The distribution of shear stress σxy in a torsion member of circular cross section is give...

The distribution of shear stress σxy in a torsion member of circular cross section is given by

where T denotes torque, J is the polar moment of inertia of the cross section, and ρ is the radial coordinate from the center O of the cross section to an interior point in the cross section. By Eqs. 5.6, 5.7, and (a), show that the strain energy UT of torsion is

 (5.6)

 (5.7)