Adding a cover plate — where the extra steel actually pays
Steel earns its keep by , so where you weld a plate matters far more than how much it weighs. Put it on one flange and you buy stiffness and asymmetry in the same move.
- Girder
- 200 × 16 flangesweb 10 × 468
- Overall depth
- 516 mmwith the plate
- Cover plate
- 250 × 16bottom flange only
Part 1 — A plate girder, then a plate under it
Four rectangles, and the fourth is the interesting one.
Start with a small welded girder — 200 mm flanges, a 10 mm web, 516 deep overall:
REC -100,16 100,32 bottom flange · REC -5,32 5,500 web · REC -100,500 100,516 top flange
Then add a cover plate under the bottom flange — 250 × 16, wider than the flange so it can be welded along both toes:
REC -125,0 125,16
That plate is 4000 mm² — about 36% more steel than the girder had.
Part 2, step 1 — A quarter more steel, half again the stiffness
Because it went where the lever arm is longest.
The bare girder has = 460.4 × 10⁶ mm⁴. With the cover plate: 656.1 × 10⁶ mm⁴ — up 43% for 36% more steel.
The reason is the parallel-axis term, and nothing else:
The plate’s own inertia is mm⁴ — utterly negligible. What it contributes is : 4 000 mm² at roughly 190 mm from the centroid is about 1.4 × 10⁸ mm⁴, three orders of magnitude more than its own stiffness.
Weld the same plate onto the WEB at mid-height and , so it would add essentially nothing to . Same steel, same weld length, no benefit. That is the whole content of “ pays”.
Part 2, step 2 — Plating one flange splits the section moduli
You bought stiffness and asymmetry together.
The plate went on the bottom only, so the centroid moved down — from 266 mm (mid-depth of the plain girder) to 197.6 mm measured from the bottom of the plate.
The two extreme fibres are now different distances away, so there are two moduli:
- Z to the top fiber = 2060332 mm³ — the far side, and the smaller value
- Z to the bottom fiber = 3320841 mm³ — the plated side, 61% larger
Under sagging the top is in compression and reaches its limit first, so the governing Z is 2060332 mm³. The cover plate improved the fiber that was already going to be fine, and improved the governing one by less. Plating both flanges keeps the section symmetric and lifts both moduli together — usually the better buy unless there is a reason the plate can only go one side.
Part 2, step 3 — The plastic axis is 130 mm away from the centroid
The most dramatic separation of the five examples.
Turn on PNA. The plastic neutral axis sits at 66 mm, while the elastic centroid is at 197.6 mm — they are 131.6 mm apart.
The reason is that the two axes weight area differently. The centroid balances — area times its distance. The plastic axis balances — area alone. A thin web spread over 468 mm contributes a lot of lever arm and not much area; the fat plate and flange at the bottom contribute the reverse.
So the equal-area line sits far down in the bottom flange region, and 2728360 mm³ is 1.32× the governing — a shape factor you could not have guessed from the 1.5 that a rectangle gives.
Hand calculation vs the tool
| Quantity | By hand | StructureCalcs | |
|---|---|---|---|
| Plain girder area | 200×16 ×2 + 10×468 = 11 080 mm² | 11080 mm² | |
| With cover plate | 11 080 + 250×16 = 15 080 mm² | 15080 mm² | |
| Centroid | must drop toward the plate | 266 → 197.6 mm | |
| Ix gain | 36% more steel | +43% stiffness | |
| Z top vs Z bottom | must differ — monosymmetric | 2060332 vs 3320841 mm³ | |
| Shape factor Sx/Zx | 1.5 for a rectangle; more here | 1.32 |
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.
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