Shear force and bending moment diagrams

Shear force and bending moment diagrams show how internal forces vary along a beam. They tell the designer where a beam needs the most steel, where bars can be curtailed and where shear links must be closer.

At any section, the shear force is the sum of the vertical forces on one side of the cut, and the bending moment is the sum of their moments about the cut. A consistent sign convention matters more than which one you choose; a common one treats sagging moment as positive.

Three relationships make the diagrams quick to draw. Under no load the shear is constant and the moment varies linearly. Under a uniform load the shear varies linearly and the moment follows a parabola. The slope of the moment diagram equals the shear, so the maximum moment occurs where the shear crosses zero. A point load causes a jump in the shear diagram equal to the load.

For a simply supported beam with a uniform load, the moment peaks at mid-span. For a cantilever, the moment is largest at the fixed end and the bars must go at the top. Getting this right is what puts steel on the correct face of a member.