Explanation Given Information: Use the single equation of equilibrium for the calculation of each force. 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 right side as positive and left side as negative in horizontal components of forces. Consider the force indicating upside is taken as positive and 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 moment about joint A and equate to zero. ∑ M A = 0 E y ( 20 ) − 3 ( 20 ) − 5 ( 15 ) − 4 ( 10 ) − 4 ( 5 ) = 0 E y = 9.75 kN Along vertical direction: Determine the vertical reaction at joint A by resolving the vertical component of forces. ∑ F y = 0 A y + E y − 2 − 4 − 4 − 5 − 3 = 0 A y + E y = 18 (I) Substitute 9.75 kN for E y in Equation (I). A y + 9.75 = 18 A y = 8.25 kN Along 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 5 m for adjacent side in Equation (II). tan θ 1 = 3 5 θ 1 = 30.96 ° Substitute 2 m for opposite side and 5 m for adjacent side in Equation (II). tan θ 2 = 2 5 θ 2 = 21.80 ° Member BC : Apply equation of equilibrium. Take moment about joint H and it will eliminate the force in the members H C and HG . ∑ M H = 0 F B C ( 3 ) + 2 ( 5 ) − 8

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 6.4, Problem 39P

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The force in members BC, HC, and HG of the truss and the state of members are in tension or compression.

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Chapter 6.4, Problem 36P

Chapter 6.4, Problem 40P

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Chapter 6 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 6.3 - In each case, calculate the support reactions and...Ch. 6.3 - Identify the zero-force members in each truss....Ch. 6.3 - Determine the force in each member of the truss....Ch. 6.3 - Determine the force in each member of the truss....Ch. 6.3 - Determine the force in each member of the truss....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 - Determine the force in each member of the truss....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 force in members BC , HC , and HG of the truss and the state of members are in tension or compression.

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