What is the direct stiffness method?

It is the matrix form of the finite element method used for pin-jointed structures. Each member contributes a 4x4 stiffness block based on its axial stiffness EA/L and orientation into one global matrix K. Solving K times u equals F gives nodal displacements, from which member forces follow.

How do Pratt, Howe and Warren trusses differ here?

They differ in how the diagonal members are arranged. Pratt diagonals slope toward mid-span and go into tension under a central load, Howe diagonals slope the other way and go into compression, and the Warren truss alternates diagonals with no verticals. Switching type rebuilds the geometry and re-solves the model.

Why does the load sweep automatically?

By default the point load sweeps back and forth across the deck so you can see how member forces and the deflected shape change as the load moves, similar to a vehicle crossing a bridge. Dragging the deck or the position slider takes over and pauses the sweep.

Home▸Engineering & Materials▸Bridge Truss FEM (2D)

Bridge Truss FEM (2D)

2D truss-bridge FEM lab: assemble the global stiffness matrix for a Pratt, Howe or Warren truss, apply a moving point load, and watch member forces colour-coded from tension to compression.

Engineering & Materials2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion runs the same direct-stiffness-method truss solver as the 3D version through a flat, top-down diagram built for reading the structural analysis clearly: pick Pratt, Howe or Warren geometry and steel or aluminium, drag the load along the deck (or let it sweep automatically like a vehicle crossing the span), and watch the deformed shape and the tension/compression colour map update from a fresh global-stiffness-matrix solve every frame.

⚙ Under the hood

2D truss-bridge FEM lab: assembles the global stiffness matrix from each member's axial stiffness EA/L and orientation, solves K·u = F by Gaussian elimination, and colours members by tension/compression.

truss bridgefinite element methoddirect stiffness methodstructural analysisstress distribution

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install