axial stress/axial force don't appear to be in agreement

Hi all, I have a little problem with a simple linear simulation : a straight vertical pipe fixed at both ends and subject to gravity, pressure and thermal expansion from 21.1 to 30 °C. So the only stresses are pure axial ones, and I activated the option to include them.

Now, for gravity and thermal expansion load cases, I get, as I expected, that the normal forces equal the stresses times the steel pipe area.

For the pressure load case on the contrary I get Fax=203476 N and sigma=39.7 N/mm2. As the steel area is 7676.6 mm2 (10" sch 40 pipe with 0 corr. all. + 0 mill. all), the normal force is far less than the stress times the area. Why does it happen?

A second thing I don't understand is how the pressure stress is calculated. The pipe is restrained at both ends, so the only axial stress arising from internal pressure should be due to the poisson effect .i.e. 0.3 (poisson coeff.) times the hoop stress. As the hoop stress is reported to be 143.3 N/mm2 the axial stress should be 43 N/mm2 and not 39.7 N/mm2. The difference is very slight but I wouldn't expect any, given such a straightfoward calculation. So how is the axial stress due to internal pressure calculated?

By the way, even assuming a pressure stress of 43 N/mm2 the axial force is different from the axial stress times the cross sectional area.

can anyone help me?

thank you

7676,6
  • Hello RKP,

    It is difficult to answer questions like this because there is some missing information required to answer your questions. For example:

    What Piping code and year are you referring to?

    What option exactly are you talking about " I activated the option"?

    To comment, your Steel Area calculation is incorrect, 10" sch 40 pipe, OD = 10.75",wall thick = 0.365", Id = 10.02", area of steel = 11.908 in sq. or 7682.76 mm sq.

    Most of the calculations used in AutoPIPE can be found at the following help location:

    Help > Contents> Contents Tab> Reference Information> Code Compliance Calculations>

    In addition, AutoPIPE's results depend heavily on the settings located at Tools> Model Options> Results>

    For your issues, suggest reviewing: "Longitudinal Pressure" and "Include axial force" settings. Ultimately understanding all the settings found under Tools> Model Options> dialogs.

    Regards,

    Mike Dattilio
    Bentley Product Advantage Group Analyst

    ===================================================

  • Mike,

    I'm sorry not to have been that clear, the code I refer to is ASME B31.3 2012. The option I activated is : Tools->model options->result-> include axial force.

    You will agree that,  even if my steel area is as much as 0.08% incorrect, the conclusions don't change too much. Pressure stresses are different from pressure axial force divided by the cross sectional area. Moreover the sign is reversed for stress and force. There should be a reason, but I cannot see it.

    Attached you find an excerpt from the report

    thank you for any help

    best regards!

  • rkp,

    You were right when you said you may be missing something. The longitudinal pressure stress calculations take in to account the axial force generated due to pressure extension and the longitudinal pressure force or end cap force. Pressure extension is calculated using thick wall formula, which would then give you the axial force which you see in the forces and moments report against pressure case say P1. The stress due to end cap force is added or subtracted from the stress due to pressure extension during the post processing. The following screen capture is from calculations performed for a similar fully restrained pipe and how the stress values are calculated:

     

    Note that AutoPIPE convention for axial forces is that compression forces are positive and tensile forces are negative. Using the above formula will also take in to account the direction of the stress when reporting the net stress due to the pressure case.

    Hope this helps.

    Regards,

    Bilal Shah

  • Hello Bilal,
    if one develops the calculation finds: sigmaP1 = Slp - Saxp = 2vP*Ap/As, i.e. the stress due to pressure extension cancels out and only contraction is considered in the stress, while both contraction and extension are considered in the force. What's the logic behind that? I couldn't find any reference in Autopipe help.
    Could you also give me some idea on where the formula for the contraction extension comes from?

    thank you very much for your help

    regards
  • rkp,

    I think you have answered your original question :). For calculation of longitudinal stress, AutoPIPE uses a combination of analysis results and post processing. The pressure extension forces are derived from the analysis, which uses thick wall formula for pressure extension:

    You can find the seventh edition of Roark's formulas online using the following link (look under table 13.5, 1b last equation):

    http://materiales.azc.uam.mx/gjl/Clases/MA10_I/Roark's%20formulas%20for%20stress%20and%20strain.pdf 


    Regards,

    Bilal Shah