Deflection of slab-on-grade
Deflection of slab-on-grade
(OP)
Is there a way to approximately calculate the deflection of an existing 5" slab-on-grade, 6" granular stone base under it, when subject to a concentrated shoring post load of about 5000 pounds)?
The soil under the granular base is quite stiff (at least 200 pounds per cubic inch coefficient of subgrade reaction). The slab-on-grade has been in place for many decades.
I ask the question because we have to temporarily support a high pressure steam line that is currently suspended at 8 foot centres from the floor above, but the floor above is about to be repaired and the suspension hangers will of course be temporarily ineffective.
The plan is to temporarily support the steam line with steel A-frames at 8 foot cetres which are supported on the existing slab-on-grade.
When the suspended slab above is demolished, its load will be transferred to the shores and from them to the slab-on-grade, which may cause a bit of deflection of the slab-on-grade thereby causing the A-frame to move down a bit. My feeling is that the movement is tiny, but I would like to have a calculation to prove that. So the question is how to calculate is my question. An approximate type of calculation method will suffice.






RE: Deflection of slab-on-grade
RE: Deflection of slab-on-grade
RE: Deflection of slab-on-grade
RE: Deflection of slab-on-grade
wmax = PL2/8k, where w = deflection and L = lambda.
L2 = SQRT (k/D), where k = modulus of subgrade reaction.
D = Eh3/12(1-nu2), where nu = Poisson's ratio for the plate/slab-on-grade and h = the plate/slab-on-grade thickness.
RE: Deflection of slab-on-grade
RE: Deflection of slab-on-grade
Thanks very much. Much appreciated.
RE: Deflection of slab-on-grade
I have verified that Hokie93's formula will give the same answer as my (infinite) spreadsheet provided in the latter you use an adequately small loaded area. So provided you satisfy Hokie's warning about the load being sufficiently away from any slab edge you should use his formula. It will be much quicker.
If your load is close to a slab edge you could use my (semi-infinite) spreadsheet, with your load applied over a small area positioned exactly at the edge.
RE: Deflection of slab-on-grade
Are there equipment nozzles or some other items that might make you worried about an exact deflection number?
Just as a rough idea of what we're talking about... Let's say you have a 6"x6" plate on your shoring. Let's project the load through the 5" thick concrete to the subgrade at a 45 degree angle, neglecting bending. Your load would be acting over a 16"x16" area of the subgrade. At 200lb/in^3 stiffness and a stress of 5000lb/256in^2 you get a deformation of about a tenth of an inch. This isn't right, but it's probably right enough. I don't think you're going to have to worry about this unless your system is really sensitive.
At 10kips/8ft of pipe, though, this is a pretty serious install.
Also, here's a fun article for structural point loads on slabs on grade:
http://www.structuremag.org/wp-content/uploads/201...
It's about strength rather than serviceability, but it still might be useful.
RE: Deflection of slab-on-grade
wmax = c * PL2/k
using the same symbols as Hokie93 used.
In this formula c is a numerically determined coefficient whose value varies slightly with Poisson's ratio as follows:
nu c
0.0 0.404
0.15 0.426
0.30 0.461
0.50 0.521
I no longer have access to Timoshenko's book. The fact that "my" c varies with nu adds raises a suspicion that the Timoshenko formula should also vary slightly with nu. If so, then presumably the given formula applies only to some particular value of nu. But then the exactness of Timoshenko's coefficient (1/8) hints otherwise.
RE: Deflection of slab-on-grade
RE: Deflection of slab-on-grade
Some polymer modified concretes can have a higher Poisson's ratio. Dynamic loading will also increase Poisson's ratio as compared to static loading.
RE: Deflection of slab-on-grade
Thanks again everyone for the help.
RE: Deflection of slab-on-grade
The A-Frames holds up part of the floor too?
I'm significantly less worried if it's a small-ish steam line.
RE: Deflection of slab-on-grade
To TLHS: No; the "A" frames hold up only the pipes. The load on the "A" frames is tiny. The issue is the load on the nearby shoring posts that temporarily hold up the slab above; these shoring posts will bring load onto the slab-on-grade, causing it to deflect; the "A" frames, being supported by the slab-on-grade will go along for the ride. I probably did not make this clear in my original description, so thank you TLHS for giving me the opportunity to clarify.
If the shoring posts (not the "A" frames) are placed at 4 feet on centres around the perimeter of the new temporary openings that will be made to get at the corroded rebar and repair it, then the load per shore (not the "A" frame) may be in the range of perhaps 5,000 pounds per shore, although that is probably grossly overestimating the load, but I don't know how to calculate that without doing a computer model, but I am only just trying to get a "rough feel" for the deflection. I think the procedures that you and Hokie93 and Denial have provided to me should suffice.
(Complicating it all is that we have now found by GPR, and confirmed by cores, that there are locations of significant voids (up to 4") under the slab-on-grade in some locations. So of course my question relates to those locations where there is no void under the slab-on-grade).