# How a Suspension Bridge Stays Up

How deck load travels through suspenders, parabolic main cables, towers and anchorages, with a live sag\-ratio slider and a stiffening\-truss comparison

By Numa

Topic: Engineering

[Open the interactive Jig](https://ask.jig.com/j/JT0qEXuEazWN)

## Guide

### 1. A road hung from two cables

A suspension bridge carries its deck by hanging it\. Dead load travels up the suspenders in tension, along two main cables to the tower saddles, down the towers in compression, and back to the anchorages\. Amber marks tension and blue marks compression throughout\. The model uses Golden Gate dimensions: 1,280 m main span, 227 m towers\.

Drag empty space to turn the bridge\.

### 2. Suspenders: deck to cable

Vertical suspender ropes at a panel spacing of about 15\.2 m pick up the deck's dead load and deliver it to the main cables\. With so many closely spaced hangers, the cable sees a nearly uniform load per horizontal metre, w\. For the Golden Gate the design dead load was 21,300 lb/ft, about 311 kN/m, or w ≈ 155 kN/m per cable\.

Each suspender carries roughly w × 15\.2 m ≈ 2\.4 MN at its cable band\.

### 3. Why the cable is a parabola

A flexible cable carrying uniform load per horizontal length takes the shape y = \(w / 2H\) x², and horizontal equilibrium makes H constant along the span\. Taking moments about midspan gives H = wL² / 8d\. Drag the sag ratio d/L: a shallow cable is cheaper in tower height but its tension rises steeply, while a deep one needs taller towers\.

Built bridges cluster around d/L ≈ 1/8 to 1/11; the Golden Gate is about 1/9\.

### 4. Tension peaks at the towers

Cable tension T = H·√\(1 \+ y′²\) is least at midspan, where the cable is level and T = H, and greatest at the saddles, where the slope is 4d/L\. The brighter amber near each tower shows that rise\. At d/L = 1/9, T\_max ≈ 1\.09 H; a cable under only its own weight would hang as a catenary, which differs little at this sag\.

Per cable the 1935 design quoted a tension of 63,000,000 lb \(≈ 280 MN\) including live load\.

### 5. Towers work in compression

At each saddle the main\-span and backstay cables meet\. Their horizontal components nearly cancel, so the tower receives mainly a vertical thrust, V = wL/2 from the main span plus H·tan θ from the backstay\. The steel legs carry it down to the piers in compression, with little bending if the saddle stays balanced\.

The design figure was 61,500 short tons \(≈ 550 MN\) on each tower from both cables\.

### 6. Anchorages resist the pull

The horizontal component H does not vanish at the towers; it continues down the backstays to the anchorages\. Each cable splays into its strands inside a massive concrete block, about 60,000 tons, which resists the pull through its weight, friction and the rock behind it\. Remove the anchorage and the whole cable system loses its tension\.

The 1935 design gave a pull of 126,000,000 lb \(≈ 560 MN\) at each anchorage for both cables\.

### 7. Live load and the stiffening truss

A moving concentrated load would pull a bare cable into a local kink, because a cable has no bending stiffness\. The deep stiffening truss \(modelled at about 7\.6 m\) spreads the load over many suspenders, so the deflection is shallow and wide\. Switch the truss off to compare; deflections are exaggerated twenty\-fold and shown qualitatively\.

Deflection theory couples cable and girder; aerodynamic stiffness also matters, as Tacoma Narrows showed in 1940\.

### 8. The complete load path

Deck to suspenders, suspenders to cables, cables over the saddles into compression in the towers, and the remaining horizontal pull into the anchorages: every member is either pulled or pushed along its length\. The idealised model holds while the cable stays elastic and deflections stay small relative to the sag\.