A truck convoy crosses a 600 m suspension span. See how the stiffening girder, the cables and the towers share the load, and what the worst case along the deck is.
Read it like a map of "how much does a 1 N load at this position bend the chosen section". Orange marks are the axles now on the span. Moment per unit load, in metres.
The science
Idealisation. The main cables carry the dead load of the deck as a parabola of sag f, so H = wd L² / (8 f). Under that load the girder is stress-free (it is "hung"). Only the live load q (the trucks) acts on the stiffening girder.
Linearised deflection theory. For a girder of stiffness EI on a cable of horizontal force H, with downward deflection v and simply supported ends at the towers: EI v'''' − H v'' + ΔH β = q, with β = 8f/L². The cable stretches as it is pulled down, so ΔH rises with the area under the deflected shape: ΔH = κ β ∫ v dx, κ = EcAc / Le. The whole thing is solved on a 5 m grid (120 intervals) with finite differences; the ΔH coupling is a rank-one update handled by the Sherman–Morrison formula, which is verified against a direct solve below.
Moment, hanger force, reactions. M = −EI v'' (sagging positive). The hangers hand p = −H v'' + ΔH β per metre to the cables. The end reactions are the shear M' at the towers. Because the system is linear, the moment influence matrix is built once; the convoy then moves over it and the envelope is the maximum and minimum of M at each point over all convoy positions (every 5 m).
Why the girder looks so small. The dimensionless βL = L √(H/EI) compares the cable and the girder stiffness. Above about 5 the cable carries most of a local load and the girder only has to smooth it; a soft girder and a strong cable approach a string (v = P a(L−a)/(L H)), a stiff girder and a weak cable approach an ordinary beam (v = P L³/(48 EI)). Both limits are checked numerically.
Stress. Chord stress is estimated as σ = M (d/2) E / EI, d = 9.6 m between the chords. Yield 355 MPa. Simplifications: a single lane line, quasi-static (no resonance, a flat dynamic amplification factor instead), linear geometry (no hanger slackening), no wind or temperature, constant EI, no shear lag or local deck bending, no secondary tower effects. The three axle loads per truck (18 % / 41 % / 41 %) are generic. This is a teaching model, not a design tool. Models built with Blender, scene by Three.js.