Statics question – change in loading

1. The problem statement, all variables and given/known data

In the structure shown, the beam is pinned at point B. Point E is a roller support. The beam is loaded with a distributed load from point A to point B of 400 N/m, a 500 N·m couple at point C, and a vertical 900 N force at point D. If the distributed load and the vertical load at D are removed, and a vertically upward force of 1700 N at point F is added, what moment at point F would be necessary to keep the reaction at point E the same?

2. Relevant equations

3. The attempt at a solution

Since the reaction Ey at point E is to be unchanged, we only need to calculate the change in loading. Also, the location of the new moment is irrelevant.

Since the reaction forces at B are unknown, it is convenient to find the change in loading by summing the moments at point B.

The distributed 400 N/m force creates an 800 N downward force 1m to the left of point B.

The changes at point B needed to counteract the removal of the 800 N force and the 900 N force, and the addition of an upward force at point F are:

∑MB = (800N)(1m) – (900N)(5.5m) + (1700N)(4.5m) = 3,500N clockwise

That’s my answer, but the book has:

-(800N)(1m) + (900N)(5.5m) + (1700N)(4.5m) = 11,800N clockwise

I’ve stared at this problem for an hour now and I can’t see how my calculation is incorrect.

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