Explanation Given: The magnitude of component force F 1 = 200 lb . The magnitude of component force F 2 = 400 lb . The magnitude of component force F 3 = 300 lb . The magnitude of component force F 4 = 300 lb . Show the free body diagram of the magnitude of component forces F 1 , F 2 , F 3 and F 4 into x and y axis components as in Figure (1). Express the magnitude of component force F 1 along the x direction using Figure (1). ( F 1 ) x = F 1 (I) Express the magnitude of component force F 1 along the y direction using Figure (1). ( F 1 ) y = 0 Express the magnitude of component force F 2 along the x direction using Figure (1). ( F 2 ) x = F 2 cos θ (II) Express the magnitude of component force F 2 along the y direction using Figure (1). ( F 2 ) y = F 2 sin θ (III) Use Figure (1) to find out the cos θ and sin θ . cos θ = 4 5 sin θ = 3 5 Express the magnitude of component force F 3 along the x direction using Figure (1). ( F 3 ) x = F 3 sin θ (IV) Express the magnitude of component force F 3 along the y direction using Figure (1). ( F 3 ) y = F 3 cos θ (V) Express the magnitude of component force F 4 along the x direction using Figure (1). ( F 4 ) x = F 4 (VI) Express the magnitude of component force F 4 along the y direction using Figure (1). ( F 4 ) y = 0 Express the magnitude of the resultant force that is measured counterclockwise from the positive x axis using Figure (1). + → ( F R ) x = ∑ F x ( F R ) x = ( F 1 ) x + ( F 2 ) x + ( F 3 ) x + ( F 4 ) x (VII) Express the magnitude of the resultant force that is measured counterclockwise from the positive y axis using Figure (1). + → ( F R ) y = ∑ F y ( F R ) y = ( F 1 ) y + ( F 2 ) y + ( F 3 ) y + ( F 4 ) y (VIII) Calculate the magnitude of the resultant force F R that is measured counterclockwise from the positive x axis. F R = ( F R ) x 2 + ( F R ) y 2 (IX) Conclusion: Substitute − 200 lb for F 1 in Equation (I)

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Chapter 2.9, Problem 3RP

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The magnitude of the resultant force acting on the gusset plate of the bridge truss (FR).

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The magnitude of the resultant force acting on the gusset plate of the bridge truss ( F R ) .

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The magnitude of the resultant force acting on the gusset plate of the bridge truss (FR).

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