Explanation Assumption: 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. Use the equation of equilibrium, wherever applicable. Entire frame: Show the free-body diagram of the entire frame as in Figure 1. Using Figure 1, Moment about the point E : Determine the vertical reaction at point A by taking the moment about the point E . ∑ M E = 0 400 ( 2 ) − A y ( 3.5 ) + 300 ( 3.5 ) + 300 ( 1.5 ) = 0 (I) Conclusion: Solve Equation (I). 800 − 3.5 A y + 1 , 050 + 450 = 0 3.5 A y = 2 , 300 A y = 657.14 N Thus, the vertical reaction component at point A is A y = 657.14 N _ . Segment CD : Show the free-body diagram of segment CD as in Figure 2. Using Figure 2, Moment about the point D : Determine the vertical reaction at point C by taking the moment about the point D . ∑ M D = 0 400 ( 2 ) − C y ( 3.5 ) = 0 (II) Conclusion: Solve Equation (II). 3.5 C y = 800 C y = 228.57 N Thus, the vertical reaction component at point C is C y = 228.57 N _ . Segment ABC : Show the free-body diagram of segment ABC as in Figure 3. Using Figure 3, Determine the value of θ : tan θ = Opposite side Adjacent side (III) Moment about the point B : Determine the horizontal reaction at point C by taking the moment about the point B . ∑ M B = 0 C x ( 2.5 ) = 0 (IV) Along the vertical direction: Determine the force in the members BD and BE by resolving the vertical component of forces. ∑ F y = 0 A y − C y − F B D sin θ − F B E sin θ = 0 (V) Along the horizontal direction: Determine the force in the members BD and BE by resolving the horizontal component of forces. ∑ F x = 0 F B E cos θ − F B D cos θ − C x = 0 (VI) Conclusion: Substitute 2.5 m for opposite side and 3.5 m for adjacent side in Equation (III). tan θ = 2 .5 3 .5 θ = 35.54 ° Solve Equation (IV). C x = 0 Substitute 657

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 6.6, Problem 76P

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The horizontal and vertical components of force which the pins at A, B, and C exert on member ABC of the frame.

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Chapter 6.6, Problem 75P

Chapter 6.6, Problem 77P

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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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The horizontal and vertical components of force which the pins at A , B , and C exert on member ABC of the frame.

The horizontal and vertical components of force which the pins at A, B, and C exert on member ABC of the frame.

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Chapter 6 Solutions