Tank wall analysis 1

[fa2070]

Hello,

Think of a circular roofless tank constructed of precast concrete panels supported on a concrete ring footing. See the following picture.

My question: How do I analyze this cylindrical shell? Is this a hinged or a fixed base? Or is it a partially fixed configuration? I recall having read in distinct sources that almost all tanks are considered hinged at the base, save those (most notably cast in place tanks) where the design contemplates monolithism between the wall, footing and floor, in which case they're analyzed with a fixed base.

Now back to my case. Although it's true there's no continuity between the floor/wall steel, it is evident X and Y translations, as well as rotation are restrained. So, how do I analyze this?
a) hinged base - free top
b) fixed base - free top
c) partially fixed base - free top

Thanks in advance.

 

[BarryEng]

Hinged base - free top.
Design using PCA publication - circular concrete tanks without prestressing.

There have been several studies done on wall to floor joints, & the results are that it is almost impossible to remotely achieve a fixed base. Even if the wall & floor are monolithic, the wall/footing/floor sits on a (essentially) elastic foundation & even doing an analysis with one of the usual computer programs with a resonable value for a sub grade elastic response, the very slight rotation that the sub grade will give, the joint will inveriably be very close to a hinged base.

Remember that the hoop stress in a hinged base - free top tank, is very close to the hoop stress in a fixed base - free top tank (so - from a hoop stress point of view, there is no advantage in either selection). All that the (apparent) fixity of a fixed base will do, is to increase the base moment dramatically. Even with a VERY high subgrade stiffness spring, the moment at the base will tend to rotate the junction & try to lift the floor marginally (causing a rotation even though the wall/floor junction is fixed at 90 degrees).

The above statements are generalities. To better answer your query, what are the dimensions of your tank - dia, tank wall thickness, etc? What is the nature (& material) of the subgrade?

 

[BarryEng]

PS I was very impressed with your drawing.
What system did you use to allow the web site to accept it?

 

[fa2070]

Thank you for your reply. I'll go the hinged base route for the analysis.
My query, however, isn't associated to any particular project. Instead, it's of generic nature so to say, as the tanks can be of varying radii and heights, and be built on sites with soils that range from solid rock to plastic clays and everything in between. My fear, though, was that bending moments on the wall could be underestimated if the mild rotation restraint at the base is fully neglected in the analysis, as is the case when it's modelled as a fully hinged base.

Now, with regard to posting images to the Eng Tips website.
The forum software doesn't allow us to embed pictures within the posts, however, it implements a specialized mini-language for presenting visual widgets and enriching what otherwise would be plain text. This mini-language, consisting of markup tags, allows us to reference graphics (more on this later), embed emoticons, present items in bulleted lists, format text as well as achieve a number of visual effects. To make use of these visual resources you have to place the markup tags whereever you want within your message. The tags are parsed, interpreted and executed behind the scenes by the forum software, arranging and styling your message accordingly and serving it to the internet browsers.
Every time you reply to an existing thread or start a new one, you'll see three links on [red]"Step 5 Options"[/red], just below the textbox where you type your message. If you click on "Process TGML", a help window will pop up showing you all the markup tags that you have at your disposal and what each of them does.
For example, if you wish to highlight a paragraph (or a word, or a group of words for that matter), you just enclose them within the corresponding markup tag, which in this case is [ignore]words to highlight[/ignore], being [ignore][/ignore] and [ignore][/ignore] the opening and closing tags respectively.

Another example. If you want to embed a picture the tag to use is [ignore]

[/ignore]. You'll have to replace [ignore]

http://www.myserver.com

[/ignore] for the actual server name that hosts your picture and mypicture.jpg for the actual filename. As Eng-tips.com doesn't offer its members the facilities to host files, you'll have to open an account in an online hosting service that does. Most of them offer free entry-level accounts. In my case the hosting service is

http://www.photobucket.com

(but there are others too).
So, once you've uploaded your picture to your hosting service, you'll get an URL (that's an internet address that uniquely references your picture) that you copy to the clipboard and then paste in the message that you're composing at eng-tips.com.
I'd recommend you read the help page that I mentioned above ("Process TGML") to get the scope of what can be done with the markup mini-language.

Finally, it's always wise to preview your message before submitting it as more often than not we don't get the markup tags right in the first attempt. When this happens, I can click on Edit Post, fix the errors and retry until I get it right.

Hope this helps.

 

[BarryEng]

Bending moments in the wall.

I have designed tanks from a few hundred m3 up to 25,000 m3. Some of these were site checked for rotation etc & the answer was always variable.

A few years ago, I designed a 25,000 m3 tank that was prestressed (65 m dia x 12 m deep). I set the precast panels on a teflon strip (within a slot in the footing) & stressed every second strand in the wall. The result was that the wall moved (slightly) inwards, but the movement was variable around the circumference (as a average, in the order of a sliding base loaded with the strand loads with some sliding restraint from friction). I then cast the base into the slot & then stressed the other strands. By doing this, I only required to design the wall for 50% of the vertical moment. In the empty condition, the wall is deflected inwards (from prestress forces). When the tank is filled, the wall is deflected from an inward movement - back to a zero movement & then an outward movement.

For a normal concrete tank, I have found that the minimum reinforcement required by the water retaining code (I use the Australian Standard - based on allowable stresses, rather than ultimate conditions, due to serviceability limit state considerations), has a bending resistance that is usually sufficient for most tanks to resist the vertical bending moment.

As I said in my previous thread, the vertical bending moment in the wall is very similar in both a fixed base & a hinged base (above the base). The major departure of the two bending moment curves, is in the location of the base. It is very difficult to develop full fixity. Perhaps if the base slab is reinforced into a rock foundation, but then the analysis would be different.

In the PCA manual (concrete tanks without prestressing) the analysis of a hinged base suggests not designing the hoop force to zero at the base of the wall (even though this is correct for the analysis of a hinged base) to allow for some translation. Remember that it is difficult to replicate the real world in the analysis, we start with discreat jumps from sliding base - hinged base - fixed base, without a transition between them.

I have compared methods of analysis of tanks from the methods used in the early 1900's (Gray & Manning etc), with the PCA manual, & in recent years, with Amin Ghali's matrix methods, & more reently with FEA methods. If you compare the graphs, there is very little difference in the results. I do like elastic methods that have stood the test of time (with results that can be verified & reproduced).

Drawing on this web site.

I'm even more impressed - I thought it might be only an imported autocad file. I did not realise it was so complicated. Thanks for the info.

 

[GBor]

I believe site management prefers that files be uploaded to the engineering.com site as an attachement (Step 3). This reduces the memory burden on Eng-Tips.