Explanation Given information: The diameter of the shaft is 40 mm. The value of shear modulus of elasticity is 75 GPa. Calculation: Determine the angle of twist ( ϕ ) of the shaft using the relation: ϕ = T L J G (1) Here, T is the torque applied, 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. 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 20 mm. Substitute 20 mm for r . J = π 2 ( 20 mm ) 4 = π 2 ( 20 mm × 10 − 3 m 1 mm ) 4 = 2.5133 × 10 − 7 m 4 Calculate the value of internal torque in the segment AB ( T A B ) of the shaft using the Figure. T A B = − ( 4 kN ) ( 50 mm ) + ( 10 kN ) ( 50 mm ) + ( 6 kN ) ( 75 mm ) − ( 2 kN ) ( 75 mm ) = 600 kN ⋅ mm = 600 kN ⋅ mm ( 10 − 3 m 1 mm ) ( 10 3 N 1 kN ) = 600 N ⋅ m The length of the segment AB of the shaft is 450 mm. Rewrite Equation (1) for angle of twist of wheel B with respect to wheel A ( ϕ B / A ) of the shaft

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Design of Shafts and Shaft Components

The shaft is basically defined as the machine element that rotates, is in circular cross-section, it is majorly used to transfer the power from one part of the system to another, or from a power generating machine to a power absorbing machine. The shaft …

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Chapter 10.4, Problem 10FP

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Find the angle of twist of wheel B with respect to wheel 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 wheel B with respect to wheel A of the shaft.

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Find the angle of twist of wheel B with respect to wheel A of the shaft.

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