If the column is fixed at both ends. The relation between equivalent length (l_e) and actual length (l) as per Euler's formula is:

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BHEL Engineer Trainee Mechanical 24 Aug 2023 Official Paper

Answer 1

Concept:

Euler buckling load for a column is given by,

Where, Le is the effective length of the column that depends on the end support conditions, and EI is the flexural rigidity of the column.

Now, effective length (Le) for different end conditions in terms of actual length (L) are listed in the following table:

Support Conditions	Effective length (Le)
Both ends hingedIpinned	Le = L
One end hinged other end fixed	Le = LI√2
Both ends fixed	Le = LI2
One end fixed and the other end free	Le = 2L

∴ For both ends fixed Effective length Le = 0.5 L