The equivalent length of a column fixed at both ends is _______. (Length of the calumn is L)

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Question

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JKSSB JE Mechanical 02 Nov 2021 Shift 1 Official Paper

Answer 1

Concept:

Euler buckling load for a column is given by,

\({{\rm{P}}_{\rm{E}}}{\rm{\;}} = {\rm{\;}}\frac{{{{\rm{\pi }}^2}{\rm{EI}}}}{{{\rm{L}}_{\rm{e}}^2}}\)

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 hinged/pinned	Le = L
One end hinged other end fixed	Le = L/√2
Both ends fixed	Le = L/2
One end fixed and the other end free	Le = 2L

∴ For both ends fixed Effective length Le = 0.5 L