A concrete bridge is a span structure that carries traffic loads across an obstacle using reinforced or prestressed concrete as the primary structural material. Modern post-tensioned concrete box girders routinely cross 150-300 m main spans, with the Stolmasundet Bridge in Norway holding a 301 m record for a cast-in-place box girder. The concrete resists compression while embedded steel resists tension, so the deck handles both its own dead weight and live traffic loads. You see the result in everything from short overpasses to the Confederation Bridge's 12.9 km crossing of the Northumberland Strait.
Concrete Bridge Interactive Calculator
Vary prestressing strand strength and jacking ratio to see the locked-in steel stress used to pre-compress a concrete bridge deck.
Equation Used
The worked example states that post-tensioned bridge strands are tensioned to 0.7 x f_pu. For a typical 1860 MPa strand, that gives about 1300 MPa of jacking stress.
- Uses the worked-example relation where strand is tensioned to a fraction of ultimate strength.
- Calculates stress only; total tendon force also requires strand area and strand count.
- Friction, anchorage slip, long-term losses, and code-specific limits are not included.
The Concrete Bridge in Action
A concrete bridge moves load from the deck surface, through girders or a slab, into piers and abutments, and finally into the foundation. The concrete itself is brilliant in compression but weak in tension — roughly 10% of its compressive strength — so the design always pairs it with steel reinforcement or prestressing tendons that pick up the tensile half of every bending moment. In a reinforced concrete deck, deformed rebar bonds to the concrete and resists tension where the slab sags between supports. In a prestressed or post-tensioned bridge, high-strength steel strands are tensioned to 0.7 × fpu (typically around 1,300 MPa for 1860 MPa strand) and locked off, putting the entire concrete section into pre-compression so it never sees net tension under service loads.
The geometry is chosen to match the span. Short spans up to 30 m use simple precast I-girders or AASHTO bulb-tees dropped onto pier caps. Mid-range spans of 30-90 m typically run continuous post-tensioned girders or precast segmental construction. Anything past 100 m main span moves into balanced cantilever post-tensioned box girder territory, where the deck is built outward symmetrically from each pier in 3-5 m segments. If the tendon profile is wrong — say the parabolic drape sits 50 mm too high at midspan — you lose the upward equivalent load that the prestress was supposed to deliver, and the deck cracks at the soffit under live load. We see this in older 1960s post-tensioned decks where grouting voids let the strands corrode, the prestress force drops, and the bridge starts behaving like an under-reinforced slab. The Ynys-y-Gwas collapse in Wales in 1985 came from exactly that failure mode.
Load path matters as much as material. Dead load — the weight of the concrete itself — is permanent and predictable, around 24 kN/m³ for normal-weight concrete. Live load follows the AASHTO HL-93 design vehicle in North America or the LM1 model in Eurocode, both of which combine a heavy truck with a lane load to envelope realistic traffic. The deck must carry both without exceeding allowable stress at service and without crushing or yielding at ultimate. Get the load combination wrong and you either over-build (wasting concrete and tendon) or under-build (cracking, spalling, and eventual repair calls 15 years in).
Key Components
- Deck slab: The riding surface that distributes wheel loads laterally to the supporting girders. Typically 200-250 mm thick reinforced concrete with top and bottom mats of 16-25 mm rebar at 150-200 mm spacing. Cover to reinforcement runs 50-75 mm in de-icing-salt environments to keep chloride out.
- Girders or box section: The primary longitudinal flexural members. Precast prestressed I-girders span 20-50 m; post-tensioned segmental box girders span 60-300 m. The web thickness must hold tendons plus 50 mm cover plus shear stirrups — typically 350-500 mm minimum for a serious box girder.
- Post-tensioning tendons: Multi-strand cables of 7-wire 15.2 mm strand, jacked to roughly 75% of ultimate after losses, draped on a parabolic profile. The drape produces an upward equivalent load that cancels much of the dead-load sag. Anchorage zones need spiral confinement to handle the 5-10 MN local bursting force.
- Piers: Vertical compression elements that carry deck reactions to the foundation. Typically reinforced concrete columns or hollow box piers for tall river crossings. Slenderness ratios above 22 trigger second-order moment amplification — you cannot ignore P-delta on a 50 m tall river pier.
- Abutments: End supports that take both vertical reaction and horizontal earth pressure from the approach embankment. They also accommodate deck thermal movement through expansion bearings or integral connection. Backfill compaction matters — under-compacted backfill settles and cracks the approach slab within 2-3 winters.
- Bearings and expansion joints: Elastomeric or pot bearings that let the deck rotate and translate without transferring unwanted moment to the substructure. A 100 m continuous concrete span moves roughly ±25 mm seasonally from thermal effects alone, and the bearing has to absorb that without binding.
Real-World Applications of the Concrete Bridge
Concrete bridges dominate medium and long-span road and rail crossings worldwide because they last 75-100 years with reasonable maintenance and don't need painting. You will find them across every kind of obstacle — rivers, valleys, rail corridors, urban interchanges, and ocean straits — and the form changes to suit the span. Short standardised spans use precast girders for speed of erection. Long crossings use cast-in-place balanced cantilever segmental construction because hauling a 200 m girder is impossible.
- Highway infrastructure: The Confederation Bridge between Prince Edward Island and New Brunswick — 12.9 km of precast post-tensioned concrete box girder segments, 250 m typical main spans, opened 1997.
- High-speed rail: The Beipanjiang Railway Bridge on the Guiyang-Kunming high-speed line uses a 445 m concrete-filled steel arch, with the approach viaducts built as continuous post-tensioned concrete box girders.
- Urban interchange: The MacKay Bridge approach viaducts in Halifax and similar precast segmental ramps used across the I-95 corridor for cloverleaf and stack interchanges.
- River crossing: The Stolmasundet Bridge in Norway — a 301 m main-span cast-in-place balanced cantilever post-tensioned concrete box girder, the world record holder for that bridge type since 1998.
- Pedestrian and light rail: Skytrain elevated guideways in Vancouver and the Calgary CTrain extensions, built as precast post-tensioned U-girders riding on single-stem concrete piers through dense urban corridors.
- Cable-stayed hybrids: The Sutong Bridge in China and the Russky Bridge in Vladivostok use concrete pylons and concrete approach viaducts paired with the steel main span — the concrete portions handle 90% of the total deck length.
The Formula Behind the Concrete Bridge
Sizing a concrete bridge deck starts with the factored design moment per unit width at midspan, which decides slab thickness, rebar quantity, and prestress force. The formula below combines dead load, superimposed dead load (asphalt wearing surface, barriers), and live load with their respective load factors per AASHTO LRFD or Eurocode. At the low end of typical highway spans — a 12 m simply-supported slab carrying a single lane — the moment stays modest and a 250 mm reinforced section handles it. At the high end — a 50 m continuous span on an arterial — the moment climbs by more than an order of magnitude and you have to move to a post-tensioned girder. The sweet spot for plain reinforced concrete sits around 15-20 m; past that, prestressing earns its keep.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Mu | Factored ultimate moment per unit width at midspan | kN·m/m | kip·ft/ft |
| γDC | Load factor for structural dead load (1.25 in AASHTO LRFD Strength I) | dimensionless | dimensionless |
| wDC | Self-weight of the concrete deck per unit area | kN/m² | psf |
| γDW | Load factor for superimposed dead load (1.50 in AASHTO LRFD) | dimensionless | dimensionless |
| wDW | Wearing surface and barrier weight per unit area | kN/m² | psf |
| γLL | Load factor for live load plus impact (1.75 in AASHTO LRFD) | dimensionless | dimensionless |
| wLL | HL-93 equivalent live load per unit area including dynamic allowance | kN/m² | psf |
| L | Effective span length between bearing centerlines | m | ft |
Worked Example: Concrete Bridge in a precast post-tensioned highway overpass deck
Sizing the midspan factored design moment for a 35 m simply-supported single-cell post-tensioned concrete box girder carrying a 2-lane rural arterial bridge over a CN rail corridor in southern Saskatchewan. Deck width is 11 m, slab thickness is 0.225 m, asphalt wearing surface plus barriers contribute 2.5 kN/m², and the HL-93 lane plus design truck combination produces an equivalent uniform live load of 9.3 kN/m² including 33% dynamic allowance.
Given
- L = 35 m
- wDC = 5.4 kN/m² (0.225 m × 24 kN/m³)
- wDW = 2.5 kN/m²
- wLL = 9.3 kN/m²
- γDC = 1.25 dimensionless
- γDW = 1.50 dimensionless
- γLL = 1.75 dimensionless
Solution
Step 1 — combine the factored loads per unit area at the nominal 35 m span:
Step 2 — apply the simply-supported beam moment formula at midspan for the nominal span:
Step 3 — at the low end of the typical operating range for this deck type, a 20 m span:
That is roughly one-third the nominal moment, and a 1.2 m deep precast I-girder with 12 strands of 15.2 mm prestress handles it cleanly. You feel this in the field as a deck that vibrates noticeably under a loaded gravel truck but never cracks at the soffit. Step 4 — at the high end of practical simply-supported precast construction, a 50 m span:
That doubles the nominal moment and pushes you past the limit of standard precast bulb-tee sections. You either go to a 2.4 m deep custom segmental box, switch to balanced cantilever continuous construction, or split the crossing with an additional pier. This is the threshold where designers stop using catalogue precast and start designing bespoke post-tensioned sections.
Result
The nominal factored midspan moment is 4,101 kN·m/m, which sizes the post-tensioned tendon force at roughly 18-22 MN per box girder web depending on the lever arm chosen. That moment pairs comfortably with a 1.8 m deep box girder and a parabolic tendon profile rising 1.2 m from soffit to anchor. Across the operating range the moment scales with L² — the 20 m low-end span needs only 33% of the nominal capacity while the 50 m high-end span needs 204%, so span choice drives section depth more than any other parameter. If your measured midspan deflection comes out 30% above predicted, suspect one of these: tendon grouting voids reducing effective prestress, creep coefficient under-estimated for the concrete mix (especially with high fly-ash content blends running creep coefficients of 2.5+ instead of 2.0), or differential temperature gradient through the deck adding an unexpected positive moment of 400-600 kN·m/m on hot summer afternoons.
Concrete Bridge vs Alternatives
Concrete is not the only way to span an obstacle. The choice between a concrete bridge, a steel girder bridge, and a composite steel-concrete bridge comes down to span length, fabrication and erection logistics, lifecycle cost, and the maintenance regime the owner can actually fund. Here is how the three compare on the dimensions that drive real selection decisions.
| Property | Concrete bridge (post-tensioned) | Steel plate girder bridge | Composite steel-concrete bridge |
|---|---|---|---|
| Practical span range | 20-300 m (segmental box girder) | 30-260 m (continuous plate girder) | 30-200 m (composite I-girder) |
| Service life with normal maintenance | 75-100 years | 50-75 years (paint cycle dependent) | 60-80 years |
| Typical superstructure cost per m² of deck | $1,500-$3,000 CAD | $2,000-$4,000 CAD | $1,800-$3,500 CAD |
| Maintenance interval (major) | 20-30 years (joint, bearing, tendon inspection) | 12-15 years (repaint, fatigue inspection) | 15-20 years (paint plus deck) |
| Self-weight of superstructure | High (24 kN/m³ concrete) | Low (steel girder + concrete deck) | Medium |
| Erection speed for a typical 40 m span | 1-3 weeks (precast) or 4-8 weeks (cast-in-place) | 3-5 days (girder launch) | 1-2 weeks |
| Vulnerability to fatigue cracking | Low (concrete is not fatigue-sensitive in compression) | High at welded details and cover plates | Medium (steel girder is fatigue-sensitive) |
| Best application fit | Long-span river crossings, urban viaducts, coastal salt environments | Long-span where weight matters, accelerated bridge construction | Medium spans, simple geometry, fast erection |
Frequently Asked Questions About Concrete Bridge
Three common causes, none of which show up in the factored moment calculation. First — prestress losses are higher than assumed. Friction losses through curved ducts, anchor set, elastic shortening, creep and shrinkage can collectively cost you 20-25% of the jacking force, and if the design used 15% you are now under-compressed at midspan and the soffit cracks under live load.
Second — differential shrinkage between the deck slab and the precast girders. The deck pour shrinks against the older girder and induces tensile stress in the soffit. Third — incomplete grouting of tendon ducts. A grouting void of even 1-2 m along the cable means that section of strand carries no bond, the prestress redistributes, and you see localised cracking. Drill and borescope the ducts before assuming a calculation error.
Below about 50 m, precast post-tensioned I-girders or bulb-tees almost always win because you can truck them in, drop them on the pier caps in a single shift, and pour the deck. Past 50 m the girder gets too long to transport on standard highway permits, and past 60 m you cannot lift it without a heavy-lift crane that costs more than the segmental forming traveller would.
Balanced cantilever takes over in the 70-200 m main span range because the deck builds itself outward from each pier and never needs ground access between the piers. That is what made it the default for river and valley crossings where falsework is impossible — the Stolmasundet Bridge at 301 m and most of the Confederation Bridge approach spans use exactly this method.
Almost always the model assumed too high a creep coefficient. Modern concrete mixes with silica fume, low water-cement ratios around 0.35, and steam curing in precast yards develop creep coefficients of 1.2-1.6 instead of the 2.0-2.5 assumed in older code-based predictions. The deck is genuinely stiffer over time than the model predicted.
Verify by pulling cylinder data from the construction record — modulus of elasticity at 28 days above 35 GPa for normal weight concrete is your tell. If the cylinders show high modulus and low creep coefficient from companion creep specimens, your bridge is fine and the model was conservative. Adjust the long-term camber prediction for the next bridge in the program.
The decision is driven by chloride exposure severity and intended service life. Epoxy-coated rebar (ASTM A775) works for moderate de-icing salt exposure on inland highway bridges, but coating damage during placement creates anodic spots that corrode faster than uncoated bar — Florida DOT banned it in marine splash zones in the 1990s after the Long Key and Niles Channel bridges showed accelerated corrosion within 12 years.
Galvanised rebar gives you 30-50 year protection in mild marine exposure. Stainless (typically 2205 duplex or 316LN) is the call for direct splash and tidal zones, and projects like the Confederation Bridge specified it for the most exposed elements. Stainless costs 4-6× black bar but lasts 100+ years without corrosion intervention, which beats a 50-year repair cycle on a structure you cannot easily access.
The AASHTO empirical distribution factors were calibrated against grillage and finite-strip analyses for typical bridge geometries. They are conservative for standard cases — beam spacings of 1.8-3.0 m, span-to-width ratios of 0.5-2.5, no skew. Your FE model captures the actual transverse load sharing and usually gives a 10-20% lower moment per girder for ordinary cases.
The trap is the reverse — for skewed bridges past 30°, for short stocky spans below 12 m, or for unusually wide girder spacing past 3.5 m, the empirical factors can under-predict. Check your geometry against the AASHTO range-of-applicability table before trusting either method, and run a grillage check whenever you are outside the calibrated range.
Lightweight concrete at 18-19 kN/m³ versus 24 kN/m³ normal weight saves roughly 25% of slab dead load, which translates to 5-8% of total superstructure moment on a typical girder bridge. That can be enough to avoid widening pier footings or replacing girders during a deck replacement.
The downsides — modulus of elasticity drops to 70-80% of normal weight at the same compressive strength, so deflections increase and prestress losses through elastic shortening go up. Permeability is also higher unless you specify a tight aggregate. Use it when the dead-load saving genuinely unlocks a structural decision (avoiding a substructure rebuild), not just because the spec sheet number looks good.
This one passes the maintenance restriction because tendon corrosion is the single most common cause of unexpected capacity loss in post-tensioned bridges, and it is directly tied to inspection frequency. The interval depends on the duct system. Bonded tendons in fully grouted metal ducts with no voids can go 20-30 years between detailed inspections. External unbonded tendons in HDPE pipes get inspected every 6-10 years because they are accessible.
The dangerous case is older 1960s-1980s grouted tendons where grouting practices were poor and voids are common. Boscombe Down, Ynys-y-Gwas, and several Florida segmental bridges all showed catastrophic strand corrosion in voids within 25-30 years of construction. For any bridge in that vintage, plan a borescope and impact-echo survey every 5-7 years and assume some strands are gone until proven otherwise.
References & Further Reading
- Wikipedia contributors. Concrete bridge. Wikipedia
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