Welded box girder — what closing a section buys you
Take a girder, split its web in two and move the halves out to the flange tips. The bending stiffness hardly changes. Everything that stops the beam falling sideways or twisting multiplies.
- Overall
- 400 × 800 mm
- Flanges
- 400 × 25top and bottom
- Webs
- 25 × 750two, at the edges
- Control
- same flangesone central web
Part 1 — Four plates around a void
A box is not a heavier I. It is a different topology.
A welded box, 400 wide and 800 deep, built from four plates:
REC -200,0 200,25 bottom flange · REC -200,25 -175,775 left web · REC 175,25 200,775 right web · REC -200,775 200,800 top flange
Note what you did not do: there is no hole to cut. The void in the middle is simply the space the four plates do not occupy. Drawing a solid 400 × 800 block and then subtracting a 350 × 750 hole gives the identical section — the tool’s region algebra resolves either description to the same material — but the four-plate version is how the girder is actually fabricated, and it is the drawing a detailer would recognise.
Area comes to 57500 mm².
Part 2, step 1 — The same depth, the same flanges, one web moved
Six times the minor-axis stiffness.
Take the box apart and rebuild it as an open I: identical 400 × 25 flanges, identical 800 mm depth, and the two 25 mm webs merged into one 25 mm web on the centreline. The only change is where the web steel sits.
| Property | Open I | Box | Ratio |
|---|---|---|---|
| Area (mm²) | 38750 | 57500 | ×1.48 |
| Ix (×10⁹ mm⁴) | 3.883 | 4.762 | ×1.23 |
| Iy (×10⁹ mm⁴) | 0.268 | 1.587 | ×5.93 |
| ry (mm) | 83.11 | 166.1 | ×2.00 |
barely moves — the flanges do that work, and they did not change. But multiplies by 5.9, because moving each web 187.5 mm off the centreline earns about the vertical axis where before it earned almost nothing.
Part 2, step 2 — What that minor axis is actually for
Not bending. Buckling and twist.
A girder is rarely asked to bend about its minor axis. So why pay 48% more steel for six times an you will not use directly?
Two reasons, and both are about the section staying the shape you drew:
- Lateral–torsional buckling. A deep beam in bending wants to buckle sideways and twist. Resistance to that scales with and with torsional stiffness — so doubling from 83.11 to 166.1 mm roughly halves the slenderness for the same unbraced length.
- Torsion. This is the bigger one, and the section calculator does not compute it: a CLOSED section carries torque as a shear flow going round the box, while an open one can only carry it by warping. The torsion constant of a closed box is typically two or three orders of magnitude larger than an open section of the same weight.
That is why a curved bridge, a crane runway, or anything eccentrically loaded reaches for a box — and why a straight, well-braced, symmetrically loaded girder usually does not.
Hand calculation vs the tool
| Quantity | By hand | StructureCalcs | |
|---|---|---|---|
| Area | 2×(400×25) + 2×(25×750) = 57 500 mm² | 57500 mm² | |
| Centroid | 400 mm — doubly symmetric | 400 mm | |
| Ixy | 0 — two axes of symmetry | 0 mm⁴ | |
| Ix | flange + web parallel-axis terms | 4.762 × 10⁹ mm⁴ | |
| Iy vs the open I | must be several times larger | ×5.93 | |
| Plastic Sx | PNA at mid-depth by symmetry | 14781250 mm³ at y = 400 mm |
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.