A real finite-element solver for beams, in the browser, with no account and no nonsense.
I teach structural mechanics. Every year I send students home with the same exercise: take this beam, these supports, these loads, and draw me the shear and moment diagrams. The math is solvable by hand. The diagrams are not optional — they're how a structural engineer learns to see what a beam is doing.
For decades, the only way for a student to check their answer was to run a commercial structural analysis package — SAP2000, RISA, ETABS — software designed for working engineers, with interfaces that look like they haven't been updated since 1998 and price tags that haven't either. Free web tools exist, but most of them are toys: simple cases only, no documentation of the math, ads on every screen.
Tension & Moment is the free beam calculator I built because my students deserved better.
Try it here — runs in any modern browser, no signup, no backend, no tracking.
Who this is for
The audience is anyone who needs to compute beam forces and deflections quickly and trust the answer. Structural engineering students checking their hand calculations. Practising engineers who want a sanity check without booting up the full software stack. Lecturers building examples for class. Anyone teaching themselves structural analysis from a textbook.
How it works
You draw a beam. You place supports — pin, roller, or fixed — wherever you want them along the span. You add loads: point forces, moments, or distributed loads with any taper from rectangular to triangular. You hit Solve.
In a few milliseconds, you get three diagrams: shear force along the length, bending moment along the length, and the deflected shape of the beam under load. Hover anywhere on the diagrams and a crosshair shows you the exact value at that position. Tap a support and you see its reaction force. Everything updates in real time as you edit.
That's the whole tool. No projects to manage, no licenses to install, no account to create. Open the page. Solve the beam.
The core idea
The principle is that engineering software shouldn't be ugly. The math underneath is beautiful — Euler-Bernoulli beam theory, finite element formulation, exact analytical solutions for the classical cases. The fact that most software wrapping that math looks like a CAD program from the early 1990s is a failure of craft, not a requirement of the discipline.
Tension & Moment uses the same finite-element solver method that runs inside the expensive commercial packages — assembled from scratch in plain JavaScript, validated against closed-form analytical solutions for every classical case in the textbook. The numbers are correct to machine precision. The diagrams render as crisp vector graphics that look right at any zoom level, on any screen.
The visual language is deliberately precision instrument. Drafting-paper cream by day, oscilloscope amber on navy by night. Monospace fonts for every number. A subtle dot grid behind everything. The interface is supposed to feel like an instrument, not an app.
The moment the diagram becomes the answer
The reason for building this is a moment that happens early in a structural engineer's training and never quite goes away. You solve the beam by hand. You compute the reactions. You sketch the shear diagram from the loads, the moment diagram from the shear, the deflected shape from the moment. Each step is mechanical. The moment of insight is when the four pictures agree with each other — when what you sketched matches what you computed.
Tension & Moment is built to make that picture instant. A student edits a beam, sees the diagrams update live, and starts building intuition: where does maximum moment occur? What happens to deflection if I add a support? Why does a cantilever behave so differently from a simply-supported beam? These are questions textbooks answer in equations. The calculator answers them in pictures, in real time.
What this is
Tension & Moment is what I wanted to give my students. A real solver, accurate to machine precision, in a tool that looks like the engineering instrument it is. No license, no install, no backend, no ads. The whole application is one self-contained file — small enough to attach to an email, fast enough to run on a phone, accurate enough to trust.
It's also a quiet argument that engineering software can look as good as anything else on the internet, if anyone decides to build it that way.
Coming next
A tutorial article and YouTube video are in production: a walkthrough of how Tension & Moment was built with AI coding agents, covering the finite-element math, the diagram rendering, and the design decisions that made it feel like an instrument instead of an app. Subscribe for when it ships.