Buckling and local stress in a leg supported vessel

[arbor]

I am working on a stress analysis for a leg supported vessel with vacuum and seismic load. Due to the vacuum and the bending moment resulted from the seismic load, the area above the leg sees axial and hoop compressive stress. I am having a hard time for the buckling check and I hope I can get some help here

To make my questions simple, I will just try to use the axial stresses here. The maximum axial compressive stress is 41.7 ksi at the corners of the leg attachment. The axial compressive stress is 25.7 ksi at the location about 15 inches above the leg and 18 ksi at the location about 40 inches above the leg. I did stress linearization at those locations, the bending stress is very small, so we can basically assume above stresses are membrane stresses. My questions are:

1.Shall I compare those stresses with the allowable stresses by ASME VIII Div 2 4.4.12.2 (c) for local buckling (or (f) if I got the equivalent stress)? The allowable stresses based on 4.4.12.2 (c) is about 13 ksi.

2.Which stress shall I use? Are there general or local membrane stresses for the compressive stress? Is 1.5S still applicable if so?

3.Is there still a 1.2 factor for seismic condition for the compressive stress?

4.In European Codes, for local buckling, they define 0.9 time of yield as the limit for total compressive stress in the area of attachments and supports where significant compressive membrane stresses are present. (for this limit to apply the loaded area has to be not greater than 1/3 of the shell circumference). Based on the European Code, I will have an allowable of 0.9*36 = 32.4 ksi. It is significantly different from 13 ksi. Which is more appropriate for this case?

I also did a buckling analysis for the same tank. Since I got so many buckling modes due to the vacuum, so I removed the external pressure and apply the load from the heads due to vacuum as axial compression to the cylinder. There is no equivalent load applied for the absence of the vacuum to the side wall. The axial compressive stress I got is about 4 psi lower so the error is not significant. The load factor I got for the buckling is 47 which means buckling is unlikely to happen. Is my approach wrong?

I have attached the stress, buckling pre stress, and bulking results.

Another off topic, ASME define a local area of SQRT(Rt) in the meridional direction, what about the circumferential direction?

Thank you

Arbor

 

[TGS4]

You've asked some good questions about the compressive stresses. I will need to think about those for a while.

Another off topic, ASME define a local area of SQRT(Rt) in the meridional direction, what about the circumferential direction?

There is no restriction in the circumferential direction. Think LTA that extends around the full circumference of a vessel - that's OK.

 

[dig1]

Arbor,

I agree with TGS4 that you have good questions. It sounds like you are on a reasonable approach.

I do have a couple of comments. With respect to the 1.2 factor for the seismic load you need to check the building code which was used to calculate the load. Some codes say that if the load combinations in the code are used you cannot take an increase in the allowable stress. If this is the case the building code would be more restrictive than ASME and the 1.2 could not be used. I have run across this before.

TGS4 is correct on the issue of the circumferential stress. Think of the local stresses at a cone to cylinder junction, they run around the entire circumference but a discontinuity longitudinally would be limited. Is your question may be in regards to a localized area such as a punching load from a leg or a general question? It may not change the answer but clarification may help explain an answer.

Without knowing what software you used I cannot say for certain, but generally a buckling load factor of above 10 indicates that buckling is not likely.

If you are using the EN (I suspect EN 13345 is what you are referencing) when you need to make sure that all the assumptions of that allowable are meet. EN 13445 Part 4 or 5 has tolerances which may apply. Also, the tolerance on a vessel subject to vacuumj is generally tighter than ASME Section VIII. Check EN 13445 Part 3, Chapter 8.

I know this does not answer your most important questions so please be patient while some more thought is given.

Thanks,

Patrick

 

[MJCronin]

arbor...

Would it be reasonable to consider either a thickened bottom course for the vessel or a dual-ring reinforcement incorporating the tops of the legs ?

I believe that the Bednar text and the Pressure Vessel Handbook have an extensive discussion of this type of design

 

[arbor]

Thank you all for the valuable comments. I have learned a lot from this forum.

Regarding the local area in the circumferential direction, it was from the stress analysis for nozzle loads or localized loads. Depends on the geometry and loads, there could be a relatively large area in the circumferential direction with high equivalent membrane stress (Mises stress). And the allowable stress would be 1.5S which is the yield strength for some materials. For the LTA, it has a thickness limit when being accepted to extend the full circumference under internal pressure. In this case, the Mises stress is about 0.8 yield since the longitudinal stress is half of the hoop stress. For stresses in the cone shell junction, it has more secondary feature. So it seems to me that it is unconservative not to limit the circumferential direction for the stresses from localized loads. More explanation about the through/theory behind this would be really appreciated.

I know the 30% stress increase has been removed from ASCE7 and the AISC manual. But in ASCE7, it says if the pressure vessel is design to ASME with ASCE7 loads included, it is deemed to satisfy ASCE7 requirements. So I think the 1.2 still applies for the stress in the vessel but not the supports. However, ASME Code only indicates 1.2 applies to tensile stress. Under compression, the shell behaves differently from under tension, I am not sure if the 1.2 is still applicable.

I am using ANSYS for the analysis. I can increase the bottom shell thickness to bring the stress down. But it still bothers me that the result by comparing the FEA stress to the Code allowable does not match with the buckling analysis result. So I hope ASME could provide more guidance for the local compressive stress evaluation.

I don’t have much experience with European Code. I was trying to understand the local compressive stress so I tried to go through some papers and Codes and found some European Codes such as PD 5500 A3.3 mention the local compressive stress. But I do need to learn more about its limitations.

Thank you all again and waiting for more inputs,

Arbor

 

[TGS4]

OK - had the weekend to think about this.

In my opinion, there are number of different things that you are doing incorrectly:
1) Where do you find a 1.2 factor on seismic? Table 5.3 has no such multiplier on E - see Design Load Combinations 5, 6 and 8.
2) From a local stress perspective, the Code makes no differentiation between compressive and tensile stresses - hence to use of an invariant. The rules in Article 5.2 are the same regardless of whether the underlying component stresses are tensile or compressive. You would NOT take the allowable stress from the general membrane compressive allowable.
3) A buckling analysis MUST be performed using all of the design loads. I am assuming that you are performing an analysis to Article 5.4 - is that correct? If so, you are required to evaluate all of the load case combinations in Table 5.3 - and there is no load case that does not include pressure (except by following Note 3). Therefore, the buckling analysis that you performed is somewhat interesting, but essentially irrelevant. You must include pressure if it acts unfavorably to you.

Regarding the limit in the different directions for the locality check (5.2.2.2(b)), if you want a better explanation, I would suggest that you check out some of the thin-shell theory work from Timoshenko. Failing that, do your own elastic-plastic analysis and demonstrate that limit to yourself. Imagine a ring of nozzles fully around the circumference - each has a local membrane stress that exceeds 1.1S - completely analogous to a full circumferential LTA - completely OK. Now imagine a row of nozzles in the longitudinal direction - not OK. Think in terms of the magnitude of the hoop vs longitudinal stresses in a cylinder...

For the LTA, it has a thickness limit when being accepted to extend the full circumference under internal pressure. In this case, the Mises stress is about 0.8 yield since the longitudinal stress is half of the hoop stress.

huh? Got a reference for that?

For stresses in the cone shell junction, it has more secondary feature.

Got a reference for that too?

 

[rhg]

Use reinfocing pads near legs, increase number of legs or design this equipment with skirt.

Make it simple

Regards

rhg

 

[jtseng123]

Why wasting your time doing FEA ? This is very simple drum with legs and any commercial programs, Compress or PV Elite will take care of it in 10 minutes, and all the answers to your questions are in the output. It cost nothing to add pads as pointed out by rhg. Ask your friends in other companies if they can do you a favor running it for you.

 

[TGS4]

jtseng123 - pray do tell what approach these programs use that would address the OP's question? How do they handle vacuum+seismic+deadweight in the design of the leg supports? You don't use a computer program without knowing exactly what is done inside it, do you?

 

[arbor]

TGS4, thank you for your explanation. First I need to apologize that I didn't give enough background of my analysis and mixed all my questions together. The stress analysis is for a pressure vessel designed to Div.1. FEA is mainly used for the local stresses. Section II Part D allowable stress for Div .1 but the acceptance criteria from Div. 2 is used.

1. 1.2 for seismic load question is from the Div. 1 code. But even in Div.1, it is only for tensile stress. Maybe not using it is the right way to go.

2. If only consider 5.2.2 requirements, my concern of the stress might go away. However, Div.2 4.4.12.1 indicates "the allowable stresses of this paragraph shall also be used as the acceptance criteria for shell subjected to compressive stress evaluated using Part 5". If using the allowable stress based on part 4, even I could use 1.5 for local area, it will still be too high.

3. For the buckling analysis, I wasn't able to get the buckling model for the shell local buckling above the leg if I put in the external pressure. There are so many modes in the general area of the shell under external pressure. Although the load factor for the first mode with all the loads is acceptable based on 5.4.1.2, thinking of the high compressive stress above the leg, it hard to understand why the load factor is not lower. Therefore, I removed the external pressure to just study the relationship of the compressive stress level with the buckling load factor. It suprised me that even at a stress level in the 20 to 30 ksi range, the load factor is so high. I wonder if the supports from the legs increase the critical buckling load at this area. This makes me think of if multipliers should be used for the local compressive stress, 1.5 times or maybe even higher. Or I just totally ignore 4.4.12? But the compressive stress is still shown there, some other engineers will question it.

The requirements for the LTA was from AD-200 of the old Div. 2. It was removed from the new Div.2. But it is still given in chapter 22 of Companion Guide to ASME BPVC by K.R.Rao. It says the thickness of the local thin area needs to be no less than 2/3 of the shell thickness calculated by DBR. Therefore, the Mesis stress calculated using hoop and longitudinal stresses will be SQRT(3)*hoop stress/2. If I didn't remember it wrong, the same requirements may also in ASME III.

Cone to shell connection is a gross discontinuity, the membrane stress includes secondary stress due to discontinuity in the full circumference. My impression about the stress in an area farther away from a local discontinuity such as small attachment, the secondary stress due to discontinuity would be much less. Please correct me if my understanding is wrong.

I know I could change the design to make lower stress and higher buckling load factor, but it will remain an unclear topic to me all the time.

Thank you,

Arbor

 

[TGS4]

1. Am I correct that you are referring to Note 12 to UG-23(d)? If so, it allows a 20% increase in allowable stress (equivalent to a load factor of 0.833). To follow your logical steps to get to Div. 2, you would go from UG-23(d) - note that you are calculating local stresses, note that Div. 1 has no provision for local stresses, which then points you to U-2(g). Going from U-2(g), you decide to approach Div. 2. Since you have decided to perform an FEA, that puts you directly into Part 5 (i.e. you skip over Part 4). Once in Part 5, in order to comply with U-2(g), you have to ensure that the methodology you follow is "as safe as" Div. 1. For local stresses (to ensure compliance with 5.2), you choose to modify Table 5.3, design load combinations 5, 6, and 8, replacing 0.7E with 0.833E. OK, so now that you're into Part 5, you have to follow it all of the way through. You check with 5.3 - can you exempt yourself by 5.3.1.1 (hopefully)? Then, into 5.4, you're stuck with how to comply with U-2(g). None of this looks anything familiar to UG-23(b) - so you choose to apply the margins directly from Div. 2 (this is the correct choice, BTW). Since you want to do an eigenvalue buckling assessment, you choose 5.4.1.2(a). Note that it says you have to follow the load case combinations in Table 5.3 (all of them...). Therefore, you MUST deal with the multiple buckling modes - hopefully the lowest is greater than ßcr. As long as the lowest eigenvalue is greater than ßcr, good to go. It doesn't matter whether or not that eigenvector (buckling mode) is related to your local load or not... Finally, don't forget 5.5, especially 5.5.6.

Ignore the old AD-200. Follow the rules, as written, in the latest edition of the Code. K.R.Rao may have it wrong, too. Follow the rules. If you're doing FEA, then dive straight into Part 5, and ignore Part 4. Likewise, if you're doing Part 4, ignore Part 5. While not mutually exclusive, the two are independent of each other; and any conflicts between the rules are intentional (about 90% serious here).

Does this make sense? There is a proper procedure to follow, which I believe has been adequately laid out here. If you choose, via U-2(g) to go to Div. 2, Part 5, then you have committed yourself to going into Part 5 whole-hog. There can be no half-a$$ed approach once in Part 5. Forget what you thought you knew, or what you read elsewhere (including previous editions of the Code) - follow the Code rules as-written. To the letter. ALL of them...

 

[arbor]

TGS4, thank you for a very clear procedure for using Part 5 of Div.2. I still have a couple of things unclear.
1. The buckling approach in Part 5 still does not cover my original questions. It has the minimum design factors for shell under axial compression and under external pressure, respectively. But not for combined loads, such as compression from bending and external pressure. That's why I looked back into Part 4 for clues which makes me confused.
2. Chapter 22 of Rao's book was authored by those big names behind the new Div.2, such as David Osage, Thomas Pastor, etc. They specifically indicated the requirements for LTA are from the old Code but still applies. So I don't think it is a mistake. But I don't understand why they removed it from the new Code.