Explanation Write the expression of radius of pressure vessel. r = d 2 (I) Here, the radius of the pressure vessel is r and the diameter of the pressure vessel is d . Write the expression of ratio of radius and thickness of pressure vessel. R = r t (II) Here, the ratio of radius and thickness of pressure vessel is R and the thickness of pressure vessel is t . Write the expression of inner diameter of the pressure vessel. d i = d − 2 t (III) Here, the inner diameter of the pressure vessel is d i . Write the expression of tangential stress acting on the pressure vessel. σ t = p ( d i + t ) 2 t (IV) Here, the pressure of the pressure release-vale is p and the tangential stress acting on the pressure vessel is σ t . Write the expression of lateral stress acting on the pressure vessel. σ l = p d i 4 t (V) Here, the lateral stress acting on the pressure vessel is σ l . Write the expression of radial stress acting on the pressure vessel. σ r = − p i . (VI) Here, the radial stress acting on the pressure vessel is σ r . Write the expression for maximum stress acting on pressure vessel using distortion-energy theory. σ ′ = 1 2 [ ( σ t − σ l ) 2 + ( σ l − σ r ) 2 + ( σ r − σ t ) 2 ] 1 2 (VII) Here, the maximum stress acting on pressure vessel using distortion-energy theory is σ ′ . Write the expression of factor of safety using the distortion-energy theory. n = S y σ ′ . (VIIII) Here, the factor of safety using the distortion-energy theory is n and the yield strength of 2024-T3 aluminum alloy is S y . Conclusion: Substitute 3 1 2 in for d in Equation (I). r = 3 1 2 in 2 = 7 4 in = 1.75 i n Substitute 1.75 in for r and 0.065 in for t in Equation (II). R = 1.75 in 0.065 in = 26.92 Since R > 10 , so the vessel can be considered as thin-wall vessel. Substitute 3 1 2 in for d and 0.065 in for t in Equation (III). d i = ( 3 1 2 in ) − ( 2 × 0.065 in ) = 3

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ISBN: 9781260163155

Author: BUDYNAS

Publisher: MCG CUSTOM

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Chapter 5, Problem 60P

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The factor of safety using the distortion-energy theory.

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The factor of safety using the distortion-energy theory.

Solution Summary: The author explains the factor of safety using the distortion-energy theory, which is 3.88.

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