Explanation Given Information: The unstretched length of spring is 0.3 m. The mass of each bar is 20 kg. Convert the mass of bar in to weight of bar using the relation. W = m g Here, the mass is m . The weight of each bar is ( 20 × 9.81 ) N . Member BC : Show the free body diagram of the member BC as in Figure (1). Using Figure (1), 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 p = k x (2) Here, the stiffness is k and the compression is x . Moment about point C : Determine the horizontal and vertical reaction at point B by taking moment about point C. ∑ M C = 0 B y ( 2 cos θ ) − B x ( 2 sin θ ) − 20 × 9.81 ( cos θ ) = 0 2 B y cos θ − 2 B x sin θ = 196.2 cos θ (3) Conclusion: Substitute 2 sin θ for d and 0.3 m for unstretched length in Equation (1). x = 2 ( 2 sin θ ) − 0 .3 = 4 sin θ − 0.3 Substitute 150 N/m for k and ( 4 sin θ − 0.3 ) for x in Equation (2). F s p = 150 × ( 4 sin θ − 0.3 ) = 600 sin θ − 45 Member AB : Show the free body diagram of the member AB as in Figure (2).

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 57P

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Find the angle θ for equilibrium.

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Chapter 5 Solutions

Statics and Mechanics of Materials (5th Edition)

Ch. 5.3 - In each ease, calculate the support reactions and...Ch. 5.3 - Identify the zero-force members in each truss....Ch. 5.3 - Determine the force in each member of the truss...Ch. 5.3 - Determine the force in each member of the truss...Ch. 5.3 - Determine the force in each member of the truss...Ch. 5.3 - Determine the greatest load P that can be applied...Ch. 5.3 - Identify the zero-force members in the truss....Ch. 5.3 - Determine the force in each member of the truss...Ch. 5.3 - Determine the force in each member of the truss...Ch. 5.3 - Determine the force in each member of the truss...

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Find the angle θ for equilibrium.

Solution Summary: The author shows the free body diagram of the member BC as in Figure (1).

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