Explanation Hint: The resultant force at pin E acting along member ED . Method adopted: Method of Joints. Assumptions: Consider the state of member as tension, where the force is pulling the member, and as compression, where the force is pushing the member. Consider the force indicating the right side as positive and the left side as negative, in horizontal components of forces. Consider the force indicating upward as positive and downward as negative, in vertical components of forces. Consider the clockwise moment as negative and the anti-clockwise moment as positive, wherever applicable. Joint C : Show the free-body diagram of joint C as in Figure 1. Using Figure 1, Determine the value of θ . tan θ = Opposite side Adjacent side (I) Along the vertical direction: Determine the force in member CD by resolving the vertical component of forces. ∑ F y = 0 F C D sin θ − 2 = 0 (II) Along the horizontal direction: Determine the force in member BC by resolving the horizontal component of forces. ∑ F x = 0 F C D cos θ − F B C = 0 (III) Conclusion: Substitute 2 m for the opposite side and 3 m for the adjacent side in Equation (I). tan θ = 2 3 θ = 33.69 ° Substitute 33.69 ° for θ in Equation (II). F C D sin 33.69 ° − 2 = 0 F C D = 2 sin 33.69 ° F C D = 3.60 kN ( C ) Substitute 3.60 kN for F C D and 33.69 ° for θ in Equation (III). 3.60 cos 33.69 ° − F B C = 0 F B C = 3 kN ( T ) Thus, the magnitude of force in member CD is F C D = 3.60 kN ( C ) _ . Thus, the magnitude of force in member BC is F B C = 3 kN ( T ) _ . Joint B : Show the free-body diagram of the joint B as in Figure 2. Using Figure 2, Along the vertical direction: Determine the force in member BD by resolving the vertical component of forces. ∑ F y = 0 F B D − 3 = 0 (IV) Along the horizontal direction: Determine the force in member AB by resolving the horizontal component of forces. ∑ F x = 0 F B C − F A B = 0 (V) Conclusion: Solve Equation (IV). F B D = 3 kN ( C ) Substitute 3 kN for F B C in Equation (V). 3 − F A B = 0 F A B = 3 kN ( T ) Thus, the magnitude of force in member BD is F B D = 3 kN ( C ) _

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 6.3, Problem 18P

To determine

The force in each member of the truss and whether the states of members are in tension or compression.

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Chapter 6.3, Problem 17P

Chapter 6.3, Problem 19P

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Chapter 6 Solutions

Engineering Mechanics: Statics

Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 3FP Ch. 6.3 - Determine the greatest load P that can be applied...Ch. 6.3 - Identify the zero-force members in the truss....Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Determine the force in each member of the truss,...Ch. 6.3 - Determine the force in each member of the truss,...

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