DESIGN OF STEEL COMPRESSION MEMBERS
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.
Euler’s formula for critical load for a pin-ended column subjected to axial load is
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 
. In the Euler equation, it is assumed that stress is proportional to strain, therefore,
Critical Stress =
Where, A= area of cross-section, and
r = radius of gyration about the bending axis
= slenderness ratio
Columns with length L and effective length 
are shown in figure below:
Maximum axial compression load permitted on a compression member,
Where, P = axial compressive load (N),
= permissible stress in axial compression (MPa)
A = effective cross-sectional area of the member 
Indian Standard IS 800: 1984
It stipulates that the direct stress on the cross-sectional area of axially loaded compression members should not exceed 
nor the permissible stress calculated using Merchant – Rankine formula.
Permissible stress in axial compression (MPa):
Where 
= yield stress of steel in MPa
= elastic critical stress in compression = 
= slenderness ratio of the member
Where, 
= 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
EFFECTIVE LENGTH OF COMPRESSION MEMBER
Table below gives the values of effective length recommended by the Indian Standard, IS 800. The actual length L of the compression member should be taken as the length from centre-to-centre of intersection of supporting members or the cantilevered length in the case of free standing struts.
Table: Equivalent length for various end conditions
| Type
| Effective length of member l
|
1
| Effectively held in position and restrained in direction at both ends.
| 0.67 L
|
2
| Effectively held in position at both ends restrained in direction at one end.
| 0.85 L
|
3
| Effectively held in position at both ends but not restrained in direction.
| L
|
4
| Effectively held in position and restrained in direction at one end and at the other end effectively restrained in direction but not held in position.
| L
|
5
| Effectively held in position and restrained in direction at one end and the other end partially restrained in direction but not held in position.
| 1.5 L
|
6
| Effectively held in position and restrained in direction at one end but not held in position or restrained in direction at the other end.
| 2.0 L
|
Note: