What is the effect of a moment on a point in a beam?

[chandran]

I have a doubt Applying moment at a point in a beam. Normally in beam theory we define moment at a point about some coordinate system.Does it mean that the point will try to accelerate around some axis in that coordinate system? The path of the point will be in a circle with centre at the coordinate system and radius as the distance between the coordinate system and the point in the beam.

if we define the moment about the coordinate system at the same point itself what will be the result?

 

[HallsofIvy]

0, of course. If your point is on the axis about which the system is rotating, it is not moving.

 

[Cyrus]

in beam theory we define moment at a point about some coordinate system.

Not quite, the moment is what is known as a "free vector" which means it can act ANYWHERE on the body and cause pure rotation. It will cause rotation of the beam irreguardless of where you put the moment.

Does it mean that the point will try to accelerate around some axis in that coordinate system? The path of the point will be in a circle with centre at the coordinate system and radius as the distance between the coordinate system and the point in the beam.

Again, the moment is a FREE vector, put it anywhere youd like to. The path is totally depended on the constraint. Is this beam fixed? if it is its not going to move around anywhere, it will just have a tendency to "want" to rotate, which is counteracted by supports. If it is free to move, it WILL rotate, in the direction that the supporting structure will alow for rotation. And it will revolve around the FIXED point on the beam to the ground. NO MATTER where the moment is placed. EVEN if the fixed point is off center on a round wheel, it will turn around that point, because its fixed, and the moment causes pure rotation.

IF the beam is floating in space, it will rotate around its center of gravity. NO MATTER Where the moment is applied.