Cylinder flat pattern

What it is

The rolled shell is the straight tube: a plate run through the rolls until both edges meet, closed with one longitudinal weld. It is the simplest part in the trade and the basis of nearly everything else — stacks, ducts, silos and tank shells are stacked cylinders.

Where it is used

Exhaust ducting, chimneys, tank and vessel shells, equipment jackets, large-diameter pipe fabricated from plate.

Measurements the calculation needs

• D Outside diameter
• H Height of the shell (its length)
• THK Plate thickness

Calculate with your own measurements

No account needed: enter the measurements in millimetres or inches and get the figures and the drawing. The scaled PDF template, the DXF for the cutting table and the 3D model take a free account.

Diameters and sides are outside measurements. The flat pattern already allows for the plate thickness, working on the mean line.

Units: mm inches

Outside diameter D (in)

Height of the shell (its length) H (in)

Plate thickness THK (in)

Calculate free

How it develops: the formulas

Plate length (circumference on the neutral axis)

L = π × (D − t) D is the outside diameter and t the plate thickness. For D = 300 and t = 3: L = π × 297 = 933.1 mm. With π × D the plate would come out 9.4 mm long.

Plate height

H = h The shell height goes in as it is: the plate is a rectangle of L by h.

Mean diameter

Dm = D − t The diameter of the neutral axis, at mid-thickness. From an inside diameter use Dm = Di + t.

Worked example

The values the form comes pre-filled with, run through the tool itself:

Outside diameter	11-13/16" (11.811)
Height of the shell (its length)	19-11/16" (19.685)
Plate thickness	1/8" (0.1181)
The flat pattern fits a plate of	36-3/4" × 19-11/16"

Result of the example

Plate	36-3/4" × 19-11/16"
Area and weight	5.0 ft² · ≈ 24.2 lb in 1/8" steel

How to mark it out on the plate

1. Work out L = π × (D − t) and mark a rectangle of L by h on the plate. Check squareness by the diagonals: both must measure √(L² + h²).
2. Mark the centre line and, if the shell takes a nozzle or branch, its position relative to the seam, before rolling.
3. Cut and bevel the longitudinal seam to suit the welding process. The template is the finished part, with no root gap.
4. Pre-bend both ends in the press before rolling, or leave stock and trim afterwards: a three-roll bender leaves the ends flat.
5. Roll until the two edges meet, check the outside circumference with a tape (π × D) and weld the seam.

Common mistakes and tolerances

Using the outside diameter for the circumference

π × D instead of π × (D − t) leaves π × t over: 9.4 mm on a 300 mm shell in 3 mm plate and 31.4 mm on 800 mm in 10 mm. The seam overlaps and the shell goes oval.

Forgetting the weld allowance

The template is the finished part on the neutral axis. Bevel, root gap and machining stock go on top, to shop practice.

Flat ends off the rolls

The first and last 50 to 100 mm stay flat on a three-roll bender. Either pre-bend the ends in the press or roll with stock and trim; otherwise the seam sits on a flat and the tube comes out with a peak.

Checking by diameter instead of circumference

A 1 mm error in circumference is 0.32 mm in diameter. On a large shell the tape on the circumference is more sensitive than callipers on the diameter.

Guides about this part

• The neutral axis of plate: why every development uses D − t, and the bend deduction
• How we check the Planichapa calculations, and who is behind them
• LITIO alternative: Planichapa develops sheet metal parts in the browser, nothing to install, now that LITIO2 is no longer sold
• Plate 'n' Sheet alternative: Planichapa develops sheet metal parts in the browser, with the price on the page
• Steel plate weight calculator, weight per m², gauges and stock plate sizes: table and formula
• Pipe ovality: a calculator, the formula, a worked example, the limits the codes use and how to measure it in the shop
• Plate rolling calculator: the blank length of a rolled shell, with the formula, a chart and a worked example
• Dished head calculator: depth, volume, blank diameter and weight of torispherical, 2:1 elliptical and hemispherical heads

Frequently asked questions

Why is the plate length not π times the outside diameter?

Because the plate neither stretches nor compresses at the neutral axis, which sits at mid-thickness. The correct length is π times the mean diameter — the outside diameter less one thickness. On a 300 mm shell in 3 mm plate that is over 9 mm, more than enough to leave the weld short.

Does the flat pattern include weld preparation?

No. The result is the finished part on the neutral axis. If your process needs a bevel, root gap or extra stock, add it to the calculated figure according to your shop practice.

What plate length does a 300 mm shell in 3 mm plate take?

π × (300 − 3) = 933.1 mm, by 500 high. With the outside diameter, π × 300 = 942.5: nine millimetres over, which overlap at the seam.

How do I check the diameter after rolling?

By the outside circumference, with a tape, which must give π × D. A 1 mm error in circumference is only 0.32 mm in diameter, so on a large shell the tape is more sensitive than callipers.