Explanation Given information: AE is constant. Assumptions: Consider that the state of member as tension where the force is pulling the member and as compression where the force is pushing the member. Consider that the force indicating 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. Apply method of joints to determine the force in each member of the truss. Express the equation for strain energy of a bar of constant cross-sectional area A and the constant internal axial load N as follows: U i = ∑ N 2 L 2 A E (1) Here, N is internal axial force, L is the length of the member, A is the cross sectional area of the member, and E is Young’s modulus or modulus of elasticity. Joint C : Show the free-body diagram of the joint C as in Figure 1. Determine the value of θ : sin θ = Opposite side Hypotenuse (2) Along the horizontal direction: Determine the axial force in the member AC by resolving the horizontal component of forces. ∑ F x = 0 − N A C cos θ + N B C cos θ = 0 N A C = N B C (3) Along the vertical direction: Determine the axial force in the member BC by resolving the vertical component of forces. ∑ F y = 0 N A C sin θ + N B C sin θ − P = 0 (4) Show the calculation of forces as follows: Conclusion: Substitute L /2 for opposite side and L for hypotenuse in Equation (2). sin θ = L 2 × L θ = 30 ° Substitute N B C for N A C and 30 ° for θ in Equation (4). N B C sin 30 ° + N B C sin 30 ° − P = 0 N B C = P ( C ) Substitute P for N B C in Equation (3)

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 14.3, Problem 14.26P

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The vertical displacement of joint C.

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