Calculate diameter of shaft in maximum direct stress:
A shaft is designed for transmitting 100 kW power at 150 rotation per minute. Shaft is supported in bearings 3 m apart and at 1 m from 1 bearing a pulley exerting transverse load of 30 KN on shaft is mounted. Obtain diameter of shaft if maximum direct stress is not to exceed 100 N/mm2.
Sol.:
Ra + Rb = 30 KN
Ra = 20 KN
Rb = 10 KN
Maximum bending moment occurs at 'C'.
MC = 20 × 1 = 20 KN-m ...(i)
The power transmitted by shaft P = 2 NT/60
100 × 103 = 2 x 150. T/60
T = 6366.19 N-m ...(ii)
Equivalent bending moment Me = ½[M + (M2 + T2)1/2]
= ½[20,000 + (20,0002 + 63692)1/2]
Me = 20494.38 N-m ...(iii)
From the bending equation Me/I = σ/y 2044.38 × 103/[ ( ?/64)d4] 100/d/2
d = 127.8 mm