Pipe Flexibility using Julia and Jupyter Jul 2022

Classical 1911 (!!) meets 'High Tech' 2022

I revisited piping flexibility factors by reading:

Advanced Strength of Materials
by J. P. den Hartog (1952) and
“Parametric Study of Flexibility Factor for Curved Pipe and Welding Elbows”
by O. Kireev, D. Kireev, and A.Berkovsky (2013)
https://repository.lib.ncsu.edu/handle/1840.20/32871
https://repository.lib.ncsu.edu/bitstream/handle/1840.20/32871/Pap_525_ver_1.pdf?sequence=1&isAllowed=y

Then I compared equations from den Hartog, from Kireev et al, and from B31.3 Table D300.

The agreement was quite good.

I had three goals:

To discover the approach used in classical mechanics to calculate the flexibility factor for curved pipe (ells, for example). Den Hartog describes the calculations performed in 1911 by von Kármán (pages 234-244) as a crowning achievement of the theory of least work.
To put Julia, and my bit of working knowledge of it, to a full test including of course the programming of mathematics and functions, but also exploring the packages Symbolics, Plots, and Plotly.
To fully explore Julia within Jupyter including how to save Plotly graphics as HTML and how to save a Jupyter notebook as a PDF. This goal was the most difficult to achieve.