When engineers are needed to make bent or curved pieces of sheet metal, they use thumb rules, company written tables and guesstimates to determine the length of straight stock needed for bending into a precisely measures curved part. But what if these methods are unavailable to some engineers ? Even if they were, the required stock length depends on material thickness, end radius and bending angle, but also on the specific material being used.

Fortunately, there is a series of equations that are valid for all materials which can calculate bend length and bend allowance. If the material's strength and ductility are known, the equations can be used directly. If not, they can be used with data from a simple test bend to determine material properties and then applied to the bend at hand.

Fortunately, there is a series of equations that are valid for all materials which can calculate bend length and bend allowance. If the material's strength and ductility are known, the equations can be used directly. If not, they can be used with data from a simple test bend to determine material properties and then applied to the bend at hand.

**How to find bend length:**
If the material bends with the neutral plane in the exact center of the sheet, bending length (BL) can be calculated from

BL = (πθ/180)(R+0.5T)

The bend allowance (Ba) for outside measurements A and B is related to bend length (BL) by

Ba = (θ/90)(2(R+T)-BL)

However when the material undergo plastic deformation, as they do in bending opeations, the neutral plane does not remain at the center of the sheet. Under these conditions, bend length can be found out from this equation

BL = (πθ/180)(R+C*0.5T)

where C is related to the material's ductility.

One indication of ductility is K, the ratio of material's yield strength to its tensile strength. Low ductility materials have K ratios approaching 1, while highly ductile materials have K ratio much less that 1. Applying linear regression with the bend length equation yields the following equation for C

C =0.668+0.326K

^{2 }.
Because sheet metals vary from batch to batch, values of K and C are best determined from test bending a material sample and computing new values rather than relying on previously established data. Both K and C are the properties of the material rather than geometry, so the best bend can be made on a sample of any convenient thickness and at any convenient radius.

Using the above equations and data from test bend, K

^{2 }can be found out from equation 2
K

^{2 }=((2(R+T)tan(θ/2)- Ba)(180/πθ)-R)((1/T)-0.334)(1/0.163)**Nomenclature :**

A = straight line dimension on one side of bend

B = straight line dimension on other side of bend

BL = bend length

Ba = bend allowance

C = ductility constant

K = ratio of yield strength to tensile strength

L = straight line length of piece before bending

R = bend radius measure on inner surface

T = material thickness

θ = bend angle

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