Explanation Given information: The curved rod has a diameter d . The rod is made of material having a modulus of elasticity of E . Consider that bending strain energy only. Assumptions: Consider that the right side force as positive and left side as negative in horizontal components of forces. Consider that the upward force as positive and downward as negative in vertical components of forces. Consider that the clockwise moment as negative and anticlockwise moment as positive. Show the free-body diagram of the cross-section as in Figure 1. Moment about the section: Determine the moment at the section by taking moment about the section. ∑ M x = 0 M − P r sin θ = 0 M = P r sin θ Here, P is the external load acting on the curved rod and r is the radius. Moment of inertia: Determine the moment of inertia of the rod using the formula. I = π d 4 64 Here, d is diameter of the curved rod. Strain energy due to Bending: Determine the strain energy in the beam due to bending using the equation. ( U i ) b = ∫ 0 s M 2 d s 2 E I (1) Here, M is the moment in the beam and I is the moment of inertia of the beam. Here, s = θ θ = π 2 d s = r d θ Substitute π 2 for s , P r sin θ for M , r d θ for d s , and π d 4 64 for I in Equation (1). ( U i ) b = ∫ 0 π 2 ( P r sin θ ) 2 r d θ 2 E × π d 4 64 = 32 P 2 r 3 π d 4 E ∫ 0 π 2 sin 2 θ d θ = 16 P 2 r 3 π d 4 E ∫

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 14.3, Problem 14.36P

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The vertical displacement of end B of the rod.

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Chapter 14.3, Problem 14.35P

Chapter 14.3, Problem 14.37P

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Mechanics of Materials

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