moment in slab on grade
moment in slab on grade
(OP)
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






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