Discussion
The same column cantilevered, fixed at one end and free at the other, would carry nearest to
Answer: D
A cantilever, fixed at one end and free at the other, has effective length \( L_{e} = 2L \): \[ P_{cr} = \frac{\pi^{2} EI}{(2L)^{2}} = \frac{\pi^{2} EI}{4L^{2}} = \frac{1}{4} \times \frac{\pi^{2} EI}{L^{2}} \] \[ = \frac{691}{4} = 173 \ \mathrm{kN} \] This is the weakest of the standard end conditions, a quarter of the pinned value and one sixteenth of the fixed-fixed value.
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