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Euler's formula for Buckling Load of a column with both ends hinged is:

Where E = Young's modulus, I = moment of inertia, L = effective length

  • A.\(\frac{\pi^{2}EI}{L^{2}}\)
  • B.\(\frac{\pi E^{2}I}{L^{2}}\)
  • C.\(\frac{\pi^{2}EI^{2}}{L^{2}}\)
  • D.\(\frac{\pi^{2}E^{2}I}{L^{2}}\)

Answer: A

Euler's buckling load for a column with both ends hinged is \(\frac{\pi^{2}EI}{L^{2}}\).

Euler's critical load is \(P_{cr} = \frac{\pi^{2}EI}{L_{e}^{2}}\), where \(L_{e}\) is the effective length. For both ends hinged \(L_{e} = L\), giving \(\frac{\pi^{2}EI}{L^{2}}\).

The other options square E or I or drop a power of \(\pi\). The load is directly proportional to the flexural rigidity EI, not to its square.

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