Cutting the member open

Imagine sawing a loaded beam in half. It would immediately fall apart, because the two halves were holding each other. Whatever forces the material was providing across that plane are the internal forces.

To find them, cut the beam at the section you care about, throw one side away, and ask what forces you would have to apply at the cut face to keep the remaining piece exactly where it is. Those forces are what the material was carrying.

At a cut in a plane member there are three of them. Normal force N acts along the member and either stretches or squashes it. Shear force V acts across the member and tries to slide one face past the other. Bending moment M is the turning effect that bends the member. In three dimensions there is also torsion, which twists it.

The cut-section method gives the normal force just as readily as the shear and moment, and it is worth drawing its own diagram when a member carries load along its length.

Cut the member, take one side, and resolve along the member instead of across it. The normal force is the algebraic sum of the axial components to that side, taken as positive in tension.

A column picking up load at each floor is the standard case. The normal force is constant between floors and steps by the load applied at each one, so the normal force diagram is a series of steps — exactly like a torque diagram, and for the same reason: point actions produce jumps, distributed ones produce slopes. A column carrying only its own self-weight, for instance, has a linearly varying normal force.