Learn how to use the Beam Solver app
Watch the complete walkthrough for setting spans, supports, loads, units, and reading the shear, moment, slope, and deflection results.
Multi-Span Beam Solver
Downward loads are positive. Any number of spans. Results via Euler–Bernoulli 1D beam FE (2 dof/node: v, θ).
Beam, Material & Mesh
Loads
Convention: P and w are downward positive. Distances are local to the chosen span and use the global length unit (m); forces use the global force unit (kN).
A point load can be inclined: pick an angle from the horizontal or enter a slope triangle (any two of run / rise / hyp). Its vertical component drives shear, moment, and deflection; its horizontal component is carried as axial force and resisted by the pin and fixed supports. Inclined loads are assumed to act along the beam axis (no eccentricity).
Moving Load
Build the train from any mix of wheels and uniform loads, in order from front to back — a lane load behind an axle group is just wheel, wheel, uniform. Each item after the first sits its gap past the end of the one before it, so a gap of 0 butts them together. A uniform load may be trapezoidal: set w₁ ≠ w₂.
Drag the train on the beam sketch, or use the slider. Shear and moment redraw as it moves. The train rolls right off either end: a wheel past the end carries nothing into the beam, and a uniform load hanging over the end is cut at the end so only the part still bearing counts. That is how you park it with a single wheel biting the edge and the rest in mid-air.
Show / Hide
Beam Sketch
The shear, moment, slope, and deflection diagrams are shown below. Hover (or tap) an internal hinge to read the vertical and horizontal forces transmitted through it.
Evaluate at x
Enter a global x measured from the left end of the beam, or drag the slider. The span is detected automatically.
The slider activates once the beam is solved.
Point Evaluation (V, M, θ, δ at user points)
Probe Results
| Span | x (m) | V (kN) | M (kN·m) | θ (rad) | δ (mm) | Exact V | Exact M | Exact θ | Exact δ |
|---|
Results
Left Support
Rleft (kN), Mleft (kN·m)
— / —
Hleft: — kN
—
Right Support
Rright (kN), Mright (kN·m)
— / —
Hright: — kN
—
Max Deflection
δmax (mm) @ x (m)
—
Stations (supports + midspans)
| x (m) | V (kN) | M (kN·m) | δ (mm) |
|---|