Explanation Given information: The inner diameter of the hollow shaft ( d 1 ) is 25 mm. The outer diameter of the hollow shaft ( d 2 ) is 60 mm. The yield strength ( τ Y ) is 145 MPa. The rigidity modulus of steel ( G ) is 77.2 GPa. The length of the solid shaft ( L ) is 5 m. Calculation: Calculate the inner radius of the hollow shaft ( c 1 ) using the relation: c 1 = 1 2 d 1 Here, d 1 is the inner diameter of the hollow shaft. Substitute 25 mm for d 1 . c 1 = 1 2 ( 25 ) = 12.5 mm = ( 12.5 mm × 1 m 1 , 000 mm ) = 0.0125 m Calculate the inner radius of the hollow shaft ( c 2 ) using the relation: c 2 = 1 2 d 2 Here, d 1 is the outer diameter of the hollow shaft. Substitute 60 mm for d 1 . c 2 = 1 2 ( 60 ) = 30 mm = ( 30 mm × 1 m 1 , 000 mm ) = 0.03 m When the plastic zone reaches the inner surface of the shaft is distributed uniformly. Find the torque using the relation: T = 2 π ∫ c 1 c 2 ρ 2 τ Y d ρ . (1). Integrate Equation (1). T = 2 π τ Y ∫ c 1 c 2 ρ 2 d ρ = 2 π τ Y [ ρ 3 3 ] c 1 c 2 = 2 π τ Y [ c 2 3 3 − c 1 3 3 ] T = 2 π τ Y 3 ( c 2 3 − c 1 3 ) . (2). Calculate the magnitude of torque ( T ' ) at unloading: T ' = 2 π τ Y 3 ( c 2 3 − c 1 3 ) Substitute 145 MPa for τ Y , 0.03 mm for c 2 , and 0.0125 mm for c 1 . T ' = 2 × π × ( 145 MPa × 1 , 000 , 000 Pa 1 MPa ) 3 ( 0.03 3 − 0.0125 3 ) = 7

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 3.8, Problem 119P

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Find the permanent angle of twist (ϕperm) of the rod.

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Chapter 3.8, Problem 118P

Chapter 3.8, Problem 120P

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Find the permanent angle of twist ( ϕ perm ) of the rod.

Solution Summary: The author calculates the permanent angle of twist of the rod. The yield strength is 145 MPa and the rigidity modulus of steel is 77.2 GPa.

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Chapter 3 Solutions