Discussion
If that column's ends are fully fixed instead of pinned, its critical load becomes nearest to
Answer: C
Fully fixed ends give an effective length \( L_{e} = 0.5L \), and the critical load varies inversely with \( L_{e}^{2} \): \[ P_{cr} = \frac{\pi^{2} EI}{(0.5L)^{2}} = \frac{\pi^{2} EI}{0.25 L^{2}} = 4 \times \frac{\pi^{2} EI}{L^{2}} \] \[ = 4 \times 691 = 2764 \ \mathrm{kN} \] Real end fittings never achieve full fixity, so the whole fourfold gain is not realised in practice; design codes use an effective-length factor above 0.5 for that reason.
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