A solid cylindrical shaft of diameter d is subjected to constant bending moment M and torq...

A solid cylindrical shaft of diameter d is subjected to constant bending moment M and torque T (see Figure 4.22). Let dsbe the diameter of the shaft at which yielding is reached according to the maximum shear-stress criterion. Also let dVM be the diameter of the shaft at which yielding is reached according to the von Mises criterion.

a. Derive an expression for the ratio dVM/dsas a function of the applied load ratio T/M.

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b. Plot the expression for dVM/ds over the range of T/M from 0.01 to 1000.

FIGURE 4.22 Comparison of criteria of failure.