Calculate and visualize shear force and bending moment diagrams for loaded beams. Supports point, distributed, and moment loads.
You set the span and support conditions, add point loads, distributed loads, or moment couples, and the tool solves the statics and draws the shear force and bending moment diagrams below the beam. Because moment is built as the integral of shear, the three curves are mutually consistent by construction. The thing that surprises most first-time users: a moment couple never shows up in the shear diagram at all, and the peak bending moment sits where the shear curve crosses zero, not under the heaviest-looking load.
A concrete input and expected output from the current implementation.
Input
Span 6, simple supports at both ends. Point load 24 at midspan (x = 3).
Expected output
Reactions 12 at each support. Shear is +12 from x = 0 to x = 3, jumps by the full 24 at the load, and stays -12 to x = 6. Bending moment is 0 at both supports, rises linearly to 36 at midspan, and falls back to 0.
Symmetry puts half the load on each support (24/2 = 12), and a central point load on a simple span peaks at PL/4 = 24 x 6 / 4 = 36 kN.m at midspan.
The tool first enforces static equilibrium: vertical forces sum to zero and moments about any point sum to zero, which fixes the reactions for statically determinate beams. Shear at any station is then the net vertical load on one side of that station, and bending moment is the accumulated area under the shear diagram, so all three outputs stay consistent with each other.
A point load makes the shear diagram jump by the load's magnitude and kinks the moment curve at that station. A distributed load slants the shear line and curves the moment parabolically. A moment couple leaves the shear diagram untouched and jumps the moment curve by the couple's value. The maximum bending moment occurs where the shear curve crosses zero.
At the point where the shear diagram crosses zero, since moment is the integral of shear. For a symmetric load on a simply supported beam that is midspan; for asymmetric loading it shifts toward the more heavily loaded side. If shear crosses zero several times, there are local peaks to compare, and the moment curve's extremum is the largest of them.
No. The beam is treated as weightless, and its material is irrelevant: reactions, shear, and moment depend only on loads, supports, and span, never on stiffness or cross-section. To include self-weight, add it yourself as a uniform distributed load. Anything needing material properties, like deflection, is outside this tool's scope.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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