2 While the exact distribution of the shearing stresses in a

Last updated: 4/25/2023

2 While the exact distribution of the shearing stresses in a hollow cylindrical shaft is as shown in Fig a an approximate value can be obtained for Tmax by assuming that the stresses are uniformly distributed over the area A of the cross section as shown in Fig b and then further assuming that all of the elementary shearing forces act at a distance from O equal to the mean radius rm 1 2 C1 c2 of the cross section This approximate value to T Arm where T is the applied torque a C2 O b a Express the ratio Tmax To of the true value of the maximum shearing stress and its approximate value to as a function of C C2 b Calculate and plot using Excel or Matlab the ratio Tmax To for values of c C ranging from 0 to 1 in steps of 0 05 c From the plot estimate the maximum Tmax To ratio and the corresponding c C2 value then calculate the maximum error in associated with the uniform stress assumption Hint When plotting set the x axis C C2 range from 0 to 1 and the y axis Tmax To range from 0 95 to 1 25 d The thickness of the so called thin walled hollow cylindrical shafts is typically less than 1 20 of the diameter Based on the above analysis do you think it is reasonable to assume uniform shear stress distribution in such shafts Briefly justify your answer