Unreinforced SOG design accounting for flue space 1

[ladisirt]

Hello,
I am designing a warehouse floor slab and the owner has requested the allowable rack load per upright. He has provided all necessary parameters, including:
- 100 pci subgrade modulus,
- 7" desired floor thickness,
- 48" x 96" rack leg spacing
- 4" x 6" baseplate size,
- 700 psi flexural concrete strength,
- 4,000 psi compressive concrete strength, and
- 2.0 factor of safety.

Sounds pretty straight forward, just use the appropriate PCA design chart and back into a maximum post load, right? My hang up is a 12" flue between racks. I have searched numerous times for a way to account for this without over conservatively assuming a single leg with double the load at the flue. Does anyone have advice on how to account for the 12" flue space?

 

[Ron]

Is the flue space a square hole in the concrete?

Why are you using a 700 psi modulus of rupture? That's not easy to get unless you use steel fibers. If you are using pumped concrete with relatively small aggregate, there's not a snowball's chance in hell you'll get it. I would use 450 or 500 psi.

As for the flue space, if my assumption is correct, find the radius of relative stiffness of the slab and if the flue space falls within that, then reinforce around the opening.

Post load will probably be on the order of 8-10 kips.

 

[ladisirt]

Ron,
The flue space is a 12" wide longitudinal space between back to back racks for fire protection purposes. The concrete slab is continuous, no holes or openings. The PCA design charts use either a single rack assumption with the same load at each post, or a double rack configuration with double the load on the middle leg. It is overly conservative to use double the load on a single post, but I also cannot ignore the close proximity of the two legs.

I am certain both post legs fall within the radius of relative stiffness, but adding reinforcing is not feasible. The owner wants flexibility in locating the racks.

The 700 flexural strength is verified by beam break. By the calculative MOR method you need a compressive strength north of 6,000 psi, which is unlikely. However, it is common in my area to see 5,000-5,500 psi compressive breaks on the 4,000 psi spec mix.

The controlling factor will be tension on the underside of the slab, as the individual post loads will not be very high. Does anyone have a recommendation on accounting for the close proximity of the post loads? I am willing to do an FEA analysis, but am unfamiliar with modeling such a situation.

 

[RHTPE]

ladisirt - What is being stored on the racks? In my experience I have found that those who work in warehouses pay little attention to the load capacity of the racking - their concern is focused on item location and how it fits into the order picking process. My previous employer had numerous rack collapses due to overloading. Perhaps your 2:1 FS will cover it. It's easier to replace a rack member than to repair a cracked floor slab.

Ralph
Structures Consulting
Northeast USA

 

[Ron]

Thanks for the clarification. Now I see the dilemma. No, isolated reinforcement would not be good.

I agree with Ralph.

I still think your 700 psi MOR is ambitious.

As for analysis, I would do an elastic layer analysis of the slab to check the tension at the bottom. This can be done by hand or by a computer program such as Everstress (free download from State of Washington DOT). You're only considering a single layer sitting on soil, so you could easily do by hand (See Yoder and Witczak "Principles of Pavement Design", 2nd edition. This will show you the influence of one load on the other.

 

[ladisirt]

Ron,
Great advice! I've downloaded Everstress and worked through a few iterations. I've modeled a two layer system, with my 7" concrete slab sitting atop the subgrade, ignoring any extra boost from my drainage course. The stresses make sense, with negligible stress at the midpoint of the slab. For the resilient modulus of the concrete, is it acceptable to use the elastic modulus in it's place? Also, I found a calculator from the American Concrete Pavement Assoc. and backed into a resilient modulus of 1940 psi for 100 pci soil. Does this sound reasonable?

Ralph,
The storage has yet to be determined. The owner wants to know what the slab can handle (and get it in writing) so as tenants come and go there is the least amount of uncertainty as possible.

Thanks again,
Bob

 

[Ron]

Bob,
I would use a higher resilient modulus for the soil. 2ksi is pretty low..comparable to a soft clay or silt.

If subgrade is reasonably competent, I'd use 8 to 10 ksi.

As for the concrete, use the elastic modulus, probably on the order of 3 x 10^6.

If you keep the tensile stress to less than 50 percent of the allowable modulus of rupture, then you don't have to worry about repetitive loads.

You might also check the forklift traffic on the slab. That's usually more rigorous than the static post loads. Consider proximity of the forklift loading to the post loads as well.