Euler's Theory of failure : ( BUCKLING FAILURE)

Euler's theory is not valid for short column because in short column, crushing occurs before buckling. For validity of Euler's theory buckling should occur before crushing, it means slenderness ratio should be greater than or equal to critical slenderness ratio.

Assumptions:

Material is isotropic, homogeneous and linearly elastic in which Hook's law is valid.
The plane cross section remains plane before and after of application
Column under the analysis is assumed to be a long column.
The failure of the column is assumed to be due to buckling.
Before loading column is perfectly straight.
Weight of column is neglected.
The load is perfectly axial and passes through the centroid of the column section

Here, E = Young's modulus
I = minimum moment of inertia about traverse axis
L= effective length or equivalent length of column

Effective length is defined as distance between two adjacent points of zero bending moment or contra flexure.

Slenderness ratio is defined as the effective length divided by the least radius of gyration.

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