Learning Goal: To use the torsion formula to relate the torque applied to a rod of circular cross section to the maximum

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Learning Goal To Use The Torsion Formula To Relate The Torque Applied To A Rod Of Circular Cross Section To The Maximum 1 (160.75 KiB) Viewed 54 times

Learning Goal: 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. 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 cross sections will remain planar and parallel. The shear strain within the shaft will vary linearly along any radial line.(Figure 1) If the material is homogenous and elastic, then the shear stress will also vary linearly along any radial line as long as the maximum shear stress is no greater than the proportional limit for the material. Since the shear stress varies linearly, the maximum will occur on the outer boundary of the cross section. The shear stress T at a point on the cross section is Tp related to the torque at the section by T = J.where p is the distance of the point from the central axis and J is called the polar moment of inertia of the cross- πT 4 sectional area. For a solid circular shaft J: Z€², where c is the shaft radius. For a circular tube with inner radius c; and outer radius co, the polar moment of inertia is J = -(co-c²). π 2 Figure T < 1 of 1 > Part A - Maximum stress A cross section of a solid circular rod is subject to a torque of T = 2.2 kN m. If the diameter of the rod is D = 7 cm, what is the maximum shear stress? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) μÅ A ? Tmax= 35.75 MPa Submit Previous Answers X Incorrect; Try Again; 2 attempts remaining Part B - Torque The maximum stress in a section of a circular tube subject to a torque is Tmax = 27 MPa. If the inner diameter is D; = 3.25 cm and the outer diameter is Do = 4.25 cm, what is the torque on the section? Express your answer with appropriate units to three significant figures. ► View Available Hint(s) НА =)? T= Value Units Submit Provide Feedback Next >