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 left side as negative in horizontal components of forces. Consider the force indicating upward is taken as positive and downward 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. If only two non-collinear members form a truss joint and no external load or support reaction is applied to the joint, the two members must be zero-force members. If three members form a truss joint for which two of the members are collinear, the third member is a zero-force member provided no external force or support reaction is applied to the joint. Joint B : Show the free-body diagram of the joint B as in Figure 1. Using Figure 1, Zero-force members: The members BC and AB are non-collinear and there is no external load and support reaction is applied to the joint. Thus, the force in the members BC and AB is zero. Thus, the zero force members are B C and A B _ . Joint H : Show the free-body diagram of the joint H as in Figure 2. Using Figure 2, Zero-force members: Three members AH , HG , and HI forming a truss joint H for which two of the members AH and HG are collinear, the third member HI is a zero-force member. Since, no external force or support reaction is applied to the joint H . Thus, the zero force members at joint H is H I _ . Joint I : Show the free-body diagram of the joint I as in Figure 3. Using Figure 3, Zero-force members: The force in the member HI is zero. Three members AI , IC , and IG forming a truss joint I for which two of the members AI and IC are collinear, the third member IG is a zero-force member. Since, no external force or support reaction is applied to the joint I . Thus, the zero force members at joint I is I G _ . Joint D : Show the free-body diagram of the joint D as in Figure 4. Using Figure 4, Zero-force members: The member DC and DE are non-collinear and there is no external load and support reaction is applied to the joint. Thus, the force in the members CD and DE is zero. Thus, the zero force members are C D and D E _ . Entire truss: Show the free body diagram of entire truss as in Figure 5. Using Figure 5, Reactions: Moment about point A : Determine the vertical reaction at point E by taking moment about point A . ∑ M A = 0 E y ( 6 ) − 6 ( 4.5 ) − 6 ( 3 ) = 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 − 6 − 6 + E y = 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). 6 E y − 6 ( 4.5 ) − 6 ( 3 ) = 0 6 E y − 27 − 18 = 0 6 E y = 45 E y = 7.5 kN Substitute 7.5 kN for E y in Equation (II). A y − 12 + 7.5 = 0 A y = 4.5 kN Section a-a : Pass a section a-a as shown in Figure 5 and consider left side of the section. Show the free body diagram of left side of the section a-a as in Figure 6. Using Figure 6, Force in the member IC : Determine the value of θ : tan θ = Opposite side Adjacent side (III) Moment about point G : Take the moment about point G , it will eliminate the force in the members GH and GI

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 6.4, Problem 39P

To determine

The zero-force members and the force in members IC and CG of the truss and the state of members are in tension or compression.

To indicate: The zero-force members in the truss.

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Chapter 6.4, Problem 38P

Chapter 6.4, Problem 40P

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Chapter 6 Solutions

Engineering Mechanics: Statics

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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The zero-force members and the force in members IC and CG of the truss and the state of members are in tension or compression. To indicate: The zero-force members in the truss.

The zero-force members and the force in members IC and CG of the truss and the state of members are in tension or compression. To indicate: The zero-force members in the truss.

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Chapter 6 Solutions

The zero-force members and the force in members IC and CG of the truss and the state of members are in tension or compression.

To indicate: The zero-force members in the truss.