Bending Angle α and Thickness s:
The bending angle a can have any value between 0° and 180°. The thickness ‘s’ decreases by approximately 20 % in the rounded portion (see Figure 1).
To obtain uniform bends on bending rails, it is recommended that only bending radii from the series below be selected. The values printed in bold are to be preferred.
| r | 1 | 1.2 | 1.6 | 2 | 2.5 | 3 | 4 | 5 | 6 | 8 | 10 | 12 | 16 | 20 | 25 | 28 | 32 | 36 | 40 | 45 | 50 | 63 | 80 | 100 |
These bending radii comply with the radii according to DIN 250.
Table 1 gives the minimum permissible bending radii to be chosen for given sheet thicknesses and materials and for the applicable bending machines. The indicated values apply for bending angles α ≤ 120°. For bending angles α> 120° the next higher value in the table shall be used, e.g. if sheets of S 275 JR according to DIN EN 10025-2 are to be bent transverse to the rolling direction, with a thickness s = 6 mm, the minimum permissible bending radius is r= 10 mm for α ≤ 120° and r = 12 mm for α> 120°.
Table 1 — Minimum permissible bending radius r (Dimensions in millimetres)
| Minimum permissible bending radius r for thicknesses s | ||||||||||||||||
| Steelgrades | For bending transverse or parallel to the rolling direction | Up to 1 | Over 1 up to 1.5 | Over 1.5 up to 2.5 | Over 2.5 up to 3 | Over 3 up to 4 | Over 4 up to 5 | Over 5 up to 6 | Over 6 up to 7 | Over 7 up to 8 | Over 8 up to 10 | Over 10 up to 12 | Over 12 up to 14 | Over 14 up to 16 | Over 16 up to 18 | Over 18 up to 20 |
| S 235 JR S 235 JO s 235 J2 | Transverse | 1 | 1.6 | 2.5 | 3 | 5 | 6 | 8 | 10 | 12 | 16 | 20 | 25 | 28 | 36 | 40 |
| Parallel | 1 | 1.6 | 2.5 | 3 | 6 | 8 | 10 | 12 | 16 | 20 | 25 | 28 | 32 | 40 | 45 | |
| S 275 JR S 275 JO s 275 J2 | Transverse | 1.2 | 2 | 3 | 4 | 5 | 8 | 10 | 12 | 16 | 20 | 25 | 28 | 32 | 40 | 45 |
| Parallel | 1.2 | 2 | 3 | 4 | 6 | 10 | 12 | 16 | 20 | 25 | 32 | 36 | 40 | 45 | 50 | |
| S 355 JR S 355 JO s 355 J2 | Transverse | 1.6 | 2.5 | 4 | 5 | 6 | 8 | 10 | 12 | 16 | 20 | 25 | 32 | 36 | 45 | 50 |
| Parallel | 1.6 | 2.5 | 4 | 5 | 8 | 10 | 12 | 16 | 20 | 25 | 32 | 36 | 40 | 50 | 63 | |
Table 2 — Permissible deviations for minimum bending radii r (Dimensions in millimetres)
| Steel grades | Permissible deviations for minimum bending radii r for thicknesses s | ||
| Up to 3 | Over 3 up to 8 | Over 8 up to 20 | |
| S 235 JR S 235 JO S 235 J2 | +0.5 0 | +1 0 | +1.5 0 |
| S 275 JR S 275 JO S 275 J2 | +0.8 0 | +1.5 0 | +2 0 |
| S 355 JR S 355 JO S 355 J2 | +1 0 | +2 0 | +3 0 |
Key to Materials:
Table 3 provides examples of materials for which suitability for cold bending, cold flanging and cold curling is guaranteed, taking into account the minimum permissible bending radii specified in Table 1.
Table 3 — Key to materials (examples)
| Type of steel | Steel grade with a minimum tensile strength a | ||
| Over 360 MPa up to 510 MPa | Over 430 MPa up to 580 MPa | Over 510 MPa up to 680 MPa | |
| Hot-rolled products of structural steels according to DIN EN 10025-2 | S 235 JR | S 275 JR | s 355 J2 |
| a For nominal thicknesses < 3 mm | |||
Minimum Leg Length:
When mechanically bending sections of sheet metal, the leg length b is approximately 4.r (see Figure 2).
Permissible Deviations for Angular Positions on Bending Sections:
Values apply for a ratio up to r : s =4. For a larger (r : s) ratio, a larger deviation due to spring back is to be expected (see Figure 3).
Table 4 — Permissible deviations of angular positions (Dimensions in millimetres)
| Leg lengths a and b (where the shorter leg length is regarded as the nominal length) | Up to 30 | Over 30 up to 50 | Over 50 up to 80 | Over 80 up to 120 | Over 120 |
| Permissible deviations of bending angle α | ± 2° | ±1° 45′ | ± 1° 30′ | ± 1° 15′ | ± 1° |
Calculation of Developed Lengths:
Developed length=a+b+𝓋. Depending on the value of the bending angle, 𝓋 varies and represents a compensating value which, at an opening angle β of 0° up to 65° (calculated value 65° 24′ 30″), can be negative or positive, and at an opening angle over 65° can only be negative.
Developed lengths shall be rounded up to the nearest full millimetre.
Opening Angle β 0° up to 90°:
Opening Angle β 90° up to 165°:
Opening Angle β 165° up to 180°:
Compensating value 𝓋 =0
The values for 𝓋 are negligibly small in this case and sufficiently accurate for practical applications.
Correction Factor k to Determine the Cut Lengths of Bent Workpieces
The correction factor k gives the deviation of the position of the neutral line s/2 and can be calculated as follows:
or can be taken from the following graphical representation in Figure 7, which represents the equation.
For r : s > 5, Equation (3) is no longer valid so that k= 1 applies.
If only minimum requirements are set for the determination of cut lengths, rounded values as grouped together in Table 5 may be used for the correction factor k.
Table 5 — Correction factor k, rounded values
| Internal bending- radius r as a function of sheet thickness s | Ratio r : s | Over 0.65 up to 1 | Over 1 up to 1.5 | Over 1.5 up to 2.4 | Over 2.4 up to 3.8 | Over 3.8 |
| Correction factor k (rounded values) | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 | |
For any value for β, r and s, the corresponding compensating values 𝓋 can also be identified by the use of the correction factor k together with the graphical representations of factors in DIN 6935, Supplement 1.
For calculated compensating values 𝓋 for several opening and bending angles based on the above formula for correction factor k, see DIN 6935, Supplement 2.
Representation and Position of Bend Lines for Developments
The bend line indicates the middle of the bending radius and shall be represented by a thin continuous line. The position of the bend line results from the abutting leg lengths a and b, with half of the positive or negative compensating value 𝓋 taken into account (see Figure 8).
Developments shall only be explicitly drawn if the shape of the cut sheet is not unambiguously determined by dimensioning and indication of the bend line.
Dimensioning and Calculation of Developed Lengths (Examples)
EXAMPLE 1:
Material: S 235 JR
Sum of leg lengths= 50 + 200 + 80 = 330
β 90°, r= 6, s=4
𝓋= 3.14 x(0.5)x ( 6+2 x 0.74)- 2×10= -8.26
β 90°, r= 20, s=4
𝓋= -13.44
𝓋total = -8.26-13.44= -21.7
Developed Length = 330-21.7= 308.3 ≈ 309
EXAMPLE 2:
Material: S 235 JR
Sum of leg lengths= 50 + 170 + 246+50 = 516
β 90°, r= 20, s=12 , 𝓋= -25,41
β 45°, r= 20, s=12 , 𝓋= -6.12
β 135°, r= 32, s=12 , 𝓋= -7.25
𝓋total = -25.41-6.12-7.25= -38.78
Developed Length = 515-38.78= 477.22 ≈ 478
Development and Marking of Bend Line Position (Example)
Material: S 355 J2
All dimensions in millimetres.
Sum of leg lengths= 45 + 50 + 32 = 127
β 45°, r= 10, s=5 , 𝓋= -1.72
β 135°, r= 10, s=5 , 𝓋= -3.00
𝓋total = -1.72-3.00= -4.72
Developed Length = 127-4.72= 122.28 ≈ 123
Position of Bend Lines:
For leg length = 45, β 45°, r= 10, s=5 , 𝓋= -1.72
45- 1.72÷2= 45- 0.86 = 44.14 ≈ 44
For leg length = 32, β 135°, r= 10, s=5 , 𝓋= -3.00
32-3.00÷2=32-1.5=30.5 ≈ 31
