Under normal operating conditions, the electric motor exerts a 12-kip·in. torque at E. Knowing that each shaft is solid, determine the maximum shearing stress in (a) shaft BC, (b) shaft CD, (c) shaft DE.
Fig. P10.9

(a)Consider the shaft BC
Calculate the polar moment of inertia for the given shaft BC
Here, J is the polar moment of inertia of the shaft,
is the radius of the shaft.
Substitute
for
Calculate the maximum shearing stress by using the following relation:
Here,
is the maximum shearing stress in BC,
is the torque exerted by the shaft BC,
is the polar moment of inertia of the shaft BC,
is the radius of the shaft BC.
Substitute
for
,
for
,
for
Therefore, the maximum shearing stress at BC is
(b)
Consider shaft CD
Calculate the polar moment of inertia for the given shaft CD
Here,
is the radius of the shaft CD.
Substitute,
for
.
Calculate the maximum shearing stress by using the following relation:
Substitute
for
,
for
,
for
Therefore, the maximum shearing stress at CD is
.
Consider shaft DE
Calculate the polar moment of inertia for the given shaft DE
Here,
is the radius of the shaft DE.
Substitute,
for
.
Calculate the maximum shearing stress by using the following relation:
Substitute
for
,
for
,
for
Therefore, the maximum shearing stress at DE is
.