Explanation Write the expression for maximum interference pressure. p max = E δ max 2 R 3 [ ( r o 2 − R 2 ) ( R 2 − r i 2 ) r o 2 − r i 2 ] (I) Here, the interference pressure is p max , the modulus of elasticity is E , radial interference is δ max , outer diameter is r o , inside diameter is r i and nominal diameter is R . Write the expression for maximum interference pressure. p min = E δ min 2 R 3 [ ( r o 2 − R 2 ) ( R 2 − r i 2 ) r o 2 − r i 2 ] (II) Here, the interference pressure is p min , the modulus of elasticity is E , radial interference is δ min , outer diameter is r o , inside diameter is r i and nominal diameter is R . Write the expression for the maximum tangential stress at transition radius for the inner cylinder. ( σ t max ) i = − p max R 2 + r i 2 R 2 − r i 2 (III) Here, the maximum tangential stress at inner cylinder is ( σ t max ) i , the maximum interference pressure is p max , the inside radius is r i and the transition radius is R . Write the expression for the minimum tangential stress at transition radius for the inner cylinder. ( σ t min ) i = − p min R 2 + r i 2 R 2 − r i 2 (IV) Here, the minimum tangential stress at inner cylinder is ( σ t min ) i . Write the expression for the tangential stress at transition radius for the outer cylinder. ( σ t max ) o = p max r o 2 + R 2 r o 2 − R 2 (V) Here, the maximum tangential stress at outer cylinder is ( σ t max ) o . Write the expression for the tangential stress at transition radius for the outer cylinder. ( σ t min ) o = p r o 2 + R 2 r o 2 − R 2 (VI) Here, the minimum tangential stress at outer cylinder is ( σ t min ) o . Write the expression for maximum radial interference. δ max = 1 2 ( d o − D i ) (VII) Here, the maximum radial interference is δ max , the inside cylinder outer diameter is d o and outside cylinder inner diameter is D i . Write the expression for minimum radial interference. δ min = 1 2 ( d o ′ − D i ′ ) (VIII) Here, the minimum radial interference is δ min , the inside cylinder outer diameter is d o ′ and outside cylinder inner diameter is D i ′ . Conclusion: Refer to Table A-5 “Physical Constants of Materials”, obtain the properties of modulus of elasticity for carbon steel as, E = 30 × 10 6 psi Substitute 1.003 in for d o and 1.001 in for D i in Equation (VII). δ max = 1 2 ( 1.003 − 1.001 ) = 0.001 in Thus, the maximum radial interference is 0.001 in . Substitute 1.002 in for d o ′ and 1.002 in for D i ′ in Equation (VIII). δ min = 1 2 ( 1.002 − 1.002 ) = 0 in Thus, the minimum radial interference is 0 in . Substitute 30 × 10 6 psi for E , 0 in for r i , 0

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

10th Edition

ISBN: 9780073398204

Author: Richard G Budynas, Keith J Nisbett

Publisher: McGraw-Hill Education

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Chapter 3, Problem 118P

To determine

The radial interferences.

The interference pressures.

The tangential normal stresses on inner side of the fit surface.

The tangential normal stresses on outer side of the fit surface.

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Chapter 3, Problem 117P

Chapter 3, Problem 119P

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Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

Ch. 3 - 31 to 34 Sketch a free-body diagram of each...Ch. 3 - 31 to 34 Sketch a free-body diagram of each...Ch. 3 - Sketch a free-body diagram of each element in the...Ch. 3 - 3-1 to 3-4 Sketch a free-body diagram of each...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - For the beam shown, find the reactions at the...Ch. 3 - For the beam shown, find the reactions at the...Ch. 3 - Repeat Prob. 36 using singularity functions...

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The radial interferences. The interference pressures. The tangential normal stresses on inner side of the fit surface. The tangential normal stresses on outer side of the fit surface.

Solution Summary: The author explains the radial interferences and the interference pressures on the inner and outer side of the fit surface.

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The radial interferences. The interference pressures. The tangential normal stresses on inner side of the fit surface. The tangential normal stresses on outer side of the fit surface.

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Chapter 3 Solutions

The radial interferences.

The interference pressures.

The tangential normal stresses on inner side of the fit surface.

The tangential normal stresses on outer side of the fit surface.