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PROBLEM (9.100) A shaft of diameter d is mounted between bearings and loaded by two pulleys
of pitch diameters D as shown in Fig.P9.100. Note that the pitch diameter refers to the diameter where belt
forces T1 and T2 act. Determine the factor of safety
s
ncorresponding to yield, applying the maximum
energy of distortion theory of failure.
Assumptions: Bearings act as simple frictionless supports. The shaft is made of cold-rolled steel with an
allowable strength of all
σ
.
Given: d = 45 mm, D = 150 mm, T1 = 2T2 , y
σ
= 600 MPa
SOLUTION
Reactions, as found from the conditions of equilibrium, are worked in Fig. a.
The critical region is between A and B.
Hence, Eq. (9.31):
22
3
32 3
4
y
s
M
T
nd
σ
π
=+
622
3
600(10 ) 32 3
(2250) (1500)
(0.045) 4
s
n
π
=+
Solving, 2.07
s
n=
Figure (a)
30 kN
100 mm
75 m
m
T=1.5 kN
⋅
m 30 kN
y
30 kN
B
30 kN
A
x
2250
x
Mz
(N⋅m)
1
/
1
100%