To determine The angle of rotation of the beam ( θ ) . Explanation Given information: The length of each rod is L . The diameter of each rod is d . The vertical force is applied at the end of the beam is P . The modulus of elasticity of material is E . Calculation: Show the free body diagram of therigid beam as in Figure 1. Refer Figure 1. Here, F A B is force of the rod AB and F C D is force of the rod CD . Calculate the moment about point F by applying the equation of equilibrium: Sum of moments about point F is equal to 0. ∑ M F = 0 ( F A B × a ) + ( F C D × a ) − ( P × 3 a ) = 0 a F A B + a F C D − 3 a P = 0 a ( F A B + F C D − 3 P ) = 0 F A B + F C D − 3 P = 0 F A B + F C D = 3 P (1) Show the geometry of the deformation diagram of the rod as in Figure 2. Refer Figure 2. Here, δ A B is deformation at AB and δ C D is deformation at CD . Calculate the forces of the rods ( F A B and F C D ) using the deformation: δ A B = δ C D F A B L A E = F C D L A E F A B = F C D Substitute F C D for F A B in Equation (1). F C D + F C D = 3 P 2 F C D = 3 P F C D = 3 P 2 Substitute 3 P 2 for F C D in Equation (1)

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 4.5, Problem 4.59P

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The angle of rotation of the beam (θ) .

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