# Why do we include the fixed-end moment when calculating the bending moment at another point on the beam?

When we calculate the bending moment in a beam with a fixed end using the the method of cuts (determining the moment at a point $$x$$ by making a cut at that point in the beam) we usually include the restoring moment as a moment about $$x$$ in the calculations.

For example for a simple cantilever with a point load at the free end. It has a restoring moment $$R=Fl$$ at the support and vertical reaction at the supports of $$A_y$$:

$$R-A_yx-M_x=0$$ would be my moments about $$x$$. Why do we include the reaction moment $$R$$ when it acts about the support of the beam and not the point $$x$$?r

Do these moments actually act on a different point than I assume or is the fixed end moment caused by some sort of couple?

## 1 Answer

Note that the restoring moment, or technically the fixed end moment, represents the total energy produced by the applied force at a distance"x = l" from the support (which is the point of x = 0). And, for any point along the beam, to maintain structural equilibrium, the sum of forces must be equal to zero, that is, 0 = the total energy (R) - the energy produced by the reaction (Ay) and the internal energy (Mx) at that location. It is depicted in the figure below. Hope this helps.