Column A has both its ends fixed, and column B has one end fixed and the other end free. The ratio of the buckling load of column A to that of column B is:

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Question

This question was previously asked in

HPCL Engineer Mechanical 04 Nov 2022 Official Paper (Shift 2)

Answer 1

Concept:

End Condition	Both end hinged	One end fixed other free	Both end fixed	One end fixed and other hinged
Effective length (Le)	L	2L	1/2	\(\frac{L}{{\sqrt 2 }}\)

Crippling load:

\(P = \frac{{{\pi ^2}EI}}{{L_e^2}}\)

Calculation:

Both end fixed for the column A,

Le = L/2

One end fixed and the other end free column B,

Le = 2L

2 - both ends fixed: Le1 = L/2

\(\frac{{{P_A}}}{{{P_B}}} = \left( {\frac{{{L_{eB}}}}{{{L_{eA}}}}} \right)_{eff}^2 = {\left( {\frac{{2L}}{{L/2}}} \right)^2}=16\)

P1: P2 = 16 : 1