Question

7.4 The tension in the cable at 80 m from the lower pier (3) [10] QUESTION 8: COMBINED BENDING AND TWISTING OF SHAFTS A hollow shaft has an outside diameter of 100 mm and a bore of 75 mm. The yield stress in shear for the material is 200 MPa. The shaft is subjected to combined twisting and bending, with the bending moment being three times the applied torque. Calculate the following: 8.1 By using a safety factor of 4, the maximum allowable bending moment and torque 8.2 The principal stress in the shaft 8.3 The diameter required if the shaft must be solid TOTAL: 100

Answer 1

GIVEN THAT • Outer diameter of shaft, Do loo mm • Inner diameter of shaft, Di = 75 mm o yield stress in shear, I = 200 MPa • Bending moment = 3 Abblied Torque M = 3T • Factor of Safety = 4 Moment of inertia (I) = a 10o – Di") = (100°-75") I = 3.355 x 10 mm 1100"-15") Polar moment of inertia ,J = (00-01) - J= 6.711 x 100 mm Tallowable = 200 MPa = 200 = 50 MPa Fos 8.1 Torque T - U - 50 X 6.71110 = 6.711x10 N-mm 50 = 6711.165 N-m Ber Moment, M = 31 - 20133.495 Nm 8. 2 using bending equation en → 165 MH - 20133. 495 x 100 x 50 To = 3 00.052 MPa 3.355 X 106

Major principal stress (0) C) = x y + = " - "y Ў+ что, Сът x , y =o , , • Туу "; * + + * + чт; з - Зоо. 055 + (20.05а +ч (50) от 308.16ч MP4 8.3:5 for solid shaft а в Т= та те 6+1] . 165 - Ta° x 5о хто 16 а- о. 08go9 м d = 88.09 mm