To use the torsion formula to relate the torque applied to a rod of circular cross section to the maximum shear stress in the rod. Part A- Maximum stress When a torque T is applied to a shaft with a circular cross section, the shaft will deform by twisting about its longitudinal axis. For small deflections, the radial lines will remain straight and the oross sections will remain planar and paralel. The shear strain within the shaft will vary linearly along any radial ine (Eigure 1) A cross section of a solid circular rod is subject to a torque of T- 23 kN m. If the diameter of the rod is D8 cm , what is the maximum shear stress? Express your answer with appropriate units to three significant figures. If the material is homogenous and elastic, then the shear stress will also vary linearly along any radal Ine as long as the maximum shear stress is no greater than the proportional imit for the material Since the shear stress varies inearly, the maximum will occur on the outer boundary of the cross section > View Available Hint(s) The shear stress r at a point on the cross section is related to the torque at the section by T=. where p is the distance of the point from the central axis and J is called the polar moment of inertia of the cross-sectional area. For a solid circular shaft J=e, where e is the shaft radius. For a circular tube with inner radius e and outer radius Ce, the polar moment of inertia is J-(-e). Value Units Submit • Part B- Torque The maximum stress in a section of a circular tube subject to a torque is T 37 MPa. If the inner diameter is D, -5 cm and the outer diameter is D.7 cm, what is the torque on the section? Express your answer with appropriate units to three significant figures. View Available Hint(s) O DI ? T- Value Units Submit Provide Feedback Next