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Pressure Vessel Design

  1. Aug 18, 2009 #1
    I have a question regarding the design of pressure vessels, which is:

    what is the 'maximum allowable working pressure'? i know the definition and all but i am struggling to understand whether the design pressure is based on the operating pressure or the MAWP?

    For example, let the given operating pressure is 100 psi
    so do we give a safety factor (of 30 psi or 10 percent) over this figure or that of the MAWP?

    secondly, should the MAWP be greater or smaller than the design pressure?
  2. jcsd
  3. Aug 18, 2009 #2


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    Hi Grey. Best way to think of this is that the ASME code requires that the vessel be protected by a relief device set at the MAWP under (I'd need to check but I think) ALL circumstances. In other words, if you run the pressure up to the MAWP, a relief device will open to relieve pressure.

    Generally, we assume the operating pressure is lower than the MAWP such that the MAWP is 110% of operating. So if you need to operate at 100 psi, the MAWP should be at least 110 psi.
  4. Aug 18, 2009 #3
    Thanks Q_Goest, for the reply...

    i think i was a bit unclear on how i phrased my question...but i ll proceed from the values you have given at the end

    assuming the required operating pressure is 100 psi
    and as you say, the MAWP is 110 psi

    and the design requirement tell us to put a margin of safety (say 30 psi), to what do we add this 30 psi for the design pressure?
    1. Do we add safety (30 psi) to the operating pressure (100 psi) and get the design pressure (130 psi)?
    2. we add safety (30 psi) to the MAWP (110 psi) and get the desing pressure (140 psi)?

    apologies if i am a bit confusing
  5. Aug 19, 2009 #4


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    I'm not sure what you mean by margin of safety. ASME code already has a safety factor figured into the design of any vessel. For a vessel with an MAWP of 110 psi, a pressure of 1.5 times that should not produce stresses in the vessel that exceed the yield stress of the material. And at 3.5 times that pressure, the stresses should not exceed the ultimate tensile strength. Generally, systems are designed to operate roughly 10% below the MAWP.
  6. Aug 19, 2009 #5
    i am confused...

    ok, i read in a text that there are:
    1. Operating Pressure. the pressure at which the vessel is going to operate
    2. Design Pressure. Operating pressure + 30psi or 10% (which ever is greater)
    3. MAWP. pressure at which the weakest element will fail
    4. hydrostatic test pressure. 1.5 x MAWP

    now, my understanding so far is that unless we have a weak part (e.g flange) as part of the whole vessel, the MAWP is equal to the design pressure. That is, the weakest part is the shell itself, but still over the operating pressure by the safety factor (10% or 30 psi thing)

    Am i right?
  7. Aug 19, 2009 #6


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    Hi Grey. Yes, all of what you said is correct.

    Just a few clarifications... Some codes, such as ASME B31.3 Process Piping, use the term "Design Pressure" (see para. 301.2). The term "design pressure" in this case is synonyomous with the term Maximum Allowable Working Pressure as used in the ASME BPV (Pressure Vessel) code.

    Hydrostatic test pressure is generally done per the code at a pressure level that is 1.5 times this design pressure or MAWP. It is done to prove that the vessel or piping material will not yield at that pressure. Note that ASME codes include as a design criteria, a factor of safety of 1.5 to yield. So if the vessel (or pipe) has a design pressure or MAWP of 100 psi, then according to the codes, it can withstand a pressure of 150 psi without yielding. This hydrostatic test is a 1 time test to prove the structural integrity of the vessel or system. Note that the codes also allow for a pneumatic test in the case where water may cause irreversible system contamination.

    Operating pressure is simply a pressure below the design or MAWP at which you wish to operate the vessel or system. You could operate at the design pressure but generally a form of pressure relief must be incorporated into your system, so you would constantly be activating your pressure relief devices. Operating pressure is typically less than or equal to 91% of design pressure (or MAWP).
  8. Aug 19, 2009 #7
    dear Q_goest

    thanks for your replies...i hope to have become wiser with this little discussion..thanks :-)
  9. Aug 19, 2009 #8
    Q Goest,

    For clarification the ASME Section 1 the hydrostatic design pressure is to be 1.5 times the MAWP stamped on the boiler.

    The method for determination is different is the vessel is designed to Section VIII Div. 1 or Div 2.

    The MAWP can be specified as Design Pressure or it can be calculated through the method provided in the ASME Code. You must be careful using this method because flanges and nozzles can severly limit the MAWP calculated for a vessel.

    I work with this code all of time and I NEVER use a calculated MAWP. I use the user/purchases supplied design pressure and I have the vessel data plate stamped with this pressure as the MAWP. (That is allowed by the code.)

    Also, relief valves are only mandatory for Section I vessels. Section VIII vessels do not require relief valves to be installed.

    If you need more specifics let me know.

    Last edited: Aug 19, 2009
  10. Aug 19, 2009 #9
    another question...design pressure or MAWP incorporate a safety factor, right? that is the difference between it and the operating pressure represents the safety, right? so if the vessel operates just over the design pressure, it should fail???? right? becoz we no longer have that safety

    then how can it be tested (the hydrostatic test) at 1.5 x the MAWP??? wouldn't it always fail?

    or do the formulas (from the Code i think) have another margin of safety within them?
  11. Aug 19, 2009 #10
    No if you exceed the design pressure the unit does not fail. The ASME has a set of allowable stress vs temperature for the materials of construction of the pressure vessel. These stresses are at, either 2/3 of yield or 90% of yield, depending on your degree of conservatism. During a hydrotest the allowable stress can and will be exceeded. You have to remember that the allowable stress for the material is plotted against a temperature and the hydrotest occurs (usually) at ambient temperature. For instance, I design pressure vessels that operate at high temperatures and the allowable stress is very small but during the hydro test the allowable stress is much higher due to the ambient temperature at which the test is performed. There is no safety factor incorporated in the MAWP, the safety is incorporated into the allowable stress values published by the ASME in Section II Part D.

    Last edited: Aug 19, 2009
  12. Aug 19, 2009 #11
    right...so basically, when we say that:

    t = PR /(SE + 0.4P) , by incorporating 'S' we have a margin becoz 'S' is far away in value to the yeild point of the material?
  13. Aug 19, 2009 #12
    Yes, that is correct.

    Also, you might want to add for anyone who reads this thread that the above equation is listed in Mandatory Appendix 1 of Section VIII Div. 1 and the R is the outside radius and that this is for the thickness of cylindrical shells under internal pressure. Lastly, E is the joint efficiency and is dependent upon the degree of radiography. (E can never exceed 1.0)

    The thickness calculation for cylindrical shells is completely different for Section I applications.

  14. Aug 19, 2009 #13


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    Right. The S is called the "stress allowable" and if you look in the material section (D I think?) you'll find the stress allowables for various materials as a function of temp.

    Per Div 1 of the code, it looks at the yield and ultimate strength of a material (304 stainless steel for example has Sy=30,000 psi and Su=75,000 psi). Then it calculates a stress allowable for both values:
    S = Sy/1.5 (304 gives 20,000 psi)
    S = Su/3.5 (304 gives 21,400 psi)

    It then publishes the lesser of those two as the stress allowable. (So for 304, it uses the lower value of 20,000 psi for S.)

    I believe Div 2 has slightly lower safety factors, but I don't generally work with that one. The same thing is done in B31.3 piping code. Other piping codes may have different factors of safety.
  15. Aug 19, 2009 #14


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    The common safety factor that I know of is for long time (5yr+) use of these things and it's 2.5, to be able to sustain damage from stress, heat and corrosion.
  16. Sep 18, 2009 #15
    Can anyone explain the following.
    when we say
    t = PR /(SE + 0.4P), the term 0.4P is a correction factor for the stress non linearity with the vessel thickness. Is that so?

    Since S = Sy/1.5 , all the vessels we design have the same factor of safety which is 1.5.

    Please correct me if I am wrong.
  17. Sep 18, 2009 #16
    No, the 0.4P term has nothing to do with non-linearity. That equation is only valid for vessels of a certain size.

    Per UG-27 "Thickness of Shells Under Internal Pressure"

    Circumferential Stress - "When the thickness does not exceed one-half the inside radius, or P does not exceed 0.385*S*E" the equation for thickness based on the circumferential is valid.

    Longitudinal Stress - "When the thickness does not exceed one-half of the inside radius, or P does not exceed 1.25*S*E" the equation above is valid.

    If you exceed the above then the vessel becomes a "thicked walled" vessel and entirely different approach is taken for it's design because the stress distribution through the wall is non-linear.

    Now about those stress values given in Section IID.

    Those values are for tension only.

    In UG-23 "Maximum Allowable Stress Values" if your vessel is in compression (a vacuum is pulled inside the vessel or the vessel is externally pressurized) the allowable stress is evaluated based on the vessel geometry and operating temperature not on the published values listed in Section IID.

    Now onto the correct forumulas for establishing the Allowable Stress Values.

    From Table 1-100 in Section IID

    Note: "Two sets of allowable stress values my be provided in Table 1A for austentic materials and in Table 1B for specific nonferrous alloys. The lower values are not specifically identified by a footnote. These lower values do not exceed two-thirds of the minimum yield strength at temperature. The higher alternative allowable stresses are identified by a footnote. These higher stresses may exceed two-thirds but do not exceed 90% of the minimum yield strength at temperature. The higher values should be used only where slightly higher deformation is not in itself objectionable. These higher stresses are not recommended for the design of flanges or for other strain sensitive applications."

    Lastly, for welds.

    UW-15 "Welded Connections" - "The allowable stress values for groove and fillet welds in percentages of stress values for the vessel material, which are used with UG-41 calculations, are as follows.

    groove-weld tension - 74%
    groove-weld shear - 60%
    fillet-weld shear - 49%

    For clarity, UG-41 is the design of welds for reinforcement calculations. Such as, nozzle to shell junction reinforcement pads.

    So as you can see the allowable stress values are not laid out to define a safety factor for the entire vessel.

    I hope this helps you out.

    FOOTNOTE: - The above information is taken from the 2007 with 2008a Addenum of the ASME code. This code changes regularly. DO NOT use the informaton above to design a vessel with. Consult the current edition of the code.

  18. Sep 18, 2009 #17

    thank you so much for the comprehensive reply.
    My understanding is, with basics we can prove the equation PR/S=t

    However 0.6p or 0.4p has been added to the denominator of this equation due to some reason.
    Obsequiously now this is a semi empirical equation.

    As the following link;

    http://books.google.co.th/books?id=...vlinks_s#v=onepage&q=later ASME added&f=false

    (pls see the page num28)

    it says the term 0.6p is added due to stress non linearity of thicker vessels. So I was curious about this.
    On the other hand depending of the shape this value /sign of this competent is varies.

    My other worry is how we can determine the safety factor of the vessel once we calculated the thickness using this equation.

    Please help me on this
    Thank You
  19. Sep 18, 2009 #18
    Well, the designer of the vessel sets the safety factor. When I design tubesheets for heat exchangers using section UHX in Section VIII Div. 1, and I get a minimum thickness of say .375" I still use a plate of .625" or 0.750" thickness. This is because I have to allow for the effects of creep and fatigue.

    Basically what I am trying to say is this. Yes, there is a built in safety factor of some value used in the determination of the allowable stress values, but the code doesn't know the all of the loading on the vessel. See UG-22 for loadings. Therefore, it is upto the designer and the end user to develope a safety factor for the vessel.

  20. Sep 20, 2009 #19
    Does anyone know how to estimate the tube sheet thickness for SQUARE TYPE tube sheets ?(like in fin tube Air coolers).

    Where can i find those calculations?

    as i know TEMA /ASME give only for circular types.
  21. Sep 21, 2009 #20
    My company uses a proprietary method for our rectangular vessels. Sorry can't give you the formulas.

    Yes, the ASME and TEMA only have procedures for circular types.

    The best method is to use a finite element analysis.

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