Explanation Given information: The stiffness of the spring is 15 lb/in . . The spring is unstretched when the angle θ is 0 ° . Calculation: Show the geometry of the segment ABC as in Figure (1). Using Figure (1), When the angle θ = 0 ° , the length is 8 + 12 = 20 in . . Use sine rule: Determine the value of α : sin α 8 = sin θ 12 (1) Determine the value of ϕ : ϕ = 180 ° − θ − α (2) Determine the length l ′ A C : l ′ A C sin ϕ = 12 sin θ (3) Conclusion: Substitute 30 ° for θ in Equation (1). sin α 8 = sin 30 ° 12 sin α = 0.333 α = 19.47 ° Substitute 30 ° for θ and 19.47 ° for α in Equation (2). ϕ = 180 ° − 30 ° − 19.47 ° = 130.53 ° Substitute 130.53 ° for ϕ and 30 ° for θ in Equation (3). l ′ A C sin 130.53 ° = 12 sin 30 ° l ′ A C = 12 × sin 130.53 ° sin 30 ° l ′ A C = 18.242 in . Joint C : Show the free body diagram of the joint C as in Figure (2). Using Figure (2), Member CB is a two-force member. Spring force: Determine the elongation of the spring, x using the equation. x = l A C − l ′ A C (4) Determine the spring force using the equation

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 59P

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Find the couple M that must be applied to AB to hold the mechanism in equilibrium when θ=30°.

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Chapter 5.5, Problem 58P

Chapter 5.5, Problem 60P

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Statics and Mechanics of Materials (5th Edition)

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Find the couple M that must be applied to AB to hold the mechanism in equilibrium when θ = 30 ° .

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Find the couple M that must be applied to AB to hold the mechanism in equilibrium when θ=30°.

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