A solid shaft is subjected to the torque T, which causes the material to yield. If the

Chapter 5, Problem 5-126

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A solid shaft is subjected to the torque T, which causes the material to yield. If the material is elastic plastic, show that the torque can be expressed in terms of the angle of twist \(\phi\) of the shaft as \(T=\frac{4}{3} T_Y\left(1-\phi_Y^3 / 4 \phi^3\right)\), where \(T_Y\) and \(\phi_Y\) are the torque and angle of twist when the material begins to yield.

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