This worked example demonstrates how to calculate the maximum shear stress and angle of twist in a solid circular shaft when subjected to a twisting moment (torque). This is fundamental to mechanical engineering shaft design.
A solid steel shaft has a radius of 0.02 m, a length of 1.5 m, and a shear modulus . It transmits a torque of . Calculate the maximum shear stress () and the angle of twist ().
Step 1: Calculate Polar Moment of Inertia (J)
mechanics-torsion not found in the Formula Registry.Step 2: Calculate Maximum Shear Stress ()
mechanics-torsion not found in the Formula Registry.Step 3: Calculate Angle of Twist ()
mechanics-torsion not found in the Formula Registry.The maximum shear stress is MPa, which the engineer must compare against the material's shear yield strength to prevent failure. Furthermore, the angle of twist is degrees. If this angle is too large, it might affect the precision of the machinery, and the shaft diameter would need to be increased.