Explanation Given information: There is a vertical force P acting at its end. JG is constant. Show the free body diagram of the cross section as in Figure 1. Geometry: Show the geometric view of the cross section as in Figure 2. Refer to Figure 1 and 2. The torsion in the curved bar is as follows: T = P r ( 1 − cos θ ) Express the equation for strain energy in terms of torsion as follows: U i = ∫ 0 L T 2 2 J G d s (1) Here, T is torsion, J is polar moment of inertia, and G is modulus of elasticity or shear modulus. Here, θ = π / 2 s = r θ d s = r d θ Substitute π / 2 for θ , r d θ for d s , and P r ( 1 − cos θ ) for T in Equation (1). U i = ∫ 0 π / 2 ( P r ( 1 − cos θ ) ) 2 2 J G r d θ = P 2 r 3 2 J G ∫ 0 π / 2 ( 1 − cos θ ) 2 d θ = P 2 r 3 2 J G ∫ 0 π / 2 ( 1 − 2 cos θ + cos 2 θ ) d θ

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external f…

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Chapter 14.2, Problem 14.19P

To determine

the strain energy in the horizontal curved bar due to torsion.

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Chapter 14.2, Problem 14.18P

Chapter 14.2, Problem 14.20P

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