The crippling load for a direction - fixed strut is

Question

Question

This question was previously asked in

BPSC AE Paper 4 (General Engineering Science) 10 Nov 2022 Official Paper

four times that of a strut with one end direction -fixed and other end free for the same length
directly proportional to the square of the length of strut
three times that of a strut with one end fixed and other pinned
four times that of a pin - ended strut for the same length

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

The crippling load for a direction - fixed strut is four times that of a pin - ended strut for the same length.