Hello,

     I'm working on a series of sheet metal parts to come up with a K-Factor for various thicknesses of sheet metal, and various number of bends.  We started with some sample pieces (6" x 6") in various thicknesses from 16GA to 3/8" Hot Roll.  In each thickness, we made several samples, (single bends, double bends, etc.) and took measurements of the bent shapes, including the resultant bend radius. I then took these measurements and used them in a mathematical equation that I've found on-line for accurately defining a K-Factor for a single bend, but when the same K-Factor is used on a piece with multiple bends, the total length of the flat pattern does not equal the 6" that we started with on our sample piece. Below is the equation that I used to find a K-Factor for single-bend pieces for each gage size and had great success with the flat pattern equalling 6.000".  A and B are the overall outside lengths of each leg and Total Flat Length is the 6" flat sample piece.

Bend Deduction = A +B – Total Flat Length

Outside Setback = (Tan(Bend Angle/2)) * (Thickness + Bend Radius)

Bend Allowance = (2 * Outside Setback) – Bend Deduction

K-factor = (-Bend Radius + (Bend Allowance / (π * Bend Angle / 180))) / Thickness

Here is the eqaution with my numbers(in inches) plugged in for 16 GA:

Bend Deduction = 3.054 + 3.056 - 6 = .110

Outside Setback = (Tan(90/2)) x (.060 + .060) = .120      (where (Tan(90/2) = Tan 45 = 1)

Bend Allowance = (2 x .120) - .110 = .130

K-Factor = (-.060 + (.130 / (3.14 x 90 / 180))) / .060 = 0.38     (where 3.14 x 90 / 180 = 1.57)

I followed this formula for each GA thickness and, with the resultant K-Factor, had a flat pattern of 6.000" each time.  But when I tried using the same K-Factor of 0.38 for a 16 GA piece with two bends, with an overall outside width of 3.595 and two legs with overall outside lengths of 1.320/1.321,  the flat pattern length grows to 6.016".  To get the flat pattern to equal 6.000", I had to use a K-Factor of 0.295.  Why is there a difference when going from one bend to 2 bends when starting with the same size flat pattern sample piece?  I have yet to start working with pieces that have 3 or more bends, because I have been stumped at 2......

Thank you in advance for any input,

Mike Knauss