In short: A built-up or tapered member has no tabulated kg/m, so its weight comes from its plates: volume of each plate × 7,850 kg/m³. For a tapered web, use the average web depth over the length. Add flanges and any cover plates the same way. In a pre-engineered building, where most of the primary steel is tapered, this is how the tonnage is worked out, and it is what MTO Generator does automatically for every tapered member in your STAAD.Pro model.
For a rolled section, steel weight is easy: look up the kg/m in the section table and multiply by length. Pre-engineered buildings (PEBs) don't work that way. Their columns and rafters are made from plates, welded into I-sections whose depth changes along the length. To get the tonnage, you go back to the plates.
This guide shows the calculation step by step, with a worked example you can check by hand.
Why built-up members need their own calculation
A tapered rafter might be 600 mm deep at the haunch and 300 mm deep at mid-span, with a 6 mm web and 200 × 10 mm flanges. There is no table entry for that. Its weight depends on:
- the web plate: thickness × average depth × length;
- the flange plates: width × thickness × length, for top and bottom;
- any cover plates added to strengthen a rolled section.
Since the depth is what drives most of the difference between a light and a heavy frame, getting the web right matters. Our article on what drives steel weight in a PEB explains why.
The basic formula
For any plate:
weight (kg) = width (m) × thickness (m) × length (m) × 7,850 kg/m³
7,850 kg/m³ is the usual density for structural steel plate. (For rolled sections, section tables are based on slightly different values; MTO Generator, for example, uses 7,833.5 kg/m³ for rolled sections and 7,850 kg/m³ for plates.)
A handy shortcut: a steel plate 1 m² in area and 1 mm thick weighs 7.85 kg.
Tapered web: use the average depth
For a web that tapers linearly from depth d₁ to d₂, the plate is a trapezoid. Its area is the average depth × length:
web weight = ((d₁ + d₂) / 2) × t_w × L × 7,850
Use the web depth, which is the overall depth minus the two flange thicknesses, not the overall depth. Using overall depth slightly overstates the weight.
Worked example: a tapered rafter
Rafter segment: overall depth 600 mm tapering to 300 mm, web 6 mm, flanges 200 × 10 mm (top and bottom), length 6 m.
1. Web depth at each end
- Deep end: 600 − 2 × 10 = 580 mm
- Shallow end: 300 − 2 × 10 = 280 mm
- Average: (580 + 280) / 2 = 430 mm
2. Web weight 0.430 × 0.006 × 6 × 7,850 = 121.5 kg
3. Flange weight (two flanges) 2 × 0.200 × 0.010 × 6 × 7,850 = 188.4 kg
4. Total 121.5 + 188.4 = 309.9 kg, about 51.7 kg/m
Notice that the flanges are more than half the weight here. A small change in flange size often changes the tonnage more than the taper does.
Cover-plated rolled sections
When a rolled beam is strengthened with a plate, add the plate's weight to the beam's:
ISMB 400 (61.6 kg/m) with a 200 × 12 mm top plate:
- Plate: 0.200 × 0.012 × 7,850 = 18.8 kg/m
- Total: 61.6 + 18.8 = 80.4 kg/m
With plates on both flanges, add both.
How to report built-up steel in an MTO
Estimators and fabricators buy plates, not "tapered rafters", so a good take-off for a PEB lists built-up members as plates:
| Item | Size | Weight |
|---|---|---|
| Web plate | PL 6 mm | 121.5 kg |
| Flange plates | PL 200 × 10 | 188.4 kg |
Summed over the frame, this gives the plate quantities by thickness, which is how the steel is ordered. It also makes the take-off easy to check: a reviewer can see straight away if a web thickness looks wrong.
Common mistakes
- Using the overall depth for the web. Subtract the flanges.
- Using the deep-end depth for the whole length. For a tapered web, use the average.
- Forgetting cover plates. They are often assigned in STAAD as a separate property and missed in a hand count.
- Counting split members twice. Analysis models often split a rafter into several segments. Make sure each segment is counted once, with its own start and end depths.
- Leaving out connection plates. End plates, base plates and stiffeners are not in the analysis model. Add them as a separate, visible allowance.
Doing it automatically from STAAD.Pro
Working this out by hand for one member is a good check. For a whole PEB, with dozens of tapered segments per frame, it is a spreadsheet job that has to be redone with every revision.
MTO Generator in SS Workbench reads the tapered and built-up sections straight from your STAAD.Pro model:
- Tapered members are broken into their web and flange plates, using each member's start and end depths.
- Cover-plated beams (top, bottom or both) are weighed with their plates.
- Rolled sections, channels, angles, tubes and pipes are weighed in the same run.
- You get every member's weight and a summary by section, in kg and MT, exported to Excel.
Select the frame in STAAD.Pro's 3D view, click Extract MTO, and export. If you combine several STAAD models, they go into one bill of materials.
For the STAAD.Pro commands that give a basic take-off, see STAAD.Pro material take off: steel weight by section.
Try it
Open MTO Generator in SS Workbench with your PEB model open in STAAD.Pro, and check the tonnage of a tapered frame against the hand calculation above.