The neutral axis
I'm Iris Xu, a Sales Manager in ZTRFM. A buyer in Qatar asked me last week why his strip needed to be 35 millimeters wider than the finished profile circumference. He had added up the outside dimensions of his Z-section and could not see where the extra steel went. The answer is bend allowance, and it is the single number that decides how wide a coil you must order.
When a strip bends, the outside of the bend stretches and the inside compresses. Somewhere between the two surfaces sits a thin layer that neither stretches nor shrinks. We call it the neutral axis. The length of that layer at the bend is the true length of material you need, and the flat blank is sized from it.
In pure bending theory the neutral axis would sit at the middle of the thickness, the 0.50 line. In real cold forming it sits closer to the inside face, typically around 0.40 to 0.50 of the thickness measured from the inside surface. Machinery's Handbook gives 0.40 to 0.50 for mild cold-rolled steel at about 60,000 psi tensile, with 0.446 as the common default. For air-bent mild steel most shops run 0.40 to 0.46, and softer aluminum runs a little lower.
The K-factor is just that position written as a decimal. K = 0.44 means the neutral axis lies at 44 percent of the thickness out from the inside face. The K-factor is the only empirical number in the whole flat-pattern problem. Everything else is geometry.
The bend allowance formula
Bend allowance is the arc length of the neutral axis through one bend. For roll forming we use the same relationship as a press brake:
BA = pi x (R + K x T) x (theta / 180)
where R is the inside bend radius, T is the strip thickness, and theta is the bend angle in degrees. Add the straight legs and you get the developed width of the strip.
Worked example: a 2.0 mm thick strip, inside radius 3.0 mm, 90-degree bend, K 0.44.
BA = 3.1416 x (3.0 + 0.44 x 2.0) x (90 / 180) = 3.1416 x 3.88 x 0.5 = 6.09 mm
That 6.09 mm is the material the bend itself consumes. Add it to the straight flange lengths and you have the cut width. Change the radius to 5 mm and the allowance grows to 7.40 mm, which is why a wider bend radius needs a wider blank even when the angle is the same.
Why the strip is wider than the profile
A closed section like a C or Z has several bends, and each one adds allowance. Take a simple C-channel with two 90-degree return flanges:
| Element | Length (mm) |
|---|---|
| Web, flat | 100.0 |
| Two bend allowances (2 x 6.09) | 12.18 |
| Two flange legs, flat | 50.0 |
| Developed strip width | 162.18 |
The outside dimension of that section is only about 127 mm across, yet the strip is 162 mm wide. The difference is the bend allowance on both corners plus the flange returns. Order the coil too narrow and the flanges will not reach, or the lip angle will be wrong.
Where it matters on the floor
Strip width drives three things. First, coil cost: you pay for every millimeter of width, so an over-wide blank is pure scrap. Second, edge trim: if the flower is designed around the wrong developed width, you cut off material you paid for. Third, the screw line: in a purlin or stud the flange must land on a hole pattern, and a few millimeters of wrong developed width shifts every hole.
Developed width is also how we set the side-roll positions and the edge guides. The blank must enter centered, and the width tells us where the bends will fall.
Roll forming versus press brake
The formula is the same, but the process differs. In a press brake the bend happens at one station and the neutral axis can shift toward the inside as the punch forces the material. In roll forming the bend is built up gradually over many stands, so the neutral axis moves much less during each pass. The K-factor we use for roll-formed strip is therefore a little more stable run to run than in brake work, though it still shifts with lubrication, temper and stand pressure.
Finding K from a test bend
If you do not trust the book value, run a test bend and measure. Form a known radius and angle, measure the flat length that produced it, then solve the formula backwards:
K = (BA / theta_in_radians) - R, all divided by T
We do this whenever a new grade arrives, because the published default assumes low-carbon steel and a V-die. A high-strength or coated coil will not match it. A five-minute test bend beats a warehouse of scrap.
Common mistakes we see
- Using the CAD default K of 0.50 for air-bent steel, which runs closer to 0.44.
- Adding outside dimensions and forgetting the bend allowance entirely.
- Ignoring that a wider bend radius needs a wider blank.
- Mixing bend deduction and bend allowance on the same drawing.
Thin stock needs more care
Below about 1.0 mm the K-factor and the radius tolerance matter more, because a small error in radius is a large fraction of the thickness. At those gauges we tighten the side-roll setup and re-check the developed width on the first coil. A half-millimeter width error on thin trim is the difference between a flush seam and a gap.
Ordering coil to the developed width
Buyers sometimes order coil to the profile width plus a rough allowance and hope the flower fits. That guessing is where scrap comes from. We prefer to calculate the true developed width, then add only the slitting tolerance the mill needs, often plus or minus 0.5 mm. A line that trims a 5 mm edge off every meter of a wide coil is throwing money into the scrap bin. Get the developed width right and the edge trim drops to almost nothing.
A note on the angle
The bend angle in the formula is the angle through which the material is bent, not the included angle of the finished profile. A 90-degree leg-up bend is a 90-degree bend. A hemmed 180-degree fold is a 180-degree bend, and its allowance is double a 90 at the same radius. Mixing the two up is a common cause of a blank that is short by a noticeable margin.
A practical takeaway
Before you order coil, let us calculate the developed width from your drawing, not from the outside dimensions. Send the section profile, the thickness and the material grade, and we will return the exact strip width plus the K-factor we used.
I will leave it there. ZTRFM builds roll forming lines and the tooling that turns a flat strip into a dimensional section, so getting the developed width right is the first step in every machine we ship. If your current line is trimming too much edge, send us a sample and we will check the flower against the real bend allowance.
