The composite shaft is made of a steel sleeve, which is bonded to a brass core.

Question

The composite shaft is made of a steel sleeve, which is bonded to a brass core. The outer diameters of the two parts are d1 = 40 mm for the brass core and d2 = 50 mm for the steel sleeve. The shear moduli of elasticity are Gb = 36 GPa for the brass and Gs = 80 GPa for the steel. Assuming that the allowable shear stresses in the brass and steel are ?b = 48 MPa and ?s = 80 MPa, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft without any material failure. The torques are applied each at the end of the shaft opposite directions.

Explanation / Answer

shear stress, = T*r/J

J= polar seconde moment of area.

for the solid shaft, J=r4/2

for the hollow shaft = J = *(r12-r22)/2

r1 = 50/2=25 mm = 0.025 m

r2 = 40/2 = 20 mm = 0.02 m

Tmax = max*J/r

maximum torque for the brass core Tmax,brass= max*J/r = (48*106)*(*0.0204/2)/0.02 = 603.2 N-m

and net torque for the composite shaft, Tmax, composite = max*J/r =  (80*106)*(*(0.0254-0.024/2)/0.025 = 1159.25 N-m

since torque is opposite in direction therefore maximum torque at the end of the steel shaft = Tmax, composite + Tmax,brass= 603.2+1159.25 = 1762.45 N-m opposite in direction of torque acting on the brass core.

hence, maximum torque at the end of the steel shaft =1762.45 N-m opposite in direction of torque acting on the brass core.

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