Equivalent Force-Couple System (Problem 03.081.b)
Step 1: Match the moment about B
Original moment about B:
MB = rxPy - ryPx
= (0.300)(-484.974) - (-0.175)(280)
= -96.492 N·m (clockwise)
To reproduce this with a vertical at A located 0.125 m left of B:
FA · dAB = |MB|
FA = 96.492 / 0.125 = 771.94 N upward
Step 2: Match the force components
Force at B components:
FBx = FBcosθ , FBy = -FBsinθ
x-direction:
FBcosθ = Px = 280 ...(1)
y-direction:
FA + FBy = Py
771.94 - FBsinθ = -484.974
FBsinθ = 1256.914 ...(2)