Concept explainers
Fig. P3.30
3.30 (a) For a given allowable shearing stress, determine the ratio T/w of the maximum allowable torque T and the weight per unit length w for the hollow shaft shown, (b) Denoting by (T/w)0 the value of this ratio for a solid shaft of the same radius express the ratio T/w for the hollow shaft in terms of (T/w)0 and c1/c2 ■
(a)
The ratio
Answer to Problem 30P
The ratio
Explanation of Solution
Given information:
The maximum allowable torque is T.
The weight per unit length of the hollow shaft is w.
Calculation:
The torsion formula for allowable shear stress in the hollow shaft
Here,
The polar moment of inertia for a hollow shaft
The area of the hollow shaft is
Substitute
Let the specific weight of the shaft be
Total weight of the shaft is
The weight per unit length of the hollow shaft is expressed as follows:
Find the ratio of
Therefore, the ratio
(b)
The ratio
Answer to Problem 30P
The ratio
Explanation of Solution
Given information:
The maximum allowable torque is T.
The weight per unit length of the hollow shaft is w.
Calculation:
The polar moment of inertia for a solid shaft
The area of the solid shaft is
Substitute
The weight per unit length of the solid shaft is expressed as follows:
Find the ratio of solid shaft
Refer part (a).
The ratio
Substitute
Therefore, the ratio
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Mechanics of Materials - With Access
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