Explanation Given information: Shaft rotates at 540 rpm. The radius at the transition of the shaft is r = 7.2 mm . The allowable shear stress is 55 MPa. Calculation: Determine the power transmitted ( P ) by the shaft using the relation: P = T ω (1) Here, T is the applied torque and ω is the angular velocity of the shaft. The expression for angular velocity of the shaft ( ω ) is shown below: ω = 2 π f (2) Here, f is the frequency of shaft’s rotation. Substitute 540 rev min for f in Equation (2). ω = 2 π ( 540 rev min ) = 2 π ( 540 rev min ) ( 1 min 60 sec ) = 56.5487 rad sec Substitute 56.5487 rad sec for ω in Equation (1). P = T ( 56.5487 rad sec ) T = P 56.5487 rad sec Let D be the larger diameter of the built-up shaft, d be the smaller diameter of the built-up shaft, and r be the radius at transition between the cross sections. The value of D is 75 mm, d is 60 mm, and r is 7.2 mm. Find the value of D d as shown below: Substitute 100 mm for D and 60 mm for d . D d = 75 mm 60 mm = 1.25 Find the value of r d as shown below: Substitute 7.2 mm for r and 60 mm for d . r d = 7.2 mm 60 mm = 0.12 Find the value of torsional stress concentration factor K : Refer Figure 5-32, “The stress concentration factor” in the textbook, to find the stress concentration factor ( K ) for the shaft with known D d and r d values. The value of D d is 1.25 and r d is 0.12, then the corresponding stress concentration factor ( K ) value is 1

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 5.10, Problem 5.122P

To determine

The maximum power the shaft can transmit.

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Chapter 5.10, Problem 5.121P

Chapter 5.10, Problem 5.123P

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Chapter 5 Solutions

Mechanics of Materials

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