Shear Force & Bending Moment Diagram | BeamMetric

Generate shear force and bending moment diagrams for beams with multiple loads and support conditions. Visualize internal forces.

How to Build a Shear and Moment Diagram

Pick the support type — simply supported, or a cantilever fixed at its left end — set the span, and add any combination of point loads and full or partial uniformly distributed loads. The calculator first solves the support reactions from static equilibrium.

It then evaluates the shear V(x) and moment M(x) along the beam: shear starts at the left reaction and drops by each load passed, while the moment accumulates as the running integral of shear. Extra sample points are inserted immediately on either side of every point load so the vertical step in the shear diagram is drawn cleanly.

Point loads produce jumps in shear and kinks in moment; distributed loads produce linearly varying shear and parabolic moment. The summary reports the extreme values Vmax, Vmin, Mmax, and Mmin together with both reactions, which is what you need for section sizing.

FAQ

Why does the shear diagram jump at a point load?

An idealized point load transfers its entire force at a single location, so the internal shear changes by exactly that force as you cross it. The calculator samples immediately on both sides of each load to capture the discontinuity instead of drawing a misleading slope between grid points.

How are shear and moment related?

The moment is the running integral of the shear: dM/dx = V. That is why the bending moment of a simply supported beam peaks where the shear diagram crosses zero, and why a constant UDL — which produces linear shear — always produces a parabolic moment curve.

Which end of the cantilever is fixed?

The left end, at x = 0; the right end is free. The fixed end resists the total of all applied loads, and the bending moment is greatest there because each load contributes in proportion to its distance from the wall.

Can I analyze several loads at once?

Yes — add as many point loads and partial uniformly distributed loads as the loading calls for. The reactions and both diagrams superpose all of them simultaneously, so you can model self-weight as a UDL plus equipment as point forces in a single run.