Problem

Under normal operating conditions, the electric motor exerts a 12-kip·in. torque at E. Kno...

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

Step-by-Step Solution

Solution 1

(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 .

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