Explanation Given information : The downward force F 1 is 400 N. The upward force F 2 is 600 N. The downward inclined force F 3 is 900 N. The upward inclined force F 4 is 400 N. Show the free body diagram of the frame as in Figure (1). Use Figure (1). Assumption : Towards the right is positive. Determine the resultant of the horizontal force using the equation of equilibrium. F R x = ∑ F x = F 3 ( 3 5 ) − F 4 ( 4 5 ) (I) Assumption : Upward is positive. Determine the resultant of the vertical force using the equation of equilibrium. F R y = ∑ F y = F 2 − F 1 − F 3 ( 4 5 ) + F 4 ( 3 5 ) (II) Determine the resultant force F R . F R = ( F R x ) 2 + ( F R y ) 2 (III) Determine the direction θ of resultant force. θ = tan − 1 ( F R y F R x ) (IV) Assumption : Clockwise is positive. Determine the line of action of resultant by taking the moment about point A . ( M R ) A = ∑ M A F R y a − F R x b = F 1 ( l 1 ) − F 2 ( l 2 ) − ( F 3 ) ( 3 5 ) ( l 3 ) + ( F 4 ) ( 4 5 ) ( l 4 ) (V) Here, the horizontal distance of F 1 is l 1 , the horizontal distance of F 2 is l 2 , the vertical distance of F 3 is l 3 , and the vertical distance of F 4 is l 4 . Show the calculation of the resultant force and the line of action as follows: Conclusion : Substitute 900 N for F 3 and 400 N for F 4 in Equation (I). F R x = 900 ( 3 5 ) − 400 ( 4 5 ) = 540 − 320 = 220 N ( → ) Substitute 600 N for F 2 , 400 N for F 1 , 900 N for F 3 , and 400 N for F 4 in Equation (II). F R y = 600 − 400 − 900 ( 4 5 ) + 400 ( 3 5 ) = 600 − 400 − 720 + 240 = − 280 N = 280 N ( ↓ ) Substitute 220 N for F R x and –280 N for F R y in Equation (III)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.8, Problem 121P

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The equivalent resultant force, the direction of the resultant force, and the line of action of the resultant that intersects a vertical line along member CB measured from C.

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Chapter 4.8, Problem 120P

Chapter 4.8, Problem 122P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The equivalent resultant force, the direction of the resultant force, and the line of action of the resultant that intersects a vertical line along member CB measured from C .

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The equivalent resultant force, the direction of the resultant force, and the line of action of the resultant that intersects a vertical line along member CB measured from C.

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