Explanation Given information: Each member of the truss is uniform and has a weight of W . Remove the external load P . Method adopted: Method of Joints. Assumptions: The weight of each member can be represented as a vertical force, half of which is applied at each end of the member. 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 the horizontal components of forces. Consider the force indicating upward as positive and downward as negative, in the vertical components of forces. Consider the clockwise moment as negative and the anti-clockwise moment as positive, wherever applicable. Distribution of self-weights: Joint A : Find the vertical force at joint A due to weight: W A = Weight of member A E 2 + Weight of member A B 2 = W 2 + W 2 = W Joint B : Find the vertical force at joint B due to weight: W B = Weight of member A B 2 + Weight of member B E 2 + Weight of member B C 2 = W 2 + W 2 + W 2 = 3 W 2 Joint C : Find the vertical force at joint C due to weight: W C = Weight of member C D 2 + Weight of member C E 2 + Weight of member B C 2 = W 2 + W 2 + W 2 = 3 W 2 Joint D : Find the vertical force at joint D due to weight: W D = Weight of member C D 2 + Weight of member D E 2 = W 2 + W 2 = W Joint E : Find the vertical force at joint E due to weight: W E = ( Weight of member A E 2 + Weight of member E 2 + Weight of member C E 2 + Weight of member E D 2 ) = W 2 + W 2 + W 2 + W 2 = 2 W Reactions: Entire truss: Show the free-body diagram of the entire truss as in Figure 1. Using Figure 1, Moment about point A : Determine the vertical reaction at point D by taking moment about point A . ∑ M A = 0 D y ( 2 L ) − W ( 2 L ) − 3 W 2 ( 3 L 2 ) − 3 W 2 ( L 2 ) − 2 W ( L ) = 0 (I) Along the vertical direction: Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y + D y − W − 3 W 2 − 3 W 2 − 2 W − W = 0 (II) Along the horizontal direction: Determine the horizontal reaction at point A by resolving the horizontal component of forces. ∑ F x = 0 A x = 0 Conclusion: Solve Equation (I). D y ( 2 L ) − 2 W L − 9 W L 4 − 3 W L 4 − 2 W L = 0 D y ( 2 L ) − ( 8 W L + 9 W L + 3 W L + 8 W L 4 ) = 0 D y ( 2 L ) = 28 W L 4 D y = 7 W 2 Substitute 7 W 2 for D y in Equation (II). A y + 7 W 2 − 7 W = 0 A y = 7 W 2 Joint A : Show the free-body diagram of joint A as in Figure 2. Using Figure 2, Determine the value of θ . cos θ = Adjacent side Hypotenuse (III) Along the vertical direction: Determine the force in member AB by resolving the vertical component of forces

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 6.3, Problem 24P

To determine

The approximate force in each member due to the weight of the truss and whether the states of members are in tension or compression.

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Chapter 6.3, Problem 23P

Chapter 6.3, Problem 25P

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Chapter 6 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - State if the members are in tension or...Ch. 6.3 - Prob. 3FP 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 - State if the members are in tension or...Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P 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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