A 20-ft-long column is made of aluminum alloy 2014-T6. If it is pinned at its top and bottom, and a compressive force \(\mathbf{P}\) is applied at point \(A\), determine the maximum allowable magnitude of \(\mathbf{P}\) using the equations of Sec. 13.6 and the interaction formula with \(\left(\sigma_{b}\right)\) allow \(=20 \mathrm{ksi}\).

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5.25 in. x- 0.5 in.- 10 in. A. P x 10 in. 0.5 in. 0.5 in.