Question

Problem 2 A prospector uses a hand-powered winch (see figure) to raise a bucket of ore in his mine shaft. The axle of the winch is a steel rod of diameter d = 0.625 in. Also, the distance from the center of the axle to the center of the lifting rope is b = 4.0 in. a) If the weight of the loaded bucket is W = 100 lb, what is the maximum shear stress in the axle due to torsion? b) If the maximum bucket load is 125 lb and the allowable shear stress in the axle is 9250 psi, what is the minimum permissible axle diameter?

Answer 1

a) Shear stress= 8344.46 psi

Tosque acting on the axle - w x b. = 100x4 = 400 lb.in T- Torque = 400 lb.in J = Polar moment of Inertia o W = 100 lb Shear stress - TR 400X0.3125 0.01498 J-(0.625)4 = 0.01498 int R= d = 0.625 -0.3125 in T = 8344. 46 psi on eblina b) maximum bucket load wa 125 lb Maximum torque T=Wb=125x4 = 500 lb.in Allowable shear stress T=9250 psi T = e dt - 112 32 Or, 11 d4 32 - - 7 16 de d3 = 16T TT . d3 = 168 500 ll x 9250 = 0.2753 Minimum dia.. d= 80.2753 = 0.650 in

b) minimum diameter = 0.650 in