A simply-supported truss bridge carries a point load P at distance a from the left support (span L = a+b). Bending stress in the bottom chord and mid-span deflection both scale with the bending moment.
M(x) = P·a·b / L (moment under the load)
δ_mid ≈ P·a²·b² / (3·E·I·L)
σ = M·c / I (flexure formula)
SF = σ_yield / σ_max
- Load magnitude — the point force applied to the deck; raises moment, stress and deflection everywhere.
- Load position — moves the load across the span; moment peaks under the load itself.
- Beam depth (I) — scales the second moment of area of each member; stiffer members deflect and stress less for the same load.
- Span length — longer spans amplify both moment and deflection for the same load.
- Roll load — animates the load sweeping across the deck so you can see which position is most critical.
Real bridges are designed so the safety factor (yield stress ÷ peak stress) stays comfortably above 1 under the heaviest expected vehicle load, with extra margin for fatigue and dynamic impact.