Analytical Formula to calculate the As-Built Shape of RC

Written by Martin Teigen.

OMAE2020-18261 proposed an analytical formula to estimate the pipe initial bending moment:


  • 𝜀𝑟 – residual strain.
  • LRC – residual curvature length.
  • H – residual lay-tension.
  • And self explanatory pipe properties (E, t, D).

The main driver to the initial bending moment is the residual lay-tension (H) pulling outwardly on the residual curvature. As such, the moment in the pipeline can also be approximated by the moment-arm relationship:

The parameters are visualized in the figure below:

This can then be substituted into the first formula to obtain an approximation for the initial deflection:

For a pipe in pipe (PIP), a good approximation can be achieved using outer pipe material properties. This is because the OP is much stiffer compared to the IP.

This formula proves useful when calibrating your FE-model to as-laid data.

The residual curvature length and strain and other parameters are known from the as laid report. If the bottom tension is uncertain, we need to perform a screening FE analysis to match with the amplitude that we observe from the survey data. Or, a good guess can then be calculated by reorganizing the formula above:

This is actually quite useful in follow-on engineering, because it will save you from a trial-and-error approach on several different lay-tensions. A good guesstimate is achieved on the first go.

Reorganizing again gives an estimate for the residual strain:

The coefficient c is available in the table below:

I hope that this can be useful for you as well, and please let me know if there is any errors in the formulae above.

I’m clocking off, have a good night!