A bridge is a structure that carries a path, a road, a railway, a footway, a pipeline, even a canal, across something that would otherwise stop it: a river, a valley, another road, a strait. The definition is deliberately plain, because everything in engineering follows from it. A bridge has one job that never changes (keep the path continuous and safe) and one thing it can never escape (gravity, acting on its own weight and on whatever crosses it).

Two words are used constantly and often mixed up. The span is the distance between two adjacent supports. The length is the whole crossing, end to end. A 2 km bridge may be forty spans of 50 m or one span of 1,500 m with approaches, and those are two entirely different structures, even though both are "2 km long".

Where does a bridge begin? Owners draw the line by size. In the United States the National Bridge Inventory treats a structure as a bridge once it measures more than 6.1 m (20 ft) along the roadway between abutment faces; anything shorter is a culvert. Other countries use similar thresholds. The reason is practical: above that size the structure needs its own inspection, load rating and maintenance programme, which is the subject of Chapter 10.

Every decision in this book, the depth of a girder, the number of piles, the sequence of a construction stage, is an answer to the same question: how do we carry the load from the path down to the ground, over this particular gap, for a hundred years, at a cost the owner can afford?

Engineers split a bridge into three families of parts. The superstructure is everything the traffic rides on: the deck, the main load-carrying members beneath it (girders, a box, a truss, an arch, cables), plus barriers, drainage and the wearing surface. The substructure holds the superstructure up: piers in the middle, abutments at the two ends. The foundations take the load into the ground, spread footings on rock or firm soil, piles or drilled shafts where the good ground is deeper.

deck on girders bearing abutment abutment pier pier footing on piles approach

Between superstructure and substructure sit the bearings: small, deliberately placed devices that let the deck expand, contract and rotate while still passing its weight down. At the ends, expansion joints let the deck breathe against the fixed approach. These are the parts that wear out first, and they get their own chapter (9).

Follow one truck wheel. Its load presses on the wearing surface, spreads through the deck slab, and lands on the nearest girders. The girders bend and carry it sideways to the supports. At each support a bearing hands the reaction to the pier cap; the column carries it down in compression; the footing or pile group spreads it into the soil until the ground can hold it. That chain is the load path, and the first duty of a bridge engineer is to make sure it is continuous, with no weak link.

wheeldeckgirderbearingpierfoundation

Along the way the load is carried by only a handful of actions: bending (a girder), shear (near the supports), compression (a column or an arch), tension (a cable or a hanger) and torsion (a curved or eccentrically loaded box). Materials are good at some of these and poor at others. Concrete is strong in compression and weak in tension, which is why we put steel bars inside it, or squeeze it in advance with prestressing. Steel is strong in both but slender pieces can buckle in compression. A cable can only ever pull.

Most of bridge design is choosing a form that puts each material where it does the work it is good at. That choice is the subject of the next section.

Strip away the details and almost every bridge ever built spans its gap in one of four ways, or in a combination of them.

beam · bendingarch · compression, thrustcable · tensiontruss · axial, in triangles

• Beam. A member laid across the gap and carrying load by bending: the top squeezes, the bottom stretches. Slab, T-beam, I-girder and box girder are all beams. Simple, cheap, and by far the most common; but bending grows quickly with span, so beams give up somewhere around 300 m.
• Arch. The curve turns load into compression and pushes outward at its springings, so an arch needs ground (or a tie) that can take that thrust. Masonry could only work this way, which is why the arch is the oldest long-lasting form. Modern steel and concrete arches reach roughly 500–600 m.
• Cable. Hang the deck from tension members. In a suspension bridge the deck hangs from a main cable draped between towers and anchored in the ground; in a cable-stayed bridge straight stays run from the tower directly to the deck. These forms hold the span records: cable-stayed past 1,200 m, suspension past 2,000 m.
• Truss. Break the beam into triangles so every member works axially, in pure tension or compression. Light, stiff, and made from small pieces, the reason railways of the nineteenth century were built on trusses.

Real bridges mix these. A cable-stayed deck is still a beam between stays; a tied arch is an arch whose thrust is taken by a beam; an extradosed bridge is a beam that borrowed a little from the cable family. The form is chosen by span, ground, materials, construction access and, never last, cost.

Everything a structure does is measured in stress: force divided by the area that carries it. Structural steel yields at 345–460 MPa; bridge concrete crushes at 30–60 MPa and cracks in tension at about a tenth of that; timber manages 20–40 MPa along the grain; good building stone takes 50–150 MPa in compression and almost nothing in tension. A design is nothing more than a set of shapes chosen so that, under the worst load, no stress anywhere exceeds what its material can take, with a margin.

A beam turns load into two opposite forces: the top is squeezed, the bottom is stretched. Together they form a couple: a compression force C and an equal tension force T, separated by a lever arm z that is roughly 0.8–0.9 of the depth. The bending moment the beam resists is M = C × z. That single equation explains the shape of every girder ever built. Double the depth and the flange forces halve; put the material far from the middle, where the stresses are, and leave the middle thin: that is the I-girder, the box girder, the truss, and the hollow arch of section 2.10.

The moment itself grows fast. For a uniform load the midspan moment is w L²/8: double the span and the moment is four times larger. To keep the stresses the same the designer must roughly double the depth or quadruple the flanges, which is why a 30 m girder is 1.5 m deep, a 60 m one is 3 m deep, and a 300 m concrete box has a 15 m web at the pier. Depth is the cheapest strength there is, and the first thing a bridge engineer estimates for any span is how deep it will have to be.

In 1675 Robert Hooke published, as an anagram, the sentence that connects the two oldest long-span forms: as hangs the flexible line, so but inverted will stand the rigid arch. A chain hung between two points takes the one shape in which every link is in pure tension. Freeze that shape, turn it upside down, and you have an arch in which every stone is in pure compression. The chain and the arch are the same structure with the sign changed.

The shape has a name. A chain under its own weight hangs in a catenary; under a load spread evenly along the horizontal, which is what a bridge deck is, it hangs in a parabola. Either way, the horizontal force at the ends is H = w L² / (8 f), where f is the sag. The formula carries a warning: make the cable flatter and the force climbs without limit. Suspension bridges settle on a sag of about a tenth of the span, and a tower height to match; the Golden Gate's cables sag 144 m over a 1,280 m span. The inverted arch obeys the same equation, and its H is the outward thrust that its foundations, or a tie, must resist. Masonry arches were built high, a rise of a fifth to a half of the span, precisely to keep that thrust manageable.

There is one difference between the two forms, and it decides how each is designed. A cable is flexible: if the load changes, the cable moves to a new shape that is once again pure tension. An arch is rigid and cannot. When traffic loads one half of an arch the true line of thrust shifts, and if it wanders outside the ring the arch cracks and, in masonry, hinges. The classic rule keeps the thrust line within the middle third of the ring so that no stone ever sees tension; the massive spandrel fill of Roman bridges did that job by making the dead load overwhelm any live load. Modern arches do it with a stiff deck or with hinges placed where the thrust line is known to pass, which is Maillart's three-hinged arch of 1930. Suspension bridges have the mirror problem: the cable is stable, but the deck hung from it is not, and needs its own stiffness against traffic and wind.

A bridge that is strong enough can still be unfit for use, and the second half of every design check is about the ways a structure lets its users down without breaking.

Stiffness. Deflection is limited long before strength is reached: highway codes hold live-load deflection to about span/800, span/1,000 where pedestrians share the deck, and railways are stricter still because a sagging track derails trains. Stiffness depends on the cube of the depth (the second moment of area I grows with d³) while strength grows only with d², so a slightly deeper girder is a far better cure for a lively bridge than a heavier one. Prestressed concrete has its own version of the problem: a girder that is stiff enough may still hog upward under its prestress, and the camber must be predicted, which brings creep into the calculation.

Stability. A slender member in compression does not crush, it buckles: it bends sideways at a load Euler wrote down in 1744, P = π² E I / (K L)², which depends on stiffness and length, not on strength at all. Buckling took down the Quebec Bridge in 1907, when the built-up compression chords of the cantilever failed at half the stress the steel could carry. It rules the webs and flanges of steel girders (which is why they have stiffeners), the deck of a steel box, an arch rib in compression, a pier column, and every girder being erected before its bracing is in place. Concrete boxes buckle too, in their thin webs and bottom slabs at the pier.

Vibration. People walk at 1.6–2.4 steps a second and lock into a bridge that sways at the same rate: London's Millennium Bridge closed two days after it opened in 2000 for exactly that reason. Wind sets off worse things: vortex shedding that rocks a deck at a fixed wind speed, galloping of iced cables, rain-and-wind vibration of stays, and flutter, the self-feeding twist that broke Tacoma Narrows in 1940. Long spans are tested as models in wind tunnels before they are built; the deck of the Great Belt and every box deck since owes its streamlined shape to that.

Fatigue. A highway bridge sees on the order of a hundred million heavy-vehicle passages in its life, and steel that is well below its strength under one load will crack under enough repetitions of it. The crack always starts at a detail: a weld toe, a cover-plate end, a cope hole, a bolt hole. Codes classify details from best to worst (AASHTO's categories A to E′) and the detail category, not the steel grade, decides the fatigue life. Concrete is more forgiving; prestressing strand at its anchorages and stay cables are not, and are tested for two million cycles before they are accepted.

Galileo saw it in 1638: make a beam twice as big in every direction and its strength grows four times, but its weight grows eight. Scale a structure up and it eventually cannot carry itself. For a bridge the arithmetic is brutal. Self-weight moment grows with w L²; to carry it the girder gets deeper, so w itself grows with L, and the moment ends up growing with roughly L³ while the section that resists it grows only with L². Somewhere every form reaches a span at which most of its capacity is spent holding up its own weight, and past that span it is no longer the cheapest answer.

The practical ceilings today are roughly: precast concrete girders 50–60 m; continuous concrete boxes 250–300 m (the Shibanpo Bridge in Chongqing reached 330 m in 2006 with a steel midspan section); steel boxes about 300 m; trusses 500–550 m (the Quebec cantilever of 1917 has never been beaten); arches 550–600 m in steel and 600 m in concrete; cable-stayed bridges 1,200 m; suspension bridges just past 2,000 m. Each ceiling is where self-weight wins. The cable forms hold the records because a cable carries load in the one action, pure tension, that wastes no material on bending.

A useful way to compare materials is the breaking length: how long a bar could hang from one end before it snapped under its own weight. For structural steel it is about 4–5 km; for the 1,770 MPa wire of a suspension cable, 23 km; for concrete in compression, under 2 km; for carbon fibre, more than 100 km. Suspension spans of 3,000–5,000 m are within reach of steel wire (the Messina design is 3,300 m), and the fact that no one has built one is a matter of cost and need, not of physics. The same number explains why Rome could not span more than 30 m in stone, and why the arrival of each stronger material in Chapter 2 immediately moved the records.

Below the records, the choice of span is an economic balance. Superstructure cost per square metre rises with span; substructure cost falls, because there are fewer piers, and falls faster in deep water or bad ground. The cheapest layout sits where the two are roughly equal, a rule of thumb old enough to appear in nineteenth-century textbooks and still the first thing a preliminary design settles.

A bridge is never designed to just carry its load. Between the load that the code writes down and the strength the code allows sits a margin, and the margin is built in layers.

• Load factors. Permanent loads are multiplied by about 1.25, traffic by 1.75 (AASHTO LRFD Strength I), because the real values are uncertain and the traffic model is a notional vehicle standing in for anything the road may carry.
• Resistance factors. Calculated strengths are multiplied by 0.9 for flexure, 0.75–0.9 for shear, 0.5–0.7 for foundations, in proportion to how well each can be predicted; foundations get the biggest cut because the ground is the least known material on the site.
• Characteristic strengths. The concrete strength on the drawings is one that 95 per cent of test cylinders exceed; the steel yield is a guaranteed minimum that mills beat by 10–20 per cent.

Stacked together these give a member a probability of failure of roughly 1 in 5,000 over its 75-year design life, which is the reliability index β ≈ 3.5 that AASHTO LRFD was calibrated to in the 1990s. The Eurocodes aim for a similar number over 50 years. That is per member and per load case; the bridge as a whole is safer still, because of the next layer.

Redundancy is the property that one broken part does not bring the bridge down. It comes in three forms: several girders side by side (load-path redundancy), continuity over the piers so a damaged span hangs from its neighbours (structural redundancy), and members built from several plates so a crack in one is arrested (internal redundancy). Where it is absent the code names the member fracture-critical: a two-girder steel bridge, a pin-and-hanger, an eyebar chain. The Silver Bridge collapse of 1967 (section 2.14) was one eyebar with one crack, and it is the reason those members are inspected by hand at arm's length. Cable-stayed bridges are designed for the sudden loss of any one stay, and modern codes ask for robustness in general: damage should stay proportionate to its cause.

Finally, the design life: 75 years in AASHTO, 100 in the Eurocodes, 120 in British practice. It is a durability target, not a strength one; nothing in the strength checks changes at year 76. In practice most bridges are replaced because they are too narrow, too weak for new traffic or too expensive to maintain, long before their steel or concrete gives out, and durability, drainage, cover, coatings and joints decides which of those it will be.

A bridge is designed for a set of loads and for the ways they combine. The list is longer than most people expect.

deadlivewindearthquaketemperaturewatercollisiontimeconstruction

dead load

The structure's own weight plus everything permanently on it, surfacing, barriers, utilities. For a long concrete bridge this is most of the load.

live load

Traffic. Design codes replace real traffic with a notional model (in AASHTO LRFD, the HL-93 truck and lane load) and add a dynamic allowance for impact.

wind

Static pressure on the deck and towers, and for slender spans the aerodynamic behaviour that famously destroyed Tacoma Narrows in 1940.

earthquake

Ground shaking that the substructure and bearings must survive without the deck falling off its seat.

temperature

Daily and seasonal expansion and contraction, a 1 km deck moves by tens of centimetres a year, plus gradients through the depth.

water

Flow pressure, ice, debris and above all scour, the erosion of soil around foundations, which is among the most common causes of bridge failure worldwide.

collision

Vehicles hitting piers, ships hitting piers, over-height loads hitting girders.

time

Fatigue from millions of load cycles, corrosion of steel, creep and shrinkage of concrete, relaxation of prestressing.

construction

Every intermediate stage, a half-built cantilever, a girder being launched, is a structure in its own right and must be checked.

Modern codes handle this with limit states: the structure is checked for strength (it must not break), service (it must not crack, sag or vibrate unacceptably), fatigue and extreme events, each with its own load factors. Chapter 4 explains the philosophy; the calculators on this site apply it.

A bridge is not designed once. It passes through a life cycle, and different people own each stage.

planningdesignconstructionoperationinspection

• Planning. The owner, a highway or railway authority, a city, a port, fixes the route, the clearances, the traffic, the budget and the required service life (typically 75 to 120 years).
• Type selection and preliminary design. Engineers compare forms for the site: span layout, ground conditions, navigation clearance, seismicity, construction access, aesthetics, cost. This is where the four families of section 1.4 compete.
• Detailed design. Every member and connection is sized against a design code, AASHTO LRFD in North America, the Eurocodes in Europe, and national codes elsewhere, and drawn for construction.
• Construction. The contractor builds it, usually by one of a dozen well-established methods (Chapter 8), each with its own temporary structures and its own risks.
• Operation. Inspection at fixed intervals (24 months is the common maximum), load rating whenever traffic or condition changes, maintenance, strengthening, and eventually replacement.

The bridge engineer's job runs through all of these. It is less about equations than about judgement: choosing the form, understanding the ground, anticipating how the thing will be built and how it will age. The rest of this book is an attempt to pass on that judgement, chapter by chapter.

The book is arranged as a tree. Chapter 1, the one you are finishing, is the root: it defines the vocabulary every later chapter uses. Chapter 2, the trunk, is the history, the timeline along which each form and material appeared. The branches are the specialist chapters, and you can read them in any order once the root is done.

Each chapter is broken into short sections that end deliberately. Read one section, stop, come back. Your place is remembered on this device. Where a section connects to a calculator, an animation, a gallery entry or a failure case on this site, there is a link at the end of it.

Nothing here is copied from a textbook. Where a number or a rule comes from a specific standard it is named, AASHTO LRFD, MBE, HEC-18, Eurocode, so you can check it, and the references chapter collects them. If you find an error, say so in the Forum.