Concept explainers
3.57 and 3.58 Two solid steel shafts are fitted with flanges that are then connected by bolts as shown. The bolts are slightly undersized and permit a 1.5° rotation of one flange with respect to the other before the flanges begin to rotate as a single unit. Knowing that G = 77.2 GPa, determine the maximum shearing stress in each shaft when a torque of T of magnitude 500 N·m is applied to the flange indicated.
3.57 The torque T is applied to flange B.
3.58 The torque T is applied to flange C.
The maximum shearing stress in the shaft AB.
The maximum shearing stress in the shaft CD.
Answer to Problem 58P
The maximum shearing stress in the shaft AB is
The maximum shearing stress in the shaft CD is
Explanation of Solution
Given information:
The modulus of rigidity of the solid shafts is
The torque applied to the flange C is
The rotation of one flange with respect to the other flange is
Calculation:
The radius of the shaft AB is
The polar moment of inertia of shaft AB of radius
The torque carried by the shaft AB
Here,
Substitute
The radius of the shaft CD is
The polar moment of inertia of shaft CD of radius
The torque carried by the shaft CD
Here,
Substitute
The clearance rotation for flange C is,
Find the torque required to remove the clearance:
Substitute
The magnitude of torque applied at the flange is
The torque
The total torque
Substitute
Substitute
Torque in the shaft AB is,
Torque in the shaft CD is,
The maximum shearing stress in the shaft AB
Substitute
Therefore, the maximum shearing stress in the shaft AB is
The maximum shearing stress in the shaft CD
Substitute
Therefore, the maximum shearing stress in the shaft CD is
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Chapter 3 Solutions
Loose Leaf For Mechanics Of Materials Format: Looseleaf
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