Octagonal and circular mats

[nicoga3000]

I've been working on the design for an octagonal mat for a storage tank over the past few days. Originally, I looked at a circular mat, but the rebar requirements were astronomical (the spacing was getting close to 3" c/c on #11 bars...so that won't work). The rebar requirements for my octagonal mat are still pretty high, but given that I can reinforce orthogonality vs radially/circumferentially, it becomes slightly more manageable. But even still, I have run into, call it, an issue. See the attached photo.

What we have is a circular shaft. After some discussion, I've decided that the circular ringwall can be reasonably assumed to be an equivalent octagon (for analysis, this is MUCH more manageable over a circular ringwall). Given the loading conditions (which are quite high) and low bearing capacity, this footing is quite large - about 63 feet in side-to-side diameter. What I've done is taken the area above what I labeled the flexure face and determined what sort of moment I'd get. Assuming a #10 bar, I figured the development length (ld) and went ld away from the flexure face. Wherever that hit, I took that area as my length of "available" beam for reinforcement. OK, fine, this part I'm comfortable with.

But if you look at the left half of the drawing, there is an area that would (I think...) have very low flexure. The requirements here are quite small in comparison. I COULD go as far as to switch bars here, but I don't know if it would be cost effective for the field crews when they're out there trying to differentiate between n number of bars. We've also got the middle of the mat to deal with. Top steel here should, in theory, be quite large. I can only think to do a strip analysis and call it a simply supported beam with a distributed pressure acting along it for loading. That would give me a fair approximation of the moment I think. It comes out to being larger than the flexure face moment, but given that the circular ringwall is 40' in diameter, it makes sense.

So my question...Does anyone have any experience in designing these sorts of foundations (octagonal OR circular mats) and have some good resources? I've read the paper on chimney foundations, but it doesn't address mats in the sense that I'm using them. I've also tried to research and read/buy every paper that's been suggested elsewhere on the internet. So far, NOTHING has given me what I consider to be a close approximation of the type of foundation and loading condition that I'm dealing with. I've tried to use STAAD.Pro to design a mat, but besides geometry issues, I just can't seem to get results that I feel comfortable with. I'm not about to put up a tank with a shoddy foundation!

Any help, suggestions, guidance, or general thoughts/ideas would be welcome. I'm more than willing to share whatever else I can in order to better guide the discussion! I feel like round and octagonal mats are like the ugly duckling of the foundation world - they seem to get pushed into the corner and never spoken about. Round and circular "things" are not always the most friendly to hand calculations I know, but anything is better than nothing I guess! Thanks all!

 

[Michel60]

Good morning nicoga,

Some one else will have to comment on the analytical approach but I will offer a few ideas on detailing:
1) keep the bar mats orthogonal if at all possible
2) I usually try to place a primary mat based upon the average demand and that is sufficient for minimum steel requirements. Run these bars continuous.
3) Place additional bars at higher moment areas at some simple division of the primary mat spacing. These bars could be a different size and would not necessarily be full length.
4) Be sure the minimum spacing between bars allows for placement of a pump hose, say 6" to 8". If you need more reinforcing add layers, don't reduce spacing. It is not unusual for thick mats the have multiple layers running in each direction. Be sure the maximum bar spacing for large mats is "walkable", say 16"max but 12"max is better.
5) Provide clear engineering diagrams of bar placement showing extents and order of layering


regards,
Michel

 

[JoshPlumSE]

Octagon foundation, in my experience, are really quite common. At least in the industrial world. .

I have not generally seen people try to reduce the size of reinforcent or increase the spacing of reinforcement in the regions of the slab which you describe. Question: what would happen if the earthquake or wind pressure where occur along a 45 degree axis rather than occurring parallel to your rebar layout. Wouldn't the steel in those areas be required to contribute to this resistance?

One other note: I have seen folks lay an extra bar or two parallel to the 45 degree faces at the edge of the slab. I believe this helps prevent temperature and shrinkage cracks along or near those edges where your orthogonal bars are not very well developed yet.

 

[BAretired]

For ease of placing, I would consider four bands of reinforcement placed at 45 degree increments. Each band would be 26' wide and 62'-6" long. I would add a few bars parallel to the edge in the low moment regions.

All band bars would be of equal length and the spacing in would be double what you would require for a purely orthogonal arrangement. The loss of effective depth as a result of having four way reinforcement would not be an issue if the footing has a reasonable thickness. Placing and vibrating concrete around the reinforcement would be much easier.

BA

 

[nicoga3000]

Thanks for the information folks!

@Michel60 - I appreciate the info. I'm making sure to work closely with our foundation department and concrete field head to make sure that we detail and lay everything out in such a way as to help our crew work as efficiently as possible.

@JoshPlum - you make a good point. I assumed that the rebar running in the XX and YY direction would cross that plane and contribute accordingly (so for XX and YY, you'd get ~40% additional reinforcement across that plane). Maybe that's an unfair assumption to make in this case, though.

@BAretired - I actually started looking at doing that this morning. The bottom mat started getting VERY heavy though (my analysis shows #10 bars required @ 7.5" O/C). When you consider that many bars, you're getting close to 60 kips of rebar on the bottom mat alone!

I still have one major concern regarding the analysis of the flexural demand on this mat. Again, I'm making some pretty rough assumptions, but if there were some information available for me to read (or some sample designs available to study?), I think I'd feel much more comfortable with my reinforcement on this beast.

 

[BAretired]

7.5" is an awkward spacing. Using 8", each band requires 26*12/8 = 39 bars (say 40). Total length = 40*63.5*4 = 10,160'. Weight = 4.3#/' for #10 bar. Total weight = 43,688# excluding perimeter steel. It is likely the most economical arrangement of bars available.

BA

 

[JStephen]

Can't pull up the image right now. But thick circular slabs under tanks are normally reinforced with orthogonal rebar mats, not radial/circumferential. Usually, the whole mat will be the same size, same spacing. Usually, the bottom mat will be the heavier of the two. If the rebar is too close, you can thicken the slab, use bigger bars, doubled bars, or a double mat.

 

[JoshPlumSE]

I've seen people do what BARetired suggested (multiple layers at 45 degrees). But, in my experience, it is not very common. The orthogonal reinforcment does contribute to bending resistance along the 45 degree line. In fact, it should be basically the same as the bending resistance along the main axes. So, I'm not sure how you can justify all that extra reinforcment. Though if he doubles the spacing then it becomes more reasonable.

The main problem is at the end of the mat (where the bars are not developed). But, there is very little flexure in that location and you probably only need to worry about temp / shrinkage cracks.

 

[JedClampett]

Is there some reason the thickness of your mat is limited? If you have #10's at 3 inches, that's telling me that you need more depth. Adding thickness to a concrete mat is very cheap, almost free. I'd try to keep the rho at less than 1.5% for one mat of steel. Plus if you're desiging an elevated water tank, that mass comes in handy for overturning, although with the size of mat you're requiring, that's probably not an issue.

 

[nicoga3000]

I've got a 4' thick pad at the moment. I may look at going to 54" to see how that helps. And you are correct JedClampett - OT on this tank is NOT an issue!

 

[OUDrew]

In terms of the analysis, you may look into Yield Line Theory. There are a lot of sources available, concrete texts and such. See the link below for a decent reference.

http://www.scribd.com/doc/95793294/18/Raft-foundations

 

[BAretired]

How is the mat supported? Only by a ring wall? Perhaps you should consider additional supports in order to reduce the maximum slab moment.

BA

 

[Michel60]

I think Jed's the one on the mark here, reinforcing in a properly sized mat foundation should just not be getting that dense. You seem to have an unusual supporting condition in terms of what I'd normally encounter, but if you make it 60" and can get bar spacing into the 10-12" range, I'd say do it . Also be sure to check the shear demand too. Trouble with moments and shear can often come in pairs for mat design.

regards,
Michel

 

[BAretired]

Increasing the mat from 48" to 54" is not going to make a huge difference in reinforcement. I am wondering if the OP is erring in his analysis.

BA

 

[nicoga3000]

Here's a simplified approach of my analysis. I'd be happy to provide additional information to anyone who may be interested in looking at things. I opted to do an upload to Imgur so others can take a peak.

http://i.imgur.com/FaVhL.jpg