(a) Explanation Given information: The radius of solid shaft is r . The solid shaft is subjected to a torque T . Inner core of the shaft resists one half of the applied torque. Calculation: The polar moment of inertia for a solid shaft of radius r is π 2 r 4 . The outer radius of the shaft is r . The torsion formula for maximum shear stress in the shaft ( τ max ) is shown below: τ max = T c J (1) Here, the internal torque is T , the polar moment of inertia is J , and the outer radius of the shaft is c . Substitute r for c and π 2 r 4 for J in Equation (1). τ max = T r π 2 r 4 = 2 T π r 3 Rearrange Equation (1) for the shear stress τ in the inner core of the shaft with radius as r ' and torque as T 2 . Substitute τ for τ max , T 2 for T , r ' for c , and π 2 ( r ' ) 4 for J in Equation (1) (b) To determine Find the radius of the inner core of the shaft r ' using the resultant of the shear-stress distribution.

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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In mechanical engineering, torque, torsion, and twisting moment are three of the most important concepts which have different meanings. Torque is the consequence of a moment of a force that produces an angular acceleration in a body or induces rotational…

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Chapter 10.3, Problem 1P

(a)

To determine

Find the radius of the inner core of the shaft r' using the torsion formula.

(b)

To determine

Find the radius of the inner core of the shaft r' using the resultant of the shear-stress distribution.

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Chapter 10.3, Problem 8FP

Chapter 10.3, Problem 2P

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Find the radius of the inner core of the shaft r ' using the torsion formula.

Solution Summary: The author calculates the polar moment of inertia for a solid shaft of radius r using the torsion formula.