Thanks CTW. So, are we saying that the method I used ("equivalent footing" method, if you will) is conservative? It seems like we're all in agreement that there is no definitive solution to my particular condition (overturning moment on a slab on grade). I'm still a little confused at what people think is the best estimated method. Equivalent footing? BOEF? FEA software? Other? I'm okay with neglecting the fact that the steel might not be exactly in the right place, etc., as I consider the safety factors to account for that. I just need a method of analysis to hang my hat on. Conservative is okay.
if it comes to it, maybe you could install a larger grouted sole or bearing plate underneath the robot base. This might not be desirable for the robot though as it will change the height of the machine.
Thanks, Toad. Yeah, I'm considering increasing the size of the baseplate. But, I'm still faced with having to analyze the slab somehow, no matter how big the baseplate is.
Let's say I can make the baseplate as big as I want it. What's the best method to analyze the slab? Does a gigantic base plate simplify the slab design any? Would that make the equivalent footing method more logical?
Toad or CTW,
Perhaps you can explain why you think my method is not conservative. It is just a spread footing, with slab on ground connected around the sides, but ignored in the analysis.
hokie66-
I'm glad you posted this question as it kept me in check. I should have re-read my initial post and slowed down a bit before I responded with "may not be conservative". I don't know where my brain was on that post as that's certainly not what I think. It's been a long week and I was tired when I responded.
So let me formally retract my last post stating the "equivalent footing" method "may not be conservative".
zstructural-
Yes, I was stating (in a round about way) that hokie66's "equivalent footing" method is conservative. What I was trying to point out was that your 4 ft cantilever may be sufficient afterall. You stated that it was "just undersized". Your analysis is based on a cantilever or single spread footing which doesn't actually exist, which isn't a bad thing. You instead have much more slab surrounding this cantilever. So the behavior is not a true cantilever and the moment used in the analysis may not be as high. Therefore the slab may be adequate. It would be a judgement call at that point but I think you can justify calling it good if your analyis results are not too far over the allowable.
I liked Ron's approach and would have started with that since it may be difficult developing enough tensile capacity from the 8" slab. But it may be fine depending on the number of bolts, type of post-installed anchor and the tension required.
If that checked out, I would have gone to hokie66's method to check the slab capacity.
There's no defined method that I'm aware of for this situation. It's going to take being confident in your assumptions, making sure those assumptions are realistic, being comfortable with your analysis method and results, and using your engineering judgement.
We don't know what actual moment or reiforcing size are used in your analysis, so only you can determine if what you've done is conservative. As long as you feel there is a sufficient safety factor to cover any unknowns, then you can probably hang your hat on your decision and methods used to arrive at your conclusion.
It's a neat problem. Keep us updated on what you decide and what methods you used in your final analysis.
when I say it "may not be conservative" I actually am wondering myself....not saying that it definitively is not conservative.
My problem is this....this problem is more along the lines of plate theory and plate stresses then a straight up cantilever bending moment. The stresses at or near the baseplate may be much higher since the slab that we are treating as a cantilever is not a true cantilever and in reality cannot rotate like a cantilever due to the constraint of the surrounding slab.
It would seem to me that the greatest stress concentrations would be very near the base plate leading me to believe that a giant "equivalent footing" may not be the best representation.
Also, the thinner the slab, the shorter the distance from the base plate I would feel comfortable using in checking overturning. Certainly if you bolted a basketball hoop or the like to your 100'x20'driveway you wouldn't count your entire driveway in checking overturning, would you? Bad and cheesy example, I know.
I don't know this for sure; just voicing concerns I might have.
Thank you everybody for your input. This has helped me, if for no other reason than to bounce it off of you, and know I'm not way out in left field - and hear that the equivalent footing method is logical (if used in a logical manner).
I feel comfortable using a large enough area to resist overturning, as long as that area checks out for the cantilever. Toad, to your basketball hoop analogy, I would say if your driveway was 24" thick with reinforcement, you could use a pretty large area to prevent overturning. In other words, as long as I can get the cantilever to check out, that distance/area would be okay to use in resisting the overturning. That's my thought process. Let me know if you disagree.
I'm ending up making the plate a little bigger so the numbers look a little better on paper, and I'm not relying too much on my engineering judgement. That way if someone screwed up the rebar 30 years ago, or something, and the slab starts cracking, I can numerically prove that what I designed, given my parameters.
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