Understanding shear force and bending moment diagrams

A shear force diagram (SFD) and a bending moment diagram (BMD) do not show the loads applied to a beam — they show the internal forces the beam itself has to resist at every point along its length, as a direct consequence of those applied loads and the reactions holding it up. Cut the beam at any point, in your head, and look at everything to one side of that cut: the shear force at that point is the net vertical force from everything on that side, and the bending moment is the net turning effect (force × distance) from everything on that side, taken about the cut.

Because both diagrams are built by sweeping along the beam from one end, they follow a few predictable rules. On the shear diagram, a point load or reaction causes a sudden vertical jump equal to that force; a uniformly distributed load causes a straight sloped line, with the slope equal to the load's intensity. Wherever the shear diagram is a horizontal line, no load is being applied along that stretch (an unloaded span between two point loads, for instance).

Why the moment diagram matters most for design

The bending moment diagram is closely tied to the shear diagram: at any point, the moment is effectively the running total of the area under the shear diagram up to that point, which is why a straight-sloped shear diagram produces a curved (parabolic) moment diagram, while a constant shear produces a straight-sloped moment diagram. The most useful rule to remember when reading one: the bending moment is at a local maximum or minimum exactly where the shear diagram crosses zero — that's the point a designer usually checks first, because it's almost always where the section needs the most flexural capacity.

This is precisely why both diagrams matter for design, not just one: the peak moment governs how much flexural (bending) reinforcement or section capacity a beam needs at that location, while the shear force — particularly near supports, where it's usually largest — governs the shear reinforcement (stirrup spacing in a concrete beam, or the web capacity check in a steel one). A beam that's comfortably strong enough in bending can still fail in shear if that check is skipped.

The Beam calculator plots both diagrams directly from whatever support and loading you set up. RC Beam Design and Steel Beam Design take that same shear-and-moment information further, using the peak values to actually size reinforcement or check section capacity against the applicable code (see the related tools below).