Pressure Vessel Engineering will complete vessel code calculations and drawings for ASME Section 1, 4 and 8 (Div 1 and 2) as well as B31.1 and 31.3. The tools we use include custom spreadsheets, Advanced Pressure Vessel, or PVElite for conventional ASME vessel code calculations. For cases not covered by the code book, we use CosmosDesigner or NozzlePro Finite Element Analysis.
NOTE: Only ASME can make interpretations on the ASME VIII-1 code. The articles in this section are for information purposes only.
Design Code Used in Repair/Alteration/Used Vessels...
Hand Calculations - How To and How Not To...
Loads On Flanges - The ASME Way...
Nozzle F Factor (UG-37)...
Origins of the ASME Area Replacement Rules...
Use of 44w Material... in Pressure Vessels...
Weld Efficiences for ASME VIII-1 Vessels...
Pressure Vessel Design Charts...
Pressure Vessel Spreadsheets...
When registering a used vessel or a repair/alteration, you must use the correct section, edition and addenda of the ASME Code.
According to National Board RC-1020 (Construction Standards), if the "original construction is the ASME Code, repairs and alterations shall conform, insofar as possible, to the section and edition of the ASME Code most applicable to the work planned".
Similarly, CSA B51-03 paragraph 11.1 states, "In all repairs or alterations, the methods employed shall retain the factor of safety determined by the ASME Code section referenced when the unit was first manufactured".
A vessel originally designed to Section VIII-1, 1995 Edition is to be modified and new components added. The 1995 Edition is not available, but material stress values have only changed once in recent times. In the 1999 Addenda to the 1998 Edition, ASME changed the factor of safety from 4 times to 3.5 times, increasing the allowable stress values. Therefore, the calculations for both new and original components are performed to the current code edition (2007 at this time), using material stress values from 1986 (our closest available edition to the original code of construction).
Pressure Vessel Engineering can perform calculations on your used or repaired/altered vessel and help with registration. Ensure that all the paperwork is available to include in the submission package. Original U-1A Form (Manufacturers Data Report), drawings showing modified vessel, photos or rubbings of the original nameplate, UT test reports, calculations and the QC certificate for the contractor performing the work.
We at PVEng use hand calculations when we do not have a program or spreadsheet or when we want to create a spreadsheet and need verification. Hand calculations are respected more than programs for audits or code submission but in my opinion, they are much more likely to be wrong. The ideas presented here are designed to reduce the most common causes of hand calculation problems:
These common problems will be investigated in more depth on the following pages.
Without references it is not possible to check if the equations are sourced right.
The correct equation is t = PR/(2SE+0.4P) not as shown above. With the references listed it is possible to go back and find this copying problem.
The illustrated intermediate step allows the reviewer to see what numbers were used for the variables. It is not possible to check what is not known.
How was the first answer calculated? What values were used for P,R,S and E -why is the first answer wrong?
Here we are assuming that the reader/reviewer understands what P, R, S and E mean, probably a good assumption. However, it would be a better assumption if the reference for the equation was included. There is no reason to provide further explanation for something that is easily looked up.
The equation should read specific gravity, not density. Without the units, it is not verifiable.
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ASME VIII-1 Appendix 2 provides a method of sizing flanges. The calculations use three loads - HT, HG & HD and two operating conditions - seating and operating. What are these loads, how are they calculated, and where are they applied to the flange? In the article below, a sample flange will be calculated using ASME Appendix 2 methods and by finite element analysis (FEA) to illustrate the application of the loads and show the resulting stresses. |
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Summary:The stresses around a nozzle located in a cylindrical shell are not the same in all directions. If a non-round nozzle is oriented in the correct direction, ASME allows us to take advantage of this. |
The area replacement rules in the ASME code books have always interested me: You can cut a hole in a vessel as long as the nozzle attached to it replaces the lost area. How can this be a rational method of designing pressure vessels?
I was re-reading a fascinating book that I first encountered when I was a kid called "The new Science of Strong Materials or Why You Don't Fall Through the Floor" by J. E. Gordon, 1968, Penguin Books. This interesting book might have had something to do with why I became an engineer. It is still in print, available at Amazon.com I was trying to understand why a crane I was working on was cracking (see more on this crane at Sample 16) when I came across the section quoted below (Page 60) dealing with tubular shapes like railway bridges and ships as well as my crane)...
A ship is a long tube closed at both ends which happens to be afloat but is not otherwise structurally very different from Stephen-son's Menai bridge. [topic of the authors previous paragraph] The support which the water gives to the hull does not necessarily coincide with the weights of engines, cargo and fuel which are put into the ship and so there is a tendency for the hull to bend. It ought to be impossible to break a ship, floating alongside a quay, by careless and uneven loading of the holds and tanks, but this has happened often enough and will probably happen again. In dry-dock ships are supported with care upon keel-blocks arranged to give even support but there is not much even support at sea where a ship may be picked up by rude waves at each end, leaving her heavy middle unsustained, or else exposing a naked forefoot and propeller at the same moment. As ships tended to get longer and more lightly built, the Admiralty decided to make some practical experiments on the strength of ships. In 1903 a destroyer, H.M.S. Wolf, was specially prepared for the purpose. The ship was put into dry-dock and the water was pumped out while she was supported, in succession, amidships and at the ends. The stresses in various parts of the hull were measured with strain-gauges, which are sensitive means of measuring changes of length, and therefore of strain, in a material. The ship was then taken to sea to look for bad weather. It does not require very much imagination to visualize the observers, struggling with seasickness and with the old-fashioned temperamental strain-gauges, wedged into Plutonic compartments in the bottom of the ship, which was put through a sea which was described in the official report as 'rough and especially steep with much force and vigour'. Her captain seems to have given the Wolf as bad a time as he could manage but, whatever they did, no stress greater than about 12,000 p.s.i. or 80 MN/m2 could be found in the ship's hull.
As the tensile strength of the' steel used in ships was about 60,000 p.s.i. or 400 MN/m2, and no stress anywhere near this figure could be measured, either at sea or during the bending trials in dry-dock, not only the Admiralty Constructors but Naval Architects in general concluded that the methods of calculating the strength of ships by simple beam theory, which had become standardized, were satisfactory and ensured an ample margin of safety. Sometimes nobody is quite as blind as the expert. Ships continued to break from time to time. A 300-foot (90 metres) ore-carrying steamer, for instance, broke in two and sank in a storm on one of the Great Lakes of America. The maximum calculated stress under the probable conditions was not more than a third of the breaking stress of the ship's material. Even when major disasters did not actually happen, cracks appeared around hatchways and other openings in the hull and decks.* These openings are of course the key to the problem. Stephenson's tubular bridge was eminently satisfactory because it is a continuous shell with no holes in it except the rivet holes. Ships have hatchways and all sorts of other openings. Naval Architects are not especially stupid and they made due allowance for the material which was cut away at the openings, increasing the calculated stresses around the holes pro rata. Professor Inglis, in a famous paper in 1913, showed however that 'pro rata' was not good enough and he introduced the concept of 'stress-concentration' which, as we shall see (Chapter 4), is of vital importance both in calculating the strength of structures and in understanding materials.[emphasis added]
What Inglis was saying was that if we remove, say, a third of the cross-section of a member by cutting a hole in it then the stress at the edge of the hole is not 3/2 (or 1.5) of the average but it may, locally, be many times as high. The amount by which the stress is raised above the average by the hole - the stress-concentration factor - depends both upon the shape of the hole and upon the material, being worst for sharp re-entrants and for brittle materials [emphasis added]. This conclusion, which Inglis arrived at by mathematical analysis, was regarded with the usual lack of respect by that curiously impractical tribe who call themselves 'practical men'. This was largely because mild steel is, of all materials, perhaps the least susceptible to the effects of stress concentrations though it is by no means impervious (Plate 3). It is significant that, in the Wolf experiments, none of the strain gauges seems to have been put close to the edge of any important opening in the hull.
Is this really the origin of the Area replacement (or pro-rata) rules that we use in pressure vessels? Is it just a set of rules that failed when applied to ships but have been successfully applied to pressure vessels? Yes these pro rata rules are still in use in the ASME pressure vessel and piping codes. Basically, when we remove some material from a vessel in the form of a nozzle opening, we look for an equal amount of extra material to replace it, in both the surrounding shell, and in the nozzle pipe.
I have a mental picture that I use to explain the development process - I do not know how accurate it is but it goes like this: The stresses in vessels were too complicated to accurately understand at the time, so a rule like area replacement is adopted from another field like naval architecture. Or it is independently developed by the original pressure vessel designers (our rules UG-36 to 43). The designs work well most of the time but occasionally a pressure vessel blows up (this is after all an experience based code). With more experience, more restrictions like appendix 1-7 are added and our vessels fail less often. Are designers ignoring the intent of the code but purely following the rules - the more specific restrictions on the geometry are added - (like UW-14 to 16). And so it goes - we are still changing the pressure vessel code today. At no point is the problem fully understood but pressure vessels gradually get more reliable. We can expect more restrictions in the future...
The ASME nozzle area replacement rules cannot be taken on their own. There are a large number of code sections that need to be considered on each nozzle - UG-36 to 43, App 1-7, UW-14 to 16, UG-45 and others. The rules explicitly only apply to circular, obround and elliptical openings - for the last two, the length cannot be more than twice the width. In practice, these limits are commonly violated.
The amount by which the stress is raised above the average by the hole - the stress-concentration factor - depends both upon the shape of the hole and upon the material, being worst for sharp re-entrants and for brittle materials [J.E. Gordon, copied from the above quote].
Brittle materials are not much of an issue with modern pressure vessels; however the shapeof- opening issues still remains. Also we do not distinguish between nozzles attached to high stress areas of vessels like knuckles on heads, or lower stress areas like straight shells. I wonder if an enterprising (or luckless) engineer could design a nozzle for a pressure vessel that meets all code rules, but is unsafe. Have we closed all the loopholes?
Note: Only ASME can make code interpretations.
More than a decade ago the then head review engineer of TSSA's pressure vessel division first told me that 44w was allowed in pressure vessels, pointing out the line in the IID code book showing CSA G20.41 38W. Today a TSSA field inspector is insisting that 44w is not acceptable for use in pressure boundaries on ASME VIII-1 pressure vessels. This memo is about a small vessel that was accidently made out of 44w materials.
44w steel is a Canadian steel grade specified in CSA-G40.21. The specification has a wide variety of grades available in plate and structural forms. The use of 44w (or 50w or other CSA G20.41 grades) has not been an issue for welded structural supports used on pressure vessels.
ASME IID lists 38w as SA/CSA-G40.21 38W (page 14 of the 2008 update) - tensile strength of 60,000 psi, 38,000 psi yield. The allowable stress at ambient is 17,100 psi, maximum temperature is 650°F.
ASME IID lists SA-36 (page 10 of the 2008 update) - tensile strength of 58,000 psi, 38,500 psi yield. The allowable stress at ambient is 16,600 psi, maximum temperature is 650°F. This is a similar but not identical material to 44w.
ASME IID does not list 44w.
38w is not practically available in Canada. 44w is common. The steel mill that made the 44w plates for this vessel had not heard of 38w before.
ASME IX lists 38w and 44w both as P 1 Gr 1 materials (page 109).
ASME IX lists 38w and 44w both as P 1 Gr 1 materials (page 109).
Both 38w and 44w are specified in CSA G20.41 spec. (numbers below are simplified, see the full CSA G20.41 spec for more detailed requirements).
| Carbon | Yield | Tensile | Elongation | |
| 38w | 0.20% max | 38 ksi min | 60 ksi min | 18% |
| 44w | 0.22% max | 44 ksi min | 65 ksi min | 18% |
| 44w MTR | 0.17% | 59 ksi | 73.5 ksi | 30% |
Note that the vessel MTR shown above could have been triple certified by the mill as 38w/44w/50w, and if that had been done (38w showing), would be acceptable for use on this pressure vessel.
38w and 44w are both listed in ASME section IV Table HF-300.1 "SA/CSA-G40.21 as specified in Section IIA grade 38W or 44W, may be used in lieu of SA-36 for plates and bars not exceeding 3/4 in. (20mm). For use at the same allowable stress values as SA-36." (page 76, 2007 edition).
The steel used from the material test report listed above was recertified by the mill as 38w/44w/50w making it a listed material. See ASME VIII-1 UG-10(a)(1).
If requested, Pressure Vessel Engineering will design pressure vessels using 44w for pressure boundaries. The drawings and calculations will state 38w and material strength allowables for 38w will be used. Be careful to review mtrs before purchasing materials to ensure that the material can be recertified by the mill under 38w. Use of other explicitly code listed materials is recommended.
The use of 44w or 50w for structural supports is currently not a problem and is common practice in Canada.
We have asked ASME to list 44w and 50w in IID to eliminate the unnecessary expense of recertifying materials.
Comment: Only ASME can make interpretations on the ASME VIII-1 Code
I have long struggled with the weld efficiencies presented in section UW of the ASME VIII-1 code. I have had more trouble with it than many other sections of the book combined. The ideas in this section are simple, but the ASME code written around it is anything but. Where ASME has not made the code readable, we must live with confused and diverging interpretations.
The problem area is sections UW-11 and UW-12 and any section of the code that references UW-11(a)(5)(b) - and there are many. What weld efficiencies to use when seams with different efficiencies intersect? I do not believe that circ weld efficiencies can affect longitudinal efficiencies however; these rules as presented in UW-12 and UW-11(a)(5)(b) exist and must be dealt with. I do believe that I will have to read the infinitely confusing sentence UW-11(a)(5)(b) many more times in my career.
I and others have tried to reason their way through this section of the code. An example can be found at Authorized Inspector I think what I present here agrees with their interpretation, but I do not like this method. Even if you agree with what is presented, then you still have to persuade others - best of luck.
Only ASME can provide interpretations as to what this code means, and someone can ask them, but - how about doing something simple instead? Samples of what the code committee wants can be found in appendix L. In specific samples L-1.5.1 through L-1.6.3 show the correct weld efficiency to use with differing radiography, and they also show the effect of circ efficiency on long seams. The meaning of UW-11(a)(5)(b) can be inferred.
This article comments on the 6 sample vessels found in Appendix L. A simple spreadsheet is introduced that calculates the same weld efficiencies. The spreadsheet can be downloaded below. Each Appendix L sample is calculated at the end of this article.
Pressure Vessel Engineering Ltd. assumes no responsibility for this sheets use, and reminds you that only ASME can provide code interpretations. We would however be very happy if everyone could use the same interpretation to this difficult code section.
Although not suited for final vessel calculations, design charts can be very useful for preliminary design and quotation purposes. The charts on this page (in pdf format) provide pressure ratings, weight and volume for various sizes and wall thicknesses of components.
To use these charts, you will need to know the rated stress for the materials you will be using. Currently, the rated stresses for pressure vessels are found in the Boiler and Pressure Vessel Code Section II part D - about six pounds of paper covering thousands of materials. The material design temperature is also required to lookup material properties. You will also need to know what joint efficiency to use.
| 20,000 psi | 18,000 psi | 16,000 psi | 14,000 psi | 12,000 psi |
| 10,000 psi | 8,000 psi | 6,000 psi | 4,000 psi | 2,000 psi |
| 20,000 psi | 18,000 psi | 16,000 psi | 14,000 psi | 12,000 psi |
| 10,000 psi | 8,000 psi | 6,000 psi | 4,000 psi | 2,000 psi |
| 20,000 psi | 18,000 psi | 16,000 psi | 14,000 psi | 12,000 psi |
| 10,000 psi | 8,000 psi | 6,000 psi | 4,000 psi | 2,000 psi |
- Pressure rating for wall thickness at E = 1.0
- Pressure rating for wall thickness at E = 0.85
- Volume per foot
- Weight per foot (for carbon steel)
| 20,000 psi | 18,000 psi | 16,000 psi | 14,000 psi | 12,000 psi |
| 10,000 psi | 8,000 psi | 6,000 psi | 4,000 psi | 2,000 psi |
| 20,000 psi | 18,000 psi | 16,000 psi | 14,000 psi | 12,000 psi |
| 10,000 psi | 8,000 psi | 6,000 psi | 4,000 psi | 2,000 psi |
| 20,000 psi | 18,000 psi | 16,000 psi | 14,000 psi | 12,000 psi |
| 10,000 psi | 8,000 psi | 6,000 psi | 4,000 psi | 2,000 psi |
The pressure vessel design tools are a series of Excel 2003 spreadsheets that allow a user to create a preliminary design of a vessel that meet the general rules and guidelines of ASME VIII Division 1. The spreadsheets do not contain all aspects of the VIII-1 code (see notes on each sheet to determine what is missing). The spreadsheets can only be used to design vessels and vessel components with interior pressure. The design tools will help the user select preliminary sizes, estimate materials and determine vessel properties such as weight and volume.
NOTE: These spreadsheets are provided for educational purposes only. Pressure Vessel Engineering Ltd. is not liable for their use.
Each design spreadsheet calculates parameters that are critical to the design and function of a pressure vessel (ex. maximum pressure, required thickness, etc).
Important: Users should read all notes and comments at the bottom of the spreadsheet before beginning to design a vessel or vessel component. Instructional comments can also be found by hovering over a cell with a red triangle in the top right corner (see illustration below).

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A sample vessel has been calculated using the design spreadsheets as reference. A simple sketch was created to indicate important nozzles and sizes that are pertinent to the vessels function. The design tools assist in the selection of the materials and sizes required to pass specified design conditions. |
Requirements for lethal service are scattered through VIII-1, the code cases and the interpretations. ASME VIII-1 section UW-2 (2007 edition) has most of the requirements for lethal service. Two definitions of lethal service are provided in UW-2:
[A] vessel is to contain fluids of such a nature that a very small amount mixed or unmixed with air is dangerous to life when inhaled[.]
By "lethal substances" are meant poisonous gases or liquids of such a nature that a very small amount of the gas or of the vapour of the liquid mixed or unmixed with air is dangerous to-life when inhaled. For purposes of this Division, this class includes substances of this nature which are stored under pressure or may generate a pressure if stored in a closed vessel.
It is up to the user to determine if a service is lethal. We at Pressure Vessel Engineering do not determine if the vessel service is lethal (but we might have opinions based on previous jobs).
When it has been determined that a vessel is in Lethal Service, some of the following code sections will apply. Other code sections might also be required.
More from UW-2:
The following Code Cases refer to lethal service for VIII-1 vessels (2007)
![]() Special lap joint stub end for lethal service |
![]() All partial penetration nozzles are prohibited |
![]() All figure UW-13.2 corner welds are prohibited |
![]() No slip on flanges |
Disclaimer: This material is provided for educational uses only. Only ASME can make code interpretations.
The Canadian CRN registration system requires that all fittings used on a vessel or included in a registered piping system carry CRNs. To register the fittings, design validation based either or code calculations, finite element analysis or proof testing is required.
When a design is based on code listed materials, the code of construction provides allowable operating stress levels. If the design of the pressure containing item is simple, the regular code rules can be used and will supply a pass/fail judgement. If no code rules exist for a complex or unusual shapes, Finite Element Analysis (FEA) can provide the stresses which can be compared with the listed allowables for a pass/fail judgement.
An alternate to code calculations is to proof test the item at stress levels far above operating. The items actual and guaranteed minimum tensile strengths are required for the proof test. The formula used is from VIII-1 UG-101(m):
Where B is the burst test pressure and P the allowed operating pressure. The burst test has to be at least 4 times the operating pressure. E is the welding efficiency if the item is welded – typically between 0.7 and 1.0. Two more pieces of information are required – Su – the specified minimum tensile strength of the material and Suavg – the tensile test results from the item under test. Typical proof test pressures are 5-6x operating pressure, a requirement far more conservative than regular code calculations or FEA.
For code listed materials, all of the required information is available for either calculations/FEA or for burst testing.
Codes B31.1 and B31.3 are useful for registering fittings because they allow unlisted materials to be adopted and because they provide fewer restrictive design rules. Be aware that ABSA has a new unpublished ruling that requires items that look like vessels (even slightly) to be registered under VIII-1 where adoption is not permitted. So far other provinces are not in agreement.
An unlisted material made to a specification can be adopted if the material’s guaranteed minimum yield and tensile strength are available. The code adopted strength is based on a formula using these two inputs resulting in allowable design strength. Or the minimum tensile strength can be used in the proof test. Using this process, almost any IID listed material can be adopted for use in B31.1 or B31.3.
This is a typical formula for adopting unlisted material in B31.3. Sy and St are the materials guaranteed minimum strength. More complex methods are used at higher temperatures where the materials creep properties need to be taken into account. Availability of elevated temperature material properties can severely limit the adoptability of unlisted materials.
Many common fittings materials are not code listed and have no guaranteed minimum tensile or yield strength information. Two common examples: SAE1010 is a carbon steel and B85 A380 is a die cast aluminum. Both are made to chemical only specifications.
To use either of these materials in Canadian registered fittings, the purchaser has to agree with the mill/foundry what minimum tensile and yield strength level is acceptable. A specification referenced or written into each material batch purchase order is required. Chosen strength levels are obviously important. Set too high and excessive batches will be rejected upon physical testing. Set to low and the parts will not pass code calculations. Also note that the ratio between the actual and minimum tensile strength impacts the required burst test pressure. The lower the minimum specified strength, the higher the required proof test. A sample purchase order or a copy of the specification would be required with the CRN application.
If all of the above fails, most Canadian jurisdictions will allow a fitting to be registered with “unknown” materials if it can be proof tested to 10x operating pressure (no tensile strength testing required). This category includes many plastics that are not covered by the piping codes, glass, ceramics and steels that cannot be adopted by the above methods.
Clearly 10x operating is a severe test not possible with many otherwise safe products. This method is reserved for products that are highly overdesigned.