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

R_min = α x DN [mm]

R_min = 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).

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

r_a = Outer radius

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

e₁ = Solid waterway wall thickness [mm] 

ɛ = Permissible strain of outer fibre [%]

Local Buckling

R_K= Minimum bending radius due to buckling [mm]

r_m = Medium pipe radius

r_m      = 

SFF= Spiral-factor [-] 
e_VW= 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:
R_min=max(R_D,R_K)

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

 Table 1

Sketch 1: Cross section of a Krah pipe

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.

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

Photo 4: Test for evaluating the spiral factor