Explanation Given information: The length of the shank is 50 mm. The torque in the shank is expressed as t = k x 2 3 . The radius of the shank is 4 mm. The applied torque at the bolt head is 50 N ⋅ m . Calculation: The torque in the shank is expressed as follows: T = ∫ 0 L t d x Substitute 50 N ⋅ m for T , k x 2 3 for t , and 50 mm for L . 50 N ⋅ m = ∫ 0 50 mm ( k x 2 3 ) d x 50 N ⋅ m = ∫ 0 0.05 m ( k x 2 3 ) d x 50 N ⋅ m = [ k x 2 3 + 1 2 3 + 1 ] 0 0.05 m 50 N ⋅ m = k ( 0.05 ) 5 3 5 3 k = 12.3 × 10 3 N m ( 2 3 ) Therefore, the value of constant k is 12.3 × 10 3 N m ( 2 3 ) _ . In general the torque is expressed as follows: T = ∫ 0 x k x 2 3 d x = ∫ 0 x ( 12.3 × 10 3 ) x 2 3 d x = 12.3 × 10 3 ( x 5 3 5 3 ) = 7.38 × 10 3 x 5 3 Find the torque at distance x from A . T ( x ) = 50 − 7.38 × 10 3 x 5 3 The polar moment of inertia for radius ( c ) of the solid shaft is π 2 c 4 . Refer the properties of A -36 steel: The value of shear modulus of elasticity of A -36 steel is 75 GPa. Determine the angle of twist ( ϕ ) of the shank using the relation: ϕ = ∫ 0 L T ( x ) d x J G Here, the torque applied at x is T ( x ) , the polar moment of inertia is J , and the shear modulus of elasticity of the material is G

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382869

Author: HIBBELER

Publisher: PEARSON

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Chapter 10.4, Problem 58P

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Find the value of constant k and the angle of twist in the shank.

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Chapter 10.4, Problem 57P

Chapter 10.4, Problem 59P

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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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