Question

3.A solid steel shaft (see Figure Q3) free at the ends has a diameter of 25 mm. LBc 500mm and Lco 250mm. The torques experienced by the shaft are T1 300Nm T2 = 550Nm and T3 = 250Nm. The modulus of rigidity of the material is G- 100GPa BC CD Figure Q3 a) Find the values of the internal torques TBc and Tco taking the anticlockwise direction as positive b) What is the maximum shear stress experienced by the shaft? Where would the minimum shear stress be and what is its magnitude. c) Find the angle of twist between B and D d) If the shaft is now replaced by a hollow circular bar of outside diameter 40mm and the allowable shear stress is 60MPa, determine the maximum possible inside diameter

Answer 1

sigma M_B = 0 = > 300 - T_BC = 0 T_BC = 300 rightarrow C C W sigma M_C = 0 = > 300 - 550 - T_CD = R_CD = -250 CW sigma_MD = 0 rightarrow 300 - 550 + 250 - T_D = 0 T_D = 0 T_BC = + 300 Nm CCW T_CD = phi - 250 Nm CW C_max = 16 T/pi d^3 CBC = 16 times 300/pi times (0.025)^3 = 97 78 Mpa C_CD = 16 times 250/pi times (0.025)^3 = 81.48 Mpa \r\n Angle of twist theta_BC = 32 TL/GJ theta_B = 32 times 300 times 0.5/100 times 10^9 times pi times (0.025)^4 = 0.0391 rad = 2.241 degree theta_CD = 32 times 250 times 0.25/100 times 10^9 times pi times (0.025)^4 = 0.0613 (C W) = 0.9338 degree theta_D theta_BC + theta_CD = 2.2411 - 0.9338 = 1 3073 shaft replaced by hollow tube BC at 300 ahs Max shear