Explanation The member AB is a two force member. The frame can be analysed by considering the members AB, BC and CD separately. 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 the upward direction as positive and the downward direction as negative in vertical components of forces. Consider the clockwise moment as negative and the anti-clock wise moment as positive wherever applicable. Apply the Equation of equilibrium wherever applicable. Member BC : Show the free body diagram of the member BC as in Figure (1): Using Figure (1), Determine the value of θ : tan θ = Opposite side Adjacent side (I) Substitute 4 m for the opposite side and 3 m for the adjacent side in Equation (I), tan θ = 4 3 θ = 53.13 ° Moment about pin B : Determine the vertical reaction at pin C by taking the moment about pin B , ∑ M B = 0 C y ( 9 ) − 15 ( 6 ) − 10 ( 3 ) = 0 9 C y − 90 − 30 = 0 (II) Moment about pin C : Determine the force in the member AB by taking the moment about pin C , ∑ M C = 0 10 ( 6 ) + 15 ( 3 ) − F A B sin θ ( 9 ) = 0 60 + 45 − 9 F A B sin θ = 0 9 F A B sin θ = 105 (III) Along the horizontal direction: Determine the horizontal reaction at pin C by resolving the horizontal component of forces. ∑ F x = 0 F A B cos θ − C x = 0 (IV) Show the calculation of force in the members as follows: Calculations: Solve Equation (II). 9 C y = 120 C y = 120 9 C y = 13.33 kN Substitute 53.13 ° for θ in Equation (III). 9 F A B sin 53.13 ° = 105 F A B = 105 7.2 F A B = 14

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ISBN: 9780134780955

Author: HIBBELER

Publisher: RENT PEARS

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The reactions at D .

Solution Summary: The author explains how the frame can be analysed by considering the members AB, BC and CD separately.

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