4c59-bf70-2fa1c8913dba",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86e2648e-f52e-4162-8ad8-a9615fc572c6/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.20.png",
"height": 376,
"width": 1291
},
{
"description": null,
"imageId": "5faec16e-18c3-4336-aaaf-92b23a315aed",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/65718f07-1206-42f2-990a-97e7e18d0547/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.20-2.png",
"height": 533,
"width": 1291
},
{
"description": null,
"imageId": "4f5fd5df-0fbe-493e-aab6-f3613ea8a079",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b2a3cfdf-9892-4c29-b6b0-a26d1f47bb22/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21.png",
"height": 701,
"width": 1327
},
{
"description": null,
"imageId": "43e6f9e6-0867-450f-86f0-447652d4cba9",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e90b12fb-ba6f-4ce8-97c3-ebca7c6212f6/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21-2.png",
"height": 696,
"width": 1322
},
{
"description": null,
"imageId": "005c3655-78cd-4a12-b72d-adb1628d298d",
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ba5f9efa-97c3-461f-b6fc-5e3fdd4f0ff9/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21-3.png",
"height": 128,
"width": 1319
}
],
"linkedItemCodenames": [
"four_point_bending_tests_on_t_beams__definition_of",
"take_idea_statica_24_0_for_a_test_drive_today"
],
"linkedItems": [],
"links": [
{
"codename": "csfm___how_it_works__code_compliance__validation_a",
"linkId": "eaab962d-ba44-4ee0-8fa7-45193c9f52b5",
"urlSlug": "csfm-explained",
"type": "support_center_article"
},
{
"codename": "theoretical_background_detail___main_assumptions_a",
"linkId": "2ebdaf9c-827f-4fd6-9f82-28bc96970a64",
"urlSlug": "main-assumptions-and-limitations-for-csfm",
"type": "support_center_article"
},
{
"codename": "theoretical_background_detail___supports_and_load_",
"linkId": "50ed723b-9b87-4870-a69f-e05b5a8a8150",
"urlSlug": "2-2-supports-and-load-transmitting-components",
"type": "support_center_article"
},
{
"codename": "theoretical_background_detail___presentation_of_re",
"linkId": "8b9399db-b927-491a-a50f-c66ad97560af",
"urlSlug": "2-8-presentation-of-results",
"type": "support_center_article"
}
],
"name": "Content",
"type": "rich_text",
"value": "<h2>引言 </h2>\n<p>本文讨论如何使用<a data-item-id=\"eaab962d-ba44-4ee0-8fa7-45193c9f52b5\" href=\"\">CSFM（协调应力场法）</a>分析少量箍筋梁的剪切破坏。为此,本文分析了 Huber (2016)、Piyamahant (2002) 以及 Vecchio 和 Shim (2004) 对简支钢筋混凝土梁所做的部分试验。这些试验涵盖了多种参数,包括不同的尺寸、剪跨比以及抗剪钢筋和纵向钢筋的配筋量。本节介绍使用 CSFM 对这些试验中的 17 个试件进行的分析,探讨 CSFM 对多种差异很大的破坏模式进行准确建模的能力,这些破坏模式包括箍筋断裂和未断裂的剪切破坏、弯曲破坏以及弯剪混合破坏。 </p>\n<p>试验装置:图 6.17 给出了所分析试验的几何尺寸、试验装置和配筋布置。表 6.10 列出了抗剪钢筋(直径 (<em>Ø</em><em><sub>t</sub></em>)、间距 (<em>s</em><em><sub>t</sub></em>) 和几何配筋率 (<em>ρ</em><em><sub>t,geo</sub></em>))、受弯钢筋(数量 (<em>n</em><em><sub>l</sub></em>) 和直径 (<em>Ø</em><em><sub>l</sub></em>))以及 几何尺寸(有效高度 (<em>d</em>)、剪跨比 (<em>a/d</em>) 和梁宽 (<em>b</em>))的相关信息。Huber (2016) 进行的试验 R1000m60 和 R500m351 采用单肢弯钩箍筋,而所有其他试验均采用双肢封闭箍筋。在所分析的 Piyamahant (2002) 的试验中,几何尺寸和受弯钢筋保持不变,而在另外两项研究中则有所变化。 </p>\n<figure data-asset-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\" data-image-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b04ab1b6-8164-42a4-8153-b0bca529109d/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.17.png\" data-asset-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\" data-image-id=\"7a127e09-323a-47c2-bb68-f6d7305df916\" alt=\"\"></figure>\n<figure data-asset-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\" data-image-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f016576c-b58f-4934-8a91-92a8f02ada8b/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%2010.png\" data-asset-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\" data-image-id=\"ae1b1eb6-ac3f-45d5-908f-58e08887a726\" alt=\"\"></figure>\n<figure data-asset-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\" data-image-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/1c39493d-2611-4b20-8595-b15bd109181c/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%2010-2.png\" data-asset-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\" data-image-id=\"460dd1dc-d307-4f49-b7d8-f46b081238f6\" alt=\"\"></figure>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"four_point_bending_tests_on_t_beams__definition_of\"></object>\n<h2>材料特性</h2>\n<p>表 6.11 汇总了 CSFM 分析中所用的抗剪钢筋、受弯钢筋和混凝土的材料特性。<a data-item-id=\"2ebdaf9c-827f-4fd6-9f82-28bc96970a64\" href=\"\">CSFM（协调应力场法）</a>分析所需的大部分材料特性可从相应的试验报告中获得。需要假定的数值已在表 6.11 中标明。 </p>\n<figure data-asset-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\" data-image-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/d40a91ae-9e7a-4cbe-9980-8bc295693359/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11.png\" data-asset-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\" data-image-id=\"8493aef1-7d61-4eca-8e25-aeda94512c10\" alt=\"\"></figure>\n<figure data-asset-id=\"b38d80f8-07f0-4992-b707-36da923011d3\" data-image-id=\"b38d80f8-07f0-4992-b707-36da923011d3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/037428f1-0d3f-4404-9321-db2a2a0f0c8c/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11-2.png\" data-asset-id=\"b38d80f8-07f0-4992-b707-36da923011d3\" data-image-id=\"b38d80f8-07f0-4992-b707-36da923011d3\" alt=\"\"></figure>\n<figure data-asset-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\" data-image-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6388402c-7243-4c35-9936-241e9bbc86e5/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.11-3.png\" data-asset-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\" data-image-id=\"78bf381f-664d-41ad-a30e-cb1dc0204a8e\" alt=\"\"></figure>\n<h2>使用 CSFM 建模</h2>\n<p>几何尺寸、钢筋、<a data-item-id=\"50ed723b-9b87-4870-a69f-e05b5a8a8150\" href=\"\">支承和加载 </a>条件均按照试验装置在 CSFM 中建模。图 6.18 以 Vecchio 和 Shim (2004) 的试验 A3 为例展示了建模过程。</p>\n<figure data-asset-id=\"be95afab-6efa-4ca2-af2d-187495214492\" data-image-id=\"be95afab-6efa-4ca2-af2d-187495214492\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ee8f6a35-2573-4491-a59a-c75249bae2ec/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.18.png\" data-asset-id=\"be95afab-6efa-4ca2-af2d-187495214492\" data-image-id=\"be95afab-6efa-4ca2-af2d-187495214492\" alt=\"\"></figure>\n<p>对每个试验,使用以下参数进行了四次数值计算:</p>\n<ul>\n <li>网格尺寸:沿梁高分别划分为 5 个(这些特定算例的默认值)、10 个和 20 个有限单元。由于默认网格已经非常粗糙,本研究仅分析更精细的网格,除 M0 外均采用 10 个单元的网格。 </li>\n <li> 是否考虑拉力刚化效应。CSFM 默认考虑拉力刚化。 </li>\n <li>是否考虑箍筋中可能存在的非稳定裂缝。考虑时(默认设置),由拔出模型 (POM) 定义箍筋的拉力刚化(所有梁的几何配筋率均低于 (<em>ρ</em><em><sub>cr</sub></em>),因此从不使用拉力弦杆模型)。不考虑时,模型通过 TCM 考虑拉力刚化。</li>\n</ul>\n<p><em>\\[ρ_{\\text{cr}} = \\frac{f_{\\text{ct}}}{f_{\\text{y}} - (n-1)f_{\\text{ct}}}\\]</em></p>\n<p>其中<em>:</em></p>\n<ul>\n <li>\\(f_y\\)<em> - </em>钢筋屈服强度</li>\n <li>\\(f_{ct}\\) - 混凝土抗拉强度</li>\n <li>\\(n = \\frac{E_s}{E_c}\\) - 模量比</li>\n</ul>\n<p>表 6.12 列出了每次数值计算所用的参数。M0 对应于采用 CSFM 默认设置的模型。</p>\n<figure data-asset-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\" data-image-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/654a5eaa-78a1-4ba4-aa24-c24a2bb360bd/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.12.png\" data-asset-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\" data-image-id=\"f066bc6c-98fe-48c4-b90d-1eb356184726\" alt=\"\"></figure>\n<h2>与试验结果的比较</h2>\n<p>本节对比了<a data-item-id=\"8b9399db-b927-491a-a50f-c66ad97560af\" href=\"\">CSFM（协调应力场法）</a>给出的极限荷载和破坏模式与试验结果。为了同时验证 CSFM 的正常使用性能和变形能力,还针对选定的梁,将模型给出的荷载-变形响应与试验结果进行了比较。</p>\n<h4>破坏模式和极限荷载</h4>\n<p>表 6.13 汇总了试验中测得的极限剪力 (<em>V</em><em><sub>u,exp</sub></em>)、CSFM 预测的极限剪力 (<em>V</em><em><sub>u,calc</sub></em>) 以及相应的破坏模式。该表还给出了各数值模型的实测极限荷载与计算极限荷载之比的平均值和变异系数 (CoV)。在所有分析中(除未考虑拉力刚化的 M3 外),CSFM 均预测箍筋发生剪切破坏。这与 Huber (2016) 和 Piyamahant (2002) 试验中观察到的破坏机理吻合良好,但与 Vecchio 和 Shim (2004) 试验中观察到的不一致。在这种情况下,未能准确捕捉破坏模式导致对极限荷载的估计略偏保守。总体而言,默认参数给出的承载力估计良好,但略偏不安全(平均偏差 6%)。</p>\n<p>图 6.19 通过试验与计算极限剪力之比 (<em>V</em><em><sub>u,exp</sub></em><em>/V</em><em><sub>u,calc</sub></em>) 展示了 CSFM 承载力预测对各数值参数的敏感性。极限荷载对所选有限单元尺寸明显敏感(见图 6.19 a)。最粗网格与最细网格(M0 和 M2)之间的最大差异达 36%(Piyamahant (2002) 的试验 4),平均差异约为 15%。采用默认参数(模型 M0 中沿梁高划分 5 个有限单元)的预测结果略高估试验承载力(约 5%)。将网格细化为沿梁高 10 个或 20 个有限单元(分别为模型 M1 和 M2)时,可获得优异的承载力预测,且结果略偏于极限荷载的安全侧。改变有限元网格尺寸时,未观察到破坏模式的变化。考虑到若干试验表现出脆性剪切破坏,而这类破坏很难用设计方法预测,即使采用默认网格尺寸的结果也非常令人满意。</p>\n<p>如图 6.19 b-c 所示,拉力刚化的考虑方式对承载力预测有着十分重要的影响。通过 POM 考虑箍筋中的拉力刚化(CSFM 的默认设置)平均而言与试验结果吻合极佳(见图 6.19 b)。然而,忽略拉力刚化会导致极限荷载平均被高估约 22%(见表 6.12)。忽略拉力刚化时,破坏模式变为弯曲破坏(见表 6.12),与观察到的剪切破坏模式不符。结果对所考虑的压力软化关系也非常敏感。如图 6.19 c 所示,在箍筋中使用拉力弦杆模型(模型 M4)而非拔出模型(模型 M1),其结果略优于忽略拉力刚化(模型 M3),但仍会将极限荷载严重高估约 15%(见表 6.12)。因此可以得出结论,在这些算例中,使用拔出模型对于正确模拟承载行为至关重要。 </p>\n<figure data-asset-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\" data-image-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/4c6d49ee-719b-4472-9a67-06b062b2df81/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13.png\" data-asset-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\" data-image-id=\"31352232-bbe5-4fb4-b54e-b0809010c318\" alt=\"\"></figure>\n<figure data-asset-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\" data-image-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/f3c49504-d203-4f82-a25e-0ab44da27aaa/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13-2.png\" data-asset-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\" data-image-id=\"2fcb4c3b-de08-410f-93c2-989b65091df0\" alt=\"\"></figure>\n<figure data-asset-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\" data-image-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/6fcfdbf1-9666-447a-988f-40df2e112587/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20table%206.13-3.png\" data-asset-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\" data-image-id=\"48a1d13e-083a-4eb5-927c-4812e5f4e37d\" alt=\"\"></figure>\n<figure data-asset-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\" data-image-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/23242854-167d-40ac-8182-edd05e68f870/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19.png\" data-asset-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\" data-image-id=\"82f061b1-5fb4-4ea7-8342-375c6db59907\" alt=\"\"></figure>\n<figure data-asset-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\" data-image-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/a1037f6e-2499-4ade-bb10-681d8ea41e54/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19-2.png\" data-asset-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\" data-image-id=\"3ccbbd8a-d639-4133-be1c-6e4e9c0abade\" alt=\"\"></figure>\n<figure data-asset-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\" data-image-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/2391dda1-eba7-4458-8142-a7ff352da592/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.19-3.png\" data-asset-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\" data-image-id=\"52e40f52-8d8f-4d36-a4c6-7885d25979c3\" alt=\"\"></figure>\n<p>图 6.20 展示了连续应力场结果(主压应力 (<em>σ</em><em><sub>c</sub></em>) 和钢筋应力 (<em>σ</em><em><sub>sr</sub></em>) 在裂缝处)(试件 A1 和 A3,来自 Vecchio 和 Shim (2004)),其中突出显示了预测的剪切破坏。这些结果采用数值参数 M1 计算(默认参数,但网格尺寸为默认值的一半)。从应力场可以看出,受弯压区中的压应力处于塑性段(99.5 %)。然而,根据所考虑的混凝土压碎准则,箍筋在混凝土压碎发生之前即已断裂。 </p>\n<figure data-asset-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\" data-image-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/86e2648e-f52e-4162-8ad8-a9615fc572c6/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.20.png\" data-asset-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\" data-image-id=\"72d9b512-35a8-4c59-bf70-2fa1c8913dba\" alt=\"\"></figure>\n<figure data-asset-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\" data-image-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/65718f07-1206-42f2-990a-97e7e18d0547/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.20-2.png\" data-asset-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\" data-image-id=\"5faec16e-18c3-4336-aaaf-92b23a315aed\" alt=\"\"></figure>\n<h2>荷载-变形响应</h2>\n<p>图 6.21 将采用 M1 数值参数(受弯钢筋采用 TCM,箍筋采用 POM)和 M3 数值参数(忽略所有拉力刚化效应)得到的计算荷载-变形响应与实测荷载-变形响应进行了比较,对应试验 R500m352、T1、A1 和 A3。荷载 <em>V</em> 对应于所施加的剪力,<em>u</em> 对应于跨中挠度(见图 6.20a)。</p>\n<figure data-asset-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\" data-image-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/b2a3cfdf-9892-4c29-b6b0-a26d1f47bb22/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21.png\" data-asset-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\" data-image-id=\"4f5fd5df-0fbe-493e-aab6-f3613ea8a079\" alt=\"\"></figure>\n<figure data-asset-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\" data-image-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/e90b12fb-ba6f-4ce8-97c3-ebca7c6212f6/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21-2.png\" data-asset-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\" data-image-id=\"43e6f9e6-0867-450f-86f0-447652d4cba9\" alt=\"\"></figure>\n<figure data-asset-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\" data-image-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\"><img src=\"https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/ba5f9efa-97c3-461f-b6fc-5e3fdd4f0ff9/Shear%20tests%20in%20beams%20with%20low%20amounts%20of%20stirrups%20fig%206.21-3.png\" data-asset-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\" data-image-id=\"005c3655-78cd-4a12-b72d-adb1628d298d\" alt=\"\"></figure>\n<p>考虑拉力刚化效应后,可较好地预测整个加载历程中的试验挠度,但峰值荷载处的挠度略被低估。特别是在 Vecchio 和 Shim (2004) 的试验 A3 中,由于数值分析首先预测到箍筋断裂,因此无法准确捕捉试验中由受弯钢筋屈服所引起的平台段。忽略拉力刚化效应会导致极限荷载和变形被高估。对于未考虑拉力刚化的分析,上述结论在采用 M4 参数(箍筋和受弯钢筋均采用 TCM)时同样成立。</p>\n<h2>结论</h2>\n<p>通过将 CSFM 的结果与所分析的少量箍筋简支梁试验中观察到的行为进行比较,可得出以下结论: </p>\n<ul>\n <li>CSFM 对极限荷载给出了良好的估计,采用默认数值参数时略有高估(平均 5%)。难以捕捉剪切与弯曲混凝土压碎相结合的组合破坏模式;CSFM 预测的是箍筋断裂破坏,这使得承载力预测偏于保守。 </li>\n <li>极限荷载的预测对有限单元网格尺寸的变化有一定的敏感性。细化默认有限单元网格时可获得最佳预测。因此,在进行最终校核时,始终建议研究有限单元尺寸对结果的影响。 </li>\n <li>忽略拉力刚化会导致对极限荷载和变形能力的高估非常明显。即使通过拉力弦杆模型对箍筋中的拉力刚化进行建模,预测的极限荷载仍明显偏于不安全。对于配筋量较少的情况,通过拔出模型考虑箍筋中非稳定裂缝的影响时,可获得最佳结果。这是 CSFM 默认采用的拉力刚化模型。 </li>\n</ul>\n<object type=\"application/kenticocloud\" data-type=\"item\" data-rel=\"link\" data-codename=\"take_idea_statica_24_0_for_a_test_drive_today\"></object>"
},
"linked_items": {
"name": "Linked items",
"type": "modular_content",
"value": [
"csfm___how_it_works__code_compliance__validation_a",
"linear_vs_csfm",
"basic_assumptions_of_csfm",
"can_you_trust_the_csfm_"
],
"linkedItems": [
"[Circular Reference]"
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "CZ/SK",
"codename": "cz_sk"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Verifications",
"codename": "verification_example"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "Detail 2D",
"codename": "detail"
},
{
"name": "Reinforcement",
"codename": "reinforcement"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 9900
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": []
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "shear-tests-in-beams-with-low-amounts-of-stirrups"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"shear-tests-in-beams-with-low-amounts-of-stirrups\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": []
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": []
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": []
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": []
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "带少量箍筋的梁的剪力试验"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "本文讨论如何使用 CSFM（协调应力场法）分析少量箍筋梁的剪切破坏。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Language translation error (when inserting into Kontent.ai)</li>\n <li>de-DE: Translated on 27.10.2026 14:30</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:23</li>\n <li>fr-FR: Translated on 27.10.2026 15:10</li>\n <li>hu-HU: Translated on 27.10.2026 18:31</li>\n <li>it-IT: Translated on 27.10.2026 15:47</li>\n <li>ja-JP: Never translated</li>\n <li>ko-KR: Translated on 15.8.2026 02:20</li>\n <li>nl-NL: Translated on 27.10.2026 17:05</li>\n <li>pl-PL: Translated on 27.10.2026 19:57</li>\n <li>pt-PT: Language translation error (when inserting into Kontent.ai)</li>\n <li>ro-RO: Translated on 27.10.2026 19:14</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Translated on 15.8.2026 00:45</li>\n <li>tr-TR: Translated on 15.8.2026 05:02</li>\n <li>vi-VN: Translated on 15.8.2026 03:36</li>\n <li>zh-CN: Translated on 27.10.2026 20:36</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "detail_verification__shear_tests_in_beams_with_low",
"collection": "default",
"id": "d92595fa-1566-4b74-91b5-7388988287a7",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:35.4331792Z",
"name": "Detail Verification: Shear tests in beams with low amounts of stirrups",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"regions": {
"name": "Region",
"type": "taxonomy",
"value": [
{
"name": "AMER",
"codename": "amer"
},
{
"name": "EMEA",
"codename": "emea"
},
{
"name": "APAC",
"codename": "apac"
},
{
"name": "CZ/SK",
"codename": "cz_sk"
}
],
"taxonomyGroup": "region"
},
"product_groups": {
"name": "Product group",
"type": "taxonomy",
"value": [
{
"name": "Reinforced concrete",
"codename": "reinforced_concrete"
},
{
"name": "Concrete",
"codename": "concrete"
},
{
"name": "Prestressed concrete",
"codename": "prestressed_concrete"
}
],
"taxonomyGroup": "product_group"
},
"support_center_article_types": {
"name": "Support center article",
"type": "taxonomy",
"value": [
{
"name": "Theoretical background",
"codename": "theoretical_background"
}
],
"taxonomyGroup": "support_center_article"
},
"expertise_levels": {
"name": "Expertise level",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "expertise_level"
},
"labels": {
"name": "Labels",
"type": "taxonomy",
"value": [
{
"name": "ACI (USA)",
"codename": "aci__usa_"
},
{
"name": "EN (Eurocode)",
"codename": "eurocode"
},
{
"name": "Geometry",
"codename": "geometry"
},
{
"name": "Load effects",
"codename": "load_effects"
},
{
"name": "Overall check",
"codename": "check"
},
{
"name": "Material settings",
"codename": "material_settings"
},
{
"name": "Corbels/Brackets",
"codename": "corbels_brackets"
},
{
"name": "CSFM",
"codename": "csfm"
},
{
"name": "Cracks",
"codename": "cracks"
},
{
"name": "Deflections",
"codename": "deflections"
},
{
"name": "Diaphragms",
"codename": "diaphragms"
},
{
"name": "Openings",
"codename": "openings"
},
{
"name": "SLS",
"codename": "sls"
},
{
"name": "Stress in reinforcement",
"codename": "stress_in_reinforcement"
},
{
"name": "TDA",
"codename": "tda"
},
{
"name": "Topology optimization",
"codename": "topology_optimization"
},
{
"name": "ULS",
"codename": "uls"
},
{
"name": "Detail 2D",
"codename": "detail"
}
],
"taxonomyGroup": "labels"
},
"attachments__files": {
"name": "Attachments",
"type": "asset",
"value": []
},
"content_priority__value": {
"name": "Content priority value",
"type": "number",
"value": 15000
},
"options": {
"name": "Options",
"type": "multiple_choice",
"value": [
{
"name": "Show Print Button",
"codename": "show_print_button"
},
{
"name": "Show Navigation",
"codename": "show_navigation"
}
]
},
"url_slug": {
"name": "Url slug",
"type": "url_slug",
"value": "theoretical-background-for-idea-statica-detail"
},
"unique_url_slug": {
"name": "Unique URL slug",
"type": "custom",
"value": "[\"theoretical-background-for-idea-statica-detail\",\"[autogenerated]\"]"
},
"content_settings__sitemap": {
"name": "Show in sitemap",
"type": "multiple_choice",
"value": [
{
"name": "default",
"codename": "default"
}
]
},
"content_settings__robots": {
"name": "Search engine indexing",
"type": "multiple_choice",
"value": [
{
"name": "default",
"codename": "default"
}
]
},
"content_settings__is_hidden": {
"name": "Hidden nested content",
"type": "multiple_choice",
"value": []
},
"content_settings__is_topped": {
"name": "Topped",
"type": "multiple_choice",
"value": [
{
"name": "yes",
"codename": "yes"
}
]
},
"metadata__page_title": {
"name": "Page title",
"type": "text",
"value": "IDEA StatiCa Detail – 混凝土不连续区的结构设计"
},
"metadata__page_description": {
"name": "Page description",
"type": "text",
"value": "IDEA StatiCa Detail 是一款用于混凝土不连续区结构设计和规范校核的混凝土设计软件。可进行混凝土构件应力分析和混凝土墙设计。"
},
"metadata__page_keywords": {
"name": "Page keywords",
"type": "text",
"value": ""
},
"metadata__canonical_url": {
"name": "Canonical URL",
"type": "text",
"value": ""
},
"metadata__og_title": {
"name": "OG:title",
"type": "text",
"value": ""
},
"metadata__og_description": {
"name": "OG:description",
"type": "text",
"value": ""
},
"metadata__og_image": {
"name": "OG:image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": [
{
"name": "Re-translate and overwrite already translated content",
"codename": "forced"
}
]
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Translated on 27.10.2026 13:49</li>\n <li>de-DE: Translated on 27.10.2026 14:30</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Translated on 27.10.2026 16:23</li>\n <li>fr-FR: Language translation error (when inserting into Kontent.ai)</li>\n <li>hu-HU: Translated on 27.10.2026 18:31</li>\n <li>it-IT: Translated on 27.10.2026 15:47</li>\n <li>ja-JP: Never translated</li>\n <li>ko-KR: Language translation error (when translating in Claude)</li>\n <li>nl-NL: Translated on 27.10.2026 17:05</li>\n <li>pl-PL: Translated on 27.10.2026 19:57</li>\n <li>pt-PT: Translated on 27.10.2026 17:48</li>\n <li>ro-RO: Translated on 27.10.2026 19:14</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Language translation error (when translating in Claude)</li>\n <li>tr-TR: Language translation error (when translating in Claude)</li>\n <li>vi-VN: Language translation error (when translating in Claude)</li>\n <li>zh-CN: Translated on 27.10.2026 20:36</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": "{\"version\":1,\"requestId\":\"9f7b9c70-6be7-4a20-a740-14eba3385087\",\"selections\":[{\"kind\":\"element\",\"path\":{\"rootElementId\":\"8c772882-d641-44d1-8dd1-be528f66940b\",\"componentIds\":[],\"elementId\":\"8c772882-d641-44d1-8dd1-be528f66940b\"}},{\"kind\":\"element\",\"path\":{\"rootElementId\":\"1dc89cef-ec7f-4a81-81ac-25c92f5d92e1\",\"componentIds\":[],\"elementId\":\"1dc89cef-ec7f-4a81-81ac-25c92f5d92e1\"}},{\"kind\":\"element\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[],\"elementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\"}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"302f228f-1aeb-4dbc-921b-df124b17c380\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"710bc53d-116f-4de0-88c4-7834b77d5b65\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"7559e62b-d910-4994-b11f-75e7e54ecdea\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"fc9ceb2a-f490-4fb7-b616-1ebdc401893d\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"24ebecce-7ccd-452f-bc0b-d0bde2109a16\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"4de200b9-c734-4e51-a0df-85457a93eb57\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"0df29264-c383-4ae1-9bfd-818e6b068c0b\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"60b56669-42bd-4ed7-a324-144032e7d2c3\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"8733400a-60b4-45e6-87c9-37bec88ceea7\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"94599007-d3a2-4dc9-88de-8d66b9ed60b0\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"04612fb2-be12-48ca-ba8c-9eec94a568ef\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"1b2e3a08-7000-480e-9b82-b4ac222dabd5\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"8450a464-07d1-4f51-ab57-ea38d40ee4ff\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"6ed55122-da89-4b63-908a-490a7d42a2c3\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"f7eba665-c2bf-495a-8464-0066a1674f2b\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"c2e4f9a0-747b-4bbc-8076-611a273bde47\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"04590655-aa1e-41f8-b8b5-4ac1774f6070\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"d5c307a1-4da1-460f-89de-6b4fad11298c\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"31d60e2e-0c2d-430b-b781-03530b44aa7b\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"d0a437ab-1aee-4e98-8227-12009b81cdd8\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"d274e5f3-5cba-4d81-a8cd-c743097abe2a\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"851a6244-4564-426e-8dc8-5db029ff842c\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"e32e2769-6251-4eff-be57-163240b39a49\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"8470c5cd-abba-485c-804a-73d71ac48ccf\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"069d7bec-24e3-4f35-8d4d-b03793aeda1b\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"b814c2ec-a807-4fbc-bb91-7d3ea5dbf5bc\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"b6f34966-cde6-414c-8235-170d5db4e98c\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"44a8bad6-959f-4694-b993-f9bee6b431d5\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"884b936f-21cc-4668-af06-477f010b7706\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"68c033a3-29b3-441c-a72a-14e04dc1bec2\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"483ed817-3824-4815-97e1-f700cbce54ed\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"276ff20a-2d54-4ba4-a26c-db0f55fb6a78\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"2255bed3-4a6a-4bd2-a3dd-c70bba5b1184\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"9f63ab5b-da73-44ba-b902-3c9693f4780c\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"14660c90-1a82-47d9-a9f4-18f7068b320b\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"a5f8b813-3923-44c0-a857-ba94cf5f4b87\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"45449fb2-efd8-4248-926c-810d30558984\"]}},{\"kind\":\"component\",\"path\":{\"rootElementId\":\"7da4e48e-b90c-4710-a37c-0a14a5a3a5eb\",\"componentIds\":[\"e8bb5777-2fd9-476b-85a6-15ecab7137a4\"]}}]}"
},
"page_tree_settings__page_label": {
"name": "Page label",
"type": "text",
"value": ""
},
"page_tree_settings__path_segment": {
"name": "Path segment",
"type": "text",
"value": ""
},
"page_tree_settings__breadcrumb_style": {
"name": "Breadcrumb style",
"type": "multiple_choice",
"value": []
},
"page_tree_settings__hide_in_breadcrumbs": {
"name": "Hide in breadcrumbs",
"type": "multiple_choice",
"value": []
}
},
"system": {
"codename": "detail_theoretical_background",
"collection": "default",
"id": "0000c94c-b603-48c4-8d31-bc56d7c95886",
"language": "zh-CN",
"lastModified": "2026-10-27T19:36:45.6092417Z",
"name": "Theoretical background Detail",
"sitemapLocations": [],
"type": "support_center_article",
"workflowStep": "published",
"workflow": "default"
}
}
]
},
"kontent_video": {
"name": "Kontent video",
"type": "asset",
"value": [
{
"name": "Beam_video_new_ui.mp4",
"description": null,
"type": "video/mp4",
"size": 27595967,
"url": "https://assets-us-01.kc-usercontent.com:443/66e7a155-be94-0096-73e6-c55dfc7e5788/0de1c262-50b9-48e0-9b7e-6de5844494d8/Beam_video_new_ui.mp4",
"renditions": null
}
]
},
"youtube_video_url": {
"name": "YouTube video URL",
"type": "text",
"value": ""
},
"image": {
"name": "Image",
"type": "asset",
"value": []
},
"translation__translation_connector": {
"name": "Translation Connector",
"type": "taxonomy",
"value": [],
"taxonomyGroup": "languages"
},
"translation__force_translation": {
"name": "Force translation",
"type": "multiple_choice",
"value": []
},
"translation__translate_standalone_nested_content_items": {
"name": "Translate standalone nested content items",
"type": "multiple_choice",
"value": []
},
"translation__last_translation": {
"images": [],
"linkedItemCodenames": [],
"linkedItems": [],
"links": [],
"name": "Last translation",
"type": "rich_text",
"value": "<p>Translation info:</p>\n<ul>\n <li>cs-CZ: Never translated</li>\n <li>de-DE: Never translated</li>\n <li>en-US: Never translated</li>\n <li>es-ES: Never translated</li>\n <li>fr-FR: Never translated</li>\n <li>hu-HU: Never translated</li>\n <li>it-IT: Never translated</li>\n <li>ko-KR: Never translated</li>\n <li>nl-NL: Never translated</li>\n <li>pl-PL: Never translated</li>\n <li>pt-PT: Never translated</li>\n <li>ro-RO: Never translated</li>\n <li>ru-RU: Never translated</li>\n <li>th-TH: Never translated</li>\n <li>tr-TR: Never translated</li>\n <li>vi-VN: Never translated</li>\n <li>zh-CN: Translated on 26.6.2026 21:21</li>\n</ul>\n<p>Publish info:</p>\n<ul>\n <li>Publish info is available only in the main language</li>\n</ul>"
},
"translation__ai_translated": {
"name": "AI translated",
"type": "multiple_choice",
"value": [
{
"name": "Translated",
"codename": "translated"
}
]
},
"translation___experimental__synchronize_content_references": {
"name": "[Experimental] Synchronize content references",
"type": "multiple_choice",
"value": []
},
"translation___experimental__selective_element_translation": {
"name": "[Experimental] Selective translation",
"type": "multiple_choice",
"value": []
},
"translation__selectivetranslationelementid": {
"name": "selectiveTranslationElementId",
"type": "custom",
"value": null
}
}