Explanation Given information : The downward inclined force F 1 is 2.5 kN. The downward inclined force F 2 is 1.5 kN. The downward force F 3 is 3.0 kN. Show the free body diagram as in Figure (1). Use Figure (1). Assumption : Towards right is positive. Determine the resultant of the horizontal force using the equation of equilibrium. ∑ F R x = ∑ F x = − F 1 ( 4 5 ) + F 2 sin θ (I) Here, the vertical resolving angle of F 2 is θ . Assumption : Upward is positive. Determine the resultant of the vertical force using the equation of equilibrium. F R y = ∑ F y = − F 1 ( 3 5 ) − F 2 cos θ − F 3 (II) Here, the horizontal resolving angle of F 2 is θ . Determine the resultant force F R . F R = ( F R x ) 2 + ( F R y ) 2 (III) Determine the direction θ of the resultant force. θ = tan − 1 ( F R y F R x ) (IV) Assumption : Counterclockwise is positive. Determine the resultant couple moment at point A using the principle of moments. ( M R ) A = ∑ M A = − F 1 ( 3 5 ) ( l 1 ) − F 2 cos θ ( l 2 ) − F 3 ( l 3 ) (V) Here, the horizontal distance of F 1 is l 1 , the horizontal distance of F 2 is l 2 , and the horizontal distance of F 3 is l 3 . Show the calculation of resultant force, direction, and moment as follows: Conclusion : Substitute 2.5 kN for F 1 , 1.5 kN for F 2 , and 30 ° for θ in Equation (I). ∑ ( F R x ) = − 2.5 ( 4 5 ) + 1.5 sin 30 ° = − 2.0 + 0.75 = − 1

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Chapter 4.7, Problem 99P

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The equivalent resultant force, direction of the resultant force, and the couple moment at point A.

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Chapter 4.7, Problem 98P

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The equivalent resultant force, direction of the resultant force, and the couple moment at point A .

Solution Summary: The author explains how to determine the equivalent resultant force, direction, and couple moment at point A using the equation of equilibrium.

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The equivalent resultant force, direction of the resultant force, and the couple moment at point A.

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