B-5Shear

IS 456:2000, Plain and Reinforced Concrete — Code of Practice

Last Updated 29 Oct 2026

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B-5.1 Nominal Shear Stress

The nominal shear stress $\tau_{v}$ in beams or slabs of uniform depth shall be calculated by the following equation:

$\tau_{v}=\frac{1}{b d}$

where

= shear force due to design loads,

$b \quad=$ breadth of the member, which for flanged sections shall be taken as the breadth of the web, and

= effective depth.

B-5.1.1 Beams of Varying Depth

In the case of beams of varying depth, the equation shall be modified as:

$V_{\pm}=\frac{M \tan \beta}{b d}$

where

$\tau_{y}, V, b$ and $d$ are the same as in B-5.1,
$M=$ bending moment at the section, and
$\beta=$ angle between the top and the bottom edges of the beam.

The negative sign in the formula applies when the bending moment $M$ increases numerically in the same direction as the effective depth $d$ increases, and the positive sign when the moment decreases numerically in this direction.

B-5.2 Design Shear Strength of Concrete

B-5.2.1

The permissible shear stress in concrete in beams without shear reinforcement is given in Table 23.

B-5.2.1.1

For solid slabs the permissible shear stress in concrete shall be $k \tau_{\mathrm{c}}$ where $k$ has the value given below:

Overall depth of slab, mm	300 or	275	250	225	200	175	150 or
Overall depth of slab, mm	more						less
k	1.00	1.05	1.10	1.15	1.20	1.25	1.30

NOTE — This does not apply to flat slabs for which 31.6 shall apply.

B-5.2.2 Shear Strength of Members Under Axial Compression

For members subjected to axial compression P, the permissible shear stress in concrete $\tau_{\mathrm{c}}$ given in Table 23, shall be multiplied by the following factor:

$\delta=1+\frac{5 P}{A_{g} f_{\mathrm{ck}}}$ , but not exceeding 1.5

where

$P=$ axial compressive force in N,
$\begin{aligned} A_{\mathrm{g}} & =\text { gross area of the concrete section in } \mathrm{mm}^{2} \\ & \text { and }\end{aligned}$
$f_{\mathrm{ck}}=$ characteristic compressive strength of concrete.

B-5.2.3 With Shear Reinforcement

When shear reinforcement is provided the nominal shear stress $\tau_{\mathrm{c}}$ in beams shall not exceed $\tau_{\mathrm{c} \max }$ given in Table 24.

Table 23 Permissible Shear Stress in Concrete

(Clauses B-2.1, B-2.3, B-4.2, B-5.2.1, B-5.2.2, B-5.3, B-5.4, B-5.5.1, B.5.5.3, B-6.3.2,B-6.3.3 and B-6.4.3 and Table 21)

100 A_t / _bd	Permissible Shear Stress in Concrete, τ_c, N/mm²
	Grade of Concrete
	M 15	M 20	M 25	M 30	M 35	M 40 and above
	(1)	(2)	(3)	(4)	(5)	(6)	(7)
≤ 0.15	0.18	0.18	0.19	0.20	0.20	0.20
0.25	0.22	0.22	0.23	0.23	0.23	0.23
0.50	0.29	0.30	0.31	0.31	0.31	0.32
0.75	0.34	0.35	0.36	0.37	0.37	0.38
1.00	0.37	0.39	0.40	0.41	0.42	0.42
1.25	0.40	0.42	0.44	0.45	0.45	0.46
1.50	0.42	0.45	0.46	0.48	0.49	0.49
1.75	0.44	0.47	0.49	0.50	0.52	0.52
2.00	0.44	0.49	0.51	0.53	0.54	0.55
2.25	0.44	0.51	0.53	0.55	0.56	0.57
2.50	0.44	0.51	0.55	0.57	0.58	0.60
2.75	0.44	0.51	0.56	0.58	0.60	0.62
3.00 and above	0.44	0.51	0.57	0.60	0.61	0.63

NOTE — A, is that area of longitudinal tension reinforcement which continues at least one effective depth beyond the section being considered except at supports where the full area of tension reinforcement may be used provided the detailing conforms to 26.2.2 and 26.2.3.

B-5.2.3.1

For slabs, $\tau_{y}$ shall not exceed half the value of $\tau_{\mathrm{cmax}}$ given in Table 24.

B-5.3 Minimum Shear Reinforcement

When $\tau_{\mathrm{y}}$ is less than $\tau_{\mathrm{c}}$ given in Table 23, minimum shear reinforcement shall be provided in accordance with 26.5.1.6.

B-5.4 Design of Shear Reinforcement

When $\tau_{\mathrm{v}}$ exceeds $\tau_{\mathrm{c}}$ given in Table 23, shear reinforcement shall be provided in any of the following forms:

a) Vertical stirrups,

b) Bent-up bars along with stirrups, and

c) Inclined stirrups.

Where bent-up bars are provided, their contribution towards shear resistance shall not be more than half that of the total shear reinforcement.

Shear reinforcement shall be provided to carry a shear equal to $V-\tau_{\mathrm{c}} . b d$ . The strength of shear reinforcement $V_{\mathrm{s}}$ shall be calculated as below:

a) For vertical stirrups

$V_{s}=\frac{\sigma_{\mathrm{sv}} A_{\mathrm{sv}} d}{S_{\mathrm{v}}}$

b) For inclined stirrups or a series of bars bent-up at different cross-sections:

$V_{\mathrm{s}}=\frac{\sigma_{\mathrm{sv}} A_{\mathrm{sv}} d}{s_{\mathrm{v}}}\left(\sin \alpha+\cos \alpha\right)$

c) For single bar or single group of parallel bars, all bent-up at the same cross-section:

$V_{s}=\sigma_{s v} A_{s v} \sin \alpha$

where

= total cross-sectional area of stirrup legs or bent-up bars within a distance,
$\begin{aligned} s_{v} & =\text { spacing of the stirrups or bent-up bars } \\ & \text { along the length of the member, }\end{aligned}$

$\tau_{\mathrm{c}}=$ design shear strength of the concrete,

$\begin{aligned} b & =\text { breadth of the member which for } \\ & \text { flanged beams, shall be taken as the } \\ & \text { breadth of the web } b_{w} .\end{aligned}$
$\begin{aligned} \sigma_{n v} & =\text { permissible tensile stress in shear } \\ & \text { reinforcement which shall not be taken }\end{aligned}$

greater than 230 N/mm²,

$\alpha \quad=$ angle between the inclined stirrup or bent-up bar and the axis of the member, not less than $45^{\circ}$ , and

effective depth.

NOTE — Where more than one type of shear reinforcement is used to reinforce the same portion of the beam, the total shear resistance shall be computed as the sum of the resistance for the various types separately. The area of the stirrups shall not be less than the minimum specified in 26.5.1.6.

B-5.5 Enhanced Shear Strength of Sections Close to Supports

B-5.5.1 General

Shear failure at sections of beams and cantilevers without shear reinforcement will normally occur on plane inclined at an angle 30" to the horizontal. If the angle of failure plane is forced to be inclined more steeply than this (because the section considered $(X-X)$ in Fig. 24 is close to a support or for other reasons], the shear force required to produce failure is increased.

The enhancement of shear strength may be taken into account in the design of sections near a support by increasing design shear strength of concrete, $\tau_{\mathrm{c}}$ to $2 d \tau_{\mathrm{c}} / a_{\mathrm{v}}$ provided that the design shear stress at the face of support remains less than the values given in Table 23. Account may be taken of the enhancement in any situation where the section considered is closer to the face of a support of concentrated load than twice the effective depth, $d$ . To be effective, tension reinforcement should extend on each side of the point where it is intersected by a possible failure plane for a distance at least equal to the effective depth, or be provided with an equivalent anchorage.

B-5.5.2 Shear Reinforcement for Sections Close to Supports

If shear reinforcement is required, the total area of this is given by:

$A_{x}=a_{y} b\left(\tau_{y}-2 d \tau_{c} / a_{y}\right) / 0.87 f_{y} \geq 0.4 a_{y} b / 0.87 f_{y}$

This reinforcement should be provided within the middle three quarters of $a_{y}$ . Where $a_{y}$ is less than $d$ , horizontal shear reinforcement will be more effective than vertical.

Table 24 Maximum Shear Stress, $\tau_{\mathrm{cmax}}, \mathrm{N} / \mathrm{mm}^{2}$

(Clauses B-5.2.3, B-5.2.3.1, B-5.5.1 and B-6.3.1)

Concrete Grade	M 15	M 20	M 25	M 30	M 35	M 40 and above
τ_c max, N/mm²	1.6	1.8	1.9	2.2	2.3	2.5

B-5.5.3 Enhanced Shear Strength Near Supports (Simplified Approach)

The procedure given in B-5.5.1 and B-5.5.2 may be used for all beams. However for beams carrying generally uniform load or where the principal load is located further than $2 d$ from the face of support, the shear stress may be calculated at a section a distance $d$ from the face of support. The value of $\tau_{\mathrm{c}}$ is calculated in accordance with Table 23 and appropriate shear reinforcement is provided at sections closer to the support, no further check for such section is required.

B-5Shear

IS 456:2000, Plain and Reinforced Concrete — Code of Practice

Last Updated 29 Oct 2026

Hover any section to copy its link or text, ask Copilot about it, or bookmark it.

B-5.1 Nominal Shear Stress

The nominal shear stress $\tau_{v}$ in beams or slabs of uniform depth shall be calculated by the following equation:

$\tau_{v}=\frac{1}{b d}$

where

= shear force due to design loads,

$b \quad=$ breadth of the member, which for flanged sections shall be taken as the breadth of the web, and

= effective depth.

B-5.1.1 Beams of Varying Depth

In the case of beams of varying depth, the equation shall be modified as:

$V_{\pm}=\frac{M \tan \beta}{b d}$

where

$\tau_{y}, V, b$ and $d$ are the same as in B-5.1,
$M=$ bending moment at the section, and
$\beta=$ angle between the top and the bottom edges of the beam.

B-5.2 Design Shear Strength of Concrete

B-5.2.1

The permissible shear stress in concrete in beams without shear reinforcement is given in Table 23.

B-5.2.1.1

For solid slabs the permissible shear stress in concrete shall be $k \tau_{\mathrm{c}}$ where $k$ has the value given below:

Overall depth of slab, mm	300 or	275	250	225	200	175	150 or
Overall depth of slab, mm	more						less
k	1.00	1.05	1.10	1.15	1.20	1.25	1.30

NOTE — This does not apply to flat slabs for which 31.6 shall apply.

B-5.2.2 Shear Strength of Members Under Axial Compression

For members subjected to axial compression P, the permissible shear stress in concrete $\tau_{\mathrm{c}}$ given in Table 23, shall be multiplied by the following factor:

$\delta=1+\frac{5 P}{A_{g} f_{\mathrm{ck}}}$ , but not exceeding 1.5

where

$P=$ axial compressive force in N,
$\begin{aligned} A_{\mathrm{g}} & =\text { gross area of the concrete section in } \mathrm{mm}^{2} \\ & \text { and }\end{aligned}$
$f_{\mathrm{ck}}=$ characteristic compressive strength of concrete.

B-5.2.3 With Shear Reinforcement

When shear reinforcement is provided the nominal shear stress $\tau_{\mathrm{c}}$ in beams shall not exceed $\tau_{\mathrm{c} \max }$ given in Table 24.

Table 23 Permissible Shear Stress in Concrete

(Clauses B-2.1, B-2.3, B-4.2, B-5.2.1, B-5.2.2, B-5.3, B-5.4, B-5.5.1, B.5.5.3, B-6.3.2,B-6.3.3 and B-6.4.3 and Table 21)

100 A_t / _bd	Permissible Shear Stress in Concrete, τ_c, N/mm²
	Grade of Concrete
	M 15	M 20	M 25	M 30	M 35	M 40 and above
	(1)	(2)	(3)	(4)	(5)	(6)	(7)
≤ 0.15	0.18	0.18	0.19	0.20	0.20	0.20
0.25	0.22	0.22	0.23	0.23	0.23	0.23
0.50	0.29	0.30	0.31	0.31	0.31	0.32
0.75	0.34	0.35	0.36	0.37	0.37	0.38
1.00	0.37	0.39	0.40	0.41	0.42	0.42
1.25	0.40	0.42	0.44	0.45	0.45	0.46
1.50	0.42	0.45	0.46	0.48	0.49	0.49
1.75	0.44	0.47	0.49	0.50	0.52	0.52
2.00	0.44	0.49	0.51	0.53	0.54	0.55
2.25	0.44	0.51	0.53	0.55	0.56	0.57
2.50	0.44	0.51	0.55	0.57	0.58	0.60
2.75	0.44	0.51	0.56	0.58	0.60	0.62
3.00 and above	0.44	0.51	0.57	0.60	0.61	0.63

B-5.2.3.1

For slabs, $\tau_{y}$ shall not exceed half the value of $\tau_{\mathrm{cmax}}$ given in Table 24.

B-5.3 Minimum Shear Reinforcement

When $\tau_{\mathrm{y}}$ is less than $\tau_{\mathrm{c}}$ given in Table 23, minimum shear reinforcement shall be provided in accordance with 26.5.1.6.

B-5.4 Design of Shear Reinforcement

When $\tau_{\mathrm{v}}$ exceeds $\tau_{\mathrm{c}}$ given in Table 23, shear reinforcement shall be provided in any of the following forms:

a) Vertical stirrups,

b) Bent-up bars along with stirrups, and

c) Inclined stirrups.

Where bent-up bars are provided, their contribution towards shear resistance shall not be more than half that of the total shear reinforcement.

Shear reinforcement shall be provided to carry a shear equal to $V-\tau_{\mathrm{c}} . b d$ . The strength of shear reinforcement $V_{\mathrm{s}}$ shall be calculated as below:

a) For vertical stirrups

$V_{s}=\frac{\sigma_{\mathrm{sv}} A_{\mathrm{sv}} d}{S_{\mathrm{v}}}$

b) For inclined stirrups or a series of bars bent-up at different cross-sections:

$V_{\mathrm{s}}=\frac{\sigma_{\mathrm{sv}} A_{\mathrm{sv}} d}{s_{\mathrm{v}}}\left(\sin \alpha+\cos \alpha\right)$

c) For single bar or single group of parallel bars, all bent-up at the same cross-section:

$V_{s}=\sigma_{s v} A_{s v} \sin \alpha$

where

= total cross-sectional area of stirrup legs or bent-up bars within a distance,
$\begin{aligned} s_{v} & =\text { spacing of the stirrups or bent-up bars } \\ & \text { along the length of the member, }\end{aligned}$

$\tau_{\mathrm{c}}=$ design shear strength of the concrete,

$\begin{aligned} b & =\text { breadth of the member which for } \\ & \text { flanged beams, shall be taken as the } \\ & \text { breadth of the web } b_{w} .\end{aligned}$
$\begin{aligned} \sigma_{n v} & =\text { permissible tensile stress in shear } \\ & \text { reinforcement which shall not be taken }\end{aligned}$

greater than 230 N/mm²,

$\alpha \quad=$ angle between the inclined stirrup or bent-up bar and the axis of the member, not less than $45^{\circ}$ , and

effective depth.

B-5.5 Enhanced Shear Strength of Sections Close to Supports

B-5.5.1 General

B-5.5.2 Shear Reinforcement for Sections Close to Supports

If shear reinforcement is required, the total area of this is given by:

$A_{x}=a_{y} b\left(\tau_{y}-2 d \tau_{c} / a_{y}\right) / 0.87 f_{y} \geq 0.4 a_{y} b / 0.87 f_{y}$

This reinforcement should be provided within the middle three quarters of $a_{y}$ . Where $a_{y}$ is less than $d$ , horizontal shear reinforcement will be more effective than vertical.

Table 24 Maximum Shear Stress, $\tau_{\mathrm{cmax}}, \mathrm{N} / \mathrm{mm}^{2}$

(Clauses B-5.2.3, B-5.2.3.1, B-5.5.1 and B-6.3.1)

Concrete Grade	M 15	M 20	M 25	M 30	M 35	M 40 and above
τ_c max, N/mm²	1.6	1.8	1.9	2.2	2.3	2.5