What is unsupported length and effective length of a column?

A column is a vertical structural member.
Its primary role is to transfer load from top to bottom.

In a framed structure, columns carry loads from slabs, beams, and upper floors.
These loads are safely transferred to the foundation.

Columns mainly resist compressive forces.
Their cross-sections are commonly square rectangular or circular.

Unsupported Length of a Column

Definition: The unsupported length $l$ of a column is the clear distance between two lateral supports.
Physical Meaning: It is the actual length of the column that is free to buckle.
Design Importance: Unsupported length directly affects column stability.

Definition: The effective length $l_{eff}$ is the design length used to study buckling behavior.
Design Role: It represents the length of an equivalent pin-ended column with the same buckling capacity.
Key Insight: The effective length $l_{eff}$ is not necessarily equal to the physical length $l$ .
Dependence on End Conditions: The value of $l_{eff}$ depends on end restraints against rotation and translation.
Codal Relation: As per IS 456 : 2000

leff=k ll_{eff} = k,lleff=kl

Sl. No.	Degree of End Restraint	Theoretical $l_{eff}$	Recommended $l_{eff}$
1	Restrained against rotation at both ends and effectively held in position	$0.50l$	$0.65l$
2	Restrained against rotation at one end and effectively held in position	$0.70l$	$0.80l$
3	Not restrained against rotation at both ends but effectively held in position	$1.0l$	$1.0l$
4	One end restrained and held other end restrained but not held	$1.0l$	$1.20l$
5	One end held and restrained other end partially restrained but not held	—	$1.5l$
6	One end held but not restrained other end restrained but not held	$2.0l$	$2.0l$
7	One end held and restrained other end neither held nor restrained	$2.0l$	$2.0l$

Buckling Behavior: Buckling depends on $l_{eff}$ not on actual length.
Load-Carrying Capacity: Increase in $l_{eff}$ reduces axial load capacity.
Slenderness Ratio:

Slenderness ratio=leffD\text{Slenderness ratio} = \frac{l_{eff}}{D}Slenderness ratio=Dleff
Design Safety: Incorrect estimation of $l_{eff}$ can lead to unsafe column behavior.

Column: Vertical member transferring compressive loads.
Unsupported Length ( $l$ ): Physical clear length.
Effective Length ( $l_{eff}$ ): Governs buckling and stability.
End Restraints: Control the magnitude of $l_{eff}$ .
Codal Guidance: IS 456 specifies recommended effective length factors.
Engineering Insight: Column design is governed more by instability than crushing.