Bending - Course: Technique of Working Sheet Metals, Pipes and Sections. Trainees' Handbook of Lessons
 (introduction...) Preliminary Remarks 1. Purpose of Bending 2. Selected Tools, Appliances and Machines 3. Processes within in the Material 4. Fundamentals of Calculation 5. Bending Techniques

4. Fundamentals of Calculation

When a workpiece is being bent, its original length may alter by a certain measure.

Therefore, the workpiece has to be cut to size very exactly before being bent The required blank length is called “stretched length” and is to be calculated from the length of the neutral axis.

Figure 20 Dimensions on parts to be bent 1 stretched length, 2 leg lengths, 3 bending radius, 4 workpiece thickness

If the bending radius is bigger than five times the workpiece thickness, the neutral axis runs in the middle of the workpiece. Hence, the neutral axis bending radius is to be calculated with the following formula:

 With RB > 5 · S RN = radius of neutral axis RB = bending radius S = workpiece thickness

If the bending radius is smaller than five times the workpiece thickness, the neutral axis is displaced to the bending internal side during the bending process.

Then the bending radius of the neutral axis can be calculated with the following formula:

With RB < 5 · S

If workpieces are bent by 360°, the length of bend is calculated with the formula for calculating the circumference:

 LB = U = D · p or LB = U = 2 · RN · p LB = length of bend U = length of circumference D = circle diameter p = constant with the value of 3.14

Hence, the following formula is used for a 180° bending:

or LB = RN · p

Hence, the following formula is used for a 90° bending:

For any optional bending, the formula of the bending angle is to be considered:

What does the term "stretched length" mean?
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How does the position of the neutral axis change when a workpiece is bent around a bending radius smaller than five times the workpiece thickness?
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Calculation example:

A flat section is to be bent for several times. Its dimensions are to be seen from the following illustration.

Figure 21 Example for dimensioning a part to be bent

For calculation, the total length is subdivided into 4 partial lengths:

 Total length - sum of all partial lengths

 L = L1 + L2 + L3 + L4

Figure 22 Subdividing the piece to be bent into partial lengths 1 partial length L1, 2 partial length L2, 3 partial length L3, 4 partial length L4

The neutral axis of partial length L1 is calculated as follows:

 L1 = 40 mm - S - RB1 L1 = 40 mm - 6 mm - 10 mm L1 = 24 mm

The neutral axis of partial length L2 is calculated with the formula derived from that to calculate the circumference for a 90° bending:

Since the bending radius RB1 is smaller than five times the section thickness, therefore RN1 is:

RN1 = 10 mm + 2 mm
RN1 = 12 mm

This means for partial length L2:

L2 = 18.84 mm

The neutral axis of partial length L3 is to be calculated as follows:

L3 = 120 mm - 2 · S - RB1 - RB2
L3 = 120 mm - 12 mm - 10 mm - 35 mm
L3 = 63 mm

The neutral axis of partial length L4 is calculated with the formula derived from that to calculate the circumference for a 180° bending:

L4 = RN2 · p

Since the bending radius RB2 is bigger than five times the section thickness, therefore RN2 is:

RN2 = 35 mm + 3 mm
RN2 = 38 mm

Now, the neutral axis of partial length L4 can be calculated as follows:

L4 = RN2 · p
L4 = 38 mm · 3.14
L4 = 119.32 mm

With the help of die partial lengths so calculated, the total stretched length of the flat section can be calculated now:

 L = L1 + L2 + L3 + L4 L = 24 mm + 18.84 mm + 63 mm + 119.32 mm L = 225.16 mm

The calculated value is always brought up to a round millimetre figure, thus the stretched length of the flat profile is 226 mm.

How is the stretched length of a workpiece calculated, if several different bends are to be made?
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