An arch truss bridge is a long-span structure that combines a curved arch with a triangulated truss to carry deck loads across a gap. The arch rib is the primary load-carrying member — it converts vertical loads into axial compression that flows down to the abutments, while the truss web stiffens the arch against bending and distributes concentrated wheel and rail loads. The hybrid exists because a pure arch flexes under unbalanced live loads and a pure truss gets uneconomical past 200 m. You see this combination on the Sydney Harbour Bridge at 503 m and the Bayonne Bridge at 504 m.
Arch Truss Bridge Interactive Calculator
Vary span, arch rise, and equivalent uniform load to see how horizontal thrust and springing force change in the arch truss bridge.
Equation Used
The equation estimates the horizontal thrust H at each arch springing for a parabolic arch under a uniformly distributed load. Increasing span L or load w raises thrust, while increasing rise f makes the arch steeper and reduces the horizontal force demanded from the abutments or tie.
- Arch behaves as a parabolic rib under an equivalent uniform vertical load.
- Load is distributed across the span by the truss web.
- Supports are at the same elevation and carry equal vertical reactions.
- SI units are used: w in kN/m, L and f in m.
The Arch Truss Bridge in Action
An arch truss bridge works by routing every vertical load — the deck weight, traffic, wind — into axial compression along the curved arch rib, which then pushes outward and downward into the foundations. The truss web sitting between the arch and the deck is what makes the system stable under realistic loading. A pure arch only behaves cleanly when the load is uniform; the moment a heavy truck sits on one quarter of the span, the thrust line wants to shift away from the arch centroid and the rib starts to bend. The truss web fights that bending by triangulating the space between the arch and the deck, so any local load gets shared across many panels of compression chord and tension tie before it reaches the rib.
Geometry is everything. The arch rise-to-span ratio normally sits between 1:5 and 1:7 — flatter than that and the horizontal thrust into the abutments climbs to numbers your foundations can't take, steeper and you waste steel because the rib gets longer for no extra capacity. The truss panel points must land exactly on the arch curve, and the hangers (in a through arch) or columns (in a deck arch) must be sized so they don't buckle under their share of the dead load and live load. Get the panel spacing wrong and you get visible deck deflection under a single semi-truck.
When tolerances drift, the bridge tells you. If the arch rib moves out of plane by more than about L/2000 during erection, the spandrel bracing starts taking lateral load it wasn't designed for and you get fatigue cracking at the gusset plates. If the tension tie on a tied arch (a bowstring arch, like the Fort Pitt Bridge) loses pretension, the abutments stop seeing balanced thrust and start to walk. The most common real-world failure modes are corrosion at the hanger anchorages, fatigue cracks at riveted gusset plates, and bearing seizure at the arch springings — all maintenance issues, not design issues.
Key Components
- Arch Rib: The primary compression member, curved to follow the funicular shape of the dead load. Typically a built-up box section in steel arches with plate thicknesses of 25-75 mm depending on span. The rib axis must stay within L/2000 of the design curve during erection or secondary bending stresses get out of hand.
- Truss Web (Spandrel Bracing): Triangulated members between the arch and the deck that stiffen the rib against unbalanced live loads. Panel spacing typically 8-15 m. The web carries shear from concentrated wheel loads and forces it back into the arch as distributed axial flow.
- Deck or Tension Tie: On a deck arch the deck sits on top of the rib; on a through arch the deck hangs below via hangers; on a tied arch (bowstring) the deck doubles as a tension tie that absorbs the horizontal thrust so the abutments only see vertical reaction.
- Hangers or Spandrel Columns: The vertical members connecting deck to arch. Hangers in a through arch are pure tension elements — usually locked-coil rope or forged eyebars of 50-150 mm diameter. Spandrel columns in a deck arch are pure compression elements with built-up box sections.
- Abutments and Skewbacks: The reinforced concrete or rock-anchored foundations that absorb the inclined arch thrust. For a 300 m span carrying highway loading, horizontal thrust can run 30-80 MN per side. The skewback face must align perpendicular to the rib axis at the springing — a 1° error puts MN-level shear into the bearing.
- Bearings (Pin or Rocker): Allow rotation at the arch springings to prevent moment buildup from temperature changes. A 500 m steel arch can grow 250 mm between -20°C and +40°C, and the bearings must accommodate that without locking up.
Real-World Applications of the Arch Truss Bridge
Arch truss bridges show up wherever a span is too long for an economical plate-girder or simple truss, but the geology gives you somewhere solid to plant the abutments. Crossings with deep water and bedrock cliffs are the classic fit — you don't want to drop piers into a 50 m deep shipping channel if you can avoid it. The hybrid form gets used for both highway and heavy rail because the truss stiffening keeps live-load deflection inside the L/800 limit codes demand for rail.
- Highway Infrastructure: Sydney Harbour Bridge (503 m main span) — through arch truss carrying 8 traffic lanes plus rail and pedestrian, opened 1932
- Highway Infrastructure: Bayonne Bridge (504 m) connecting Staten Island to Bayonne, NJ — steel through arch truss raised 64 ft in 2017 to clear post-Panamax ships
- Rail Infrastructure: Hell Gate Bridge, New York (298 m) — heavy rail through arch truss, the prototype for the Sydney Harbour Bridge design
- Highway Infrastructure: Fort Pitt Bridge, Pittsburgh — double-deck tied arch (bowstring) truss carrying I-376 over the Monongahela
- Long-Span River Crossing: New River Gorge Bridge, West Virginia (518 m) — deck arch truss, steel weathering Cor-Ten construction
- Heavy Rail / Mining Haul: Garabit Viaduct, France (165 m) — Eiffel-designed wrought iron arch truss, still in active rail service since 1884
The Formula Behind the Arch Truss Bridge
The single most useful equation in arch design is the horizontal thrust at the springings under a uniformly distributed load. This number drives your foundation design, your bearing selection, and whether the site geology will even support the bridge. At the low end of typical rise ratios — say a flat 1:8 arch — horizontal thrust climbs steeply because the geometry is fighting the load with a small lever arm. At a steep 1:4 ratio, thrust drops but you've added rib length and steel tonnage. The sweet spot for most steel arch trusses sits at a rise-to-span ratio of about 1:6, where thrust is manageable and steel weight is near minimum.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| H | Horizontal thrust at each abutment | N (or kN, MN) | lbf (or kip) |
| w | Uniformly distributed load along the span (dead + live) | N/m | lbf/ft |
| L | Span between abutment centerlines | m | ft |
| f | Rise of the arch (vertical distance from springing to crown) | m | ft |
Worked Example: Arch Truss Bridge in a 300 m highway arch truss
You're sizing the abutment thrust for a 300 m steel through arch truss carrying a 4-lane highway across a river gorge, similar in scale to the Lupu Bridge approach studies. Total uniformly distributed load (deck self-weight, truss steel, wearing surface, plus AASHTO HL-93 live load averaged over the span) works out to 220 kN/m. You want to know what horizontal thrust the skewback foundations must resist, and how that number swings if the architect pushes the rise ratio toward flatter or steeper geometry.
Given
- L = 300 m
- w = 220 kN/m
- fnom = 50 (rise ratio 1:6) m
- fflat = 37.5 (rise ratio 1:8) m
- fsteep = 75 (rise ratio 1:4) m
Solution
Step 1 — compute the total span moment numerator (w × L2), which is the same for all three rise cases:
Step 2 — compute horizontal thrust at the nominal 1:6 rise (f = 50 m), which is where most modern steel arch trusses settle:
That's roughly the weight of 5,000 fully loaded semi-trucks pressing horizontally into each skewback. It's a number that needs solid bedrock or a large mass-concrete foundation to absorb — but it's well inside what real bridges of this scale handle every day.
Step 3 — at the flat end of the typical range, rise ratio 1:8 (f = 37.5 m):
A 33% jump in thrust from the nominal case. On poor geology this can be the difference between a buildable site and a non-starter — you'd be looking at massive post-tensioned anchors or rock dowels just to hold the abutment in place.
Step 4 — at the steep end, rise ratio 1:4 (f = 75 m):
Thrust drops by a third versus nominal, but the arch rib is now 75 m tall at midspan. Steel tonnage goes up, wind area goes up, and erection cost climbs because you need taller falsework or longer cable-stay temporary supports during closure.
Result
Horizontal thrust at the nominal 1:6 rise ratio comes out at 49. 5 MN per abutment — a number that defines the entire foundation design and locks in whether the site is viable. In practice that means the skewback bearing assemblies need to react about 50 MN horizontal plus roughly 33 MN vertical at each end, which is why you see the massive granite-faced concrete piers under bridges like the Sydney Harbour and Hell Gate. The flat 1:8 case pushes thrust to 66 MN and the steep 1:4 case drops it to 33 MN, so the rise ratio is the single biggest lever you have for matching the bridge to the site geology — the sweet spot at 1:6 balances thrust against steel tonnage. If your in-service measured thrust comes in 10-20% above predicted, the most common causes are: (1) thermal lock-up at a seized rocker bearing forcing thrust up under temperature swings, (2) tension tie elongation on a tied arch transferring unintended thrust back into the abutments, or (3) settlement of one skewback rotating the rib axis and pushing the thrust line off the centroid.
Arch Truss Bridge vs Alternatives
An arch truss isn't always the right answer — the choice between arch truss, simple truss, and cable-stayed depends on span, geology, depth available below deck, and what you're willing to pay per meter. Here's how the real engineering numbers compare for medium-to-long highway spans.
| Property | Arch Truss Bridge | Simple Truss Bridge | Cable-Stayed Bridge |
|---|---|---|---|
| Economical span range | 150-550 m | 40-250 m | 200-1100 m |
| Required foundation strength (horizontal reaction) | High — full arch thrust into skewback | Low — vertical reactions only | Moderate — anchor pier resists cable pull |
| Steel tonnage per m2 of deck (typical) | 180-260 kg/m2 | 140-200 kg/m2 | 200-300 kg/m2 |
| Live-load deflection (L/x limit) | L/800 to L/1000 | L/600 to L/800 | L/400 to L/500 |
| Service life (steel, properly maintained) | 100+ years (Hell Gate, 1916) | 75-100 years | 50-80 years (cables replaced at 30-50) |
| Erection complexity | High — cantilever or falsework | Low — panel-by-panel | High — staged cable tensioning |
| Best site fit | Deep gorge, rock abutments | Shallow river, multiple piers OK | Wide channel, single-tower viable |
Frequently Asked Questions About Arch Truss Bridge
Textbooks describe the ideal funicular arch — one shaped exactly to the load it carries. Real arches are shaped for the dead load only, because that's the only load that's actually constant. The moment you put a truck on one half of the span, the load distribution stops matching the rib curvature and the thrust line shifts off the rib centroid. That offset times the axial force gives you bending moment.
This is exactly why the truss web exists in an arch truss. The web takes that secondary bending and converts it back into axial flow distributed over many members. If your model still shows large rib moments, check whether you've correctly connected the web members to both the arch and the deck — a missing rigid connection at the panel points will throw the load redistribution off completely.
Geology decides it for you. If you have rock or stiff soil at the abutment elevation that can take 30-80 MN horizontal, build a true arch — it's lighter, simpler, and lasts longer. If the abutments are alluvial soil, a poor riverbank, or you're spanning between two flat approach viaducts where there's no foundation mass to push against, you go tied arch and let the deck absorb the thrust.
Rule of thumb: if your geotechnical report shows allowable lateral bearing pressure below about 500 kPa at the springing elevation, default to tied arch. The Fort Pitt Bridge is tied because the Pittsburgh riverbanks couldn't take the thrust of a true arch at that span.
The simple formula assumes a parabolic arch under a perfectly uniform load with both springings at the same elevation. Real bridges violate at least one of those assumptions. The biggest single source of the discrepancy is usually that live load isn't uniform — patch loading on one half of the span shifts the thrust line and increases the peak abutment reaction beyond the average.
Second cause is rib shape: a true catenary or polynomial rib under a deck-plus-spandrel load distribution doesn't behave exactly parabolically. Run your finite element model with the actual load patterns (HL-93 truck plus lane load) rather than averaging — you'll see the formula is a good first-pass sizing tool but the real number always lands 10-20% higher for design.
Rail is far stricter. AREMA and most national rail codes demand L/800 to L/1000 live-load deflection for ballasted track and even tighter — L/1500 — for direct-fixation high-speed track. Highway codes (AASHTO) accept L/800 for vehicular and L/1000 only when there's significant pedestrian use.
The reason is that rail wheelsets won't tolerate the angular discontinuity at the deck joints if the span flexes more than that. A 300 m arch deflecting L/600 means 500 mm of midspan sag — the rail joints at the bridge ends would see angles that derail trains at speed. Size your truss web members for the rail limit even if the arch itself easily meets the deflection target on its own.
Hangers on a through arch are tension-only members, but they see live-load cycling every time a truck or train crosses. The connection detail at the rib end — usually a riveted gusset plate or a forged eyebar pin — concentrates stress at the rivet hole edges. Over millions of cycles, the stress concentration factor of 3-4 at the hole edge eats into the fatigue life.
The Hell Gate Bridge and similar early-1900s arches had hanger connections detailed before fatigue was well understood. Modern retrofits use welded high-strength steel hangers with machined sockets, which moves the fatigue-critical detail away from the hole edge. If you're inspecting an older arch, the hanger anchorage is the first place to put dye penetrant — long before you worry about the rib itself.
It works structurally but it's almost never economical. Below about 100 m a simple Warren or Pratt truss does the same job with a quarter the foundation cost — you don't need the arch action because the truss alone has enough depth-to-span ratio to carry the load with reasonable steel tonnage. Building an arch under 100 m means paying for skewback foundations that weren't necessary.
Exceptions exist when aesthetics drive the decision — pedestrian bridges in parks and architectural showpieces routinely use short-span tied arches because the bowstring shape is visually distinctive. But on pure engineering economics, short arch trusses lose to plate-girder and simple-truss alternatives every time.
References & Further Reading
- Wikipedia contributors. Arch bridge. Wikipedia
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