39limit state of collapse: compression

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

Last Updated 29 Oct 2026

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39.1 Assumptions

In addition to the assumptions given in 38.1 (a) to 38.1 (e) for flexure, the following shall be assumed:

a) The maximum compressive strain in concrete in axial compression is taken as 0.002.
b) The maximum compressive strain at the highly compressed extreme fibre in concrete subjected to axial compression and bending and when there is no tension on the section shall be 0.0035 minus 0.75 times the strain at the least compressed extreme fibre.

39.2 Minimum Eccentricity

All members in compression shall be designed for the minimum eccentricity in accordance with25.4. Where

calculated eccentricity is larger, the minimum eccentricity should be ignored.

39.3 Short Axially Loaded Members in Compression

The member shall be designed by considering the assumptions given in 39.1 and the minimum eccentricity. When the minimum eccentricity as per 25.4 does not exceed 0.05 times the lateral dimension, the members may be designed by the following equation:

following equation: $P_{\mathrm{o}}=0.4 f_{\mathrm{ck}} \cdot A_{\mathrm{c}}+0.67 f_{y} \cdot A_{\mathrm{sc}}$

where
$P_{u}=$ axial load on the member,
= characteristic compressive strength of the concrete,
$A_{\mathrm{c}}=$ Area of concrete,
$f_{y}=$ characteristic strength of the compression reinforcement, and
= area of longitudinal reinforcement for columns.

39.4 Compression Members with Helical Reinforcement

The strength of compression members with helical reinforcement satisfying the requirement of 39.4.1 shall be taken as 1.05 times the strength of similar member with lateral ties.

39.4.1

The ratio of the volume of helical reinforcement to the volume of the core shall not be less than $0.36\left(A_{s} / A_{c}-1\right) f_{\mathrm{c}} / f_{y}$

where

$A_{\mathrm{g}}=$ gross area of the section,
$A_{\mathrm{c}}=$ area of the core of the helically reinforced column measured to the outside diameter of the helix,
$f_{\mathrm{ck}}=$ characteristic compressive strength of the concrete, and

= characteristic strength of the helical reinforcement but not exceeding 415 N/mm².

39.5 Members Subjected to Combined Axial Load and Uniaxial Bending

A member subjected to axial force and uniaxial bending shall be designed on the basis of 39.1 and 39.2.

NOTE— The design of member subject to combined axial load and uniaxial bending will involve lengthy calculation by trial and error. In order to overcome these difficulties interaction diagrams may be used. These have been prepared and published by BIS in 'SP : 16 Design aids for reinforced concrete to IS 456'.

39.6 Members Subjected to Combined Axial Load and Biaxial Bending

The resistance of a member subjected to axial force and biaxial bending shall be obtained on the basis of assumptions given in 39.1 and 39.2 with neutral axis so chosen as to satisfy the equilibrium of load and moments about two axes. Alternatively such members may be designed by the following equation:

$\left[\frac{M_{u x}}{M_{u x l}}\right]^{a_{x}}+\left[\frac{M_{u y}}{M_{u y l}}\right]^{a_{y}} \leq 1.0$

where

$M_{u x}, M_{u y}$ = moments about $x$ and $y$ axes due to design loads,
$M_{u x l}, M_{u y l}=$ maximum uniaxial moment capacity for an axial load of $P_{u}$ , bending about $x$ and $y$ axes respectively, and

$\alpha_{\mathrm{n}}$ is related to $P_{\mathrm{u}} / P_{\mathrm{uz}}$

where $P_{u z}=0.45 f_{c k} \cdot A_{c}+0.75 f_{y} \cdot A_{s c}$

For values of $P_{\mathrm{u}} / P_{\mathrm{uz}}=0.2$ to 0.8 , the values of $\alpha_{\mathrm{u}}$ vary linearly from 1.0 to 2.0 . For values less than 0.2, $\alpha_{\mathrm{u}}$ is 1.0 ; for values greater than 0.8, $\alpha_{\mathrm{u}}$ is 2.0 .

39.7 Slender Compression Members

The design of slender compression members (see 25.1.1) shall be based on the forces and the moments determined from an analysis of the structure, including the effect of deflections on moments and forces. When the effect of deflections are not taken into account in the analysis, additional moment given in 39.7.1 shall be taken into account in the appropriate direction.

39.7.1

The additional moments $M_{a x}$ and $M_{a y}$ shall be calculated by the following formulae:

$M_{\mathrm{ax}}=\frac{P_{u} D}{2000}\left\{\frac{l_{\mathrm{ex}}}{D}\right\}$
$M_{a y}=\frac{P_{u} b}{2000}\left\{\frac{l_{e y}}{b}\right\}^{2}$

where

$P_{\mathrm{u}}=$ axial load on the member,
= effective length in respect of the major axis,
= effective length in respect of the minor axis,
$D=$ depth of the cross-section at right angles to the major axis, and

= width of the member.

For design of section, 39.5 or 39.6 as appropriate shall apply.

NOTES

1 A column may be considered braced in a given plane if lateral stability to the structure as a whole is provided by walls or bracing or buttressing designed to resist all lateral forces in that plane. It should otherwise be considered as unbraced.
2 In the case of a braced column without any transverse loads occurring in its height, the additional moment shall be added to an initial moment equal to sum of 0.4 $M_{u 1}$ and $0.6 M_{u 2}$ where $M_{u 2}$ is the larger end moment and $M_{u 1}$ is the smaller end moment (assumed negative if the column is bent in double curvature). In no case shall the initial moment be less than $0.4 M_{u 2}$ nor the total moment including the initial moment be less than $M_{u 2}$ . For unbraced columns, the additional moment shall be added to the end moments.
3 Unbraced compression members, at any given level or storey, subject to lateral load are usually constrained to deflect equally. In such cases slenderness ratio for each column may be taken as the average for all columns acting in the same direction.

39.7.1.1

The values given by equation 39.7.1 may be multiplied by the following factor:

$k=\frac{P_{u z}-P_{u}}{P_{u z}-P_{b}} \leq 1$

where

= axial load on compression member,
$P_{\mathrm{ur}}=$ as defined in 39.6, and
$\begin{aligned} P_{\mathrm{h}} & =\text { axial load corresponding to the condition } \\ & \text { of maximum compressive strain of } \\ & 0.00035 \text { in concrete and tensile strain of } \\ & 0.0002 \text { in outer most layer of tension steel. }\end{aligned}$

39limit state of collapse: compression

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.

39.1 Assumptions

In addition to the assumptions given in 38.1 (a) to 38.1 (e) for flexure, the following shall be assumed:

a) The maximum compressive strain in concrete in axial compression is taken as 0.002.
b) The maximum compressive strain at the highly compressed extreme fibre in concrete subjected to axial compression and bending and when there is no tension on the section shall be 0.0035 minus 0.75 times the strain at the least compressed extreme fibre.

39.2 Minimum Eccentricity

All members in compression shall be designed for the minimum eccentricity in accordance with25.4. Where

calculated eccentricity is larger, the minimum eccentricity should be ignored.

39.3 Short Axially Loaded Members in Compression

following equation: $P_{\mathrm{o}}=0.4 f_{\mathrm{ck}} \cdot A_{\mathrm{c}}+0.67 f_{y} \cdot A_{\mathrm{sc}}$

where
$P_{u}=$ axial load on the member,
= characteristic compressive strength of the concrete,
$A_{\mathrm{c}}=$ Area of concrete,
$f_{y}=$ characteristic strength of the compression reinforcement, and
= area of longitudinal reinforcement for columns.

39.4 Compression Members with Helical Reinforcement

The strength of compression members with helical reinforcement satisfying the requirement of 39.4.1 shall be taken as 1.05 times the strength of similar member with lateral ties.

39.4.1

The ratio of the volume of helical reinforcement to the volume of the core shall not be less than $0.36\left(A_{s} / A_{c}-1\right) f_{\mathrm{c}} / f_{y}$

where

$A_{\mathrm{g}}=$ gross area of the section,
$A_{\mathrm{c}}=$ area of the core of the helically reinforced column measured to the outside diameter of the helix,
$f_{\mathrm{ck}}=$ characteristic compressive strength of the concrete, and

= characteristic strength of the helical reinforcement but not exceeding 415 N/mm².

39.5 Members Subjected to Combined Axial Load and Uniaxial Bending

A member subjected to axial force and uniaxial bending shall be designed on the basis of 39.1 and 39.2.

39.6 Members Subjected to Combined Axial Load and Biaxial Bending

$\left[\frac{M_{u x}}{M_{u x l}}\right]^{a_{x}}+\left[\frac{M_{u y}}{M_{u y l}}\right]^{a_{y}} \leq 1.0$

where

$M_{u x}, M_{u y}$ = moments about $x$ and $y$ axes due to design loads,
$M_{u x l}, M_{u y l}=$ maximum uniaxial moment capacity for an axial load of $P_{u}$ , bending about $x$ and $y$ axes respectively, and

$\alpha_{\mathrm{n}}$ is related to $P_{\mathrm{u}} / P_{\mathrm{uz}}$

where $P_{u z}=0.45 f_{c k} \cdot A_{c}+0.75 f_{y} \cdot A_{s c}$

39.7 Slender Compression Members

39.7.1

The additional moments $M_{a x}$ and $M_{a y}$ shall be calculated by the following formulae:

$M_{\mathrm{ax}}=\frac{P_{u} D}{2000}\left\{\frac{l_{\mathrm{ex}}}{D}\right\}$
$M_{a y}=\frac{P_{u} b}{2000}\left\{\frac{l_{e y}}{b}\right\}^{2}$

where

$P_{\mathrm{u}}=$ axial load on the member,
= effective length in respect of the major axis,
= effective length in respect of the minor axis,
$D=$ depth of the cross-section at right angles to the major axis, and

= width of the member.

For design of section, 39.5 or 39.6 as appropriate shall apply.

NOTES

1 A column may be considered braced in a given plane if lateral stability to the structure as a whole is provided by walls or bracing or buttressing designed to resist all lateral forces in that plane. It should otherwise be considered as unbraced.
2 In the case of a braced column without any transverse loads occurring in its height, the additional moment shall be added to an initial moment equal to sum of 0.4 $M_{u 1}$ and $0.6 M_{u 2}$ where $M_{u 2}$ is the larger end moment and $M_{u 1}$ is the smaller end moment (assumed negative if the column is bent in double curvature). In no case shall the initial moment be less than $0.4 M_{u 2}$ nor the total moment including the initial moment be less than $M_{u 2}$ . For unbraced columns, the additional moment shall be added to the end moments.
3 Unbraced compression members, at any given level or storey, subject to lateral load are usually constrained to deflect equally. In such cases slenderness ratio for each column may be taken as the average for all columns acting in the same direction.

39.7.1.1

The values given by equation 39.7.1 may be multiplied by the following factor:

$k=\frac{P_{u z}-P_{u}}{P_{u z}-P_{b}} \leq 1$

where

= axial load on compression member,
$P_{\mathrm{ur}}=$ as defined in 39.6, and
$\begin{aligned} P_{\mathrm{h}} & =\text { axial load corresponding to the condition } \\ & \text { of maximum compressive strain of } \\ & 0.00035 \text { in concrete and tensile strain of } \\ & 0.0002 \text { in outer most layer of tension steel. }\end{aligned}$