Discussion
According to Euler's formula, the bending load 'P' for a column of length 'l' with both ends hinged (I = least moment of inertia of the section of the column, E = Young's modulus of the material ) of the column is :
Answer: D
For a column with both ends hinged, the Euler load is \(\frac{\pi^{2}EI}{l^{2}}\).
Euler's formula is \(P = \frac{\pi^{2}EI}{l_{e}^{2}}\), where the effective length \(l_{e}\) depends on the end conditions. With both ends hinged (pinned), the column bends in a single half sine wave and \(l_{e} = l\).
The other options are other end conditions or errors. With both ends fixed, \(l_{e} = l/2\), giving \(\frac{4\pi^{2}EI}{l^{2}}\). With one end fixed and the other free, \(l_{e} = 2l\), giving \(\frac{\pi^{2}EI}{4l^{2}}\). \(\frac{2\pi^{2}EI}{l}\) is dimensionally wrong; the fixed-hinged case is \(\frac{2\pi^{2}EI}{l^{2}}\).
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