Sheet metal
Rolled plate length calculator
In short
The blank of a rolled shell course is a rectangle of length L = π × Dn + gap and height H. The neutral-fibre diameter is Dn = Dint + e = Dext − e; the mass follows m = L × H × e × ρ.
Calculation
Example calculated with the tool’s default values.
Inputs
- Diameter
- 500 mm
- The diameter entered is
- Inside
- Thickness
- 5 mm
- Shell height (plate width)
- 1000 mm
- Root gap of the longitudinal seam
- 0 mm
- Material
- Carbon steel
- Number of shells
- 1
- Number of generator lines
- 12
Results
- Blank length (neutral fibre)
- 1586.5 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Neutral-fibre Ø
- 505.0 mm
- Inside Ø
- 500.0 mm
- Outside Ø
- 510.0 mm
- Blank width
- 1000.0 mm
- Mass of one shell
- 62.27 kg
- Total mass
- 62.27 kg
- Length with DIN 6935 K
- 1586.5 mmr/t = 50.00 → k = 1.000, K = 0.500
- Residual flat, pinch machine (min)
- 7.5 mm1.5 to 2 times the thickness at each end per the maker; a pyramid roll leaves more
- Residual flat, pinch machine (max)
- 10.0 mm
- Usual pre-bend length (min)
- 102 mm4 to 10 in on the pre-bend pass (roll maker)
- Usual pre-bend length (max)
- 254 mm
- Generator line pitch on the blank
- 132.2 mm12 divisions; outside chord 132.0 mm
- Pre-bending: the plate ends stay flat when rolling. Pre-bend both ends, or leave extra length to cut off after rolling. Indicative roll-maker figures.
Step-by-step calculation
Neutral-fibre diameter
Dn = Dint + e
Dn = 500.0 + 5.0 = 505.0 mm
Blank length
L = π × Dn + jeu
π × 505.0 + 0.0 = 1586.5 mm
Mass
m = L × H × e × ρ
1586.5 × 1000 × 5.0 mm³ × 7850 kg/m³ = 62.27 kg
Check with DIN 6935 K
L = 2π (ri + K e), K = k / 2
2π × (250.0 + 0.500 × 5.0) = 1586.5 mm
Generator lines
x = π Dn × i / n ; corde = D sin(π i / n)
π × 505.0 / 12 = 132.2 mm
Generator lines: 12 divisions of the circumference (blank: from the edge; rolled shell: arc and chord from line 0)
| No. | Angle (°) | On blank (mm) | Arc out (mm) | Chord out (mm) | Arc in (mm) | Chord in (mm) |
|---|---|---|---|---|---|---|
| 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 1 | 30.0 | 132.2 | 133.5 | 132.0 | 130.9 | 129.4 |
| 2 | 60.0 | 264.4 | 267.0 | 255.0 | 261.8 | 250.0 |
| 3 | 90.0 | 396.6 | 400.6 | 360.6 | 392.7 | 353.6 |
| 4 | 120.0 | 528.8 | 534.1 | 441.7 | 523.6 | 433.0 |
| 5 | 150.0 | 661.0 | 667.6 | 492.6 | 654.5 | 483.0 |
| 6 | 180.0 | 793.3 | 801.1 | 510.0 | 785.4 | 500.0 |
| 7 | 210.0 | 925.5 | 934.6 | 492.6 | 916.3 | 483.0 |
| 8 | 240.0 | 1057.7 | 1068.1 | 441.7 | 1047.2 | 433.0 |
| 9 | 270.0 | 1189.9 | 1201.7 | 360.6 | 1178.1 | 353.6 |
| 10 | 300.0 | 1322.1 | 1335.2 | 255.0 | 1309.0 | 250.0 |
| 11 | 330.0 | 1454.3 | 1468.7 | 132.0 | 1439.9 | 129.4 |
| 12 | 360.0 | 1586.5 | 1602.2 | 0.0 | 1570.8 | 0.0 |
How to use it
- Enter the diameter and say whether it is inside, outside or on the neutral fibre.
- Enter the plate thickness and the shell height (plate width).
- Set the root gap of the longitudinal seam, the material and the number of shells.
- Read the blank length on the neutral fibre.
Frequently asked questions
How do I calculate the rolled plate length of a shell?
Use the neutral-fibre diameter, at mid-thickness: Dn = Dint + e, or Dn = Dext − e. The blank length is L = π × Dn + gap, the gap being the root gap of the longitudinal seam. Example: 500 mm inside Ø, 5 mm plate: Dn = 500.0 + 5.0 = 505.0 mm and L = π × 505.0 = 1586.5 mm.
What is the plate rolling calculation formula?
L = π × Dn + gap, with Dn the neutral-fibre diameter and the root gap of the longitudinal seam. The gap is added to the blank: the finished neutral-fibre perimeter stays π × Dn. The blank width is the shell height H.
How do I calculate the mass of a shell course?
m = L × H × e × ρ. For a steel shell 1000 mm high, 1586.5 mm blank, 5 mm plate and ρ = 7850 kg/m³: 1586.5 × 1000 × 5.0 mm³ × 7850 kg/m³ = 62.27 kg. With several shells, M = m × n.
Should the plate ends be pre-bent before rolling?
Yes: the plate ends stay flat when rolling. On a pinch machine, the residual flat is 1.5 to 2 times the thickness at each end per the maker, and a pyramid roll leaves more. Pre-bend both ends, over 4 to 10 in (101.6 to 254 mm) according to a roll maker, or leave extra length to cut off after rolling.
When is the neutral fibre no longer at mid-thickness?
When the inside radius is below 5 times the thickness: the DIN 6935 table then puts the neutral fibre towards the inside, with L = 2π (ri + K e), K = k / 2 and k = 0.65 + 0.5 log10(r/e). The calculation gives this length as a check; the real blank can be shorter, calibrate on a trial piece.
Limits
Indicative results. The neutral fibre is taken at mid-thickness; the DIN 6935 correction is only a check when the inside radius is below 5 t. Residual flats and pre-bend lengths are indicative roll-maker figures (WDM). Calibrate the blank on a trial piece.
Sources
- Calcul du flan d’une virole sur la fibre neutre : π × diamètre moyen (Dint + e = Dext − e) : Formation chaudronnier, module 2 chapitre 2 (cylindre, cône, piquage) (link)
- Facteur de correction k de DIN 6935 (k = 0,65 + 0,5 log10(r/e), K = k / 2) : DIN 6935 ; table et formule (link)
- Méplats résiduels (1,5 à 2 e en rouleuse à pincement) et pré-cintrage sur 4 à 10 pouces : WDM, « Roll Bending Tips » (guide du constructeur), sections 3 et 5 (link)