How Can I Move a Moment About One Point to Another Point?

Unless your beam is accelerating in rotation (which it's not, I assume ) the sum of all moments is zero. So if you have a moment at one spot, you have to have the opposite moment at another spot to cancel it.

Let assume that we:

a beam (lenght=l)

a constrain in the point A which gives a Moment Ma (unknown)

an external force F applied at a distance x from A

A constrain in B which gives me the moment Mb

Now. You say: So if you have a moment at one spot, you have to have the opposite moment at another spot to cancel it.

So in B we have
F(l-x)+Mb which is "the moment at one spot"

you have to have the opposite moment at another spot to cancel it so Ma is the opposite of F(l-x)+Mb?

That cannot be true because then in A we get as equilibrium:

Ma= Fx+Mb

F(l-x)+Mb=Fx+Mb
Fl=0

It would be helpful to have the configuration of your beam such as end constraints and load type. From what you have described it sounds like the ends are fixed and there is a point load between them. The following is taken from my Engineering Formulas book by Kurt Gieck:

Hopefully this will be clear enough. But the load (W) is located a distance 'a' from one end (A) and 'b' from the other end (B) with a span of 'l' between them.

Reactions:

R_A = W*b²/l²*(3-2*b/l)

R_B = W*a²/l²*(3-2*a/l)

Moments:

M_A = W*a*b²/l²

MB = W*b*a²/l²

This image should be more clear, but it uses 'P' instead of 'W' for the applied load and 'L' instead of 'l' for the span between constraints.

Let me try to clarify. All you really need to know, in a static situation, is that about any point:

1. The sum of forces = 0.

2. The sum of moments = 0.

3. Moments are calculated as lever arm x force.

Don't forget the forces (and moments) at points A and B, the supports.

Some supports only supply a force, e.g., a beam resting on two points. Others also supply a moment. A cantilever is a good example, where the internal forces within the beam provide an equalizing moment for the other forces involved.

I hope this helps.

Rixter has got it. Its a conservation thing.