moment in slab on grade

[structures333]

Hey guys - I have a floating slab on grade (independent of structure) with 250psf LL and 75psf DL. I always designed sog's with t&s reinforcement, shear checks and other parameters like those in PCA Concrete Floors on Ground. I have a reviewing agency that wants to see a moment calculation for this slab... How do I provide a moment for something that is essentially fully supported and doesn't have a "span"? Thanks

 

[Ussuri]

Typically ground slabs are loaded discretely. If you had a true uniform load then there would be no bending in the slab. In reality your slab is subject to multiple point loads from vehicle wheels, legs of storage racks etc.

The modulus of subgrade reaction is not infinite so there will be 'some' movement at the point the loads are applied. The spacing of the loads also has an effect.

A publication used in the UK is "Design of Floors on the Ground" by JWE Chandler. It is a fair age now though, so there may be an update. It is however based on US research. In particular, JJ Panak and JB Rauhut, Behaviour and design of industrial slabs on grade, Journal of the ACI, Vol 72 No 5. How this stands up to more modern practice though I couldn't say.

Not withstanding this you may have pockets under your slab where, over time, you may get settlement or a ground water flow may effect it leaving voids, or the bloke driving the roller had an off day.

 

[civilperson]

Try a 7000 pound wheel load supported by a square of slab on grade concrete 5 foot on a side. See if temperature and shrinkage steel area/location gives sufficient moment capacity.

 

[UcfSE]

It's not fully supported. It's supported on an elastic medium that can deform (soil). Look for information on beams and plates on elastic foundations.

 

[youngstructural]

The above suggestions seem to be reasonable, and probably much more appropriate than what I will offer, however, in some cases you really just need a quick check. Not all slabs or loading situations justify/require more complicated analysis and design methods. I leave that decision to your engineering judgment.

A quick and dirty way of checking required moment is to invert the problem: Treat the supporting strata as a UDL and apply a point load (to be treated as a column). Then use yield line theory.

I personally wouldn't design this way, but if you've already designed your slab to your satisfaction, you might be able to satisfy the reviewing engineer.

You need to make absolutely certain that you understand the root of their concern(s). If you fail to catch something that later results in a failure which could have been caught through a check you were asked to make, I should imagine that there wouldn't be any recourse or defense.

Good luck,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[ExtremeFiber]

You can model your slab in a finite element program such as STAAD and model the elastic behaviour of the soil with the modulus of subgrade reaction. I have done this in the past with STAAD but it has been several years so I don't remember the particulars. I remember STAAD had a special function that would convert the MSR into spring supports automatically. I imagine other FEA programs have something similiar. Try doing a search in your FEA help menu for modulus of subgrade reaction and then read up on it. I remember it was a relatively quick process. Once you have your model you will be able to output any moment their little hearts desire anywhere on the foundation.

 

[minorchord2000]

There is good treatment of this in an old concrete textbook by Nilson I believe (from the 60s) that uses the work of Westergaard. He postulated a few good equations which account for modulus of subgrade values, proximity to edge of slab, and to interior joints. The equations give concrete tensile stress values which you can compare with 7.5 root divided by a factor of safety.

 

[youngstructural]

Hey Minorchord;

I'm very interested in your post, but can't quite understand. Care to provide a little mor detail? What do you mean by 7.5 root? Is this a reference to a code clause?

Cheers,
And thanks in advance,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[Galambos]

I would suggest reading the ACI 360 publication.

 

[minorchord2000]

Youngstructural:

I wish I were in the office where I can give you an exact reference, but alas I am home. However, when I say compare the results to 7.5 root, I mean that the results obtained from these empirical equations will be the resulting tensile stress in the concrete. Compare this result to what allowable the concrete code requires. 7.5 root is the 7.5*square root f'c/divided by a safety factor. Personally, I limit my tensile stress to 3 root. The treatment by Westergaard also include expression for the bending stress, fb, which you can compare to an appropropiate allowable concrete stress.

Hope this helps. Maybe tomorrow, I can give you the edition and page number of my reference.

 

[youngstructural]

Minorchord:

Thanks for that, and I would very much appreciate the reference if you are able...

I assume that the formula you have offered up is an empiracle, imperial units formula? Otherwise your resulting tensile stress would almost always be higher than your compression stress! I see that it would work much better in imperial units... Are you checking root ksi and yielding psi? I was always taught that the tensile capacity of comcrete is approx the root of the compressive strength. Thus in metric Limit States Design I would have:

fc' = 25MPa, tensile strength = phi*Root(fc')
thus = 0.85*root(25 MPa) = 4.25 MPa

An imperial equivalent from your 7.5*root would be:

Tension Strength = 7.5*root(25MPa*145psi/MPa)
= 7.5*root(3625) = 452 psi
= 3.11 MPa

Keen to see your reply since I find your tensile strenght to be VERY conservative compared to a metric formula equivalent... Might have missed something though, and I'm always keen to be corrected! How else can we learn of our mistakes before something goes wrong?

Looking forward to your reference, if possible.
Cheers,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[OldPaperMaker]

minorchord2000,

I have a copy of Design of Concrete Structures, seventh edition by George Winters, L.C. Urquhart, C.E. O'Rourke & Arthur H. Nilson published in 1964.
On pages 225 to 231 he talks about Slabs on Ground and refers to the work of Westergaard.

In the first chapter of this book the authors refer to the split-cylinder strength of concrete, f'sp, given by 6 to 7 times the sq. root of f'c and the true tensile strength, f't being 0.5 to 0.6 times f'sp.

I think that this text book introduced one to ACI's first crack at Ultimate Strength Design, which became Strength Design.

I hope that this helps.

 

[Miner99er]

I like this book.

Designing Floor Slabs on Grade: Step-By-Step Procedures, Sample Solutions, and Commentary (Paperback)
by Boyd C. Ringo (Author), Robert B. Anderson (Author)

 

[OzEng80]

My design code (Australian) permits a design stress based on a flexural tensile strength of 0.6 root f'c (with 1.6 S.F) for 'plain concrete' members. This is appropriate for 'members in which a crack will not induce collapse'. I have never understood how this can be adopted for cracked sections (which i have always assumed a SOG is assumed to be)....

 

[minorchord2000]

Oldpapermaker:

That is the correct reference. I mistakenly attributed it Nilson, but I have the same book that you referenced. It was my college concrete text. The equations in section 4.2 are, in fact, empirical.


Younstructural: you have to use different equations when using metric values. 7.5 root for US units will not be the same for metric units. You should use whatever your code allows you to use for the modulus of rupture. For the metric equivalent, use 0.62* sq root f'c in MPa. So for 30 MPa concrete, this equates to 3.40 MPa or 493 psi.