Explanation Method adopted: Method of joints. Assumptions: Keep P as unknown. 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 upward force which is taken as positive and the downward force which is taken as negative in vertical components of forces. Consider clockwise moment as positive and anti-clock wise moment as negative wherever applicable. Find the reactions: Show the free body diagram of the truss as in Figure (1). Using Figure (1), Take the moment at E and equate it to zero. ∑ M E = 0 P ( d ) − A x ( 3 2 d ) = 0 A x = 0.667 P Along the vertical direction: Determine the vertical reaction at the Joint E by resolving the vertical component of forces. ∑ F y = 0 E y − P = 0 E y = P Along the horizontal direction: Determine the horizontal reaction at the joint E by resolving the horizontal component of forces. ∑ F x = 0 A x − E x = 0 Substitute 0.667 P for A x . 0.667 P − E x = 0 E x = 0.667 P Joint E : Show the free body diagram of the Joint E as in Figure (2). Using Figure (2), Determine the value of tan θ : tan θ = Opposite side Adjacent side (I) Substitute 3 d 2 for the opposite side and d for the adjacent side in Equation (I). tan θ 1 = 3 d 2 d θ 1 = 56.31 ° Along the horizontal direction: Determine the force in the member EC by resolving the horizontal component of forces. ∑ F x = 0 F E C cos θ 1 − E x = 0 (II) Along the vertical direction: Determine the force in the member ED by resolving the vertical component of forces. ∑ F x = 0 E y − F E D − F E C sin θ 1 = 0 (III) Conclusion: Substitute 56.31 ° for θ 1 and 0.667 P for E x in Equation (II). F E C cos 56.31 ° − 0.667 = 0 F E C = 1.20 P ( T ) Thus, the magnitude of force in the member EC is 1.20 P ( T ) _ . Substitute P for E y , 1.20 P for F E C , and 56.31 ° for θ 1 in Equation (III). P − F E D − 1.20 P sin 56.31 ° = 0 F E D = 0 Thus, the magnitude of force in the member ED is zero _ . Joint C : Show the free body diagram of the Joint C as in Figure (3). Using Figure (3), Substitute d 2 for the opposite side and d for the adjacent side in Equation (I). tan θ 2 = d 2 d θ 2 = 26.57 ° Substitute 3 d 2 for the opposite side and d for the adjacent side in Equation (I). tan θ 3 = 3 d 2 d θ 3 = 56.31 ° Substitute d 2 for the opposite side and d for the adjacent side in Equation (I). tan θ 4 = d 2 d θ 4 = 26.57 ° Along the vertical direction: Determine the force in the members CD and CB by resolving the vertical component of forces. ∑ F y = 0 F E C sin θ 3 − F C D sin θ 2 + F B C sin θ 4 − P = 0 (IV) Along the horizontal direction: Determine the force in the members CD and CB by resolving the horizontal component of forces. ∑ F x = 0 − F E C cos θ 3 + F C D cos θ 2 + F B C cos θ 4 = 0 (V) Conclusion: Substitute 1.20 P for F E C , 56.31 ° for θ 3 , 26.57 ° for θ 2 , and 26.57 ° for θ 2 in Equation (IV)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 6.3, Problem 23P

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The force in each member of truss in terms of P and the state of members are in Tension or Compression.

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Chapter 6.3, Problem 22P

Chapter 6.3, Problem 24P

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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 each member of truss in terms of P and the state of members are in Tension or Compression.

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The force in each member of truss in terms of P and the state of members are in Tension or Compression.

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Chapter 6 Solutions