Effective length of Column- Under Different condition of Fixed-Rotation

The effective length of the column is defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

It depends on the boundary conditions of the column. A pin ended elastic column has a bulked configuration of a sinusoidal wave. The distance between the contra flexure is critical in evaluating the stability of the column.

The effective length given in the code is generally greater than the theoretical values, as full rigidity at supports is difficult, if not possible, to achieve.

According to table 28 of IS code 456:2000, the effective length of the column for different end conditions are shown below:

Effective length of Column

Effective length of Column- Table

S.NDegree of End restrain of
compressive number
Theoretical value of effective lengthRecommended value of effective length
1)Effectively held in position and restrained against rotation in both ends.0.50L0.65L
2)Effectively held in position at both ends restrained against rotation at one end.    0.70L0.80 L
3)Effectively held in position at both ends but not restrained against rotation.  1.00L1.00L
4)Effectively held in position and restrained against rotation at one end, and at the other restrained against rotation but not held in position.1.00L1.00L
5)Effectively held in position and restrained against rotation at one end, and at the other partially restrained against rotation but not held in position.
_
1.50L
6)Effectively held in position at one end but not restrained against rotation and at the other end restrained against rotation but not held in position.  2.00L2.00L
7)Effectively held in position and restrained against rotation at one end but not held in position nor restrained against rotation at the other end.  2.00L2.00L
Effective length of Column
Effective length of Column
Effective length of Column

Theoretical analysis is used in the idealized end restraints, whose translational and rotational stiffness are set to rather zero or infinity.

In this case, it may be acceptable for the designer to assume a column has these idealized end restraint conditions, especially for preliminary design purposes when a more rigorous analysis is to follow but care is needed due to the substantial influence that end restraints have on the buckling capacity.

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