(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 = (c1 + C2)] of the cross section. This approximate value to = T/Arm, where T is the applied torque. Tmax (a) C2 (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 C1/C2. (b) Calculate and plot (using Excel or Matlab) the ratio Tmax/To for values of c/c2 ranging from 0 to 1 in steps of 0.05. (c) From the plot, estimate the maximum (Tmax/To) ratio and the corresponding c/cz value, then calculate the maximum error (in %) associated with the uniform stress assumption. [Hint: When plotting, set the x-axis (C1/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.