Explanation Given information: The diameter of the shaft is 50 mm. Calculation: Sketch the torque diagram for the shaft as shown in Figure 1. Refer Figure 1. The value of torque T A D = − 800 N ⋅ m , T D C = − 1 , 000 N ⋅ m , and T C B = − 600 N ⋅ m . Determine the angle of twist ( ϕ ) of the shaft using the relation: ϕ = T L J G Here, the torque applied is T , the length of the shaft is L , the polar moment of inertia is J , and the shear modulus of elasticity of the material is G . Rearrange Equation for the angle of twist of end A . ϕ A = ∑ T L J G = ( T A D L A D + T D C L D C + T C B L C B ) J G (1) Refer the properties of A 992 steel: The value of shear modulus of elasticity of A 992 steel is 75 GPa. The polar moment of inertia for a solid shaft of radius r is π 2 r 4 . The value of radius of the solid shaft is 25 mm. Substitute π 2 r 4 for J in Equation (1). ϕ A = ( T A D L A D + T D C L D C + T C B L C B ) ( π 2 r 4 ) G = 2 ( T A D L A D + T D C L D C + T C B L C B ) ( π r 4 ) G Substitute − 800 N ⋅ m for T A D , 600 mm for L A D , − 1 , 000 N ⋅ m for T D C , 600 mm for L D C , − 600 N ⋅ m for T C B , 300 mm for L C B , 25 mm for r , and 75 GPa for G

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 41P

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

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Chapter 10.4, Problem 40P

Chapter 10.4, Problem 42P

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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 angle of twist of end A of the shaft using the relation: cvarphi.

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

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Chapter 10 Solutions