Concept explainers
(a)
Find the magnitude
(a)
Answer to Problem 116P
The magnitude of the maximum residual shearing stress
The location of the maximum residual shearing stress
Explanation of Solution
Given information:
The radius of the solid shaft
The shear stress
The rigidity modulus of steel (G) is 77.2 GPa.
The length of the solid shaft
The angle of twist
Calculation:
Calculate the maximum shearing strain
Here, c is radius of solid shaft,
Substitute 16 mm for c,
Calculate the shearing strain
Here,
Substitute 145 MPa for
Calculate the distribution of shearing strain using the relation.
Modify the Equation (1).
Here,
Substitute
Find the polar moment of inertia (J) using the relation.
Here, c is radius of solid shaft.
Substitute 16 mm for c.
Calculate the magnitude of torque
Substitute
Calculate the magnitude of torque in unloading
Substitute
Calculate the shearing stress in unloading
Substitute
Calculate the shearing stress in unloading
Substitute
Calculate the angle of twist in unloading
Substitute
Calculate the residual shearing stress
Substitute 145 MPa for
Find the residual shearing stress
Substitute 145 MPa for
Comparing the above
The magnitude of the maximum residual shearing stress
The location of the maximum residual shearing stress
(b)
Find the permanent angle of twist
(b)
Answer to Problem 116P
The permanent angle of twist
Explanation of Solution
Given information:
The angle of twist
Calculation:
Calculate the permanent angle of twist
Here,
Substitute
The permanent angle of twist
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Chapter 3 Solutions
Mechanics of Materials, 7th Edition
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