Composite bridge deck — a concrete slab on a steel plate girder
The same steel girder, connected to a slab that was going to be cast anyway, is three times stiffer. That factor is the entire commercial argument for composite construction — and it rests on one dimensionless number and a row of shear studs.
- Girder
- 300×20 flangesweb 12 × 600
- Slab
- 2 000 × 200EFFECTIVE width
- 200 GPa
- ≈ 28.6 GPa
- 1/7
Part 1 — A girder, a slab, and one number that joins them
Two materials, drawn edge to edge.
A welded plate girder, drawn as three rectangles about the centerline:
REC -150,0 150,20 bottom flange 300 × 20 · REC -6,20 6,620 web 12 × 600 · REC -150,620 150,640 top flange 300 × 20
Then the slab, sitting on the top flange: REC -1000,640 1000,840 — 2 000 wide, 200 thick.
Now the part that makes it composite. In the Material group, add a second material, set its modular ratio to n = 0.1429 (that is 1/7, taking GPa and GPa), select the slab, and press Assign. Give it a grey fill so the drawing reads like a section through a deck.
The properties panel immediately changes its heading to Transformed section, which is the tool telling you that every number below it is now an equivalent-steel number.
Part 2, step 1 — One ratio turns two materials into one section
And the arithmetic is short enough to check.
Concrete is roughly a seventh as stiff as steel, so a square millimetre of it carries a seventh of the force at the same strain. The transformed section trades area for that:
Steel 19200 mm², concrete 400000 mm²:
Then the centroid is the area-weighted average, exactly as always:
The steel’s own centroid is at 320 mm and the slab’s at 740 mm. The transformed centroid lands at 634.4 mm — pulled up out of the steel and into the top flange region, which is the whole reason the girder gets stiffer.
Part 2, step 2 — Three times the stiffness, for concrete you already had
This is why shear studs exist.
The bare steel girder has = 1.370 × 10⁹ mm⁴. Acting compositely with the slab, the same steel gives 4.095 × 10⁹ mm⁴ — a factor of 2.99.
Nothing was added to the steel. The slab was going to be cast regardless; all that changed is that it is now connected to the girder well enough to act with it. That connection is a row of welded shear studs, and its entire job is to carry the horizontal shear at the interface so the two do not slide past one another.
Without studs the two bend independently, and you are back to 1.370 × 10⁹ plus a slab spanning transversely. With them, you get the number above.
Part 2, step 3 — Getting real stresses back out
The transform is a device; the materials are real.
The transformed section gives stresses in the reference material — steel here — directly from the familiar formula:
For the concrete you have to undo the transform. The trick works because strain is continuous across the interface while stress is not:
With , concrete at the same height carries a seventh of the steel stress — which is the point of putting it in compression at the top, where concrete is good, and leaving the tension to the steel at the bottom, where it is not.
The section moduli tell the same story: 6455472 mm³ to the steel soffit against 19915338 mm³ to the top of the slab, because the centroid has moved so far up that the bottom fibre is now much further away than the top.
Hand calculation vs the tool
| Quantity | By hand | StructureCalcs | |
|---|---|---|---|
| Steel area | 300×20 + 12×600 + 300×20 = 19 200 mm² | 19200 mm² | |
| Concrete area | 2 000 × 200 = 400 000 mm² | 400000 mm² | |
| Transformed area | 19 200 + 400 000/7 = 76 342.9 mm² | 76343 mm² | |
| Transformed centroid | area-weighted, between 320 and 740 | 634.4 mm | |
| Bare steel Ix | the control | 1.370 × 10⁹ mm⁴ | |
| Composite Ix | must be several times the bare value | 4.095 × 10⁹ mm⁴ · ×2.99 | |
| Plastic modulus Sx | needs f_y per material — NOT n | not reported (see below) |
Every value was worked by hand with the classical method, then checked against this site’s solver — the same engine the Try it button opens. This agreement is re-run automatically on every build.
Now make it yours
Open this exact model in the calculator — then change a load, drag a support, and watch every diagram update in real time. The best way to build intuition is to break it and see what happens.
Take it with you
Export this worked example as a PDF, or download it as a .screport and open it in the Report Builder — the model travels inside the file, so you can reconstruct it, re-solve, and build your own report from it.