modulus of subgrade reaction

[nate2003]

I am relocating a vertical CNC milling machine in my plant and am trying to determine the adequacy of the floor where I plan on placing it.

From old engineering drawings of my plant, the floor is six inches deep concrete reinforced with 6 in. x 6 in. WWF. Talking to my local city engineer (actually the city built this building years ago) he said that most likely there was 4 ft of "silty clay" that was dug out and replaced with 2.5 ft. of "pit run" (sandy gravelly mixture, compacted) and then 18 in. of compacted gravel.

I have an Army/Air Force technical manual that has some design guidelines in it. Based on what I can figure, my application would be considered to be a very heavy stationary live load. Based on that classification, I found a formula that says that

w = 257.876 * s * (square root of (kh/E))
where:
w is the maximum allowable live load (psf)
s is the allowable extreme fiber stress in tension, assumed to be equal to half of the normal 28 day concrete flexural strength, psi
k is the modulus of subgrade reaction, psi
h is the slab thickness, in
E is the modulus of elasticity (4E6 psi)

My problem is this: I do not know what to use for k (modulus of subgrade reaction), neither do I know what to use for s (allowable extreme fiber stress in tension.)

From values listed on a table in the technical manual, k can have values that range from 25 to 300 lb/in^3. Also, the flexural strength for concrete ranges from 550 to 700 psi. (This is where "s" is calculated from.)

I made a spreadsheet that calculated the maximum allowable loads for the entire range of k values and the entire range of flexural strengths. The worst case would be a k value of .25 with the weakest concrete (550 psi). I did this and got a maximum live load of 434 psi. Best case would be a k value of 300 and 700 psi concrete. This gives me a maximum live load of 1915 psi. Obviously quite a difference.

I have two scenarios that I am considering.
1) Placing the machine directly on the floor. The weight of the machine is 26455 lb and outside area of the machine is 92 x 54 inches. This gives me a projected area of 34.5 ft^2, and an average load of 765 psf. However the machine would be on feet and jacks, so there would obviously be higher concentrated loads at certain points.

2) Placing the machine on a steel plate several inches thick to evenly distribute the weight. This plate would be 120 x 150 inches and 3 to 5 inches thick. This would give me a live load of 334 to 436 psf depending on the thickness of the steel plate.

The first option takes me past the max allowable live load at the worst case. The second takes me almost exactly to the limit at worst case.

And finally the question:
Does anyone have a reasonable guess as to what k value I should use? Do these calculations seem reasonable? I have a degree in mechanical engineering and work as a manufacturing engineer/programmer, so I have no background at all in concrete design. I would like an expert in this area to let me know if I am heading in the right direction.

Thanks. One final comment. I only signed up with this site yesterday and listed my field as "mechanical". I would like to target geotechnical engineers with this question, but don't know to do it. I'm not sure how this works. Any ideas?

 

[DriveThru]

I'm new to this site too, but I think you need to cut and paste your question into a new thread in the geotechnical forum.

 

[SlideRuleEra]

nate2003 - The terms in the equations that you have sound like they may be from the days (1950's and before) when concrete structures were designed by working stress theory instead of current ultimate strength methods. Working stress is a technique for concrete similar to Allowable Stress Design (ASD) used with structural steel.
However back to your situation - Could you consider having a structural engineer design a suitable reinforced concrete mat that rests directly on the old floor? Perhaps it could be sized to reduce concerns about the allowable soil bearing pressure. Also it may give the opportunity to embed anchor bolts or tie downs if needed.
Best Wishes with your project.

 

[jheidt2543]

Here are a few thoughts to consider:

1. Does your CNC machine inpart any dynamic loads to the foundation? If so, I would not set it directly on the floor, use a separate foundation.

2. If the floor should fail under the machine, which is more expensive to repair the floor or your machine? Use a separate foundation.

3. Even if you don't have dynamic loads, it is difficult to know what the condition of the floor is. So, I would first verify the thickness of the floor. Secondly, verify the soil conditions with a soil boring or two.

4. When all is said and done, it is really better to cut out the floor, compact the subgrade and pour an isolated, separate foundation for the machine. I would GUESS that the foundation would be about 120" x 78" x 18"-24" thick with one mat of #6 rebar. I think that would be cheaper and easier to install than the 3" to 5" thick steel plate.

 

[Focht3]

An interesting question.

Regarding the modulus of subgrade reaction values: the range is pretty reasonable, although in general the low end could be lower and I have seen very few soil sites with values that approach anything near 300 pci for large machines or building foundations. High values of k are usually associated with small loaded areas, such as field CBR tests and plate load tests. Keep in mind that there is no such thing as "the" k value for a given soil. The use of k values represents a convenience to the designer. Please don't confuse k values with "real" soil parameters...


First, you need to look at the economics as [blue]jheidt2543[/blue] suggested. If you can tolerate the risk of floor failure and dynamic behavior is not a concern, then I would suggest that you go about 2 feet beyond the perimeter of your machine and saw cut all the way through the slab. (This is a larger area than [blue]jheidt2543[/blue] had indicated.) This will isolate the CNC machine and floor slab from the surrounding areas, limiting any damage to a specific zone. Frankly, I am more concerned about "failure" from consolidation settlement that some kind of dramatic, and catastrophic, slab failure.

If dynamic performance is an issue, then I'd strongly consider replacement similar to [blue]jheidt2543[/blue]'s suggestion. A large, shallow footing will give you better dynamic performance than deeper footings, driven piles, or drilled piers. You will need expert advice on the dynamic performance of that design...



Please see FAQ731-376 by [blue]VPL[/blue] for tips on how to make the best use of Eng-Tips Fora.

 

[cbosy]

It would also be a good idea to get a boring at the new location to find out what you really have.

 

[Focht3]

Oops! OF COURSE you need a boring - probably to a depth of about 15 to 20 feet; but you need to talk to your geotech about the depth and testing program...



Please see FAQ731-376 by [blue]VPL[/blue] for tips on how to make the best use of Eng-Tips Fora.

 

[BigH]

For dynamic analyses, depth of embedment of foundation is a very important and almost "overpowering" property. The damping coefficients due to geometry are much larger than the damping due to the soil. The old adage of foundation sizing: foundation to be 3x weight of machine - then, I'd think of embedding it sufficiently - say 1.2m or so. Ensure that backfill to foundation is well done.

 

[cbosy]

Focht3 did I catch you off guard?

 

[Focht3]

Yup. Serves me right, too! (How could I have overlooked field exploration and testing! Sheesh!)

No more posting messages after my bedtime! (Yeah, right!)



Please see FAQ731-376 by [blue]VPL[/blue] for tips on how to make the best use of Eng-Tips Fora.

 

[nate2003]

Thank you all for your responses. They are a lot of help. It is amazing to me all the responses that I got in such a short amount of time. I think that the most cost effective route for me to go is to saw out the floor to the manufacturer's recommended area, dig out the area to 2 feet, pack the gravel and pour 24" of concrete with two layers of rebar spaced 12" o.c. The original intent was to have something that was fast and mobile in case the machine moved again. That would save the jackhammering time and curing time for the concrete. However, the concrete is only half the cost and even less than that by the time I get cores done and hired a professional to evaluate it. Like jheidt2543 said, I think that it would be better on a separate foundation and if I try the plate and it doesn't work, then I'm out even more.

Thanks again to all.

 

[Focht3]

Hmmm,

You never indicated the machine's weight. You still have long term settlement issues to address -

You still need a geotechnical study.



Please see FAQ731-376 by [blue]VPL[/blue] for tips on how to make the best use of Eng-Tips Fora.

 

[dig1]

Equipment weight is mentioned at about 26.5 kips.

Totally agree that a geotech study is necessary.

After reading all of the above, I think you are taking risks that I would not take if it was my machine.

Consider the losses due to downtime if the machine is out of service due to settlement, if alignment causes parts to be machined incorrectly, etc.

I am aware of a project in my area where a few of borings and a good geotech report (not just soil boring logs!!) would have saved the owner over a million US dollars and several months schedule. The steel structure started to settle INCHES even before the siding, equipment, roof, etc was put on. They put the building over an old canal that had filled in and did not know about it until borings were done and a very old map reviewed. Piles and grouting was the backout solution.

 

[jheidt2543]

nate2003,

You should notice in my response above that my GUESS at the size of the machine foundation was made AFTER a borings and a soils investigation was suggested. We all hear war stories of problems resulting from ASSUMING things. Two borings and a soils report are cheap insurance!