So for any structure, simply supported beam, three hinge frame, cantilever etc. where there is a uniformly distributed load. For example, for a simply supported beam with uniform load of w along the length of x. Why is the bending moment equation w(x)(x/2)? I understand that the magnitude of the force is given by w(x), but is the reason for the (x/2) is because the magnitude acts halfway through the load?
Now I know that shear force and bending moment are related, with the shear force being the derivative of the bending moment, so I can just integrate the shear force equation to get w(x)(x/2), but I want to confirm through fundamentals as to why the equation is as it is.