Compensate for bend shortening by stretching the length
When a straight tube is bent in a bending machine, it inevitably shortens. The shortening increases with the bend and the number of radii inserted. It is therefore important to calculate this shortening in advance. This reliably prevents the finished bent pipe from being too short for installation. The selected pipe has the “stretched length” when straight. After processing, the pipe has been shortened to the desired length and fits into the desired installation position.
Why do pipes shorten by bending?
The “neutral fiber” runs through the middle of a pipe. Imagine this imaginary line as a string. It can be stretched or laid in radii, it does not change its length. However, the outer section of the pipe angle must cover a longer distance. How long this path is depends on the diameter of the pipe. The more pipe section is “consumed” by the elbow, the more the pipe is shortened overall. The point opposite the stretched length is called the “compressed length”. However, this is of no interest for the calculation and is neglected.
Calculate stretched length
Simple circular mathematics is used to calculate the stretched length. For a circle calculator, you only need the bending radius, the pitch circle diameter and the pipe diameter. The larger the diameter of the pipe, the greater the effect of shortening the pipe.
The formula for the bend shortening in ONE bend with a 90° angle is as follows:
L = a’+b’+ (?/2)(r+t/2)
L = Total length of the pipe section
a’= Straight section before the bend
b’= Straight section after the bend
r = Inside radius of the bend
t = Diameter of the pipe
If it is not a 90° bend, the bending angle must be included in the calculation. To do this, the circle calculator is supplemented by the factor b°/360°. In summary, the formula is as follows:
L= t x ? x b° / 360°
Correction factor for narrow pipes or sheets
The narrower the sheets or the smaller the diameter of the pipes, the further the neutral fiber shifts towards the inside of the bend. Therefore, a correction factor must be added to the stretched length to ensure the calculation is correct. This complicates the calculation considerably. To make matters worse, this calculation has to be repeated as often as bends are introduced into the pipe. For this reason, there are now apps, tools and programs that make it much easier to calculate the stretched length. A well-known tool with which you can create such a calculation aid yourself is Excel, for example.
In practice, however, pipes are often designed so that they start or end with a straight piece. A longer pipe is simply selected for production and then shortened until it fits the desired installation location. This is the usual procedure used by heating engineers, plumbers, steel fabricators and shipbuilders.
Where the stretched length must be calculated
Calculating the stretched length is important if the finished bent pipe is to be installed in a fixed bond on both sides. The more firmly the pipe is installed, the more relevant its exact calculation becomes. This is especially true for welded-in pipes. An incorrectly calculated pipe would build up stresses that are particularly visible in the bending radius of the bends. However, straight pipes can also cause undesirable stresses. In pipelines that are several kilometers long, even slight thermal expansion leads to considerable compressive stress in the system. This is why expansion loops are inserted into the pipe systems at regular intervals. Their task is to expand or contract in a defined manner in response to temperature fluctuations. This relieves the pressure on the long pipe and dissipates accumulated stresses.
Calculation not always necessary
Drainage pipes consist of prefabricated, standardized angles, bends and sections. A stretched length does not occur here, as an assembled plastic pipe does not derive from a straight long pipe.
If one side of the pipe protrudes into the open air, a further calculation can be dispensed with if the pipe is long enough. For this reason, this time-consuming process can be avoided, for example when replicating exhaust pipes for vehicles.
Calculation possible, but difficult
The large number of factors that influence the stretched length makes its calculation complicated. In most cases, the work is saved and the finished bent pipe is simply adjusted at the installation site. However, if the stretched length needs to be calculated, the use of a tool is recommended. This avoids calculation errors and guarantees precise results. Experienced Excel users can also use this program to create such a calculation tool themselves.
