Are slabs on-grade really this strong? (Punching Shear) 3

[Kilgore]

One of my fellow engineers wants to place a 75-kip concentrated load on our 250 psf-rated floor. At first, I thought it unwise (okay, downright stupid) to load to 300 times the rating, but then I ran a column punching shear calc and found it to be plenty strong. Can this be true?

Here are the numbers:
Load is placed on a 1’ x 1’ bearing pad
8” thick slab on grade – 3” cover = 5” to bars (assume #4@12” is sufficient reinforcement)
f’c=4000 psi, soil bearing=3000psf,

So, the shear cone spreads to 12” + 2.5” + 2.5” = 17” (square). At 3000 psf, the soil can take 6.0 kips (already huge compared to 250 lb for 1 sq ft of load)
The surface area of the shear cone is 17” x 4 sides x 5” = 340 in2
Shear strength is 4 x sqrt(f’c) = 253 psi, so the concrete can resist another 86 kips.

So, our 250 lb/ft2 floor can take a 92000 lb load on 1 square foot. Bearing is fine. Are slabs always this strong? Is there some failure mode I’m forgetting?

 

[OHIOMatt]

Your analysis approach makes the assumption that the slab is infinitley rigid and thus the soil supporting it will be uniformly loaded resulting in pure shear. It is not this simple. I would suggest you research the Westergaard Method of analyzing slabs on grade.

In the Westergaard Method you will model the soil as a series of compression only springs. This will result in slab bending as well as shear.

Bearing capacity will not be the primary soil property that you need to run this analysis. You will need the modulous of subgrade reaction (usually between 100 and 200 pci).

 

[cap4000]

If you can check ACI-360 it uses a Modulus of Rupture and a Safety Factor with a Radius of Relative Stiffness formula. Yes your number is high.

 

[ron9876]

Also don't forget your load factors and phi factors.

 

[JoshPlumSE]

I tend to look at it a little bit differently than you.

1) I calculate the puchning capacity of the slab (4*bo*d*sqrt(fc) = 86 kips) and reduce it by my phi factor. That gives me a base punching shear design capacity of 0.75*86 = 64.5 kips

2) I can increase this slighly based on the ACTUAL bearing pressures (due to regular loading of your slab). However, I do NOT use the soil bearing CAPACITY to do this.

My rational is that the punching shear and soil failure happen at different deflection levels. The puching shear is a brittle failure that happens at very low deflection levels. Whereas there would likely be some decent displacement that would have to occur before the soil can be considered to be fully loaded.

I suppose this is similar to what OhioMatt is saying.

 

[BAretired]

I go along with "unwise (okay, downright stupid)".

BA

 

[Kilgore]

Thanks, folks.
Okay, fair enough on the soil pressure. Thanks for the Westergard tip. I think the pre-pour site prep and tamping, as well as the current floor loads give some continuity to the soil resistance, but I wouldn't mind leaving it out of this estimate since it's small compared to shear in the concrete.

Thanks for the reminder about understrength/overload factors. I can't imagine a slab failure resulting in anything dangerous - just expensive. But thanks for at least checking my order of magnitude. 75 is sooo much bigger than 0.25. I really needed a sanity check.

 

[ToadJones]

what is the load from?

If a column, you should probably install a proper foundation.

 

[slickdeals]

You might also be interested in this article from StructureMag

http://www.structuremag.org/article.aspx?articleID=613

 

[ishvaaag]

An evaluation as per Menetrey in ACI SJ, pdf printout

 

[ishvaaag]

The same with the blackboxed calculations expanded to be seen

 

[ishvaaag]

And the Mathcad 2000 Professional worksheet just in case someone wants to get it

 

[Kilgore]

Thanks, Slick. That's probably the most appropriate article in the visible universe.

Ishvaaag: I'm an engineer, not some fancy theoretical scientist! Seriously, great analysis! It shows how the code shortcuts are based in reality. Thanks for that.

 

[RareBugTX]

Thanks for the File ishvaaag!, am just going to convert to USCU.