Multiple choice

A pin-ended column of length L, modulus of elasticity E and second moment of the cross-sectional area I is loaded centrically by a compressive load P. The critical buckling load $|(P_{cr})|$ is given by

  1. $P_{cr}=\frac{EI}{x^2L^2}$
  2. $P_{cr}=\frac{x^2EI}{3L^2}$
  3. $P_{cr}=\frac{\pi EI}{L^2}$
  4. $P_{cr}=\frac{x^2EI}{L^2}$
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D Correct answer
Explanation

$\text{Here both ends are hinged,}\\ So,\hspace{2.6cm}C=1\\ \text{Substitute in equation(i), we get} \\ \hspace{3cm}P_{cr}=\frac{\pi^2EI}{L^2}$

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