sm9 93

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PROBLEM (*9.93) The gear A attached to the steel shaft AB with an allowable shear strength all
τ
= 10 ksi is acted upon by a vertical load Fy = 300 lb (Fig. P9.93). Determine:
(a) The value of the torque T required to support the loading.
(b) The required shaft diameter d using the maximum shear stress theory of failure.
Assumption: Bearings at C and B act as simple supports.
*SOLUTION
(a) Reactions as obtained
from equilibrium
conditions, are marked
in Figure (a).
(b) From Fig. (a):
800TNm=⋅
Critical section is at C. Equation (9.30):
22
316
all
dMT
πτ
=+
Substituting the numerical
values (see Fig.b):
1
22
3
16
[ (2.186) (1.2) ]
(10)
d
π
=+
1.083 .in=
y
x
A
C
B
z
D
R
By=128.6 lb
R
Cy=428.6 lb
T= 800 N⋅in.
E
400 lb
R
Cz=114.3 lb
2 in.
3 in.
300 lb
R
Bz=285.7 lb
4 in. Figure (a)
T
(kip
⋅
in.)
x
x
My
(kip
⋅
in.)
1.2
0.237
B
D
A
C
0.625
B
A
x
Mz
(kip
⋅
in.) 2.186
Figure (b)