Solve Example 7.15 using the Tsai-Hill criterion instead of the maximum stress criterion. That is, determine the largest torque \(T\) that can be transmitted by the shaft without failure, according to the Tsai-Hill criterion. Also indicate which plies fail first (i.e., the \(+45^{\circ}\) or the \(-45^{\circ}\) plies), according to the Tsai-Hill criterion. You may use any relevant results from Examples 7.15 and 7.5 without repeating their derivations, but you must clearly explain your analysis procedure.

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EXAMPLE 7.15 The composite power transmission shaft shown in Figure 7.44 has mean radius R = 50 mm and wall thickness t = 1 mm. The material is filament- wound AS/3501 carbon/epoxy, and the wall of the shaft has a symmet- ric angle-ply [+45/-45/-45/+45] lay-up sequence (same as the material in Example 7.5) for maximum torsional stiffness. Determine the largest torque T that can be transmitted by the shaft without failure, according to the maximum stress criterion.