The forces in anchors including prying forces are determined by finite element analysis, but the resistances are checked using code provisions of IS 1946:2025.
The check of anchors is provided according to IS 1946:2025. Although the code does not specifically provide some formulas for cast-in anchors, the same formulas are used for cast-in anchors as well. This approach is considered conservative since in all other codes, such as ACI 318 or EN 1992-4, cast-in anchors have slightly higher resistance than post-installed anchors.
Cracked or uncracked concrete can be selected in Project settings. Cracked concrete is conservatively assumed as default. Concrete cone breakout check in tension and shear may be disregarded in Project settings, which means the force is assumed to be transferred via reinforcement. User is provided with the magnitude of this force. Due to the use of concrete cone breakout resistance in the formula in concrete pry-out failure check, this check is also disregarded.
Following checks of anchors loaded in tension are not provided and should be checked using information in relevant Technical Product Specification:
- Pull-out failure of fastener (for all anchors),
- Blow-out failure (for headed anchros),
- Combined pull-out and concrete cone failure (for post-installed bonded anchors),
- Concrete splitting failure.
Concrete pryout failure in shear is also not provided and should be checked using information in relevant Technical Product Specification.
Steel failure in tension
Steel failure in tension is checked according to IS 1946:2025 – 9.2.2.2:
\[N_{Rd,s} = \frac{N_{Rk,s}}{\gamma_{Ms}} \]
where:
- \( N_{Rk,s} = A_s \cdot f_u \) – characteristic resistance of a fastener in case of steel failure
- \( A_s \) – tensile stress area of the anchor bolt
- \( f_u \) – ultimate strength of the anchor bolt
- \(\gamma_{Ms} = \frac{1.2 \, f_y}{f_u} \geq 1.4 \) – partial safety factor for steel failure in tension
- \( f_y \) – yield strength of the anchor bolt
- \( f_u \) – ultimate strength of the anchor bolt
Concrete breakout resistance of anchor in tension
Concrete breakout resistance of anchor in tension is checked according to IS 1946:2025 – 9.2.2.3 and is provided for the group of anchors (where applicable). The design strength of the tensioned fasteners in a group or a single fastener is:
\[N_{Rd,c} = \frac{N_{Rk,c}}{\gamma_{Mc}}\]
\[N_{Rk,c} = N^{0}_{Rk,c} \cdot \frac{A_{c,N}}{A^{0}_{c,N}} \cdot \psi_{s,N} \cdot \psi_{re,N} \cdot \psi_{ec,N} \cdot \psi_{M,N}\]
where:
- \( N^{0}_{Rk,c} = 7.2 \, \sqrt{f_{ck}} \, h_{ef}^{1.5} \) for cracked concrete, \( N^{0}_{Rk,c} = 10.1 \, \sqrt{f_{ck}} \, h_{ef}^{1.5} \) for uncracked concrete – characteristic strength of a fastener, remote from the effects of adjacent fasteners or edges of the concrete member; concrete condition can be set in Project settings
- \( f_{ck} \) – ccharacteristic cube compression strength of concrete
- \( h_{ef} = \min \left[ h_{emb}, \max\left( \frac{c_{max}}{1.5}, \frac{s_{max}}{3} \right) \right] \) – effective embedment depth
- \(c_{\max}\) – maximum distance from the center of the anchor to the edge of concrete member
- \(s_{\max}\) – the maximum center to center distance between anchors
- \( A_{c,N} \) – concrete breakout cone area for group of anchors
- \( A^{0}_{c,N} = (3.0 \, h_{ef})^2 \) – concrete breakout cone area for single anchor not influenced by edges
- \(\psi_{s,N} = 0.7 + 0.3 \, \frac{c'}{c_{cr,N}} \leq 1\) – parameter related to the distribution of stresses in the concrete due to the proximity of the fastener to an edge of the concrete member
- \( c' \) – minimum distance from the anchor to the edge
- \( c'_{cr,N} = 1.5 \, h_{ef} \) – characteristic edge distance for ensuring the transmission of the characteristic resistance of an anchor in case of concrete break-out under tension loading
- \(\psi_{re,N} = 0.5 + \frac{h_{emb}}{200} \leq 1\) – parameter accounting for the shell spalling
- \( h_{emb} \) – embedment depth
- \(\psi_{ec,N} = \psi_{ec,N,x} \cdot \psi_{ec,N,y}\) – modification factor for anchor groups loaded eccentrically in tension
- \(\psi_{ec,N,x} = \frac{1}{1 + \frac{2 e_{N,x}}{s_{cr,N}}}\), \(\psi_{ec,N,y} = \frac{1}{1 + \frac{2 e_{N,y}}{s_{cr,N}}}\) – modification factors in x and y directions
- \( e_{N,x}, e_{N,y} \) – load eccentricities
- \( s'_{cr,N} = 3.0 \, h_{ef} \) – characteristic spacing of anchors to ensure the characteristic resistance of the anchors in case of concrete cone failure under tension load
- \(\psi_{M,N}\) – parameter accounting for the effect of a compression force between the fixture and concrete; \(\psi_{M,N}=1.0\) if either of the following criteria is met:
- \(c' < 1.5 \cdot h_{ef}\) – the anchor is located close to the edge
- \( \frac{N_c^n}{N_{Ld}} < 0.8\)
- \(\frac{z}{h_{ef}} \ge 1.5\)
- \(N_c^n\) – compressive force in the base plate
- \(N_{Ld} \) – sum of tension forces of anchors with common concrete breakout cone area
- \(\psi_{M,N} = 2- \frac{z}{h_{ef}} \ge 1 \) – otherwise
- \(z\) – internal lever arm
- \(\gamma_{Mc} = \gamma_c \cdot \gamma_{inst}\)
- \( \gamma_c \) – partial safety factor for concrete editable in Project settings
- \( \gamma_{inst} \) – installation safety factor editable in Project settings
The concrete breakout cone area for group of anchors loaded by tension that create common concrete cone, Ac,N, is shown by red dashed line.
Steel failure in shear
Steel failure in shear is determined according to Cl. 9.2.3. It is assumed that the anchor is made of threaded rod with the same material properties as bolts.
Shear force without lever arm
Shear resistance is checked according to IS 1946:2025 – 9.2.3.1:
\[V_{Rd,s} = \frac{V_{Rk,s}}{\gamma_{Ms}}\]
\[V_{Rk,s} = k_1 \cdot V^{0}_{Rk,s}\]
\[V^{0}_{Rk,s} = 0.5 \cdot A_s \cdot f_u\]
where:
- \( V_{Rk,s} \) – characteristic resistance of a fastener in case of steel failure
- \( k_1 \) – product dependent factor assumed \( k_1 = 1\)
- \( V^{0}_{Rk,s} \) – the characteristic shear strength
- \( A_s \) – tensile stress area
- \( f_u \) – ultimate strength of the anchor bolt
- \( \gamma_{Ms} \) – partial safety factor for steel failure for shear loading
- \( \gamma_{Ms} = \frac{1.0 \, f_y}{f_u} \geq 1.25 \) for \(f_u \le 800\) MPa and \(f_y/f_u \le 0.8\)
- \( \gamma_{Ms} = 1.5\) for \(f_u > 800\) MPa or \(f_y/f_u > 0.8\)
- \( f_y \) – yield strength of the anchor bolt
Shear force with lever arm
Shear resistance is checked according to IS 1946:2025 – 9.2.3.2:
\[V_{Rd,s} = \frac{V_{Rk,s}}{\gamma_{Ms}}\]
\[V_{Rk,s} = \frac{\alpha_M \cdot M_{Rk,s}}{l}\]
where:
- \( V_{Rk,s} \) – characteristic resistance of a fastener in case of steel failure with lever arm
- \( \alpha_M \) – factor accounting for the degree of restraint of the fastener, assumed \( \alpha_M = 2\) because anchor is clamped by two nuts and base plate is more rigid than the anchor
- \( M_{Rk,s} = M^{0}_{Rk,s} \cdot \left( 1 - \frac{N_{Ld}}{N_{Rd,s}} \right) \) – characteristic flexural strength of the fastener influenced by the axial load
- \( N_{Ld} \) – design tension load
- \( N_{Rd,s} \) – tensile strength of a fastener to steel failure
- \(M^{0}_{Rk,s} = 1.2 \cdot Z_{el} \cdot f_u\) – characteristic flexural strength of the fastener
- \( Z_{el} = \frac{\pi \, d_{a,r}^3}{32} \) – elastic section modulus of the fastener
- \( d_{a,r} \) – anchor diameter reduced by threads
- \( f_u \) – ultimate strength of the anchor bolt
- \(l = 0.5 \cdot d_a + t_g + \frac{t_p}{2}\) – length of the lever arm
- \( d_a \) – anchor diameter
- \( t_g \) – thickness of grout layer
- \( t_p \) – base plate thickness
- \( \gamma_{Ms} \) – partial safety factor for steel failure for shear loading
- \( \gamma_{Ms} = \frac{1.0 \, f_y}{f_u} \geq 1.25 \) for \(f_u \le 800\) MPa and \(f_y/f_u \le 0.8\)
- \( \gamma_{Ms} = 1.5\) for \(f_u > 800\) MPa or \(f_y/f_u > 0.8\)
- \( f_y \) – yield strength of the anchor bolt
Concrete edge failure
Concrete edge failure resistance is checked according to IS 1946:2025 – 9.2.3.4. If concrete cones of fasteners intersect, they are checked as a group. The edges in the direction of the shear load are checked. All load at a base plate is presumed to be transferred by a fastener near the checked edge.
\[V_{Rd,c} = \frac{V_{Rk,c}}{\gamma_{Mc}}\]
\[V_{Rk,c} = V^{0}_{Rk,c} \cdot \frac{A_{c,V}}{A^{0}_{c,V}} \cdot \psi_{s,V} \cdot \psi_{re,V} \cdot \psi_{ec,V} \cdot \psi_{h,V} \cdot \psi_{\alpha,V}\]
where
- \( V^{0}_{Rk,c} \) – initial value of the characteristic shear strength of the fastener
- \( V^{0}_{Rk,c} = 1.55 \cdot d_a^{\alpha} \cdot h_{ef}^{\beta} \cdot \sqrt{f_{ck}} \cdot (c'_1)^{1.5} \) for cracked concrete
- \( V^{0}_{Rk,c} = 2.18 \cdot d_a^{\alpha} \cdot h_{ef}^{\beta} \cdot \sqrt{f_{ck}} \cdot (c'_1)^{1.5} \) for uncracked concrete
- \( d_a \) – anchor diameter
- \( \alpha = 0.1 \cdot \left( \frac{h_{ef}}{c'_1} \right)^{0.5} \) – factor
- \( h_{ef} = \min(h_{emb}, 20 \cdot d_a) \) – parameter related to the length of the fastener
- \( h_{emb} \) – embedment depth
- \( \beta = 0.1 \cdot \left( \frac{d_a}{c'_1} \right)^{0.2} \) – factor
- \( f_{ck} \) – characteristic cube compression strength of concrete
- \( c'_1 \leq \max \left( \frac{c_{2,max}}{1.5}, \frac{D}{1.5}, \frac{s_{2,max}}{3} \right) \) – edge distance of fastener in direction 1 towards the edge in the direction of loading
- \( D \) – concrete member thickness
- \( c_{2,max} \) – larger of the two distances to the edges parallel to the direction of loading
- \( s_{2,max} \) – maximum spacing in direction 2 between fasteners within a group
- \(A^{0}_{c,V} = 4.5 \cdot (c'_1)^2\) – reference projected area of failure cone
- \( A_{c,V} \) – actual area of idealised concrete break-out body
- \(\psi_{s,V} = 0.7 + 0.3 \cdot \frac{c'_2}{1.5 \cdot c'_1} \leq 1\) – parameter related to the distribution of stresses in the concrete due to the proximity of the fastener to an edge of the concrete member
- \( c'_1 \) – edge distance of fastener in direction 1 towards the edge in the direction of loading
- \( c'_2 \) – edge distance perpendicular to direction 1 that is the smallest edge distance in a narrow member with multiple edge distances
- \(\psi_{re,V} = 1.0\) – parameter accounting for the shell spalling effect, no edge reinforcement or stirrups are assumed
- \(\psi_{ec,V} = \frac{1}{1 + \frac{2 e_V}{3 \cdot c'_1}} \leq 1\) – modification factor for anchor groups loaded eccentrically in shear
- \( e_V \) – shear load eccentricity
- \( \psi_{h,V} = \left( \frac{1.5 \cdot c'_1}{D} \right)^{0.5} \geq 1 \) – modification factor for anchors located in a shallow concrete member
- \(\psi_{\alpha,V} = \sqrt{\frac{1}{(\cos \alpha_V)^2 + (0.5 \cdot \sin \alpha_V)^2}} \geq 1\) – 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
- \(\gamma_{Mc} = \gamma_c \cdot \gamma_{inst}\) – partial safety factor for concrete failure
- \( \gamma_c \) – partial safety factor for concrete
- \( \gamma_{inst} \) – installation safety factor of an anchor system in shear
Interaction of tensile and shear forces in steel
The interaction of tensile and shear forces in steel is performed for anchors with stand-off: Direct according to IS 1946:2025 – 9.2.4:
\[\left( \frac{N_{Ld}}{N_{Rd,s}} \right)^2 + \left( \frac{V_{Ld}}{V_{Rd,s}} \right)^2 \leq 1.0\]
where:
- \( N_{Ld} \) – design tension force
- \( N_{Rd,s} \) – fastener tensile strength
- \( V_{Ld} \) – design shear force
- \( V_{Rd,s} \) – fastener shear strength
Steel interaction is not required in case of shear load with lever arm. It is covered by shear load with lever arm equation.
Interaction of tensile and shear forces in concrete
Interaction of tensile and shear forces in concrete is checked according to IS 1946:2025 – 9.2.4:
\[\left( \frac{N_{Ld}}{N_{Rd,i}} \right)^{1.5} + \left( \frac{V_{Ld}}{V_{Rd,i}} \right)^{1.5} \leq 1.0\]
where:
- \( \frac{N_{Ld}}{N_{Rd,i}} \) – the largest utilization value for tension failure modes
- \( \frac{V_{Ld}}{V_{Rd,i}} \) – the largest utilization value for shear failure modes
- \( \frac{N_{Ld,g}}{N_{Rd,c}} \) – concrete breakout failure of anchor in tension
- \( \frac{V_{Ld,g}}{V_{Rd,c}} \) – concrete edge failure
Anchors with stand-off: Gap
Anchors with stand-off: gap in tension are designed according to IS 1946:2025, and anchors in compression are designed as a beam member according to IS 800: 2007 with partial safety factor of anchors. The assumed length of the member is the sum of the height of gap, half of nominal diameter thickness and half of the base plate thickness. Stand-off anchors are usually checked at a construction stage before grouting.
Steel failure in tension is checked according to IS 1946:2025 – 9.2.2.2:
\[N_{Rd,s} = \frac{N_{Rk,s}}{\gamma_{Ms}} \]
Steel failure in compression is checked according to IS 800:2007 – 7.1:
\[P_d = A_s \cdot f_{cd}\]
where:
- \( A_s \) – anchor area reduced by thread
- \( f_{cd} = \frac{\chi \cdot f_u}{\gamma_{Ms}} \) – design compressive stress
- \(\chi = \min \left( \frac{1}{\phi + \sqrt{\phi^2 - \lambda^2}}, 1 \right)\) – buckling reduction factor
- \(\phi = 0.5 \cdot \left[ 1 + \alpha \cdot (\lambda - 0.2) + \lambda^2 \right]\) – value to determine buckling reduction factor
- \( \alpha \) – imperfection factor
- \(\lambda = \sqrt{\frac{f_u}{f_{cc}}}\) – relative slenderness
- \(f_{cc} = \frac{\pi^2 \cdot E}{\left( \frac{K L}{r} \right)^2}\) – Euler buckling stress
- \( E \) – elastic modulus
- \(K L = 2 \cdot l\) – buckling length
- \( l = 0.5 \cdot d_a + t_g + \frac{t_p}{2} \) – length of the lever arm
- \( d_a \) – anchor diameter
- \( t_g \) – thickness of grout layer
- \( t_p \) – base plate thickness
- \(r = \sqrt{\frac{I}{A_s}}\) – radius of gyration of the anchor bolt
- \( I = \frac{\pi \cdot d_{a,r}^4}{64} \) – moment of inertia of the bolt
- \( d_{a,r} \) – anchor diameter reduced by threads
- \(\gamma_{Ms} = \frac{1.2 \, f_y}{f_u} \geq 1.4 \) – partial safety factor for steel failure for tension loading
- \( f_y \) – yield strength of the anchor bolt
- \( f_u \) – ultimate strength of the anchor bolt
Shear resistance is checked according to IS 1946:2025 – 9.2.3.1:
\[V_{Rd,s} = \frac{V_{Rk,s}}{\gamma_{Ms}}\]
\[V_{Rk,s} = k_1 \cdot V^{0}_{Rk,s}\]
\[V^{0}_{Rk,s} = 0.5 \cdot A_s \cdot f_u\]
Bending resistance is checked according to IS 1946:2025 – 9.2.3.2:
\[M_{Rd,s} = \frac{M_{Rk,s}}{\gamma_{Ms}}\]
where:
- \( M^{0}_{Rk,s} = 1.2 \cdot Z_{el} \cdot f_u \) – characteristic flexural strength of the fastener
- \( Z_{el} = \frac{\pi \cdot d_{a,r}^3}{32} \) – elastic section modulus of the fastener
- \( d_{a,r} \) – anchor diameter reduced by threads
- \(\gamma_{Ms} = \frac{1.0 \, f_y}{f_u} \geq 1.25\)
- \( f_y \) – yield strength of the anchor bolt
- \( f_u \) – ultimate strength of the anchor bolt
Interaction of loading for anchors in tension (IS 1946:2025 – 9.2.4):
\[\frac{N_{Ld}}{N_{Rd,s}} + \frac{M_{Ld}}{M_{Rd,s}} \leq 1.0\]
where:
- \( N_{Ld} \) – design tension force
- \( N_{Rd,s} \) – design tensile resistance
- \( M_{Ld} \) – design bending moment
- \( M_{Rd,s} \) – design bending resistance
Interaction of loading for anchors in compression (IS 1946:2025 – 9.2.4):
\[\frac{P}{P_d} + \frac{M_{Ld}}{M_{Rd,s}} \leq 1.0\]
where:
- \( P \) – design compression force
- \( P_d \) – design compression resistance
- \( M_{Ld} \) – design bending moment
- \( M_{Rd,s} \) – design bending resistance
Concrete-related failure modes, including their interaction, are checked as for the standard anchors according to IS 1946:2025.
Detailing
If anchors with \(f_u \ge 1000\) MPa are used, steel strength for shear load may not be accurate, use steel strength from AR instead.