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 ds be the diameter of the shaft at which yielding is reached according to the maximum shear-stress criterion. Also let deps be the diameter of the shaft at which yielding is reached according to the maximum principal strain criterion.

a. Derive an expression for the ratio deps/ds as a function of the applied load ratio T/M. Assume that Poisson’s ratio ν is nonzero.

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b. Plot the expression for deps/ds over the range of T/M from 0.01 to 100 for ν = 0.0, 0.25, and 0.40.

FIGURE 4.22 Comparison of criteria of failure.