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 segment: Show the free-body diagram of the entire segment as in Figure 1. Using Figure 1, Moment about the point B : Determine the horizontal reaction at point A by taking the moment about the point B . ∑ M B = 0 A x ( 0.2 ) − 800 ( 1 + 0.05 ) = 0 (I) Along the vertical direction: Determine the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 A y − B y − 800 = 0 (II) Along the horizontal direction: Determine the horizontal reaction at point B by resolving the horizontal component of forces. ∑ F x = 0 B x − A x = 0 (III) Conclusion: Solve Equation (I). 0.2 A x = 840 A x = 4 , 200 N A x = 4 , 200 N × 1 kN 1,000 N A x = 4.20 kN ( ← ) Substitute 4,200 N for A x in Equation (III). B x − 4 , 200 = 0 B x = 4 , 200 N B x = 4 , 200 N × 1 kN 1,000 N B x = 4.20 kN ( → ) Thus, the horizontal reaction at point A is A x = 4.20 kN ( ← ) _ . Thus, the horizontal reaction at point B is B x = 4.20 kN ( → ) _ . Segment AC : Show the free-body diagram of segment AC as in Figure 2. Using Figure 2, Moment about the point C : Determine the vertical reaction at point A by taking the moment about the point C . ∑ M C = 0 A x ( 0.2 ) − 800 ( 0.05 ) − A y ( 0.2 ) = 0 (IV) Along the vertical direction: Determine the vertical reaction at point C by resolving the vertical component of forces. ∑ F y = 0 A y − C y = 0 (V) Along the horizontal direction: Determine the horizontal reaction at point C by resolving the horizontal component of forces

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 6.6, Problem 66P

To determine

The horizontal and vertical components of force that the pins at A, B, and C exert on their connecting members.

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Chapter 6.6, Problem 65P

Chapter 6.6, Problem 67P

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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 that the pins at A , B , and C exert on their connecting members.

The horizontal and vertical components of force that the pins at A, B, and C exert on their connecting members.

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Chapter 6 Solutions