Explanation Given Information: The force F of 50 lb is applied to the pads at A and C . The unstretched length of the spring is 1 ft. Spring force: Determine the elongation of the spring, x using the equation. x = 2 d − Unstretched length (1) Determine the spring force using the equation. F s = k x (2) Here, the stiffness is k and the compression is x . Conclusion: Substitute 1 ft for unstretched length in Equation (1). x = 2 d − 1 Substitute 150 lb/ft for k and ( 2 d − 1 ) for x in Equation (2). F s = 150 × ( 2 d − 1 ) Geometry: Show the geometry of triangle as in Figure (1). Using Figure (1), Determine the value of sin θ : sin θ = Opposite side Hypotenuse (3) Determine the value of cos θ : cos θ = Adjacent side Hypotenuse (4) Conclusion: Substitute d for opposite side and 1 ft for hypotenuse in Equation (3). sin θ = d 1 sin θ = d Substitute 1 − d 2 for adjacent side and 1 ft for hypotenuse in Equation (4). cos θ = 1 − d 2 1 cos θ = 1 − d 2 Joint B : Show the free body diagram of the joint B as in Figure (1). Using Figure (2), Along the horizontal direction: Determine the force in the member AB in terms of the force in the member BC by resolving the horizontal component of forces. ∑ F x = 0 F A B cos θ − F B C cos θ = 0 (5) Along the vertical direction: Determine the force in the member AB by resolving the vertical component of forces. ∑ F y = 0 F A B sin θ + F B C sin θ − F s = 0 (6) Conclusion: Substitute 1 − d 2 for cos θ in Equation (V). F A B 1 − d 2 − F B C 1 − d 2 = 0 F A B = F B C (7) Substitute d for sin θ , F B C for F A B , and 48.59 ° for θ 1 and 150 × ( 2 d − 1 ) for F s in Equation (6). F B C ( d ) + F B C ( d ) − 150 ( 2 d − 1 ) = 0 2 F B C ( d ) = 300 d − 150 F B C = 150 d − 75 d (8) Joint C : Show the free body diagram of the joint C as in Figure (3)

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 5.5, Problem 54P

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Find the smallest dimension d required for the equilibrium.

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Chapter 5.5, Problem 53P

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Chapter 5 Solutions

Statics and Mechanics of Materials (5th Edition)

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Find the smallest dimension d required for the equilibrium.

Solution Summary: The author explains the smallest dimension d required for equilibrium. The unstretched length of the spring is 1 ft.

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Find the smallest dimension d required for the equilibrium.

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