Explanation Given information: Set P 1 = 500 lb and P 2 = 100 lb . 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 the horizontal components of forces. Consider the force indicating upward as positive and downward as negative, in the vertical components of forces. Consider the clockwise moment as negative and the anti-clockwise moment as positive, wherever applicable. Joint B : Show the free-body diagram of the joint B 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 the members AB and BC by resolving the vertical component of forces. ∑ F y = 0 F A B sin θ 2 + F B C sin θ 1 − P 1 = 0 (II) Along the horizontal direction: Determine the force in the members AB and BC by resolving the horizontal component of forces. ∑ F x = 0 − F A B cos θ 2 + F B C cos θ 1 − P 2 = 0 (III) Conclusion: Substitute 8 ft for opposite side and 8 ft for adjacent side in Equation (I). tan θ 1 = 8 8 θ 1 = 45 ° Substitute 8 ft for opposite side and 6 ft for adjacent side in Equation (I). tan θ 2 = 8 6 θ 2 = 53.13 ° Substitute 53.13 ° for θ 2 , 45 ° for θ 1 , and 500 lb for P 1 in Equation (II). F A B sin 53.13 ° + F B C sin 45 ° − 500 = 0 0.80 F A B + 0.707 F B C = 500 (IV) Substitute 53.13 ° for θ 2 , 45 ° for θ 1 , and 100 lb for P 2 in Equation (III). − F A B cos 53

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 6.3, Problem 2P

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 1P

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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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