Rectangular Tube Bending Calculator
About Rectangular Tube Bending Calculation
The calculator performs a geometric calculation of rectangular tube bending based on two specified dimensions of the finished element: width B and rise height H in mm. Based on these values, it determines the bending radius R, the segment angle φ, and the arc length L, which is useful for preliminary layout of arches, canopies, greenhouses, awnings, and other bent elements.
The calculation is intended specifically for a circular arc. The calculator does not assess strength, does not check the feasibility of cold bending, and does not account for springback after unloading, wall thickness change, local ovalization, or the technological limits of a specific tube bender.
Guidelines and recommendations
Geometric model
Calculation principle. The algorithm treats the finished element as a segment of a circle. This means that the specified width B is taken as the chord of the arc, and the specified height H is taken as the sagitta of that chord. All other values are then derived from circle geometry without empirical correction factors and without safety coefficients.
Units of measurement. All input and output linear dimensions in the calculation are expressed in mm, and the segment angle is expressed in degrees. This keeps width, height, radius, and arc length in one unit system and allows them to be used directly for layout and machine setup.
Calculation sequence
Bending radius. First, the circle radius R corresponding to the arc is calculated from width B and height H:
R = H / 2 + B2 / (8 × H)
The meaning of this formula is that it reconstructs the circle radius from a known chord and its sagitta. The greater the height H at the same width B, the steeper the arc and the smaller the resulting radius.
Central angle. After the radius is found, the segment angle φ corresponding to the same arc is calculated:
φ = 2 × arcsin(B / (2 × R))
Inside the calculation, the arcsin function returns the angle in radians, after which the result is converted into degrees. This angle shows what part of the full circle the calculated arc occupies.
Arc length. The actual length of the bent tube section is then calculated using the circle arc formula:
L = R × φ
Here the angle φ is used in radians. The meaning of the result is simple: it is the length of the middle geometric line of the arc between its ends, that is, the length of the curved section rather than the straight span between supports.
How to choose final dimensions for practical work
Arc width. In the calculation, the value B is the straight distance between the end points of the arc. For arches and frames, this is usually the installation span that must be covered by the bent element.
Rise height. The value H is the maximum rise of the arc above the line connecting its ends. If a flatter shape is required, H is usually reduced at the same B, and if a steeper arch is needed, it is increased.
Practical parameter selection. For roller or tube bender setup, the main reference is usually the calculated radius R. To verify compliance with the design, the angle φ and the arc length L are also used, because the same radius can apply to arcs with different lengths and different opening angles.
What the calculation does not include
Technological deformation. The calculator does not apply a correction for metal springback after bending. In practice, for steel and aluminum, the actual radius after unloading is often slightly larger than the calculated one, so for repeated work a test piece is usually made and the machine setup is adjusted.
Tube section. The algorithm does not use the profile dimensions, wall thickness, steel grade, weld position, or bending method. Therefore, the calculation is suitable for arc geometry, but it does not replace a check of the minimum permissible bending radius for a specific profile tube.
Blank development. Arc length L shows the geometric length of the bent section, but it does not include allowances for straight ends, cutting, fitting into joints, or local technological sections. For manufacturing, these additions are usually specified separately.
Normative references
European framework. When the result is used for metal structures, the geometric calculation is usually considered together with the requirements of EN 1993-1-1 Eurocode 3. Design of steel structures. General rules and rules for buildings, EN 1090-2 Execution of steel structures and aluminium structures. Technical requirements for steel structures, and EN 10219 Cold formed welded structural hollow sections of non-alloy and fine grain steels.
These documents do not directly provide formulas for this geometric task, but they serve as the normative framework for selecting the section, checking manufacturability, tolerances, fabrication quality, and the suitability of the element for actual service conditions.
FAQs
Why does the calculator use a circular arc?
Because for most arches made from profile tube and bent on rollers, a circular bending scheme is used. It creates an unambiguous relationship between width, height, radius, and arc length and is suitable for a quick engineering calculation.
Can this calculation be used for bending without making a test piece?
For one-off work, the calculator provides a good geometric basis, but in production a test run is usually made. This is related to metal springback, machine characteristics, and the actual behavior of the specific profile tube during bending.
What is the difference between arc length and width?
Width B is the straight distance between the ends of the element. Arc length L is always greater than this value because it is measured along the curved line of the tube.
Is this calculation suitable for canopies, greenhouses, and arched frames?
Yes, this type of profile tube arc calculation is often used for canopies, greenhouses, awnings, and light arched structures. The main condition is that the element shape should be close to a circular arc rather than an arbitrary curve.
Why is there no strength check in the calculator?
Because this is a bending geometry calculation, not a load-bearing capacity calculation. To check strength, stability, and permissible stresses, additional input data are needed: tube section, wall thickness, material, support scheme, and loads according to Eurocode 3.