(Solution) - A cylindrical pressure vessel with flat ends is subjected to -(2025 Original AI-Free Solution)

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A cylindrical pressure vessel with flat ends is subjected to a torque T and a bending moment M (see figure). The outer radius is 12.0 in. and the wall thickness is 1.0 in. The loads are as follows: T = 800 k-in., M = 1000 k-in., and the internal pressure p = 900 psi.
Determine the maximum tensile stress (t, maximum compressive stress (c, and maximum shear stress Tmax in the wall of the cylinder.