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Bending and curving of Krah Pipes

The high flexibility is already very known for Krah-Pipes, and a basic reference for the bending is given by R=50 x DN/ID for long term and even R=25 x DN/ID for short term.

So technically these two cases have to be diveded, in long and short term examination. The long term is to reduce fittings (bends) and the shirt term aspect is during the installation e.G. using the S-sinking method in water applicaitons, relining. What is a easy way to make a detailed calculation, to be sure that the pipe will not fail. How to calculate the minimum bending radius for a Krah-Pipe with profiled wall structure, in helical style?

Short-term bending conditions, the welding was done  outside and now the pipe is moved into the trench DN/ID 1200 mmPhoto 1: Short-term bending conditions, the welding was done
outside and now the pipe is 
moved into the trench DN/ID 1200 mm

Rmin = α x DN [mm]

Rmin = minimum bend radius [mm]
α      = bend ratio [-]
DN/ID = Nominal pipe diameter, here inside pipe diameter [mm]

The minimum bend radius is defined as the smallest radius to which the pipe may be safely curved.

A maximum of total strain elongation should not exceed: 
ɛ =2,5 [%] (long term, 20°C) and 
ɛ =5,0 [%] (short term, 20°C).

Long-term conditions, of a bended Krah Pipe DN/ID 1300 mm
Photo 2: Long-term conditions, of a bended Krah Pipe DN/ID 1300 mm

Strain of the outer fiber 
RD = Minimum radius against strain of the outer fiber [mm]

rd equation

ra = Outer radius

nominal pipe diameter

e1 = Solid waterway wall thickness [mm] 
ɛ = Permissible strain of outer fibre [%]

e1 = Solid waterway wall thickness [mm] 

ɛ = Permissible strain of outer fibre [%]

 

Principle of a Krah pipe bendingSketch 2: Principle of a Krah pipe bending

Local Buckling

RK= Minimum bending radius due to buckling [mm]

rk equation

rm = Medium pipe radius

rm      = medium pipe radius

SFF= Spiral-factor [-] 
eVW= Equivalent wall-thickness

Spiral-factor:

The spiral-factor (SFF) is a factor of the equivalent solid wall reduction for Krah Pipes.
This factor considers the helical profile around the pipe, together with the usage of the equivalent wall thickness. The factors are:

The spiral factor for other profile distances are available on request.

Result:
Rmin=max(RD,RK)

The minimum bending radius is the maximum of RD and RK. This mathematical approach can be used for corrugated pipes with ribs.

 table factorsTable 1

profil sketchSketch 1: Cross section of a Krah pipe


Sample Calculation:

sample calculation

The minimum bending radius for this pipe is 37,6 m for long and short-time at 20°C.
This calculation will be implemented in our next Mickey software.

 Deployment of a Krah Pipe DN/ID 2400 mm
Photo 3: Deployment of a Krah Pipe DN/ID 2400 mm

Test for evaluating the spiral factor
Photo 4: Test for evaluating the spiral factor 

Author:
Alexander Krah
CEO Krah Pipes GmbH & Co. KG