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Hi Hady,
The idea of providing expansion loop to limit the expansion stress is good.
The method of analyzing seems to be non-standard. I think u may refer the ASME codes to do the stress analysis, for liquid transportation u may refer ASME B31.4, in this std u may find the equations thats are necessary for the pipeline stress analysis instead of using the general formulas.
Also regarding the pipe stress analysis, its a complex analysis due to non-linearity. Doing by hand calculation is not so easy, for moderate results u have to go for analytical method as prepared by M.W. Kellogs or Grinnell and for accurate analysis u have to use Computer programs....
Regards,
Paldex
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