SPAN — The Alpine Crossing
Keep the footbridge safe as load, wind and weather evolve across the gorge.
Deck profile / live vs analytic
Vertical displacement · metresAnchor demand / operating envelope
Tension · kN / mission timeThe science · equations, assumptions & limits
Core relationships
δmax = 5 q L⁴ / (384 E I) · ideal simply-supported beam under uniform load; δ in m.
δ(x) = q x (L³ − 2 L x² + x³) / (24 E I) · analytic shape used as the graph overlay.
Fwind = ½ ρ Cd A v² · approximate aerodynamic drag; force in N.
SF = capacity / demand · dimensionless reserve indicator.
m ÿ + c ẏ + K y = F(t) · deck nodes integrated with a 1/120 s fixed step (semi-implicit Euler).
Model boundary
The deck is a 9-node finite-difference beam with three simplified vertical hanger springs. Material flexural rigidity E·I is adjustable directly; mass and geometry are lumped for speed.
Pedestrian loading is approximated as a moving-weight envelope; wind is reduced to a vertical disturbance for deck response and a separate lateral drag estimate. The analytical overlay assumes a simply-supported beam and uniform loading, so it is a reference, not a prediction of this cable-supported system.
Not a structural design tool. No fatigue, torsion, resonance certification, nonlinear cable sag, connection failure, or code checks are modelled. Use professional engineering analysis for real structures.
All values are educational approximations.
Credits: procedural geometry, original simulation code and synthesised ambience.