Question

The figure shows a crank loaded by a force F 300 lbr that causes twisting and bending on the solid circular shaft, % in diameter, fixed to a support. For a stress element at "A" a Calculate applied bending and torsional stresses and their angles of orientation. b Draw the initial stress element. c- Draw a complete principle stress element d Draw a complete shear stress element. 1.5 in in dia. in dia in It in 4 in 5 in

Answer 1

Data from the given question is F = 300 lbf. diameter = 3/4 in. (a) Bending moment at point A m_A = F times 1.5 + F times 5 = (300 times 1.5) + (300 times 5) = 450 + 1500 m_A = 1950 lbF in \r\n Bending stress. sigma_b = m_A y/I = 32 mA/pi D^3 = 300 times 6.5 times 32/pi (3/4)^3 = 62400/1.32535 sigma_b = 47081.56 lbF/in^2 Torsional shear stress T_F = 16T/pi D^3 T = F times 4 = 300 times 4 T = 1200 lbF in T_F = 300 times 4 times 16/pi times (3/4)^3 T_F = 19200/1.32535 T_F = 14486.63 lbF/in^2 \r\n Bending stress is perpendicular to cross section at A and torsional stress is parallel to cross section at Point A. At point A sigma_b = sigma_bT (Tensile stress) T_F = torsional shear stress = T_max = 16T/pi D^3 T_d = direct shear stress = 0 \r\n (b) Initial stress element at A