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 3/16 × 3/16 in, and the centroidal axis of the beam describes a curve of the form r = 0.75 + 0.4375 θ/Ï€, where r and θ are in inches and radians, respectively (0 ‰¤ θ ‰¤ 4Ï€). The curved beam has a machined surface with yield and ultimate strength values of 60 and 110 kpsi, 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 againstyield.

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16 2.5 (Dimensions in inches