Question

Problems 1. (Subtotal: 21 points) A steady torque of 1500 Ibf in is transmitted by a machined shaft made of steel with an ultimate tensile strength of 100 kpsi. The transverse cross section at the location of a shoulder against which a gear sits is subjected to a bending moment which is a sinusoidal function of time with a maximum of 800 lbf-in. Furthermore, this cross section is the location for the maximum von Mises stress. The smaller diameter at the shoulder, d, is 1.3 in, and the theoretical stress concentration factors of this shoulder step for normal stresses and for shear stresses, Ki and Ks, are given respectively by K 1.7 and Ka 1.5, with a notch sensitivity factor for normal stresses -0.86 and a notch sensitivity factor for shear qshar 0.89. For a reliability goal of 0.90, determine the fatigue factor of safety by using the distortion energy theory combined with the modified Goodman criterion. 1 D)

Answer 1