Explanation Given information: Refer Figure 5-26, to consider the thin-walled tube. Use the formula for shear stress, τ a v g = T 2 t A m (Equation 5-18). The general equation of shear strain energy is U i = ∫ V τ 2 2 G d V (Equation 14-11). Express the equation for strain energy in terms of shear stress as follows: U i = ∫ V τ 2 2 G d V (1) Here, τ is shear stress, G is modulus of elasticity or shear modulus. Express the average shear stress as follows: τ = T 2 t A m Substitute T 2 t A m for τ in Equation (1). U i = ∫ V ( T 2 t A m ) 2 2 G d V = ∫ V T 2 8 t 2 A m 2 G d V = T 2 8 A m 2 G ∫ A 1 t 2 d A ∫ 0 L d x = T 2 8 A m 2 G ∫ A 1 t 2 d A [ x ] 0 L = T 2 L 8 A m 2 G ∫ A 1 t 2 d A (2) Refer to Figure Figure

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ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 14.2, Problem 14.14P

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To show: that the twist of the tube is ϕ=TL4Am2G∫dst .

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Chapter 14.2, Problem 14.13P

Chapter 14.2, Problem 14.15P

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that the twist of the tube is ϕ = T L 4 A m 2 G ∫ d s t .

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To show: that the twist of the tube is ϕ=TL4Am2G∫dst .

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Chapter 14 Solutions