Shear force is the transverse companion to the bending moment: cut a beam anywhere and the vertical forces on one side of the cut must be balanced by an internal shear across the section. By the common convention, shear is positive when the net force to the left of the cut acts upward, with downward loads and upward reactions counted positive when summing equilibrium.
Its maxima come from the same statics that give the reactions. A simply supported beam under a central point load P carries a constant shear of P/2 between each support and the load; under a full-span UDL the shear peaks at wL/2 at the supports and passes through zero at midspan. A cantilever sees its largest shear at the fixed end — P for a tip load, wL for a distributed one.
The shear-force diagram (SFD) makes the distribution visible: it steps abruptly at every concentrated load — from +50 kN to −50 kN across a 100 kN midspan load on a symmetric span — and slopes linearly through distributed loads. Reading the SFD alongside the bending-moment diagram identifies which cross-sections govern, since the moment is largest where the shear crosses zero.