Explanation Method adopted: Method of section. 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 upside is taken as positive, and the downside 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. Show the free body diagram of truss as in Figure (1). Using Figure (1), Find the reaction: Take the moment about joint A and equate it to zero. ∑ M A = 0 G y ( 12 ) − 6 ( 10 ) − 8 ( 8 ) − 5 ( 4 ) − 4 ( 2 ) = 0 G y = 152 12 G y = 12.67 kN Along the vertical direction: Determine the vertical reaction at joint A by resolving the vertical component of forces. ∑ F y = 0 A y + G y − 4 − 5 − 8 − 6 = 0 A y + G y = 23 (I) Substitute 12.67 kN for G y in Equation (I). A y + 12.67 = 23 A y = 23 − 12.67 A y = 10.33 kN Along the horizontal direction: Determine the horizontal reaction at joint A by resolving the horizontal component of forces. ∑ F x = 0 A x = 0 Pass a section aa as shown in Figure (1) and consider the left side of the section. Show the free body diagram of left side of the section as in Figure (2). Using Figure (2), Determine the value of θ : tan θ = Opposite side Adjacent side (II) Substitute 3 m for opposite side and 2 m for adjacent side in Equation (II). tan θ = 3 2 θ = 56.31 ° Member CD : Apply the equation of equilibrium. Take the moment about joint J and it will eliminate the force in the members KJ and CJ . ∑ M J = 0 F C D ( 3 ) + 5 ( 2 ) + 4 ( 4 ) − A y ( 6 ) = 0 3 F C D − A y ( 6 ) = − 26 (III) Conclusion: Substitute 10

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ISBN: 9780137514724

Author: HIBBELER

Publisher: PEARSON

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Chapter 6, Problem 48P

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The force in members JK, CJ, and CD of the truss and whether the states of members are in tension or compression.

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Chapter 6, Problem 47P

Chapter 6, Problem 49P

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The force in members JK , CJ , and CD of the truss and whether the states of members are in tension or compression.

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The force in members JK, CJ, and CD of the truss and whether the states of members are in tension or compression.

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