Explanation Given information: The diameter of the shaft is 80 mm. The value of shear modulus of elasticity is 75 GPa. Calculation: Let the internal torque at a section with distance x from the end A be T ( x ) . Consider a section at a distance of x from the end A of the shaft as shown in Figure 1. Use Equilibrium equation to find the internal torque at x . Sum of moments at x is equal to 0. ∑ M x = 0 T ( x ) − ( 5 kN ⋅ m / m ) ( x m ) = 0 T ( x ) = ( 5 kN ⋅ m / m ( 10 3 N 1 kN ) ) ( x m ) T ( x ) = 5 , 000 x N ⋅ m The polar moment of inertia of a shaft with radius ( r ) is expressed as follows: J = π 2 r 4 Radius of the shaft is 40 mm. Substitute 40 mm for r . J = π 2 ( 40 mm ) 4 = π 2 ( 40 mm × 10 − 3 m 1 mm ) 4 = 4.0212 × 10 − 6 m 4 Determine the angle of twist ( ϕ A / B ) of end A of the shaft using the relation: ϕ A / B = ∫ 0 L T ( x ) d x J G Here, L is the length of the shaft, J is the polar moment of inertia of the shaft, and G is the shear modulus of elasticity of the material

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 10.4, Problem 13FP

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Find the angle of twist of end A of the shaft.

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Chapter 10 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 10.3 - Determine the internal torque at each section and...Ch. 10.3 - Determine the internal torque at each section and...Ch. 10.3 - Prob. 3PP Ch. 10.3 - Prob. 4PP Ch. 10.3 - Prob. 1FP Ch. 10.3 - The hollow circular shaft is subjected to an...Ch. 10.3 - Prob. 3FP Ch. 10.3 - Prob. 4FP Ch. 10.3 - Determine the maximum shear stress in the shaft at...Ch. 10.3 - Prob. 6FP

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Find the angle of twist of end A of the shaft.

Solution Summary: The author calculates the polar moment of inertia of a shaft with radius ( r) by using the Equilibrium equation.

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Find the angle of twist of end A of the shaft.

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