MACHINERY FOOTPAD LOADING 1

[JT-1995]

I would like to toss out a conundrum that I have worked myself into. It is is unfortunately somewhat related to a 2022 post "Weight Distribution Over Six Points" that ended up being a time consuming adventure for several folks. My question relates to the footpad reactions that we structural engineers are given by equipment vendors. Often these machines are supported by several footpads, I have seen 5,6,8, often. So the footpad loading is given by the manufacturer, how they determined that may be a question (see the mentioned post from 2022) but they are what they are. Now we take those loads (as gospel?) and start to design a grid of steel and concrete to support the machine.

My question is, for the indeterminate foot pad layout of the machine that is assumed to be a very rigid weldment, would the actual load to the steel not be redistributed based on the relative stiffness of the steel support structure?

As an example, the hypothetical equipment vendor may tell us their 20ftx20ft machine is supported by 4 legs each having a footpad load of 10k. Lets say the NORTH two footpads are bearing on a concrete wall and the SOUTH two footpads are supported by a steel beam spanning 20ft. Is it accurate to say that that the two footpads on the very rigid concrete will "attract" more load than the two pads on the relatively flexible beam? If so, ok in this case the beam would be designed for a higher than needed load (designed for the two 10k), but replace the concrete with a steel beam that is 2x stiffer than the 20ft member in the original case and now the second beam is being design for 10k but in reality it would "attract" more load than that because of stiffness. In many cases the difference in this loading may not be enough to cause a failure (we don't design that tight typically) but what if the machine has very high levelness tolerance. Now the beam that has attracted more load will now deflect more than planned when analyzed at 10k loadings, is that true?

 

[JStephen]

If the machine just has 4 legs with stiffer supports on one side, it would just rotate slightly and supporting loads would remain about the same rather than "attracting" more load.
If there are stiffness requirements or deflection limits or levelness requirements associated with the operation or design of the equipment, those need to be communicated to the foundation/support designer as well as the loads themselves. If no criteria are given, I would assume there are no requirements. It might be prudent to confirm with the supplier. Those limits might be based on maintaining levelness, limiting loads, or more likely, vibration concerns.

 

[human909]

Is it accurate to say that that the two footpads on the very rigid concrete will "attract" more load than the two pads on the relatively flexible beam?

Not really.

If you only have 4 pads one in each corner with the COG in the centre then the stiffness of the beams aren't going to play a significant role unless there is a separate beam with different stiffness's under EACH foot. 4 pads is relatively easy though it is still indeterminate. 8 pads or even more is where it really is complicated.

But you really need to start thinking about what is happening at those 'pads'. Are they adjustable feet? Compressible elastomer? Something else? I can't say I've overthought the support for such machines, I design for the suitable load at each point while keeping deflections even and reasonable.

Things became fun when I was moving a 2mx4m 20tonne machine across a steel floor using 4 skates. I felt it was prudent to design for the full load bearing on only 2 skates. 10tonne bearing on a 100mm x200mm area creates an fun punching load for a steel deck and joists.

 

[milkshakelake]

In the case of a strong support versus a weak support, you can think of the supports at the two ends as springs. But however, we idealize them as pinned. In a pinned condition, they are equally stiff and will receive loading based on tributary width or whatever you get out of classical beam mechanics loading and shear/moment formulas.

If the supports are very weak springs, this will cause rotation in the beam (i.e. the mechanical equipment) and affect the loading onto the supports. The supports themselves, if loaded differently, will have differential settlement and cause further rotation and further imbalance. This would also possibly induce moments into the equipment. For the magnitudes of loading you're hypothetically talking about (10k and 20k), I think all of these effects negligible. They'd even be negligible in the realm of 500k. I think it's only worth considering if there is a strict requirement about deflection.

Also consider that the soil under the footings may have variable bearing pressure. Uniform bearing pressure is a myth, though a pretty well-substantiated one with a century of experience. It's just to say that I think the effects you're thinking of are wishy-washy at best, and a strict engineering analysis of it is more trouble than it's worth because all of this falls under tolerance criteria. (I might piss off some people saying that; sorry in advance.)

If you do want to do this analysis, it's very complicated because it will require a holistic model of both the subgrade bearing with soil spring stiffness and the equipment itself. And how do you analyze the stiffness of the equipment? There's basically no way. The mechanical equipment people I work with have their fancy ANSYS models of tanks and other stuff, and they just give us the resultant loading, not a beam model with I and E.

 

[BAretired]

My question is, for the indeterminate foot pad layout of the machine that is assumed to be a very rigid weldment, would the actual load to the steel not be redistributed based on the relative stiffness of the steel support structure?

Partly, but also based on the relative stiffness of the supports. If one footpad is bearing on soft soil, it may carry a reduced load, or no load at all. That leaves three supports, and with three supports, reactions are determinate irrespective of the relative stiffness of the superstructure or the foundation. With more than three supports, the problem is indeterminate.

 

[JT-1995]

Thanks for all of your thoughts.

Agreed, perhaps the 4 footpad hypothetical was a bit too "determinate". The issue is arising from a real world 70k cutting machine that is leveled and plumbed with lasers to within 0.001" using adjustable pads (there are 12 footpads under the machines). The support structure deflection is expected (historically) to be in the neighborhood of 0.05" as the machines are installed to allow the footpad adjustment to relevel the machine. So the variables that have started to cause me disbelief in ever being able to definitively know the footpad load is that the load on the footpad is related to the installation torque on the footpad installation bolt, the stiffness of the support itself, the stiffness of the machine body (it is indeed built with very heavy components and connections), and the relative locations of the footpads to the CG. I think that during installation each footpad is not in contact, rather key locations are used to level the machine and then the remaining footpads are lowered into contact (to some degree) and welded in place. I am afraid I am over thinking this.

I did make an FEA of the machine using extremely ridged framing and all of the footpads. I placed the machine on steel framing and ran the model. Things really looked ok on the surface (ie reasonable deflections in the steel where you would expect), but when I dove into individual member forces of the "machine model" things looked crazy. It seemed the extremely ridged members used to model the machine were attracting load back into the machine and transferring that elsewhere. Maybe that really is what should be expected, the loads will be redistributed based on machine/support frame stiffness? It seemed that in some cases the machine was cantilevering from one location over to a distant footpad and actually supporting the floor.

Maybe I need to stipulate on my drawings that the installation torque on each footpad needs to be within 10% of each other to at least try to control one of the variables. I can also design the stiffness of the support steel to be within 10% at each location under the machine. That way there are no "hard or soft spots" under the machine that will try to attract or shed load. Again, this seems overthought.

If the substructure needs to be designed to such a small deflection the proper loads are critical.

 

[milkshakelake]

If the deflections are that critical, I'd use a monolithic mat foundation instead of 4 individual footings. It takes a bit of guesswork out of figuring out the subgrade stiffness. The mat will also have rotational stiffness by itself.

 

[JT-1995]

Thanks for the thought but the machine has to be elevated about 10ft above grade and schedule does not allow concrete to cure. So steel will be needed to support the load down to elev 0.

 

[TLHS]

Yes, if you put a really stiff thing on a bunch of flexible supports, you're going to attract load based on the stiffness of the supports. The equipment either needs to be able to deal with that, or you need to make the supports

(a) more rigid than the equipment (which is likely not possible unless you're going to do a block, mat or wall style support
(b) contain a rigid element as the top-most point that will evenly bear against the equipment and distribute loads to the support (a big concrete block or deep steel skid on top of the support system) or
(c) do a reasonably good job of making the stiffnesses of the supports similar

With flexible supports and option c, you might have a hard time levelling the eqiupment, though, and you'd likely lose the expected load distribution during the process of levelling. It all depends on the amount of flexibility we're talking about, though.