The joists of a floor in a warehouse are to be selected using square timber beams made of oak. If each beam is to be designed to carry \(90 \mathrm{lb} / \mathrm{ft}\) over a simply supported span of \(25 \mathrm{ft}\), determine the dimension \(a\) of its square cross section to the nearest \(\frac{1}{4}\) in. The allowable bending stress is \(\sigma_{\text {allow }}=14 \mathrm{ksi}\) and the allowable shear stress is \(\tau_{\text {allow }}=125\) psi.

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90 lb/ft 25 ft