What is the Sign Convention for Moments in Free Body Diagrams?

[theone]

Homework Statement

In the picture, I am confused with the sign of the moments. When taking moments about D, the moment due to the 100N is taken as positive, but when they take moments about B, its negative.

Homework Equations

The Attempt at a Solution

Shouldn't both cases be negative since in either case, they cause a clockwise moment about the pivot?

 

[Infinitum]

Not quite. It doesn't really matter whether you choose clockwise or anticlockwise to be the positive direction for both, as the two equations do not depend on each other. Even if you assumed the moment due to the 100 N force to be negative for both cases, you would still end up with the same answer, as the sign corresponding to the other forces for the first equation would change as well. Do try it out and convince yourself.

 

[Doc Al]

Shouldn't both cases be negative since in either case, they cause a clockwise moment about the pivot?

If they followed a consistent sign convention, yes. But it really doesn't matter, as long as within each equation all clockwise moments have the same sign. (After all, you can multiply both sides of the equations by -1, which switches the sign, and nothing really changes.)

 

[theone]

but what if, instead of taking moments about B like they have, Dy was found by summing forces in the y direction.

wouldn't the convention chosen to get By lead to different answers for Dy, because of the sign of By?

 

[Doc Al]

but what if, instead of taking moments about B like they have, Dy was found by summing forces in the y direction.

Try it and see. You get the same answer.

wouldn't the convention chosen to get By lead to different answers for Dy, because of the sign of By?

The convention used for the forces is that up is positive. That was used consistently. (The unknown forces By and Dy were initially assumed to point upward, which is why By came out negative.)