Circular slab on grade 2

[Logan82]

Hi!

I have previously designed a standard slab on grade using ACI 360. But how would you calculate a circular slab on grade with rebars on top and bottom?

Are there some ACI provisions or some code provision for this type of slab on grade?

Thank you!

 

[dik]

I would treat it in a similar manner as a normal slab... with temperature steel moment resistance the same at 90degrees... (isotropic reinforcing). I would sawcut it radially into parts roughly equal to the annular width, assuming the annular width isn't too wide. If the annular width needed an intermediate sawcut, I'd reduce the radial ones to match that, not going greater than mayby 1.2. Depending on the geometry, the tangential sawcut may include 2 of the smaller radial parts. (I'm not sure that makes sense, but I understand it; I hope I described it OK).

It would behave in a similar fashion to a regular SOG.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[HTURKAK]

I would model the circular slab with FEM and analize it. The elements in this case would be part of a circle ..

The excerpt below to show the concept (from BOWLES , Foundation analysis and design )

 

[dik]

Unless there are unusual loads, I'm not sure that modelling it as an FEM model would serve any purpose.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[Logan82]

The annular slab on grade is supporting an old heavy alternator that was used in an hydroelectric powerplant (it is now used for display in front of a museum on a slab on grade). Dik, I agree that it needs to be sawcut radially for crack control, without cutting through the top rebars. But I would have thought that the shape would have had an impact on the reinforcement calculation (not sure though).

Thank you for the reference HTURKAK. Which software are you using to calculate slab on grade using FEM?

 

[HTURKAK]

My favorite software for FEM and analysis is, SAP 2000..

 

[dik]

I usually use 2" top cover and 1-1/2" dp sawcuts... if your slab is thick, then use greater depth of sawcuts and greater cover. Unless your load is exceptional, I don't think it will matter if the slab is annular or rectangular (considering edge effects of the latter). The kicker is that your orthogonal moment resistances are similar. With equal moment resistances in both x and y, the moment resistance at any angle is the same (or very nearly). If your loading is extremely high, or irregular, then an FEM picture is worth a thousand words... HTURKAK's FEM approach is good if it's a heavily loaded slab. Also his element pattern could be similar to the sawcut pattern for a large slab... with sawcuts at 15' or 20'; I suspect the slab could be 10" or more thick with the two layers of rebar.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[Logan82]

HTURKAK, I checked the section in your reference on ring foundations. In this document, they find the internal loads inside of each node, but they don't cover the modified resistance of the slab due to the shape. For instance, for curved steel beams, the resistance is reduced. I would have thought it would have been the same for ring foundation.

HTURKAK, how do you model the supports given by the ground in SAP2000? In fact how would you model a slab on grade using SAP2000?

I would model the circular slab with FEM and analize it

Would you say that FEM would be required if the loadings are simple (no moment, just downward force acting in a circle halfway between outside diameter and inside diameter)?

If your loading is extremely high, or irregular, then an FEM picture is worth a thousand words..

Why is it important to use FEM if the loading is high? Also what would be some example of irregular loadings that would require FEM?

 

[HTURKAK]

-you will assign vertical springs to each node. ( WINKLER MODEL) the same ref. book explains the concept..the same concept is applied to SOG.

- the nodes supported on Winkler springs for vertical.. you may assign some horizontal springs or horizontal supports at halfway nodes for stability

- FEM is applicable for all loading and foundation types . In your case , if the dia of ring foundation / width of ring is large
enough , and the loading at midway ,you may analize for a unit width ..

 

[JStephen]

If the slab is small enough, consider making it square instead of circular, and the easier analysis, forming, and rebar layout may offset additional concrete.
If the hole is small enough, consider eliminating the hole, running rebar straight at 90 degrees instead of radial/circumferential. The easier analysis, elimination of the inside forming and easier rebar setting may offset the concrete cost to fill the hole.
If the hole is large enough, you can neglect the curvature and treat it as a straight beam, a similar idea to HTURKAK's last sentence above.
If you treat the foundation as rigid on an elastic foundation, you can cut a cross section through the center and find total moment at that point.
Roark's Formulas For Stress and Strain includes circular plates with holes. The problem is, it does not address elastic foundations nor non-symmetrical loading like wind or seismic overturn.
Roark also includes curved beams, but still with sufficient limitations that it is not a useful tool for this.