BIZOMAT MAKEOS · Fabrication
Tube Bending Plan (Length, Wall Thinning, Strain and Overbend)
How long a tube do I cut for this bent part, how thin will the outside wall get, is the bend radius tight enough to crack the tube, and how far do I overbend?
Plan for rotary-draw or press bending of a round tube: developed length from straights and bend arcs (as the tube bend length tool), outer and inner wall thickness after bending and the thinning share (as the tube bend thinning tool), outer-fibre strain against the tube’s elongation, the centreline radius ÷ diameter and diameter ÷ wall ratios, and the angle to bend to with your springback allowance.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tube outside diameter | mm | Outside diameter of the tube. |
| Wall thickness | mm | Wall thickness before bending. |
| Centreline bend radius | mm | Radius of the bend measured to the tube centreline. |
| Bend angle | ° | Angle of each bend. |
| Number of bends | Number of bends of this radius and angle. | |
| Total of straight lengths | mm | Sum of all the straight lengths between and beyond the bends. |
| Least wall thickness allowed | mm | Least wall the part may have after bending (pressure rating, code). |
| Smallest bend radius ÷ diameter allowed | Tightest radius as a multiple of diameter your tooling can bend without mandrel problems (your value). | |
| Elongation of the tube material | % | Tensile elongation of the tube material (from the certificate). |
| Springback allowance | % | Extra angle to bend beyond the target, as a share of the angle, for springback (your value from trial bends). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Tube outside diameter
- What it is
- The outside diameter of the round tube before bending, from the tube specification or a measurement.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger diameter raises outer-fibre strain and thinning at the same bend radius.
- Get it right
- Use the outside diameter, not the bore or nominal pipe size.
What this means: Wall thickness
- What it is
- The nominal wall thickness of the tube before bending.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The thinned outer and inner walls are proportional to it.
- Get it right
- It must be less than half the diameter, or the tool stops.
What this means: Centreline bend radius
- What it is
- The bend radius measured to the centreline of the tube, set by the bend die. It is used for the arc length, wall thinning and strain.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger radius lengthens each arc and reduces thinning and strain.
- Get it right
- Do not use the inside radius of the bend; the centreline radius is half a diameter larger.
What this means: Bend angle
- What it is
- The finished angle of each bend, measured as the change in direction of the tube centreline.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 180°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Arc length and the bend-to angle grow in proportion.
- Get it right
- Use the change in direction (90° for a right-angle bend), not the included angle between the legs.
What this means: Number of bends
- What it is
- How many bends of this same radius and angle are in the part. Each one adds an arc length to the developed length.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 50. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Bends of a different radius or angle are not covered; plan them separately.
What this means: Total of straight lengths
- What it is
- The sum of all straight tube lengths between and beyond the bends, measured along the centreline to the tangent points.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds directly to the developed length.
- Get it right
- Measure each straight to the tangent points, not to the intersection of the legs.
What this means: Least wall thickness allowed
- What it is
- The thinnest wall the bent part may have, set by its pressure rating, a design code or the drawing. The outer wall after bending is checked against it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 50 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Smallest bend radius ÷ diameter allowed
- What it is
- The tightest centreline bend radius your tooling can bend well, stated as a multiple of the tube outside diameter. It comes from your machine, dies and trial experience.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- This is a ratio, radius ÷ diameter, not a radius in millimetres.
What this means: Elongation of the tube material
- What it is
- The tensile elongation of the tube material, the stretch at fracture in a tensile test, from the mill certificate or material data sheet. Outer-fibre strain is compared with it.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 80%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type the percentage itself, for example 30 for 30 %, not 0.3.
What this means: Springback allowance
- What it is
- The extra angle you bend beyond the target to allow for springback, as a percentage of the bend angle. Take it from trial bends with the same tube and tooling.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 30%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The bend-to angle rises in proportion.
- Get it right
- Type a percentage of the angle, not extra degrees.
Method and formulas
- Developed length = straights + bends × π R θ ÷ 180 (as the tube bend length tool).
- Outer wall ≈ t R ÷ (R + D ÷ 2); inner wall ≈ t R ÷ (R − D ÷ 2) (as the tube bend thinning tool).
- Outer-fibre strain ≈ (D ÷ 2) ÷ R.
- Bend-to angle = angle × (1 + springback share).
- Example: cut 776.99 mm; the outside wall thins to 1.6552 mm (17.241%) with 20.833% outer strain; bend to 92.7°.
Limitations
- Simple thinning estimate; mandrels, wipers and pressure dies change the real wall.
- Ovality is not calculated; thin-walled tubes at tight radii need a mandrel.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Cut tube to length for a bent part
- Check whether a tight bend will thin or crack the tube
- Set the bend angle on the bender
Who it is for
- Fabricators
- Tube bender operators
- Design engineers
What you get
- Developed (cut) length
- Wall thickness after bending and the thinning share
- Strain, ratios and the angle to bend to
Interpreting the result
- Thinning and strain fall quickly as the bend radius grows: one size larger die is often the easiest fix.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1382–1386. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Bending tube
In Yield and Plastic Flow by the Numbers
What it covers: How a tube wall thins on the outside and thickens on the inside of a bend, how to check strain and wall against limits, and why a check with the nominal wall passed tubes that came out too thin.
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Open the Tube Bending Plan (Length, Wall Thinning, Strain and Overbend) calculator