Truss elevation coloured by member force, deflected shape, utilisation along a crossing and deflection against span.
Compares the stiffness-solver bottom-chord force at midspan with the exact method-of-sections value (P/2) x / h for spans of 4 to 16 panels, and the deflection ratio against beam theory.
Not run yet.
The science
Model. A pin-jointed 2D truss (Warren-type panels with verticals, 3.05 m panel length, 1.45 m story height) is solved with the direct stiffness method: K u = f, member axial force N = (EA/L)((ub − ua)·ê), with a pin at the left support and a roller at the right. The solver is the module of the 3D lab, copied unchanged. Loads are one truss line's share: dead load as nodal loads plus the vehicle axles distributed to the two nearest bottom-chord joints.
Capacity. Tension capacity is A fy and compression capacity is the smaller of that and the Euler load π² E I / L² (pinned-pinned). Utilisation is |N| divided by the relevant capacity; the load rating is the largest multiple of the vehicle mass that keeps every member within capacity / safety factor, scanned along the crossing. Section properties are generic, so ratings are for teaching, not for design.
Method-of-sections check. For a point load P at midspan the reactions are P/2, and cutting the truss in the bay next to midspan gives the bottom-chord force exactly as F = (P/2) x / h, with x the distance from the support to the opposite top joint and h the truss depth. The experiment compares this closed form with the stiffness solver for several spans. The midspan deflection of the truss exceeds the Euler–Bernoulli beam value P L³ / 48 E Ieq because of shear deformation of the web; the ratio falls towards 1 for long, slender spans.
Honest simplifications. Linear elasticity, pinned joints, no joint slip or connection capacity, no lateral or torsional behaviour, a static (quasi-static with an impact factor) vehicle, no fatigue; the 3D page adds the Blender-built scene. This is an independent educational model of generic modular steel panel bridges, not affiliated with any manufacturer and not a design tool.