Ask a bridge engineer how deep a beam needs to be and you will usually get a number with a slash in it: span over twenty, span over twenty-five. These ratios are the first thing anyone reaches for at concept stage. They let you sketch a structure in a few minutes and sanity-check someone else's proposal before the meeting ends. They are also easy to misuse. Knowing where the numbers come from, and where they stop being reliable, is what turns a rough guess into a defensible first estimate.
What a depth-to-span ratio actually describes
The ratio is span divided by depth, written as L/d, and always quoted with the depth on the bottom. The catch is that "depth" can mean two quite different things. Girder depth is the steel beam or concrete beam on its own — what the fabricator or precaster cares about. Total construction depth includes the deck slab, any haunch, waterproofing and surfacing, and it is what determines whether you fit under the existing bridge or over the road below.
On a composite steel bridge, the slab and surfacing can easily add 300 mm or more on top of the girder. A girder sized at span/25 might produce a total depth nearer span/20. Get into the habit of asking which depth a quoted ratio refers to, and say which one you mean when you use it yourself.
Ratios were never meant to design anything. They exist to stop you wasting a week on an idea that was never going to fit.
Rules of thumb for steel and concrete
The numbers below are typical starting points for ordinary highway loading and normal girder spacings. Treat them as a range to bracket, not a figure to defend.
Steel plate girders and box girders
For a simply supported composite plate girder bridge, the steel girder depth commonly lands between span/20 and span/25. Short spans of twenty to thirty metres often sit near the span/20 end. Continuous spans can be a little shallower, because hogging over the piers trims the midspan moment, so span/25 to span/30 is a fair opening bid. Steel boxes, being torsionally stiff, tend to follow similar figures but let you push further on curved or skewed alignments.
Prestressed concrete beams
Precast prestressed units — the Y-beams and U-beams you see on UK widening schemes — typically fall around span/15 to span/20. Post-tensioned box girders do better because the prestress is spread through an efficient section, and a starting range of span/20 to span/25 is reasonable, with continuous boxes slipping slightly shallower again. Prestressing is what buys the extra slenderness; without it, concrete has to be deeper.
Reinforced concrete
Ordinary reinforced concrete needs the most depth for a given span, because the concrete in the tension zone is cracked and doing nothing useful. Short solid slab bridges often sit around span/15 to span/20, while reinforced concrete beams are closer to span/12 to span/15. That is fine for a small stream crossing. It becomes expensive fast on anything longer.
Why steel and concrete end up with different numbers
Two things drive the gap. The first is stiffness. Steel has a modulus roughly five to six times that of concrete, so a steel beam of the same depth deflects far less under the same load. The second is self-weight. Concrete is heavy, so adding depth adds load, which needs more depth — a loop that catches you out on longer spans. Steel's lightness is why it dominates the long-span end of the beam bridge market, while concrete stays competitive in the middle ranges and where low maintenance matters.
Deflection often governs rather than stress, and that is where the two materials diverge again. A slender steel girder may pass every stress check and still fail a live-load deflection limit. A prestressed concrete beam can be tuned with camber and eccentricity to control the same movement.
What pushes you away from the rule of thumb
Any of these can move the starting depth by ten or fifteen per cent either way:
- Loading. A footbridge is nothing like a trunk road bridge with an abnormal load route.
- Girder spacing. Wider spacing means each girder carries more deck, so it needs to be deeper.
- Continuity and span arrangement. A short end span beside a long one redistributes moment in ways a simple ratio ignores.
- Skew and curvature. Both introduce torsion, which pushes you towards box sections or more depth.
- Headroom and clearance. Often the site fixes the total depth, and the structure has to work around it.
- Construction method. Launching, craneage and delivery limits on precast units all constrain what you can actually build.
- Vibration. Pedestrian comfort on footbridges can govern slender decks well before strength does.
A quick sizing routine you can follow
- Fix the span, the arrangement (simple or continuous) and the total depth available on site.
- Set out the girder layout and work out how much deck each girder carries.
- Calculate a depth using the deeper ratio and the shallower one, so you have a bracket rather than a single number.
- Turn the depth into something real: an approximate flange and web for steel, or a standard precast unit for concrete.
- Estimate self-weight and check it does not wreck your assumed loads. One iteration is usually enough at this stage.
- Compare your answer with a similar bridge you can actually point to. If it is wildly different, find out why.
When a rule of thumb is not good enough
Ratios are for preliminary sizing and nothing else. They become genuinely misleading on curved or heavily skewed decks, on long or unusually slender spans, on bridges carrying exceptional loads, and anywhere vibration, fatigue or seismic action matters. Assessment work on an existing structure is a different discipline again, and so is any attempt to shave depth to win headroom.
Real design means analysis to the relevant code — in the UK, the Eurocodes with their National Annexes — carried out and checked by a competent engineer. If a depth estimate is going to influence a cost plan, a planning application or a commitment to a client, it needs to be verified properly. Nobody minds a rough number in a sketch scheme. People mind a rough number in a contract.
Making the estimate earn its keep
Write your assumptions down, every time: the ratio used, the loading, the girder spacing, whether the depth is the girder or the whole construction. Keep a small library of spans you have seen built, with a note on why they came out that depth. Build the calculation into a spreadsheet so the second iteration takes a minute rather than an afternoon.
Then use the number for what it is good at. Ratios tell you whether a scheme fits, roughly what it weighs and whether the geometry is plausible. They do not tell you what the beam should be. That answer comes from analysis, detailing and a conversation with someone who has designed one before.
Photo: Didgeman / Pixabay
