If I have a cantilever beam of length L fixed at the left end to a wall and I hang a weight W from it's right free end then why should the bending moment at a point x units to right of the wall be W(L-x)?
If I understand correctly, the bending moment at a point on the beam should be the total torque of the forces acting on cross surface at that point about an axis passing through the geometric center and perpendicular to the plane of bending, then how is this equal to W(L-x)?
Best Answer
If you split the beam in two at the position $x$ and do Free Body Diagrams you will understand why the internal moment is such.
Each split body needs to be in balance. To balance the part of the beam between the split and the end where the load is applied a moment of $F \left( \ell -x \right)$ is needed.