A structural member loaded axially in compression is generally called a compression member. Vertical compression members in buildings are called columns, posts or stanchions. A compression member in roof trusses is called struts and in a crane is called a boom.

compression member

Columns which are short are subjected to crushing and behave like members under pure compression. Columns which are long tend to buckle out of the plane of the load axis.


Euler’s formula for critical load for a pin-ended column subjected to axial load is

critical load for columns

Where, L = length of column between the hinged ends,

E = modulus of elasticity, and

I = moment of inertia of the column section.

The column will become unserviceable if the loads are larger than clip_image006. In the Euler equation, it is assumed that stress is proportional to strain, therefore,

Critical Stress =

critical stress in columns

Where, A= area of cross-section, and

r = radius of gyration about the bending axis

clip_image010= slenderness ratio


Columns with length L and effective length clip_image012 are shown in figure below:

End conditions in columns and their critical load

Strength of an Axially Loaded Compression Members

Maximum axial compression load permitted on a compression member,


Where, P = axial compressive load (N),

clip_image018 = permissible stress in axial compression (MPa)

A = effective cross-sectional area of the member clip_image020

Indian Standard IS 800: 1984

It stipulates that the direct stress on the cross-sectional area of axially loaded compression members should not exceed clip_image022 nor the permissible stress calculated using Merchant – Rankine formula.

Permissible stress in axial compression (MPa):

permissible stress in compression in steel

Where clip_image026 = yield stress of steel in MPa

clip_image028 = elastic critical stress in compression = clip_image030

clip_image032= slenderness ratio of the member

Where, clip_image012[1]= effective length of the member

r = appropriate radius of gyration of the member

E = modulus of elasticity = 200000 MPa, and

n = a factor assumed as 1.4