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 left side as negative in horizontal components of forces. Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces. Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable. Apply the Equation of equilibrium wherever applicable. The member AC is a two-force member. Member AB : Show the free-body diagram of the member AB as in Figure 1. Using Figure 1, Determine the value of θ : tan θ = Opposite side Adjacent side (I) Moment about point B : Determine the force in the member AC by taking moment about point B . ∑ M B = 0 2 ( 0.5 ) + 2 ( 1 ) + 2 ( 1.5 ) + 2 ( 2 ) − F A C sin θ ( 1.5 ) = 0 (II) Along the vertical direction: Determine the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 F A C sin θ − 2 − 2 − 2 − 2 + B y = 0 (III) Along the horizontal direction: Determine the horizontal reaction at point B by resolving the horizontal component of forces. ∑ F x = 0 − F A C cos θ + B x = 0 (IV) Conclusion: Substitute 2 m for opposite side and 1.5 m for adjacent side in Equation (I). tan θ = 2 1 .5 θ = 53.13 ° Substitute 53.13 ° for θ in Equation (II). 1 + 2 + 3 + 4 − F A C sin 53.13 ° ( 1.5 ) = 0 F A C = 10 1.5 × sin 53.13 ° F A C = 8.33 kN Substitute 8.33 kN for F A C and 53.13 ° for θ in Equation (III). 8.33 sin 53.13 ° − 8 + B y = 0 B y = 1.34 kN Substitute 8.33 kN for F A C and 53.13 ° for θ in Equation (IV). − 8.33 cos 53.13 ° + B x = 0 B x = 5 kN Thus, the vertical reaction component at point B is B y = 1.34 kN _ . Thus, the horizontal reaction component at point B is B x = 5 kN _ . Point A : Show the free-body diagram of the point A as in Figure 2. Using Figure 2, Along the vertical direction: Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 F A C sin θ − A y = 0 (V) Along the horizontal direction: Determine the horizontal reaction at point A by resolving the horizontal component of forces. ∑ F x = 0 A x − F A C cos θ = 0 (VI) Conclusion: Substitute 8.33 kN for F A C and 53.13 ° for θ in Equation (V). 8.33 sin 53.13 ° − A y = 0 A y = 6.67 kN Substitute 8.33 kN for F A C and 53.13 ° for θ in Equation (VI). A x − 8.33 cos 53.13 ° = 0 A x = 5 kN Thus, the vertical reaction component at point A is A y = 6

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 6.6, Problem 72P

To determine

The horizontal and vertical components of force at pins A, B, and C, and the reactions at the fixed support D of the three-member frame.

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Chapter 6.6, Problem 71P

Chapter 6.6, Problem 73P

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Engineering Mechanics: Statics

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The horizontal and vertical components of force at pins A , B , and C , and the reactions at the fixed support D of the three-member frame.

The horizontal and vertical components of force at pins A, B, and C, and the reactions at the fixed support D of the three-member frame.

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Chapter 6 Solutions