sm9 95

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PROBLEM (9.95) A solid circular shaft-pulley assembly is supported by frictionless supports at C
and D and acted upon by tensile forces through the belts as depicted in Fig. P9.95. If the allowable shear
stress is all
τ
= 20 ksi, what is the required minimum shaft diameter d according to the maximum shear
stress criterion of failure?
SOLUTION
The reactions and the torques, as found by the equations of statics, are marked in
Fig. a. Moment and torque diagrams are shown in Fig.(b). Critical sections is at C.
Eq. (9.32) is thus
222
316 zy
all
dMMT
πτ
=++
1
22 2
3
3
16
[ ( 950 300 ( 60) )]
(20 10 )
π
=++−
×
or
0.633 .din=
Figure (a)
100 lb
95 lb 60 lb
⋅
in.
95 lb
60 lb⋅in.
190 lb
y
z
B
D
A
C
x
T
(kip⋅in.)
x
x
My
(kip⋅in.)
-60
950
C
D
A
C
600
B
x
Mz
(kip⋅in.)
300
B
Figure (b)