The pulleys fixed to the shaft are loaded as shown. If the journal bearings at \(A\) and \(B\) exert only horizontal and vertical forces on the shaft, determine the required diameter of the shaft to the nearest \(\frac{1}{8}\) in. Use the maximum distortion energy theory of failure, \(\sigma_{\text {allow }}=20 \mathrm{ksi}\).

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150 lb 250 lb A B 0.5 ft 0.5 ft 1 ft -5 ft 2 ft. 250 lb 150 lb