The science
Method. The bridge is idealised as two identical plane trusses with frictionless pin joints, loaded only at the joints. Each member is an axial spring of stiffness EA/L. The global equation is solved with a Cholesky factorisation of the reduced stiffness matrix:
K u = f , Nmember = (EA/L) [(ub - ua) . (cos, sin)]
Deck stringers are simply supported between transoms, so a wheel load between two joints is shared linearly ((1-f)P and fP). Each truss line carries half of an axle.
Influence lines. Because the model is linear, the force in a member for a unit load at joint j is its influence ordinate. The graph plots these ordinates; the live force is the sum of axle loads times ordinates, plus self-weight.
Beam analogy. The chords act like the flanges of a deep girder, so for a midspan point load
delta = P L^3 / (48 E Ieq) , Ieq = sum Achord y^2 , chord force = M / h
Deflection scales with L3, so doubling the span multiplies it by eight. The real truss deflects more than the analogy because the web members also stretch and shorten (shear), which the experiment shows as a ratio above 1.
Buckling. A compression member fails by Euler buckling long before it yields if it is slender:
Pcr = pi^2 E I / L^2 , capacity = min(A fy, Pcr)
Safety factor and rating. SF = capacity / |N|. The load rating is the largest multiple of the vehicle that keeps every member below capacity divided by the design factor, searched over vehicle positions on the span. When any member has SF below 1 the bridge is flagged overloaded and that member turns red; nothing is destroyed in the model.
Simplifications. Generic steel (E = 200 GPa, fy = 345 MPa), generic section sizes and weights, a Pratt-type web instead of the exact panel layout, pinned joints with no bolt slip or deck bending, a static analysis with a constant impact factor, and no wind, temperature or fatigue. Several side-by-side truss plies are modelled as one truss with multiplied member areas. This is a physics and engineering teaching model, not a design or rating tool for any real bridge.