An arched deck truss bridge is a span where the deck rides on top of a curved truss that combines arch action with triangulated truss members. Highway and rail engineers reach for this configuration when a deep gorge or river valley gives them the headroom underneath but demands a clean roadway profile up top. The arch carries most of the load in compression into the abutments, while the truss web stiffens the arch against asymmetric live loads. The result is a long, stiff, economical span — the New River Gorge Bridge in West Virginia uses exactly this principle to clear 876 ft.
Arched Deck Truss Bridge Interactive Calculator
Vary span, rise ratio, truck load, and load position to see arch rise, abutment thrust, and compression change in the bridge diagram.
Equation Used
The calculator uses the article rise-to-span relationship r/L, expressed as L:r = n, then estimates horizontal abutment thrust for a point truck load on a simplified three-hinged arch. Lower n means a deeper arch and usually lower thrust demand; higher n means a shallower arch with higher foundation thrust sensitivity.
- Simplified teaching estimate for a three-hinged arched deck truss.
- Truck load is treated as a single vertical point load.
- Horizontal thrust is estimated from crown bending relief, not a final bridge design check.
- Deck, web, and arch are assumed to share load through ideal pinned truss action.
Operating Principle of the Arched Deck Truss Bridge
An arched deck truss bridge does two jobs at once. The arch — a curved chord running from abutment to abutment — pushes load outward and downward into the foundations as compression. The truss web — diagonals and verticals tying the arch to the deck above — stops that arch from buckling sideways or snapping through when a heavy truck rolls across one lane and not the other. The deck sits on top of the whole assembly, supported by short spandrel posts that transfer wheel loads down into the arch.
Why build it this way instead of a plain arch or a plain truss? Because a bare arch is brittle under unbalanced live loads — put a 40-ton lorry on one quarter-point and the arch wants to deform into an S-shape. The triangulated truss web fixes that. And a bare truss across the same span would need vastly more steel because every member would carry tension or bending instead of letting the arch geometry do the work in pure compression. You get a stiffer span for less tonnage of steel.
Tolerances matter. The rise-to-span ratio typically sits between 1:5 and 1:8 — go shallower than 1:10 and the horizontal thrust at the abutments climbs steeply, which means bigger, more expensive foundations. Camber must be built into the truss during fabrication so that under full dead load the deck sits at the design profile. If the camber is off by even 30-50 mm on a 200 m span, you'll see a visible dip and the expansion joints at the abutments will bind. Common failure modes are abutment movement (the arch loses its line of thrust and the truss starts carrying loads it wasn't sized for), corrosion at the deck-to-spandrel connections where road salt drips through, and fatigue cracking at gusset plates on highway bridges that see millions of load cycles a year.
Key Components
- Arch chord (lower curved member): The primary load path. Carries the bulk of dead and live load as axial compression into the abutments. Built-up box sections or wide-flange shapes are typical, with plate thicknesses sized so the slenderness ratio KL/r stays below 80 to prevent buckling.
- Upper deck chord: Runs roughly horizontal at deck level. Combines with the arch and the web members to form the truss. Carries tension under symmetrical loading and reverses to compression under some live-load patterns, which is why fatigue detailing matters here.
- Web members (diagonals and verticals): Tie the arch to the deck chord and triangulate the depth between them. Stop the arch from buckling out of plane and resist the unbalanced shear that comes from live loads on one half of the span. Member sizing is set by the highest-shear panel near the quarter points.
- Spandrel posts: Short vertical columns transferring deck load down into the arch at panel points. Spaced typically 6-12 m apart depending on stringer span. Pinned at top and bottom on older bridges, welded on modern designs.
- Abutments and skewbacks: Resist the horizontal thrust from the arch — often 40-60% of the vertical reaction. Founded on rock or deep piles. A 1 cm outward movement on a 200 m span can drop the crown by 30-50 mm, so foundation design is unforgiving.
- Deck system (stringers, floor beams, deck slab): Carries wheel loads from the riding surface to the spandrel posts. Floor beams span between trusses, stringers span between floor beams, slab spans between stringers. On a highway bridge the slab is typically 200-250 mm of reinforced concrete.
Where the Arched Deck Truss Bridge Is Used
Arched deck trusses show up wherever the terrain offers deep clearance below and the engineer wants a flat road or rail surface above. River gorges, rocky valleys, and mountain crossings are the classic settings. The configuration is also the right pick when navigation clearance is needed — nothing hangs below the deck except the arch itself, and the arch springs from points well above the waterline on the gorge walls.
- Highway infrastructure: The New River Gorge Bridge on US-19 in West Virginia — a 924 m steel arch with a deck truss carrying 4 lanes 267 m above the river. Built by US Steel American Bridge Division, opened 1977.
- Railway crossings: The Hell Gate Bridge approach spans in New York use deck-truss arch geometry to carry Amtrak's Northeast Corridor over the East River channel approaches.
- Mountain road crossings: The Cold Spring Canyon Bridge on California SR-154 — a 213 m steel deck arch truss spanning the canyon at 122 m above the floor, carrying 2 lanes of state highway.
- Hydroelectric and reservoir crossings: Service bridges across dam tailrace canyons where the deck must stay flat for vehicle access but the arch can spring from the bedrock walls — common on TVA and Bureau of Reclamation projects.
- Pedestrian and park infrastructure: Long-span footbridges in national parks where designers want minimal visual interruption above the deck — the arch tucks below, and walkers see only railings and roadway.
- Heavy industrial haul roads: Mine and forestry haul-road crossings over deep ravines, where loaded ore trucks of 200-400 tons demand a stiff, unbalanced-load-tolerant span — exactly what the truss web of a deck arch provides.
The Formula Behind the Arched Deck Truss Bridge
The single most important number in sizing an arched deck truss bridge is the horizontal thrust at the abutments — the inward push the arch generates when it carries load. This number drives foundation cost, abutment size, and whether you can even build the bridge on the available rock. The thrust depends on the rise-to-span ratio: shallow arches (rise/span around 1:10) generate enormous thrust and need massive abutments, while deep arches (rise/span around 1:4) generate manageable thrust but eat into clearance and lengthen the truss web. The sweet spot for highway deck-truss arches sits around rise/span = 1:5 to 1:6 — deep enough to keep thrust reasonable, shallow enough not to overshoot the available headroom.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| H | Horizontal thrust at each abutment | kN | kip |
| w | Uniformly distributed load (dead + live) per unit length of span | kN/m | kip/ft |
| L | Clear span between abutment centrelines | m | ft |
| r | Rise of the arch from springing line to crown | m | ft |
Worked Example: Arched Deck Truss Bridge in a 180 m steel deck-truss arch over a forested canyon
You're sizing the abutment thrust for a 180 m steel arched deck truss bridge carrying a 2-lane forest service road across a canyon in interior British Columbia. The combined dead plus live load works out to 95 kN/m along the span. You want to check the horizontal thrust at three candidate rise values to see which one your bedrock foundations can actually carry.
Given
- L = 180 m
- w = 95 kN/m
- r (low) = 18 m (rise/span = 1:10)
- r (nominal) = 30 m (rise/span = 1:6)
- r (high) = 45 m (rise/span = 1:4)
Solution
Step 1 — compute the total uniform load × span squared term that's common to all three cases:
Step 2 — at the nominal rise of 30 m (rise/span = 1:6, the typical sweet spot for a highway-class deck-truss arch):
That's roughly 1,290 tonnes of horizontal push at each abutment — large, but well within what a competent rock-anchored skewback can handle on solid granite or basalt.
Step 3 — at the low end of the typical range, a shallow arch with rise = 18 m (rise/span = 1:10):
The thrust jumps by 67% — about 2,150 tonnes per abutment. On marginal rock or a fractured rockmass that means oversized skewbacks, possibly post-tensioned rock anchors, and a real risk that abutment cost alone kills the project. This is why you almost never see rise/span shallower than 1:8 on a deck-truss arch.
Step 4 — at the high end, a deep arch with rise = 45 m (rise/span = 1:4):
Thrust drops to about 870 tonnes per abutment — friendly to the foundations. But now the truss web is 45 m deep, which means more steel, more wind-load surface, and potential clearance problems if the canyon isn't deep enough. The geometry stops being economical even though the abutments love it.
Result
The nominal horizontal thrust at each abutment is 12,825 kN — about 1,290 tonnes per side, which sets the size of your skewback and the rock-anchor requirements. Compare that to 21,375 kN at the shallow 1:10 rise (foundations get punishing) and 8,550 kN at the deep 1:4 rise (steel tonnage gets punishing) — the 1:6 nominal really is the sweet spot for a typical canyon crossing in this size class. If your measured thrust at commissioning differs from the predicted value, the usual culprits are: (1) abutment settlement of even 10-20 mm shifting the line of thrust and redistributing load into truss members that weren't sized for it, (2) camber error during fabrication leaving the arch in a non-funicular shape under dead load so live loads ride on a kinked geometry, or (3) temperature-induced thrust changes — a 30 °C swing on a 180 m steel span moves the crown by 50-60 mm and changes H by several percent if expansion bearings aren't releasing as designed.
Arched Deck Truss Bridge vs Alternatives
An arched deck truss isn't always the right pick. Compare it against the two most common alternatives for the same span range — a through-truss arch (where the deck hangs inside the arch) and a continuous plate-girder bridge — on the dimensions that actually matter when you're choosing.
| Property | Arched Deck Truss Bridge | Through-Arch Truss | Continuous Plate Girder |
|---|---|---|---|
| Economical span range | 120-550 m | 150-800 m | 40-180 m |
| Required clearance below deck | High (arch sits below) | Low (arch sits above deck) | Moderate |
| Steel tonnage per m2 of deck (typical highway) | 280-380 kg/m2 | 320-420 kg/m2 | 200-280 kg/m2 |
| Abutment / foundation cost | High (large horizontal thrust) | High (large horizontal thrust) | Low (vertical reactions only) |
| Stiffness under unbalanced live load | Excellent | Excellent | Moderate |
| Service life with proper detailing | 100+ years | 100+ years | 75-100 years |
| Fatigue-sensitive details | Gusset plates, deck-spandrel joints | Hanger connections, gusset plates | Welded flange splices |
| Best application fit | Deep gorge/canyon crossings | River crossings with low gorge walls | Multi-span valley or urban viaducts |
Frequently Asked Questions About Arched Deck Truss Bridge
Because the worst shear in the truss happens at the quarter points, not at the crown. When live load sits on only half the span — one heavy truck on the left side, no traffic on the right — the arch wants to deform into an S-shape. The truss web members at the quarter points fight that deformation in shear, and shear demand peaks roughly at L/4 from each abutment.
At the crown, the arch is mostly carrying axial compression and the web members aren't doing much. Designers sometimes taper the truss depth to save steel, but only after running an unbalanced-live-load case to confirm the quarter-point web members aren't governed by buckling.
Look at what's underneath the deck. If you have a deep gorge with rock walls well above the waterline or valley floor, a deck-truss arch is almost always cheaper and stiffer — the arch springs from the rock, the deck stays flat up top, and there's no need for hangers. New River Gorge is the textbook case.
If you have a shallow river crossing where you don't have anywhere to spring an arch from below the deck, a tied (through) arch makes sense — the arch goes above the deck, hangers carry the floor system, and a horizontal tie absorbs the thrust internally so abutments only see vertical reactions. Sydney Harbour and Hell Gate work this way.
Rule of thumb: if (gorge depth) > (span / 6), favour a deck-truss arch.
The most likely cause is abutment outward movement during decentering, not fabrication camber error. When the falsework comes out and the arch picks up its own weight for the first time, the horizontal thrust hits the abutments suddenly. If the rock or skewback compresses or rotates outward by even 10-15 mm, the arch geometry flattens and the crown drops several times that amount — the geometry amplification factor on a typical 1:6 rise arch is around 5-6×.
Check abutment movement first with survey monuments set before decentering. If the abutments held position, look next at fabrication shop drawings — camber is usually built in by shimming the arch chord segments at fabrication, and a missed shim plate at one panel point will show up as crown sag under dead load.
The shallow limit is foundation economics. As rise drops, horizontal thrust climbs hyperbolically — H is inversely proportional to r. Below 1:8 the thrust starts demanding rock anchors, post-tensioned tie-downs, or massively oversized skewbacks. At 1:10 the thrust is roughly 25% higher than at 1:8, which often pushes total project cost above competing bridge types entirely.
The deep limit is steel and wind. As rise grows, the truss web gets deeper, member lengths grow, the projected wind area increases, and lateral bracing systems get more expensive. Beyond about 1:4 you're paying more in superstructure than you saved in abutments.
Because the spandrel post connection sees concentrated wheel loads on every truck pass — millions of load cycles a year on a busy highway — while the arch chord sees a smoothed-out average load. Fatigue is a cycle-count problem, not a peak-stress problem, and the spandrel post tops cycle through the highest stress range per truck.
It's also the place where road salt and runoff drip through deck joints onto the connection plates, so corrosion accelerates fatigue. AASHTO Category C or D detailing here means you're rationing fatigue life. Modern designs use Category B welded details and waterproof the deck joints aggressively, but on a 1960s-era bridge this is the first place an inspector should look.
Sometimes, but the abutment thrust is usually the binding constraint. If your live-load increase pushes total uniform load up by 20%, horizontal thrust rises by 20% with it — and the original abutments were sized with maybe 10-15% reserve. So a structural assessment of the abutments is mandatory before you upgrade anything in the superstructure.
The web members and deck system can often be strengthened with bolted cover plates or FRP wraps at moderate cost. The arch chord itself usually has reserve capacity because it was sized for buckling, not strength. But if the abutment check fails, you're either rebuilding abutments, post-tensioning rock anchors to add capacity, or accepting a load posting. There's no cheap way around the thrust math.
Because the arch is a horizontally restrained structure — the abutments hold the arch ends fixed in the longitudinal direction. When the steel heats up and wants to expand, it can't push the abutments apart, so the expansion gets converted into vertical crown rise. A 30 °C temperature swing on a 180 m steel span produces about 60 mm of crown movement, which changes the arch geometry, which changes the thrust distribution.
A simple-span beam bridge just slides on its bearings — the expansion goes into bearing movement, not into geometry change. That's why deck-truss arches need careful expansion bearing design at the deck level (where the deck stringers meet the abutment) even though the arch itself is fixed at the springing line.
References & Further Reading
- Wikipedia contributors. Truss arch bridge. Wikipedia
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