Explanation Given information: The height of the rigid rod AB is h = 450 mm . The distance between the point A and the hinge is d = 300 mm . The mass of the rigid rod AB is m = 200 kg . Calculation: Show the deflection of the rod AB due to the spring as in Figure 1. Here, the change of angle of the bar is θ . Use the geometry of the triangle; δ 1 = h sin θ δ 2 = d sin θ Find the spring constant ( k ) by taking moment about point A . ∑ M A = 0 k δ 2 ( d cos θ ) + k δ 2 ( d cos θ ) − m g ( δ 1 ) = 0 Substitute h sin θ for δ 1 and d sin θ for δ 2 . k ( d sin θ ) ( d cos θ ) + k ( d sin θ ) ( d cos θ ) − m g ( h sin θ ) = 0 2 k d 2 cos θ − m g h = 0 2 k d 2 cos θ = m g h k = m g h 2 d 2 cos θ For small deformations, cos θ ≈ 1

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 10, Problem 118RP

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Find the range of values of k for which the equilibrium of rod AB is stable in equilibrium.

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Chapter 10, Problem 117RP

Chapter 10, Problem 119RP

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Chapter 10 Solutions

Mechanics of Materials, 7th Edition

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Find the range of values of k for which the equilibrium of rod AB is stable in equilibrium.

Solution Summary: The author calculates the deflection of the rod AB due to the spring by taking moment about point A.

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Find the range of values of k for which the equilibrium of rod AB is stable in equilibrium.

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Chapter 10 Solutions