The torsional coupling in the figure is composed of a curved beam of square cross section that is welded to an input shaft and output

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The torsional coupling in the figure is composed of a curved beam of square cross section that is welded to an input shaft and output plate. A torque is applied to the shaft and cycles from zero to T. The cross section of the beam has dimensions of 5 by 5 mm, and the centroidal axis of the beam describes a curve of the form r = 20 + 10 θ/π, where r and θ are in mm and radians, respectively (0 ≤ θ ≤ 4π). The curved beam has a machined surface with yield and ultimate strength values of 420 and 770 MPa, respectively.
(a) Determine the maximum allowable value of T such that the coupling will have an infinite life with a factor of safety, n = 3, using the modified Goodman criterion. (b) Repeat part (a) using the Gerber criterion.
(c) Using T found in part (b), determine the factor of safety guarding against yield.