Code-check of anchors according to Chinese standard

Four anchor bolt types are available:

• Straight 
• Washer plate - Circular 
• Washer plate - Rectangle 

Code-check of anchors is performed according to JGJ 145-2013 for post-installed anchors irrespective of selected anchor type.

In the Project settings, settings are available to activate/deactivate concrete cone breakout checks in tension and shear. If the concrete cone breakout check is not activated, it is assumed that the dedicated reinforcement is designed to resist the force. The magnitude of the force is provided in formulas for the current load effect. 

Furthermore, the concrete can be set as cracked or uncracked. Uncracked concrete should be in permanent compression that prevents shrinkage cracks. The resistances of uncracked concrete are higher. 

Note that some checks are not performed because these are determined by testing and can be provided only by the manufacturer and found in relevant Technical Product Specification. Some failure modes may be avoided by proper detailing (e.g., anchor pitch or distance of an anchor to an edge). These checks are:

• Pull-out failure of fastener (for post-installed or mechanical anchors)
• Combined pull-out and concrete failure (for post-installed bonded anchors)
• Concrete splitting failure
• Concrete blow-out failure

Anchor tensile resistance

An anchor in the form of a threaded rod is assumed. Anchor tensile resistance is checked according to JGJ 145-2013 – 6.1.2:

$$N_{Rd,s} = \frac{N_{Rk,s}}{\gamma_{Rs,N}}$$

$$N_{Rk,s}=f_{yk}\cdot A_s$$

where:

• $N_{Rk,s}$ – characteristic resistance of a fastener in case of steel failure
• $\gamma_{Rs,N} = 1.3$ – partial safety factor for steel failure in tension editable in Project Settings
• $f_{yk}$ – characteristic yield strength of the anchor bolt
• $A_s$ – anchor tensile stress area

Concrete breakout resistance of an anchor in tension 

The check is performed for a group of anchors that form a common tension breakout cone according to JGJ 145-2013 – 6.1.3:

$$N_{Rd,c} = \frac{N_{Rk,c}}{\gamma_{Rc,N}}$$

$$N_{Rk,c} = N_{Rk,c}^0\cdot \frac{A_{c,N}}{A_{c,N}^0} \cdot \psi_{s,N} \cdot \psi_{re,N} \cdot \psi_{ec,N}$$

Where: 

• $N_{Rk,c}^0 = 7.0 \cdot \sqrt{f_{cu,k}} \cdot h_{ef}^{1.5}$ – characteristic strength of a fastener in cracked concrete, remote from the effects of adjacent fasteners or edges of the concrete member 
• $N_{Rk,c}^0 = 9.8 \cdot \sqrt{f_{cu,k}} \cdot h_{ef}^{1.5}$ – characteristic strength of a fastener in uncracked concrete, remote from the effects of adjacent fasteners or edges of the concrete member 
• $f_{cu,k}$ – characteristic concrete compressive cubic strength 
• $h_{ef} = \min \left( h_{emb}, \max \left( \frac{c_{a,max}}{1.5}, \frac{s_{max}}{3} \right) \right)$ – depth of embedment

  • $h_{emb}$ – anchor length embedded in concrete 
  • $c_{a,max}$ – maximum distance from the anchor to one of the three closest edges 
  • $s_{max}$ – maximum spacing between anchors
• $A_{c,N}$ – concrete breakout cone area for group of anchors 
• $A_{c,N}^0 = (3.0 \cdot h_{ef})^2$ – concrete breakout cone area for single anchor not influenced by edges 
• $\psi_{s,N} = 0.7+0.3\cdot \frac{c}{c_{cr,N}}$ – parameter related to the distribution of stresses in the concrete due to the proximity of the fastener to an edge of the concrete member
• $c$ – minimum distance from the anchor to the edge 
• $c_{cr,N}=1.5\cdot h_{ef}$ – characteristic edge distance for ensuring the transmission of the characteristic resistance of an anchor in case of concrete break-out under tension loading 
• $\psi_{re,N} = 0.5+\frac{h_{ef}}{200}\le 1.0$ – parameter accounting for the shell spalling
• $\psi_{ec,N} = \psi_{ec,N,x} \cdot \psi_{ec,N,y}$ – modification factor for anchor groups loaded eccentrically in tension
• $\psi_{ec,N,x} = \frac{1}{1+2\cdot \frac{e_{N,x}}{s_{cr,N}}}$ – modification factor that depends on eccentricity in x-direction 

  • $e_{N,x}$– tension load eccentricity in x-direction 
  • $s_{cr,N}$ – characteristic spacing of anchors to ensure the characteristic resistance of the anchors in case of concrete cone failure under tension load 
• $\psi_{ec,N,y} = \frac{1}{1+2\cdot \frac{e_{N,y}}{s_{cr,N}}}$ – modification factor that depends on eccentricity in y-direction 

  • $e_{N,y}$ – tension load eccentricity in y-direction 
• $\gamma_{Rc,N} = 3.00$ – partial safety factor for concrete breakout in tension editable in Project settings

Shear resistance

Anchor shear steel resistance checked according to JGJ 145-2013 – 6.1.14. Friction is not taken into account. Shear with and without a lever arm is recognized as dependent on base plate manufacturing operation settings. 

For stand-off: direct, the shear without lever arm is assumed:

$$V_{Rd,s} = \frac{V_{Rk,s}}{\gamma_{Rs,V}}$$

$$V_{Rk,s} = 0.5 \cdot f_{yk} \cdot A_s$$

where:

• $f_{yk}$ – yield strength of the anchor bolt 
• $A_s$ – tensile stress area 
• $\gamma_{Rs,V} = 1.3$ – partial safety factor for steel failure in shear editable in Project settings

For stand-off: mortar joint, the shear with lever arm is assumed:

$$V_{Rd,s} = \frac{\min(V_{Rk,s1}, V_{Rk,s2})}{\gamma_{Rs,V}}$$

$$V_{Rk,s1} = 0.5 \cdot f_{yk} \cdot A_s$$

$$V_{Rk,s2} = \frac{\alpha_M \cdot M_{Rk,s}}{l_0}$$

where:

• $V_{Rk,s1}$ – characteristic resistance of a fastener in case of steel failure without lever arm
• $V_{Rk,s2}$ – characteristic resistance of a fastener in case of steel failure with lever arm
• $\gamma_{Rs,V} = 1.3$ – partial safety factor for steel failure in shear editable in Project settings
• $f_{yk}$ – yield strength of the anchor bolt 
• $A_s$ – tensile stress area 
• $\alpha_M=2.0$ – factor accounting for the degree of restraint of the fastener – full restraint is assumed
• $M_{Rk,s} = M^0_{Rk,s} \cdot \left(1 - \frac{N_{sd}}{N_{Rds}}\right)$ – characteristic flexural strength of the fastener influenced by the axial load 

  • $N_{sd}$ – design tension load 
  • $N_{Rds}$ – tensile strength of a fastener to steel failure 
  • $M^0_{Rk,s} = 1.2 \cdot W_{el} \cdot f_{yk}$ – characteristic flexural strength of the fastener 
  • $W_{el} = \frac{\pi \cdot d_s^3}{32}$ – elastic section modulus of the fastener 
  • $d_s$ – anchor diameter reduced by threads 
• $l_0 = 0.5 \cdot d + t_g + \frac{t_p}{2}$ – length of the lever arm 

  • $d$ – anchor diameter 
  • $t_g$ – thickness of grout layer 
  • $t_p$ – base plate thickness

Concrete pryout resistance 

Concrete pryout resistance is performed for a group of anchors on a common base plate according to JGJ 145-2013 – 6.1.26. All anchors are assumed in tension in the calculation of $N_{Rk,c}$. That is why it may differ from the calculation of concrete cone breakout in tension.

$$V_{Rd,cp} = \frac{V_{Rk,cp}}{\gamma_{Rcp}}$$

$$V_{Rk,cp} = k \cdot N_{Rk,c}$$

Where: 

• $k = 2.0$ – factor taking into account fastener embedment depth 
• $N_{Rk,c}$ – characteristic concrete cone failure of a fastener or a group of fasteners; all anchors are assumed to be in tension 
• $\gamma_{Rcp} = 2.50$ – partial safety factor for concrete pryout failure editable in Project settings

Concrete edge failure resistance

Concrete edge failure is a brittle failure, and the worst possible case is checked, i.e., only the anchors located near the edge transfer the full shear load acting on a whole base plate. If anchors are positioned in a rectangular pattern, the row of anchors at the investigated edge transfers the shear load. If anchors are positioned irregularly, the two anchors nearest to the investigated edge transfer the shear load. Two edges in the direction of the shear load are investigated, and the worst case is shown in the results.

Investigated edges in dependence on the direction of the shear force resultant 

The check is performed according to JGJ 145-2013 – 6.1.15.

$$V_{Rd,c} = \frac{V_{Rk,c}}{\gamma_{Rc,V}}$$

$$V_{Rk,c} = V_{Rk,c}^0 \cdot \frac{A_{c,V}}{A_{c,V}^0} \cdot \psi_{s,V} \cdot \psi_{h,V} \cdot \psi_{\alpha,V} \cdot \psi_{re,V} \cdot \psi_{ec,V}$$

Where:

• $V_{Rk,c}^0 = 1.35 \cdot d^{\alpha} \cdot l_f^{\beta} \cdot \sqrt{f_{cu,k}} \cdot c_1^{1.5}$ – initial value of the characteristic shear strength of the fastener in cracked concrete
• $V_{Rk,c}^0 = 1.9 \cdot d^{\alpha} \cdot l_f^{\beta} \cdot \sqrt{f_{cu,k}} \cdot c_1^{1.5}$ – initial value of the characteristic shear strength of the fastener in uncracked concrete
• $d$ – anchor diameter
• $\alpha = 0.1 \cdot \left( \frac{l_f}{c_1} \right)^{0.5}$ – factor
• $l_f = \min(h_{ef}, 8 \cdot d)$ – parameter related to the length of the fastener

  • $h_{ef}$ – anchor length embedded in concrete
• $\beta = 0.1 \cdot \left( \frac{d}{c_1} \right)^{0.2}$ – factor

  • $f_{cu,k}$ – characteristic concrete compressive cubic strength
  • $c_1$ – edge distance of fastener in direction 1 towards the edge in the direction of loading
• $A_{c,V}$ – actual area of idealised concrete break-out body
• $A_{c,V}^0 = 4.5 \cdot c_1^2$ – reference projected area of failure cone
• $\psi_{s,V} = 0.7 + 0.3 \cdot \frac{c_2}{1.5c_1} \leq 1$ – parameter related to the distribution of stresses in the concrete due to the proximity of the fastener to an edge of the concrete member

  • $c_2$ – edge distance of fastener perpendicular to direction 1 that is the smallest edge distance in a narrow member with multiple edge distances
• $\psi_{h,V} = \left( \frac{1.5 \cdot c_1}{h} \right)^{0.5} \geq 1$ – modification factor for anchors located in a shallow concrete member

  • $h$ – concrete member thickness
• $\psi_{\alpha,V} = \sqrt{ \frac{1}{(\cos \alpha_V)^2 + (0.4 \cdot \sin \alpha_V)^2} } \geq 1$ – modification factor for anchors loaded at an angle with the concrete edge

  • $\alpha_V$ – angle between the applied load to the fastener or fastener group and the direction perpendicular to the free edge under consideration
• $\psi_{re,V} = 1.00$ – parameter accounting for the shell spalling effect, no edge reinforcement or stirrups are assumed
• $\psi_{ec,V} = \frac{1}{1 + \frac{2e_V}{3c_1}} \leq 1$ – modification factor for anchor groups loaded eccentrically in shear

  • $e_V$ – shear load eccentricity
• $\gamma_{Rc,V} = 2.5$ – partial safety factor for concrete edge failure modifiable in Project settings

Interaction of tension and shear in steel 

The interaction of tension and shear for post-installed fasteners is determined separately for steel and concrete failure modes. Interaction in steel is checked according to JGJ 145-2013 – 6.1.28. The interaction in steel is checked for each anchor separately.

$$\left ( \frac{N_{sd}}{N_{Rd,s}} \right )^2 + \left ( \frac{V_{sd}}{V_{Rd,s}} \right )^2 \le 1.0$$

Interaction of tension and shear in concrete

 Interaction in concrete is checked according to JGJ 145-2013 – 6.1.29.

$$\left ( \frac{N_{sd}}{N_{Rd,i}} \right )^{1.5} + \left ( \frac{V_{sd}}{V_{Rd,i}} \right )^{1.5} \le 1.0$$

The largest value of $N_{Ed} / N_{Rd,i}$ and $V_{Ed} / V_{Rd,i}$ for the different failure modes shall be taken. Note that values of $N_{Ed}$ and $N_{Rd,i}$ often belong to a group of anchors.

Anchors with stand-off

An anchor with stand-off is designed as a bar element loaded by shear force, bending moment, and compressive or tensile force. These internal forces are determined by the finite element model. The anchor is fixed on both sides, one side is 0.5×d below the concrete level, and the other side is in the middle of the thickness of the plate. The buckling length is conservatively assumed as twice the length of the bar element. Plastic section modulus is used. The bar element is designed according to GB 50017-2017. The shear force may decrease the yield strength of the steel but the minimum length of the anchor to fit the nut under the base plate ensures that the anchor fails in bending before the shear force reaches half the shear resistance. The reduction is, therefore, not necessary. The linear interaction of bending moment and compressive or tensile strength is assumed.

Shear resistance (JGJ 145-2013 – 6.1.14):

$$V_{Rd,s} = \frac{V_{Rk,s}}{\gamma_{Rs,V}}$$

$$V_{Rk,s} = 0.5 \cdot f_{yk} \cdot A_s$$

where:

• $f_{yk}$ – yield strength of the anchor bolt 
• $A_s$ – tensile stress area 
• $\gamma_{Rs,V} = 1.3$ – partial safety factor for steel failure in shear editable in Project settings

Tensile resistance (JGJ 145-213 – 6.2.1):

$$N_{Rd,s} = \frac{N_{Rk,s}}{\gamma_{Rs,N}}$$

$$N_{Rk,s}=f_{yk}\cdot A_s$$

where:

• $N_{Rk,s}$ – characteristic resistance of a fastener in case of steel failure
• $\gamma_{Rs,N} = 1.3$ – partial safety factor for steel failure in tension editable in Project Settings
• $f_{yk}$ – characteristic yield strength of the anchor bolt
• $A_s$ – anchor tensile stress area

Compressive resistance (GB 50017-2017 – 7.2.1):

$$N_{c,Rd,s} = \frac{\varphi \cdot A_s \cdot f_{yk}}{\gamma_{Rs,N}}$$

where:

• $\varphi = \frac{1}{2 \cdot \lambda_n^2} \cdot \left[ (\alpha_2 + \alpha_3 \cdot \lambda_n + \lambda_n^2) - \sqrt{(\alpha_2 + \alpha_3 \cdot \lambda_n + \lambda_n^2)^2 - 4 \cdot \lambda_n^2} \right]$ – buckling reduction factor (GB 50017-2017 – D.0.5)
• $\alpha_1 = 0.73$ – coefficient for class c (GB 50017-2017 – Table D.0.5)
• $\alpha_2$  – coefficient for class c, $\alpha_2 = 0.906$ for $\lambda_n \le 1.05$ and $\alpha_2 = 1.216$ for $\lambda_n > 1.05$ (GB 50017-2017 – Table D.0.5)
• $\alpha_3$  – coefficient for class c, coefficient for class c, $\alpha_3 = 0.595$ for $\lambda_n \le 1.05$ and $\alpha_3 = 0.302$ for $\lambda_n > 1.05$ (GB 50017-2017 – Table D.0.5)
• $\lambda_n = \frac{\lambda}{\pi} \cdot \sqrt{\frac{E}{f_{yk}}}$ – relative slenderness (GB 50017-2017 – Equation (D.0.5-2))
• $\lambda = \frac{l_{cr}}{i}$ – anchor bolt slenderness (GB 50017-2017 – Equation (7.2.2-1))
• $l_{cr} = 2 \cdot l_0$ – buckling length (it is assumed on a safe side that the bolt is fixed in the concrete and able to freely rotate at the base plate)
• $l_0 = 0.5 \cdot d + t_g + \frac{t_p}{2}$ – length of the lever arm
• $d$ – anchor diameter
• $t_g$ – gap height
• $t_p$ – base plate thickness
• $i = \sqrt{\frac{I}{A_s}}$ – radius of gyration of the anchor bolt
• $I = \frac{\pi \cdot d_s^4}{64}$ – moment of inertia of the bolt
• $d_s = \sqrt{4 \cdot A_s / \pi}$ – diameter reduced by thread
• $A_s$ – anchor area reduced by thread
• $f_{yk}$ – anchor yield strength
• $E$ – elastic modulus
• $\gamma_{Rs,N} = 1.30$ – partial safety factor for steel failure in tension editable in Project settings

Bending resistance (JGJ 145-2013 – 6.1.26):

$$M_{Rd,s} = \frac{M_{Rk,s}}{\gamma_{Rs,V}}$$

$$M_{Rk,s} = 1.2 \cdot W_{el} \cdot f_{yk}$$

• $W_{el}= \frac{\pi d_s^3}{32}$ – elastic section modulus of the bolt
• f_yk – bolt yield strength
• γ_Rs,V =1.3 – partial safety factor for steel failure in shear editable in Project settings

Anchor steel utilization

$$\frac{N_{sd}}{N_{Rd,s}} + \frac{M_{sd}}{M_{Rd,s}} \le 1$$

where:

• N_sd – tensile ($N_{sd}$) or compressive ($N_{c,sd}$) design force
• N_Rd,s – tensile (positive) or compressive (negative sign) design resistance
• M_sd – design bending moment
• M_Rd,s = M_pl,Rd – design bending resistance