Meaning
Internal force distribution resulting from a twisting moment applied to a structural member acts parallel to the cross sectional area.
Shear Calculation
Shear stress magnitude depends on the applied torque, the distance from the center and the polar moment of inertia of the section. For a hollow tube the torsional shear stress is more uniformly distributed which makes it a more efficient shape for transmitting power. Designers use these formulas to select the correct material and diameter for automotive drivetrains.
Metals Response
Metals typically fail in shear when the applied torsional shear stress exceeds the shear yield strength of the alloy. In brittle materials the failure often occurs along a forty five degree angle because the maximum tensile stress is oriented in that direction. Ductile materials show a characteristic flat break perpendicular to the axis where the microstructural shear reaches its limit.
Fatigue Safety
Fatigue analysis must account for the cyclic nature of torsional shear stress in rotating machinery. Fluctuations in torque can lead to the initiation of cracks even if the peak stress is well below the yield point. Using surface treatments like nitriding or rolling can increase the resistance to these stresses and extend the operational life of the part.
