If a column is fixed at one end and free at the other end, the effective length is ______ the original length.

Question

Question

This question was previously asked in

NHPC JE Mechanical 6 April 2022 (Shift 2) Official Paper

Answer 1

Explanation:

Buckling load:
The load at which column buckle is termed as buckling load. Buckling load is given by:

\({P_b} = \frac{{{\pi ^2}EI}}{{L_e^2}}\)
where E = Young's modulus of elasticity, Imin = Minimum moment of inertia, and Le = Effective length

End conditions	Le	Buckling load
Both ends hinged	Le = L	\({P_b} = \frac{{{\pi ^2}EI}}{{L_e^2}}\)
Both ends fixed	Le = L/2	\({P_b} = \frac{{{4\pi ^2}EI}}{{L_e^2}}\)
One end fixed and another end is free	Le = 2L	\({P_b} = \frac{{{\pi ^2}EI}}{{4L_e^2}}\)
One end fixed and another end is hinged	\({L_e} = \frac{L}{{\sqrt 2 }}\)	\({P_b} = \frac{{{\pi ^2}EI}}{{2L_e^2}}\)