multi cell circular concrete structure

[bjb]

We are considering taking on a project that involves the design of a multi-cell circular concrete structure, specifically a combined digester and settling basin. The chambers are separated by concrete slab, which has a hole in the middle through which a shaft passes that drives scrapers. The diameter is about 40 feet, the overall height is about 30 feet, with the slab located about 10 feet down from the top. I have checked the PCA document for the design of circular concrete tanks, but the slab with the hole seems to put this structure beyond the scope of the PCA book.

My question: Is anyone aware of a design guide for a structure as described above? I have contaced PCA and have not heard back from them yet. ACI 350 doesn't give any design aids for the design of environmental structures.

 

[tincan]

?does one chamber sit abover the other? would the slab at 10' depth be supported by the claifier ring only or have column supports below? if supported by the ring it probably will be a circular plate/fixed end conditions.
have done similar but with rectangular configuration, or single circular only.
best, tincan

 

[bjb]

one chamber sits above the other, and the slab is only supported at the exterior wall of the vessel. My problem is that at the moment I don't know how to accurately analyze a circular slab with a 4 foot diameter hole in the middle, and I don't want to try to model it on computer without knowing how to do it by hand. I figure the fixed end moment at the perimeter of the slab could be resolved in the tank wall with a compression ring at the slab bearing and a tension ring at the base of the tank wall.

 

[JStephen]

Check "Formulas For Stress and Strain", which does have formulas for circular plates with holes, also cylindrical shells. It will get a bit involved tying the two together (ie, analyzing the two together). You will have tension at the interface (from expansion of the wall) as well as shear and moment.

I assume you mean that the lower chamber could be empty while the upper chamber was full, which of course puts substantial loads on the slab (and on the footing under the shell). If operating conditions were such that both chambers would always be filled, the only load would be the dead weight of the slab, which shouldn't be hard to support.

In the steel tank business, we periodically get inquiries from people that want to divide tanks, either with a diaphram across as you indicate, or with an inner and outer tank, or with a vertical divider. In all cases, it estimates out cheaper to build two separate tanks. In the case of concrete, I think the inner-outer annular tanks would work okay, but otherwise, I'd suggest comparing cost to two separate tanks as an option. Unless, as mentioned, the chambers are maintained full at all times.

 

[tincan]

A 4' diameter hole would be akin to a hatch or MH lid. I think PCA has something on circular caps for. Will check and reply.
Tincan

 

[tincan]

Check PCA (Portland Cement Assn.) for a bulletin on "Circular Concrete Tanks" they give the radial and tangential moment coefficients for moments in a circular slab without center support. Don't have the exact title, mine has been misplaced/borrowed. However, the coefficients are:
POINT
0.0R 0.1R 0.2R 0.3R 0.4R 0.5R 0.6R 0.7R 0.8R 0.9R 1.0R
Radial Moment Mr
.075 .073 .067 .077 .043 .025 .003 -.023 -.053 -.087 -.125
Tangential Moment Mt
.075 .074 .071 .066 .059 .050 .039 .026 .011 -.006 -.025

Moment = Coeff x pR^2 (p = uniform loading)
+sign denotes compression in surface loaded.
0.0R denotes center of slab,
best, Tincan

 

[bjb]

Thanks tincan. I contacted the PCA, but they have not gotten back to me yet. I am concerned about the effect of the hole in the middle of the slab. Roark's Formulas for Stress and Strain does consider circular slabs with holes in them, but I don't think that concrete meets the assumptions that the formulas are based on. I'm thinking that we might pass on this project.

 

[JStephen]

Note that the above is for a slab without a hole in it. Case 10b, Table 24, in the 5th Edition of "Formulas for Stress and Strain".