Explanation Calculation: Show the free body diagram of the bent rod as in Figure (1). Determine the vector component of force F 1 . F 1 = − F 1 cos θ j − F 1 sin θ k (1) Here, the angle of force F 1 is θ , the vector component of force F 1 in the y direction is j , and the vector component of force F 1 in the z direction is k . Substitute 300 lb for F 1 and 45 ° for θ in Equation (1). F 1 = − 300 1 cos 45 ° j − 300 sin 45 ° k = ( − 212.1 j − 212.1 k ) lb Determine the vector component of force F 2 . F 2 = F 2 cos θ 1 sin θ 2 i + F 2 cos θ 1 cos θ 2 j − F 2 sin θ 1 k (2) Here, the angle of force F 2 is θ 1 and θ 2 and the vector component of force F 2 in the y direction. Substitute 45 ° for θ 1 and 30 ° for θ 2 in Equation (II). F 2 = F 2 cos 45 ° sin 30 ° i + F 2 cos 45 ° cos 30 ° j − F 2 sin 45 ° k = 0.3536 F 2 i + 0.6124 F 2 j − 0.7071 F 2 k Use Figure (1). Apply equation of equilibrium in the x axis. ∑ F x = 0 A x + B x + ( F 2 ) x = 0 (3) Here, the horizontal reaction at A is A x , horizontal reaction at B is B x , and the vector component of force F 2 in the x direction is ( F 2 ) x . Apply equation of equilibrium in the y axis. ∑ F y = 0 A y + C y + ( F 1 ) y + ( F 2 ) y = 0 (4) Here, the vertical reaction at A is A y , the vertical reaction at C is C y , the vector component of force F 1 in the y direction is ( F 1 ) y , and the vector component of force F 2 in the y direction is ( F 2 ) y Apply equation of equilibrium in the z axis. ∑ F z = 0 B z + C z + ( F 1 ) z + ( F 2 ) z = 0 (5) Here, the reaction at B along the z direction is B z , the reaction at C along the z direction is C z , the vector component of force F 1 in the z direction is ( F 1 ) z and the vector component of force F 2 in the z direction is ( F 2 ) z Take the moment along the x axis. ∑ M x = 0 − B z ( x 1 ) − A y ( x 2 ) − ( F 1 ) x ( x 3 ) − ( F 1 ) x ( x 3 ) = 0 (6) Here, the horizontal distance reactions and force along the x axis is x 1 , x 2 , and x 3 . Take the moment along the y axis. ∑ M y = 0 C z ( y 1 ) + A x ( y 2 ) = 0 (7) Here, the vertical distance of reactions along the y axis is y 1 and y 2

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382593

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.6, Problem 35P

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Chapter 4.6, Problem 34P

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Chapter 4 Solutions

Statics and Mechanics of Materials (5th Edition)

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Find the magnitude of force F 2 .

Solution Summary: The author shows the free body diagram of the bent rod as in Figure (1). Determine the vector component of force F_1

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