Cylindrical Steel Tank under External Fluid Pressure 5

[mastruc]

Hi, folks!

I'm looking for some literature to better understand the mechanics and design of circular tanks under net external pressure (i.e. an empty or partially empty tank that is fully or partially submerged.) Presumably it will be a stiffened steel shell. I'm unsure of the extent to which this is treated in the literature, so any information that you fine people can point me towards would be very appreciated.

 

[fegenbush]

ASME Section VIII Division 1 UG-27 (unstiffened shells) and UG-28 (stiffened shells) are a good practice for the design of these items. Special care must be taken since you do not have uniform stress throughout the height of the tank shell.

 

[dhengr]

Mastruc:
Take a look at Timoshenko’s several different texts on Theory of Elasticity; Timoshenko and Gere, “Theory of Elastic Stability;” Timoshenko and Woinowsky-Krieger, “Theory of Plates and Shells;” F. Bleich, “Buckling Strength of Metal Structures;” all from McGraw-Hill. Any, number of Advanced Strength of Materials and Theory of Elasticity texts. And, “Tubular Steel Structures, Theory and Design,” by M.S. Troitksky, from Lincoln Arc Welding Foundation.

 

[JStephen]

The general theory is treated extensively in the literature (important for submarine design). The specifics for tanks, less so.

Refer to API-650 Appendix V for some discussion. It is less conservative than ASME.

If the tank in question has a steel bottom, that gets to be a problem. Refer to Roark's Formulas for Stress and Strain, and in particular, a section large deflections in circular plates.

 

[SAIL3]

If I remember correctly, ASME design usually has a FS of about 3 due to the possibility of high pressures and the ensueing consequences of failure. The OP's post does not indicate pressures anywhere close to these pressures and may be temporary in nature. All of dhengr's references are excellent and should give you a background and understanding of the design. Other factors that may influence the design would be the presence of hazardous fluid and possibility of any personnel working inside the vessel under this external pressure.

 

[mastruc]

Thanks for pointing me in some good directions. This is all extremely preliminary, as A) we don't yet have the project, B) the structure in question was described to me in the vaguest of terms, and C) once the requirements are clearer, it may become obvious that the design work would be best performed by someone with more explicit experience with this sort of project. For the time being, I'm treating it as a brain teaser that'll gain me some fluency on the topic.

The proposed conditions, as described to me, consist of several tank cells arranged like a pie-chart with a circular hole in the middle. That is, essentially, two concentric circular tanks connected by radial walls. The central (smaller) circular tank was the element I was concerned with in my question. Naturally, I anticipate that the critical load condition for the central tank won't be "empty central tank, full exterior 'radial' tanks", but rather some combination of full and empty "radial" tanks causing buckling of the empty stiffened central tank. Analyzing the shear/moment/deflection/buckling/etc. of a ring-shaped object experiencing several loads normal to its surface is something I've never explicitly solved for before, so I'm trying to tease out some of the mechanics in my off-time.

 

[JStephen]

Mastruc,
Usually, where a whole tank shell is loaded from the outside, you'll have stiffeners to keep it from buckling. In your case, those stiffeners will also be acting in bending, when one or more of the radial cells are empty, and that may be the controlling case.
The radial dividers between the cells will also have large stiffeners to support them, and may be more of a design issue than the center circular tanks.
The outer shell would normally be designed assuming uniform loading all around, and can become a similar design issue when only loaded in segments.
Steel tanks are very efficient as normally used, with uniform internal loading. Putting dividers into them turns them into very inefficient applications. The ideal solution is to just build a number of small circular tanks rather than putting dividers and stiffeners into a larger tank.

 

[dhengr]

Mastruc:
Are you a fabricator, or the contractor who would install these tanks? Won’t these tanks some to you already designed and detailed for the most part, maybe not piece details, of course? This sounds to me like a set settling tanks or clarifier tanks. The waste water and potable water industries (AWWA) will have some codes and specs. specific the their industries and tankage. I agree with Jstephen’s last post. However, I wonder if the radial dividers aren’t actually part of the stiffening system, not really water tight partitions, and don’t really cause small pie shaped segments/cells to remain full while others can be empty; i.e. each annular tank (ring) volume is at a constant water level, while other rings may be higher or lower. As Jstephen suggest any segmental (pie shaped tank volumes) loading really complicates the tank design problem.

 

[Sawbux]

The ASME section referenced is the one I have used in the past. However you will need to be careful in your application. With a thin shell, very litle external pressure can be resisted. Small variations or imperfections in the circularity can initiate buckling. The ASME, I believe, is developed for uniform external pressure - you have a different situation with triangular hydrostatic load distribution.
You have the benefit of the radial walls which will act as stiffeners in your case, which will help the situation. You could conservatively consider the walls as flat plates.

 

[curiocity]

Also Introduction to Continuum Mechanics by Lai, W.Michael; Rubin, David; Krempl, Erhard has some reference formulas for Circular Cylinder under internal and external pressure

 

[atomorama]

In italian "Belluzzi, Scienza delle Costruzioni vol 3"

Great book!