Bending basics: Dissecting bend deductions and die openings

Why precise bend deductions and die openings matter

The FABRICATOR September 2012
September 3, 2012
By: Steve Benson

Changing the die opening can dramatically change results during air forming. In precision sheet metal fabrication, choosing the correct die opening should not be a guessing game.

Bending basics: Dissecting bend deductions and die openings -

Figure 1: In the bend allowance calculation, you use the complementary bend angle.

Editor’s Note: This is the first article in a series on press brake operation basics. The information comes from the Fundamentals of Press Brake Operations e-Fab online training program, presented by Steve Benson of ASMA LLC and available from the Fabricators & Manufacturers Association. Material also comes from FMA’s Precision Press Brake Certificate Program, presented by Benson and held at locations across the country. For more information, visit or call 888-394-4362. Figures are courtesy of ASMA LLC, 2952 Doaks Ferry Road N.W., Salem, OR 97304, 503-399-7514,, smartphone

Bottoming and coining with the press brake had its heyday. But over the past several decades, air forming has become the industry standard. So when air forming, how do you select your bottom die opening? Do you choose a die opening that’s 6 times the material thickness, 8 times, 10 times, or even 12 times?

The narrower the die opening, the more tonnage it will take to bend a part. If you’re a new operator, or if you’re worried about exceeding tonnage limits, you might choose an opening that’s 10 to 12 times the material thickness; if you’re not worried about tonnage, you may reach for a die opening that’s only 6 times the thickness.

Almost every press brake comes with a tonnage chart, and many toolmakers publish information on maximum tonnage for every tool they make. You use a formula to calculate tonnage requirements for a specific job to ensure you don’t push your machine beyond the tooling load limit as well as what the press brake manufacturer’s ram load limit specifies (see Tonnage Matters sidebar). Tool placement on the bed, type of bending operation, and other factors come into play.

But in press brake air forming, the die opening does far more than affect available tonnage per foot. So which is the perfect die opening—6, 8, 10, or 12 times material thickness? A widely held rule of thumb is that 8 times material thickness is a perfect die opening. Well, this is correct, but only when there’s a one-to-one relationship between the material thickness and the desired inside radius. But if you want to put a 3-in. radius into 0.036-in.-thick material, that 8-times-material-thicknes rule of thumb just won’t work.

Here’s why. In bottoming, the punch profile effectively stamps the material at slightly more than material thickness. In coining, the punch presses so hard into the material that it thins the material and actually realigns the molecular structure of the metal, which is why coining is rarely performed these days, at least on purpose. In air forming, though, the die opening sets the radius of the bend.

This becomes obvious when you see air forming in action. To air-form, the punch descends to a certain point, but unlike bottoming, the workpiece doesn’t conform tightly around the punch radius; rather, the inside radius is produced as a percentage of the die opening. If you change the die opening, you change the inside bend radius you produce—sometimes significantly. If you change the inside bend radius, you change the amount of material elongation within each bend; the bend deduction (BD) in turn changes your part, and you will then be unable to form the part to the desired dimensions.

The 20 Percent Rule

The 20 percent rule shows just how dramatically small changes in the die opening affect the resulting inside bend radius. This rule states that the inside bend radius of an air-formed part will be 20 percent of the die opening. Unlike most rules of thumb in the trade, this one isn’t based on cold-roll steel, but instead uses 304 stainless steel as the baseline. In cold-rolled steel, it’s 15 to 17 percent, soft aluminum (50 series) 14 to 16 percent, 304 stainless 20 to 22 percent, and hot-rolled pickled and oiled 12 to 14 percent.

Here, it’s still helpful to use 60,000-PSI-tensile-strength cold-rolled steel as a baseline. If you are working with another material, you can multiply the tensile by this baseline. So, if your metal is 120,000-PSI tensile, that’s twice the tensile strength of cold-rolled steel. So you multiply 15 percent by 2, and find your inside radius will be approximately 30 percent of the die opening.

Because alloy characteristics can vary, the rule covers a range of percentages, so you can start with the median value and adjust as necessary over time. Say you have three test pieces of 16-gauge cold-rolled steel (all with the same grain direction) and bend them using a 1⁄32-in.-radius punch using the median percentage value for three different die openings. A 0.473-in. die opening may produce an inside bend radius of 0.70 in. A 0.551-in. opening produces an inside bend radius of 0.082 in. And a 0.984-in. opening may produce an inside bend radius of 0.147 in. That’s a huge radius variation, and the die width changed by about half an inch.

Bending basics: Dissecting bend deductions and die openings -

Figure 2: Every bend has two outside setbacks (OSSB). So to calculate the bend deduction, multiply the OSSB by 2, and then subtract the bend allowance (BA), which is the length of bend along the neutral axis.

Bend Deduction Basics

Each bend elongates—it’s often called growth or stretch, though elongate is the technically accurate term. Because of this, you must deduct certain amounts of that value from the flat blank size so that when the material bends, it elongates to the dimension required by the print. The elongation occurs because the bend’s neutral axis shifts toward the inside radius.

Each bend consists of a bend angle and inside bend radius. If two bends on a part have the same bend angle and inside radius, both will have the same bend deduction. If another bend on the part has a different angle/inside radius combination, it will require its own bend deduction calculation.

Although modern bend deduction charts are relatively accurate, older charts have serious variances. More than 100 bend deduction charts have been published over the decades, and not one of them agrees entirely with another. Say you’re putting a 0.063-in. radius in 0.060-in-thick cold-rolled steel. One chart may give a bend deduction of 0.106, another 0.136—that’s a difference of 0.030 in. This might not be a big deal if you’re working with loose tolerances and have a limited number of bends. But in a part with multiple bends, that 0.030-in. variance will stack up, eventually making it impossible to form a part to print.

True, customers may not care about the inside radius. The part print may specify a specific radius, but as long as the part matches up and works as intended, they’re probably not about to get out their radius gauges to measure each bend. But if you determine the precise bend deduction needed for a particular radius, you effectively make manufacturing easier and reduce the number of inherent mistakes. Hence, your throughput goes up and you are much more productive.

To start, you need to know what happens to sheet metal when it bends. During each bend, the material’s neutral axis—where the material neither compresses nor expands—shifts inward toward the inside radius. The bend allowance is the length of the bend as measured on the material’s neutral axis.

Here is where geometry and trigonometry come into play. Bend allowance = [(0.017453 × Inside bend radius) + (0.0078 × Material thickness)] × Complementary Bend angle. You can insert the value of the inside bend radius as determined by the 20 percent rule. For the bend angle, you use the complementary angle (see Figure 1). (This formula incorporates the K factor and other mathematical functions that will be covered in future articles in this series.)

Next, you need to know the bend’s outside setback, which is the distance from the apex, where the two planes of the bend intersect on the inside surfaces, to the tangent point of the bend, where flat metal transitions to curved metal. Here’s the formula, easily workable with any scientific calculator: Outside setback = [tangent (degree of bend angle / 2)] × (Material thickness + Inside bend radius).

At this point you know the outside setback and the bend allowance. You’re now ready to calculate bend deduction: again, the amount of material deducted from the flat blank to account for material elongation during each bend (see Figures 2 and 3).

Here’s the formula: Bend deduction = (2 × Outside setback) - Bend allowance. With the bend deduction in hand, you can determine the appropriate flat blank size, and program the press brake so that the backgauge fingers accommodate for material elongation during each bend.

The Bedrock of Bending

Geometry and trigonometry calculations like these represent the bedrock of press brake operation. Of course, modern controls and software can automate a lot of these calculations. But in your fabrication career, such modern equipment may not always be available. Moreover, just because a machine is old doesn’t mean it can’t be productive.

Bending basics: Dissecting bend deductions and die openings -

Figure 3: This shows the basics of flat blank development. Dimension x and y go to the apex. To account for bend elongation, add x and y, and then subtract the bend deduction. The bend deduction is double the outside setback (OSSB + OSSB) minus the bend allowance.

And this is only the beginning. As a press brake operator, you have so many variables to worry about. What type of bend is it—sharp, radius, or profound? What’s the grain direction? The list goes on. (Editor’s note: These topics and more will be covered in future installments of this series.)

Most important, if you know the math, you know exactly what goes into each bend. Charts and rules of thumb are useful, but in precision metal fabrication, you should, well, be precise. The more knowledge you have, the better and more productive you can be.

Tonnage Matters

When you choose a die opening, you still change the available tonnage, of course. To ensure an application isn’t pushing the tonnage limits of your machine or tooling, you need to know how much tonnage a job really takes.

For this, it’s back to the math. Note how in the following equation the material thickness is squared. A little more material thickness can go a long way in increasing the required tonnage.

[(575 × Material thickness squared)/ V die width]/12 × Material factors × Bending method factors = Tonnage per inch. In this calculation, air forming mild steel is the baseline. Other bending methods and materials are above or below this baseline.

Material Factors
Mild steel, 1.0
Copper, 0.5
H series aluminum, 0.5
T6 series aluminum, 1.28
304 stainless, 1.4

Method Factors

Air forming, 1.0
Urethane tooling operations, 4.0
Bottom bending, 5.0+
Coining, 10+

Once you know the tons per inch, you can calculate the tonnage needed for the job at hand: The length of the bend × Tons per inch = Total tonnage.

All this is rooted in a 90-degree bend in a standard die. Maximum tonnage isn’t obtained immediately. In most cases, about 80 percent of total tonnage is achieved within the first 20 degrees of bend angle. In other words, even with a slight angle, a bend can put immense pressure on tooling and equipment.

As always, tooling and press brake manufacturers have the final word when it comes to the tonnage capabilities of their equipment. You should never—ever—exceed the maximum allowable tonnage for a tool set or press brake.

Steve Benson

Steve Benson

2952 Doaks Ferry Road N.W.
Salem, OR 97301-4468
Phone: 503-399-7514
Fax: 503-399-7514
Steve Benson is a member and former chair of the Precision Sheet Metal Technology Council of the Fabricators & Manufacturers Association International®. He is the president of ASMA LLC, 2952 Doaks Ferry Road NW, Salem, OR 97301, Benson also conducts FMA’s Precision Press Brake Certificate Program, which is held at locations across the country. For more information, visit, or call 888-394-4362. For more information on bending, check out Benson’s new book, The Art of Press Brake: the Digital Handbook for Precision Sheet Metal Fabrication, © 2014, available at

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The FABRICATOR is North America's leading magazine for the metal forming and fabricating industry. The magazine delivers the news, technical articles, and case histories that enable fabricators to do their jobs more efficiently. The FABRICATOR has served the industry since 1971.

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