Question

2. The solid 50-mm-diameter shaft is used to transmit the torques applied to the gears as shown in Figure 5. Determine the absolute maximum shear stress in the shaft. (15 marks)

Answer 1

The diam eter of the shaft is50 mm The polar moment of inertia of the shaft, 22J 0.05 6.1136 x 10 m The applied torques sati sfies the moment equilibrium about the shaft axis Let us draw the free body diagrams for sections AB, BC and CD of the shaft Secti on AB 250N-m TAB250N-m Section BC 250N-m 75N-m Tac= 175N-m Section CD, 150N-m From the free body diagrams the maximum internal torque is developed in section AB Hence the absolute m aximum shear stress occurs in A The absolute maximum shear stress, (250) (0.025) 6.1136 x 10 = 10.19×106 Pa =10.19MPa Hence the absolute m aximum shear stres 10.2MPa