Propane Storage Sphere
File:PVE-4092
Date: Aug 10 2010
By: LB
Pressure Vessel Engineering was hired to prepare calculations for both pressure containment and supports for wind and seismic loads on a series of large propane storage spheres for Conrex. The vessel wall thickness and nozzle supports were calculated using standard ASME code calculations. The vessels supports were constructed using industry standard designs but Finite Element Analysis (FEA) was used for the analysis instead of existing design rules.
 The standard storage sphere analyzed for Conrex |
 The experimental sphere subject of this report |
The standard design method uses an increased wall thickness at the equator of the vessel to support the additional stresses caused by the attachment of the legs. Our FEA runs for this support method verified that this design method is valid. The question raised was - "Is it possible to design a vessel where the equator of the vessel does not have to be made thicker?" After the produced design was finished, this experimental FEA report and calculation set was run to experiment with the following:
- Shorter legs - the legs are still attached to the equator plates, but not as high up. The leg to foundation pitch circle is reduced resulting in shorter legs but increasing the overturning stresses on the legs.
- Reduced leg diameter - The bottoms of the legs are reduced in diameter to the size required to support the load. This is smaller than usually used for this type of vessel but...
- Larger legs at the shell attachment - The leg size at the top was increased until the vessel stresses at the attachment were reduced to an acceptable level. A conical transition was placed between the two different sizes of leg pipe. The reduced leg diameter at the bottom has a minimal cost impact so future production is likely to be based on a straight pipe from attachment to foundation based on the larger diameter.
- Rectangular tubing cross bracing - This high strength method of cross bracing was developed by Conrex and used in the production vessel. The bracing method shown here is identical. The appendix to the FEA report shows the excellent results obtained with this design feature.
- V plate location - for this experimental report the cross bracing leg v-plates were moved from the leg to directly attach to the shell. This design change reduces twisting at the shell attachment and is one of the keys to not requiring thicker equator plates. The v plates create local stresses in the shell which are acceptable in this experimental vessel, but could be further optimized if put into production.
- All dimensions and operating conditions of the original vessel were changed for this sample to protect Conrex's customer's process confidentiality.
 Standard Leg to Sphere Attachment |
 The experimental attachment showing the v-plate directly attaching to the shell and the reduced lower leg diameter |
Some comments on the FEA are in order. At the time this report was first done in 2009, it was one to the largest models we had run. It was run entirely as solid elements which increased the mesh complexity but allowed study of model details impossible if a shell mesh was used. Although the model has more than 1/2 million elements and 1 1/2 million nodes, it meshes in less than 5 minutes and solve it in an additional 5 minutes. This quick response time allowed rapid experimenting with different design alternatives. Clearly a half model could have also provided the same results with shorter run times, but some of the preliminary designs we analyzed did not have symmetrical leg supports which required the full model to check for side sway effects.
 Solid mesh elements were used for the full model |
 Solid mesh details |
The report shows the 6 load cases that were applied to the model to comply with ASME VIII-2 Table 5.3 requirements. The load cases were also based on Conrex's field experience with hydro testing. Seismic and wind loads are from IBC 2009 for San Diego. Studying these loads by FEA provides a much greater insight into how a vessel reacts to these loads than is possible by using standard rule based design procedures. This does not invalidate the use of rule based design but allows one to go beyond the level of understanding available using them. This experimental design would not have been derived using rules based analysis.
An ASME calculation report is included which covers the scope of the shell thickness and nozzle reinforcement. Even if FEA could demonstrate savings in materials these design rules are mandatory and must be followed. The shell thickness was set to the minimum required by the code for pressure requirements. No increase in thickness was required for the equator plates for leg support loads. However the top plate was made the same thickness as the bottom plate as an inexpensive method to reduce the amount of reinforcing required.
We at Pressure Vessel Engineering Ltd are very grateful to Conrex for allowing us to post this experimental study. Conrex can be contacted at www.conrexsteel.com or 416-747-4665. sales@conrexsteel.com >
Downloads (pdf format):
Sample 2 - Audit Vessel
File: Samples/Sample2
Last Updated: June 16, 2010
Laurence Brundrett
A Standard Audit Vessel?
If there is a standard for ASME U stamp Audit vessels this is it. It is so common that it is known in slang as a "Hartford Submarine" in honor of the Hartford Steam Boiler Inspection and Insurance Co. This is the type of vessel a shop builds when it has no vessels on order that it can use for an audit, or when it is first seeking ASME certification. The vessel, calculation set and drawings are simple. The materials are easy to source. The manufacture is easy. The audit team has seen it before.
We have seen many of these vessels built for ASME U-Stamp audits and discarded. A renewal audit based on any in production U-Stamp vessel is usually a better idea and more economical. We can also design other vessel configurations that would be useful after the audit - such as vertical air receivers.
A Vessel for Your Audit
The drawing and calculations can be updated to the latest code and addenda if you want this vessel. (Do not use these out of date calculations for an audit!) We can also re-design the vessel to use more economical material thicknesses, change nozzle configurations as desired or to demonstrate radiography.
Verification of Software
We usually do audit vessel calculations using our spreadsheet calculations because we can provide the full hand calculated verification sets (see the downloads section on this page for the calculations, but not the hand calculated verifications). The VIII-1 code book does not specifically indicate if hand verification sets are required (from VIII-1 forward page xxv):
The Code neither requires nor prohibits the use of computers for the design or analysis of components constructed to the requirements of the Code. However, designers and engineers using computer programs for design or analysis are cautioned that they are responsible for all technical assumptions inherent in the programs they use and they are responsible for the application of these programs to their design.
In previous years, we have been asked to show hand calculations to meet this requirement. Lately, verification by comparison between two different programs is being accepted. To be cautious we provide the hand calculations, even if two different programs are being used. Some audits will not request this information at all.
We can also provide the calculation sets in Advanced Pressure Vessel or PVElite if desired (the verification will be by our spreadsheets which are verified by hand calculations).
What is Expected
To date all of our Audits have been successful, but somehow they never seem to become stress free. In the last few years we have seen increasing time spent on the review and revision of the QC manual (including manuals that have gone through many audits) and much less time spent on the engineering or drawing review (written in 2009).
Contact us for a quote on the drawings, calculations and verification set on your next audit.
Downloads (pdf format):
Sample 3 - Horizontal Retention Vessel
File: Samples/Sample 3
Last Updated: June 16, 2010
Laurence Brundrett
This sample is based on a real vessel. The operating conditions and dimensions have been altered for this sample.
Contact Tank:
This 8ft diameter contact tank (or retention vessel) keeps water and chlorine in contact for a guaranteed minimum safe amount of time at the maximum possible flow rate. A longer contact time (with reduced pressure vessel volume) is achieved by providing a serpentine flow path (this can be seen in the drawings). The baffles prevent short circuiting of the flow from the input to output.
Usually a tank in this service does not need to be code stamped. This vessel was designed and built to ASME VIII-1 per the customer's specification but not registered.
Flexible Saddles and Saddle Design:
Per ASME VIII-1 appendix G-l:
A vessel supported in a vertical or horizontal position will have concentrated loads imposed on the shell where the supports are attached... Calculations to resist the forces involved are not given here because they involve so many variables depending upon the size and weight of vessels, the temperature of service, the internal pressure, the arrangement of the supporting structure, and the piping attached to the vessel as installed.
Saddles for horizontal tanks are usually designed based on the work of L.P. Zick "Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports" first published in September 1951 "THE WELDING JOURNAL RESEARCH SUPPLEMENT." http://www.codeware.com/support/papers/zick.pdf
The good news about the Zick analysis is that it calculates all of the support stresses that are required to design a horizontal vessel.
- Beam type bending of the vessel between the supports (S1)
- Tangential Shear in shell (S2)
- Tangential Shear in Head (S3)
- Saddle Horn stress in shell (S4) - often the highest stress in the vessel
- Circ bending stress in bottom of shell (S5)
With a spreadsheet or program, the Zick analysis is easy to perform.
The bad news about the Zick analysis is that it usually underestimates the peak stress in the saddle horn, often by a factor of 2 or more. Real stresses in vessels with large diameters and thin walls can be high enough to reduce the long-term cycle life of a vessel. A simple check is to assume that Zick underestimates the true saddle horn stress by 3x. For many small vessels this is not a problem. This 8ft vessel which has relatively thick walls would not have excessive horn stresses but is large enough to justify examining the horn stresses beyond the methods provided by Zick.
Rigid Saddle - an economical choice for small diameter vessels with heavy walls - stresses are higher at the saddle horn than Zick analysis predicts, but this is not important for small vessels.
Flexible Saddle - the shear plate extends beyond the vertical supports. The saddle wear plate extends beyond the vertical plates. The saddle flexibility increases further away from the vessel vertical centerline. Horn stresses are reduced - this is important for large diameter or thin walled vessels.
This sample has been calculated using our in house spreadsheets, Advanced Pressure Vessel (APV) and PVElite (sample calculations can be downloaded below). Actual projects would only provide one calculation set - our preference is to use APV with additional spreadsheets added as required.
More Information on Flexible Saddles (External Links):
- The Support of Horizontal Vessels Containing High-Temperature Fluids A Design Study
- Peak Stress and Fatigue Assessment at the Saddle Support of a Cylindrical Vessel
Downloads (pdf Format):
Sample 4 - Vertical Vessel
File: Sample 4
Last Updated: June 16, 2010
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This 5 ft diameter vertical vessel is based on a combination of different jobs. It has features often found on softener and filter vessels, although the combination presented here is unlikely to be used on one vessel.
The vessel leg supports are calculated using IBC-2000 seismic methods. The correct Seismic R factors for a vessel can be found in Table 15.4-2 of ASCE Standard 7-05.
Pad flange nozzle calculations are shown in the Spreadsheet version of the calculations. The pad flange is calculated to pass both the rules of nozzles (page 11) and flanges (page 12).
Sample calculations for APV, PVElite and PVEng spreadsheets as well as the vessel drawing can be downloaded below.
More Information on Seismic Response Factors:
Downloads (pdf format):
Sample 5 - Vessel with a Large Opening
File: Sample 5
Last Updated: June 16, 2010
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A Collection of Unusual Design Features
This sample vessel is not modeled after a real vessel. It is a collection of difficult design features and obscure code requirements: large nozzles, swing bolt covers, cone discontinuities, use of bar stock for nozzles (code case 2148) and the use of sanitary ferrules in vessels. Refer to the calculation sets for more details.
Unusual Flanges
The swing bolt cover is analyzed as an appendix 2 flange. The bolt circle is outside of the flange, which is a length of increased wall thickness pipe. The bolt loads try to twist the pipe inside out - the Appendix 2 calculations check for this. Additional calculations are run for the attachment lug weld and shear pin stress. Flange C is also a custom flange calculated to Appendix 2.
Ferrules
Ferrules and sanitary connections can not be calculated by the rules provided by Appendix 24 which requires metal to metal contact outside the gasket. Typically, ferrules need to be proof tested, or calculated by Finite Element Analysis. For this vessel, the manufacturer of the 2" ferrule has provided a CRN number covering the design. The CRN implies that either proof testing or some other calculation method was used to prove the design. The 8" ferrule does not have a CRN, here a proof test is specified.
Large Nozzles
The side nozzle C is checked against the rules of Appendix 1-7 because it is larger than 1/2 of the vessel body diameter. The rules of Appendix 1-7 are confusing and very difficult to interpret, so in this case, all the conditions regarding moments of inertia and area replacement have been applied.
Bar Stock
The rules that allow the use of bar stock in pressure vessel bodies or nozzles have been changing. At the time this sample was made, bar stock could only be used with code case 2148. This code case has since been annuled and later reinstated as 2148-1. See UG-14 and App 2-2(d) for up to date information on the use of bar stock in pressure vessels.
Example calculation sets using Advanced Pressure Vessel (APV), PVElite, and PVEng Spreadsheets can be downloaded from the links to the left.
Downloads (pdf format):
Sample 6: A Step by Step Introduction to FEA
File: Sample 6
Last Updated: June 16, 2010
LB
Why FEA?
Pressure vessel code rules exist for the analysis of simple objects like pipes and heads and more complex objects like flanges and nozzles. Where the code rules exist, they have to be used. However, most code rules do not calculate real stresses. The best they can do is provide pass/fail acceptance criteria. Code rules do not exist for many pressurized objects.
Finite Element Analysis (FEA) provides a method of analyzing complex geometry, and when the results are interpreted correctly, pass/fail criteria can be determined. Because the FEA calculates stresses, the results can also be used to predict a cycle life.
PVEng sample #6 is a simple manifold block. A simplified description of the FEA process follows. The report has these and other pictures and more in depth analysis. This is a step by step description of the process used in the analysis.
Other samples on our web site show more complex analysis involving multiple bodies connected with bolting, studies with thermal stresses, and objects with higher stresses where the interpretation of stresses to code rules is more difficult.
Step 1 - Create a solid model of the object |
 A solid model of the manifold block has been created. The manifold has a series of pipe thread ports. The manifold will have pipes attached in service so here pipes have been added to the model to simulate the loads that they generate. Many of the model shots that follow have the pipes hidden. The stress in the pipes is not a concern in this report. At PVEng we use SolidWorks to make the solid model. |
Step 2 - Check the Drawing (Hold Point) |
The first quality control step is to create a drawing from the solid model. Once dimensioned, the drawing can be compared to the original part for accuracy. |
Step 3 - Mesh the model. |
The FEA program divides the solid model into small regular shapes - here 3 sided pyramids are used. Although no stress formula exists for the complex manifold shape, formulas do exist for the small pyramids. The FEA program can calculate the deformation (and then stresses) in each small simple pyramid and combine the results for the overall complex object deformation (and stress). At PVEng we use SolidWorks Simulation (Former known as COSMOS Designer) to do the meshing and the following stress analysis. Here Cosmos has meshed the manifold and pipes into 290,000 solid pyramids each approximately 1/8" on a side. Two material properties for the SA-479 316 stainless material are required 1) the modulus of elasticity (28,000,000 psi) and 2) Poisons ratio (0.27). Cosmos uses this information to calculate how much each element deforms under load, and from that, what the stresses of the elements will be. The code allowable stress for this material is 20,000 psi. |
Step 4 - Apply Loads and Restraints |
The manifold and all pipes are pressurized on the inside. Here a pressure of 300 psi is applied to the inside of all the manifold and pipe surfaces. |
One pipe has no cap. It is fixed to anchor the whole model. This location will have zero displacement and reaction forces will be created here. More complex models can have many more boundary conditions, and if they are symmetrical, can be split in half to reduce the run time. Here the manifold is not symmetric, so the model has not been split in half. |
Step 5 - Run the Model and 2 Quality Checks |
COSMOS calculates the displacement and stress for each element (pyramid) in the model. But before looking at the results, some quick quality checks: firstly quality check #2 - check the error plot for elements with potentially high errors. The zones of high error (>5% for pressure vessels) are limited to areas where the shape of the model is rapidly changing (sharp edges or tight radii or other changes in shape known as discontinuities). All large areas have less than 5% error therefore the 1/8" mesh is acceptable (a courser mesh could have been used for this model). The presence of elements with >5% error highlights a fact of life: FEA never produces perfect results "All FEA results are wrong" but with good techniques, the results can be very good and very useful. |
We are anxious to get to the stress results, but first, quality check #3 - check the reaction forces. In theory, the anchored end of the pipe creates a force equal to the inside area of the pipe x the pressure - here 3.36in^2 x 300psi = 1008 lbs (imagine the pipe exploding with this force if it was cut). This matches the FEA reaction force for the model at 1009.6 lbs and indicates a very good run. This simple quality control check is extremely powerful for catching models with improper anchoring or missed pressurized areas or other wrong loads. |
Step 6 - Last Quality Check - Displacement Plots |
COSMOS calculates the displacement of the model and then from that the stresses. It follows that if the displacement results are bad, so are the stress results. Quality check #4 - check the displacement plot. This is the last quality check before getting to the stresses! Here the displacement of the model is magnified 500x. The model is stretching longer. It is bulging out around the large internal passage. The attached pipes are expanding. All of this makes sense - the stress results should make sense too. |
Step 7 - Stress Results |
COSMOS converts the deformation results into stress results. The stresses can be seen to be higher in areas that have more local deformation. The stress in every location of this model is below the code allowable membrane stress so it passes. Higher stressed models will have stresses up to 3-4x nominal code allowables - but limited to small areas. The art of pressure vessel FEA is interpreting when these areas of high stress are acceptable. This is often the hardest part of FEA. |
Step 8 - Fatigue Life |
ASME has published tables of fatigue life for many materials including the 316 stainless for this manifold block. The Fatigue life is calculated from the highest stress found in the model. A peak stress of 3095 is found on the inside at one of the nozzle ports. |
The 316 fatigue curve predicts an infinite cycle life for this low peak stress value.
Step 9 - The Report
Pressure vessel calculations and FEA results are usually reviewed by Authorized Inspectors and/or third party engineers. The province of Alberta has released guidelines for writing reviewable FEA reports. See our web site for samples like this and other much more complex ones written to the Alberta guidelines.
Downloads (pdf format):
Sample 7 - SolidWorks Vessel
File: Sample 7
Last Updated: June 6, 2010
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We first started using SolidWorks to make solid models for Finite Element Analysis. We are gradually doing more of our regular drafting work in it.
This sample vessel is our first vessel drawn entirely in SolidWorks. From scratch, the SolidWorks drawing took about twice as long as a comparible AutoCAD drawing. Changing the dimensions and conditions to those shown here was faster than possible in Autocad, and the results look better. We still also offer drafting service in AutoCAD.
This vessel is an aluminum storage tank. B16.5 flanges are not available in aluminum, so the flanges are custom designed but drilled to B16.5 patterns - they ended up thicker than comparable B16.5 flanges. The main body flange is a custom VIII-1 Appendix Y design for use with an O-ring seal.
Downloads (pdf format):
Sample 8 - NozzlePro FEA
File: Sample 8
Last Updated: June 16, 2010
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This sample vessel is drawn using Solidworks. We also offer drafting services using AutoCAD.
This vessel has a large nozzle located on the straight shell. The diameter of the nozzle requires Appendix 1-7 calculations. The nozzle also has large loads and moments specified by the customer. Nozzle PRO has been used to calculate the resulting stresses. The Nozzle PRO results are much more accurate than using WRC-107 methods.
Since this sample was made, ASME introduced new App 1-8 and 1-10 methods which can also be used to calculate area replacement in large nozzles.
Downloads (pdf format):
Sample 9 - B16.5 Flange
File: Sample 9
Last Updated: June 16, 2010
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A B16.5 flange's pressure at temperature ratings are taken straight from the B16.5 standard. But what if this same flange is calculated by VIII-1 Appendix 2 rules? And how does this compare to FEA results?
This standard 12" Class 150 B16.5 flange's rating was compared with Appendix 2 and FEA. Although we would not normally run FEA or Appendix 2 rules on a B16.5 flange, the comparison is interesting...
A common saying in our office is that you cannot run B16.5 flange calculations using VIII-1 Appendix 2 rules, and here is yet another example of a B16.5 flange that does not pass VIII-1 design rules. Going farther the FEA shows interesting stress patterns and vividly illustrates how a standard flange deforms under load.
This report shows how to accurately apply all of the Appendix 2 flange loads - seldom done correctly in FEA analysis. Also shown is how to combine the seating and operating conditions to get higher allowable bolt loads as allowed by VIII-2 Appendix 4 rules - required to get high seating bolt loads to pass.
We would not run Appendix 2 rules or Finite Element Analysis on a standard B16.5 flange, but we use the methods outlined here regularly on custom flanges that can not be run to the rules of Appendix 2.