# Calculation of the Minimum Bending Radius of Profiles

In actual work, it is often encountered that various curves and flanges are bent with profiles. For example, most thin-walled pipes with a wall thickness δ<2mm are used for angle steel flanges. However, when bending flanges with angle steel, it is often found that the angle steel is too large or too small when it is bent halfway, which will cause a lot of waste. Most workers judge the size of material selection based on experience, which is very unscientific. In fact, we can use profiles to make curves and flanges by combining simple calculation and lofting, which can avoid waste and unnecessary losses.

## For example, the formula for calculating the minimum radius of the outer bend of the angle steel

Cold bending

Min.Bending.Radius = [ (b – Z0)/ 0.04] – Z0

Hot bend

Min.Bending.Radius = [ (b – Z0) 0. 14 ] – Z0

## Calculation formula for minimum radius of angle steel inner bend

Cold bending

Min.Bending.Radius = [ (b – Z0)/ 0.04] – b + Z0

Hot bend

Min.Bending.Radius = [ (b – Z0)/ 0.04] – b + Z0

Note:
b is the width of the angle steel;
Z0 is the center of gravity of the angle steel.

## Calculation formula for minimum bending radius of flat steel

Cold bending

Hot bend

Note: a is the width of the flat bar.

## Calculation formula for minimum bending radius of steel pipe

Hot bend

Cold bending

Note: d is the diameter of the steel pipe.

Wall thickness δ> 2mm

1. For those with a diameter of Φ5mm～Φ35mm: Min.Bending.Radius = 3d;
2. Diameter is Φ35mm～Φ60mm: Min.Bending.Radius = 4d;
3. The diameter is Φ60mm～Φ140mm: Min.Bending.Radius = 5d.

The above calculation formulas have been widely used in practical work, practical and reliable, and can be used for reference.

## Tube bending formulas and angle steel bending formulas

### Tube Bending Formulas

1. Bend Allowance (BA): BA = (π/180) × B × (R + K × T) Where:
• B = Bend Angle in degrees
• K = K-factor (material property)
• T = Material Thickness
2. Bend Deduction (BD): BD = BA × Tan(B/2) Where:
• BA = Bend Allowance
• B = Bend Angle in degrees
3. Bend Angle Calculation: B = 2 × Tan^(-1)(BD / BA) Where:
• BD = Bend Deduction
• BA = Bend Allowance
4. Chord Length (CL): CL = 2 × R × Sin(B/2) Where:
• B = Bend Angle in degrees
5. Outside Setback (OSB): OSB = R × Tan(B/2) Where:
• B = Bend Angle in degrees

### Angle Steel Bending Formulas

1. Bend Allowance (BA): BA = (π/180) × B × (R + K × T) Where:
• B = Bend Angle in degrees
• K = K-factor (material property)
• T = Material Thickness
2. Bend Deduction (BD): BD = BA × Tan(B/2) Where:
• BA = Bend Allowance
• B = Bend Angle in degrees
3. Bend Angle Calculation: B = 2 × Tan^(-1)(BD / BA) Where:
• BD = Bend Deduction
• BA = Bend Allowance
4. Outside Setback (OSB): OSB = R × Tan(B/2) Where: