Concept explainers
Fig. P3.27 and P3.28
3.28 A torque T = 900 N m is applied to shaft AB of the gear train shown. Knowing that the allowable shearing stress is 80 MPa, determine the required diameter of (a) shaft AB, (b) shaft CD, (c) shaft EF.
(a)
The required diameter of the shaft AB.
Answer to Problem 28P
The required diameter of the shaft AB is
Explanation of Solution
Given information:
The torque applied to the shaft AB is
The allowable shear stress is 80 MPa.
Calculation:
The torsion formula for maximum shear stress in the solid shaft AB
Here, T is the applied internal torque in the shaft AB, J is the polar moment of inertia of the shaft, and c is the radius of the shaft AB.
The polar moment of inertia for a solid shaft AB
Substitute
The torque in the shaft AB is
Substitute
Diameter of the shaft AB is twice the radius of the shaft AB.
Therefore, the required diameter of the shaft AB is
(b)
The required diameter of the shaft CD.
Answer to Problem 28P
The required diameter of the shaft CD is
Explanation of Solution
Given information:
The torque applied to the shaft AB is
The allowable shear stress is 80 MPa.
Calculation:
The torsion formula for maximum shear stress in the solid shaft CD
Here, T is the applied internal torque in the shaft CD, J is the polar moment of inertia of the shaft, and c is the radius of the shaft CD.
The polar moment of inertia for a solid shaft CD
Substitute
The torque in the shaft CD is expressed as follows:
Here,
Substitute 75 mm for
Substitute
Diameter of the shaft CD is twice the radius of the shaft CD.
Therefore, the required diameter of the shaft CD is
(c)
The required diameter of the shaft EF.
Answer to Problem 28P
The required diameter of the shaft EF is
Explanation of Solution
Given information:
The torque applied to the shaft AB is
Allowable shear stress is 80 MPa.
Calculation:
The torsion formula for maximum shear stress in the solid shaft EF
Here, T is the applied internal torque in the shaft EF, J is the polar moment of inertia of the shaft, and c is the radius of the shaft EF.
The polar moment of inertia for a solid shaft EF
Substitute
The torque in the shaft EF is expressed as follows:
Here,
Substitute 90 mm for
Substitute
Diameter of the shaft EF is twice the radius of the shaft EF.
Therefore, the required diameter of the shaft EF is
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Chapter 3 Solutions
Mechanics of Materials, 7th Edition
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