Question

The solid cylindrical shaft AB of 1.5 in-diameter supports of two pulleys as shown. Find the principal normal stresses and the maximum shear stress in the critical section of the shaft. Free Body Diagram Roy 300 lbf 1 6-in D wa 50 lbf SSM 27 lbf a Roz 360 lbf :D Fe = 350 lbf Fc = 387 lbf D. Coin 1 RAZ Tec = (300-50)x8/2 = 1000 in-Ib

Answer 1

RAY $350lbf - Roy HBus + $u$ 7619_, EMA zo at of) (8 in) - (Roy) (22 m) zo Roy = 127.27 lbf EFy zo 1+ 350 – Ray – 127.27=0 RAY = 222. 73 lbf Roy - 127.21 Bonding moment at B (MB)y = - Ray x8 = -222-7378 = -1781.84cbtowy Benderig moment at C, My = - Royx 6 = +27-27*6 = - 763.64 165 un 387167 ola Sur * si buni Roz EM430 Ut 63876f) Cl6ws) + Roz) (22wi)=0 Roz = 281.45 lbf F2=0 1+ RA2 — 387 + Rp2=0 RAZ = 387- RD2=387-281.45 RA2 = 105.55 lbf Bending moment at B, MB2 = RA2X = 105.55x8 = 844.34 Bending moment at c (MC2= Rozx6=281-45x6 =1688.71bl.is

Combining the bending moments form both planes at BB and Bcb find critical location MB = 1 €1781.84)+(844.363 = 1971.77 (bf-ws MC = 1763.64) 7 1688.72 = 1853.93 lbf.us The critical location is at B. Torque transmitted, T= 300-50) 4 = 1000lb.us 2M 32 (197177) = 5950.9 psi T X 1.53 = 5.951 kpsi - = 1 509 psi x 1.53 = 1.509 kpsi tid 3 Z= II 165 Td² 16 x 1000 TX 1.S T1216 x 1000 6= +JE+z3 = 5.991 +59521715092 161 = 6.312 kpsi] 82 = 0 - J 7-1² = Sesi (5.951 37 1.5092 1027 -0.36 kpsi Trans 19537 - Essay #1.50? Tmax = 3.336 kpsi