Suspension Bridge 2D — Parabolic Cable Sag & Tension

Traffic Load

Live load w 10 kN/m

Geometry

Span L 600 m

Design sag ratio f₀/L 0.10

Hangers 16

Main Cable

Axial stiffness EA 4200 MN

Live Readouts

within limits

Sag f

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Horizontal tension H

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Tower tension T_max

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Total deck load

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How it works

The main cable of a suspension bridge carries a deck load that is (nearly) uniform per horizontal metre, so between the towers it hangs as a parabola rather than a true catenary: y = 4·f·x·(L−x)/L², where f is the sag at midspan. For a horizontal load w spread over span L, the horizontal tension component is H = w·L²/(8f) — constant along the whole cable — while the vertical shear grows linearly toward the towers, so the total tension T(x) = √(H² + w²(L/2−x)²) is lowest at midspan and highest at the towers.

y(x) = 4·f·x·(L−x) / L²      (parabolic cable shape)
H     = w·L² / (8·f)          (horizontal tension, constant)
T(x)  = √(H² + w²(L/2−x)²)    (total tension, max at towers)
s(f)  ≈ L·(1 + 8(f/L)²/3)     (cable arc length)

The cable itself is elastic, not rigid: its unstretched length is fixed once built, so a heavier live load stretches it slightly, which is exactly what lets the sag increase — more load forces the same physical cable to hang a little lower to find a new equilibrium between arc length and elastic strain s = L₀·(1+H/EA). This simulator solves that equilibrium numerically every time a slider moves, so sag and tension respond the way a real suspended cable would: heavier traffic increases both f and every tension reading, while a stiffer cable (higher EA) resists that extra sag far more.

Vertical hangers, evenly spaced along the deck, carry the deck's own share of the load up to the main cable — they are what actually turns a curved cable into a flat, drivable roadway.

Low tension High tension (near towers)