Discussion
The minimum axial compressive load, P, required to initiate buckling for a pinned-pinned slender column with bending stiffness EI and length L is
Answer: B
The critical load is \(P = \dfrac{\pi^{2}EI}{L^{2}}\).
Euler's buckling load is \(P = \dfrac{\pi^{2}EI}{L_{e}^{2}}\), where the effective length \(L_{e}\) depends on the end conditions. For a column pinned at both ends \(L_{e} = L\), which gives the result above.
The other options belong to other end conditions. \(\pi^{2}EI/4L^{2}\) is for a column fixed at one end and free at the other (\(L_{e} = 2L\)). \(4\pi^{2}EI/L^{2}\) is for both ends fixed (\(L_{e} = L/2\)). \(3\pi^{2}EI/4L^{2}\) matches no standard case.
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