Multiple choice

A long structural column (length = L) with both ends hinged is acted upon by an axial compressive load P. The differential equation governing the bending of column is given by $Ei \frac{d^2y}{dx^2} = - py$where y is the structural lateral deflection and EI is the flexural rigidity. The first critical load on column responsible for its buckling is given by

  1. $\pi^2 EI/L^2$
  2. $\\sqrt{2} \pi^2 EI/L^2$
  3. $2 \pi^2 EI/L^2$
  4. $4 \pi^2 EI/L^2$
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A Correct answer
Explanation

The governing differential equation for a column with hinged ends leads to the Euler buckling load formula. For both ends hinged, the effective length is equal to the actual length L, resulting in P_cr = pi^2 * EI / L^2.

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