Changing structures over time 3

[Danielsp]

Hello folks

I am a civil Engineer, M.SC. in structures Engineering and I model and design structures, mostly using FEM.

Right now I am interested in static modeling structures that change over time. Some cases are really simple, for instance:

1) If you load a structure then remove some part of it while keeping the same load, then the new moments, shear forces and strains can be easily obtained by simply ignoring the original structure. You load the new structure and that's it.

2) If you apply Load 1 on Structure 1, then add a structural element to it and finally apply a new Load 2, then the final state of forces and displacements is obtained by adding L1 on Structure 1 to L2 on structure 2.

So far, no big deal.
But what if after the first load you add a new part to the structure while loaded and then remove an old one?

 

[driftLimiter]

Well I suppose you go ahead an analyze the resulting structure to get internal forces and deflections?
I think you need to be a bit more specific with your question, I am sure that your not looking for such a trivial answer.

 

[rb1957]

"2) If you apply Load 1 on Structure 1, then add a structural element to it and finally apply a new Load 2, then the final state of forces and displacements is obtained by adding L1 on Structure 1 to L2 on structure 2." ... no, I don't see the displacements of Structure1 being relevant to Structure2.
Structure1 under Load1 gives Displacement1 (or 11)
Structure2 under Load1 gives Displacement1' (or 12)
Strcuture2 under Load2 gives Displacement2 (or 22)
Structure2 under load1 and Load2 is Displacement1'+Displacement2

"But what if after the first load you add a new part and then remove an old one?" remove the old what ?

And this assumes small displacements. Superposition can fail under large displacements.


"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Danielsp]

rb1957, remove any part of the original structure after you added a new part. Could be a beam, a plate, a shell, whatever.

 

[Danielsp]

driftLimiter, but how exactly do you go about that?
If you apply the load to the new structure, it will not lead to the results you are loooking for.

 

[driftLimiter]

To be honest I have no idea what your asking. How is the structural model supposed to know or care about what some other version of it was? Are you trying to envelope the results from multiple configurations? If thats what your after you need a structural analysis toolkit that allows for phased construction.

 

[XR250]

I have no idea what you are talking about.
Seems like what we normally do in the process of optimizing structures.

 

[BAretired]

I think you must use good engineering judgment about how the modified structure will behave. When in doubt, be conservative.

BA

 

[rb1957]

"rb1957, remove any part of the original structure after you added a new part. Could be a beam, a plate, a shell, whatever."

so you're asking "But what if after the first load you add a new part and then remove an old one?" to paraphrase ... create structure 2 by adding to and removing pieces of Structure 1 ... a new structure needs a new FEA. Structure1 displacements are irrelevant to Structure2.

Now you can remove the effect of a structural component by, knowing the load in it in Structure1, applying an opposite load to the Strcuture1' ...
Structure1 under Load1 gives Displacement1, and the load in ElementA is PA
Structure1' is Strcuture1 with ElementA removed
Strcuture1' under Load-PA gives Displacement2
summing Displacement2 and Displacement1 gives you the displacements for Structure1' under Load1 ... although why you'd bother is beyond me.

Something similar we do is "Fail Safe Structure Analysis" where we'll fail discrete elements and see how the load redistributes through the structure.
Running several models under the same loads.

As before, superposition assumes small displacements.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Danielsp]

driftLimiter

The model "knows" what the previous version is because the new part whas added while the load was applied! Stresses, strains, displacements... the whole shabang. Then you have a new structure with old parts already under stress and a new one that is not. Finally, you remove another part of the structure. Like I said, the order matters.
1) Apply load
2) Add new part to structure
3) Remove old one.

 

[Danielsp]

rb1957, you not only create a new structure... you create a new structure in which some elements are stressed and others aren't. You keep missing the critical part, which is the fact the you do not deload at any point in time.
Simple removal of items in a structure while under a given load is really the same as if you deload and reload in between. It really doesn't change final results.
But if you ADD new parts to a structure that is already loaded and the load is never removed, the results are quite different from deloading, then adding the new part and loading again. Any part that you add to a structure while loaded will not be under any stress or displacement.

 

[Danielsp]

Maybe some of you might be confused by the fact that in the particular case of structures that both begin and end as isostatic, the order of events in time doesn't really make any difference whatsoever to the final results. But in the case of hyperstatic (indeterminate) structures, the order matters.

BTW, rb1957... your proposal does not include the adding of a new part. That is crucial. If you only remove stuff, then the problem is trivial.

 

[phamENG]

You keep missing the critical part, which is the fact the you do not deload at any point in time.

When did you state that? It's not reasonable to assume it. Normal practice is to remove as much load as possible while making these sorts of modifications. Two reasons off the top of my head: 1) safety of the workers (welding on a transfer girder carrying a few hundred kips doesn't sound like a good idea to me) and 2) simplification of analysis.

But to your question...which I think is most applicable to shoring applications...you just have to maintain awareness of the state of stress in each member in the system as you modify it.

1) Analyze the system and determine stresses in the members at critical points (or just come up with the bending and shear diagrams so you can derive stresses at critical points later).
2) Add a support. If the load doesn't change and you didn't jack it up at all, your stresses will remain the same. This is where an understanding of the situation is required. Is there full live load on it when the post is installed? Full dead load? If full live load, then it gets interesting because when live load is removed you'll have uplift at the new support. So you have to figure out the most plausible scenario(s) (and/or code required scenario(s)) and determine the state of stresses for those.
3) Remove the other support. If you have multiple scenarios, you'll be getting into multiple permutations to figure out the final stress. As long as you're in the linear elastic range, you can just use superposition here.

Probably best to use judgement to figure out what the 'worst case' permutations will be and envelope it.

 

[Danielsp]

phamENG, I edited my opening post to make it even clearer. There are no multiple scenarios, just the one load.

I see no way to use superposition here, what exactly would you superpose to what?

 

[phamENG]

In that case, it's really simple.

For a case where you start with a simply supported beam, add a support somewhere between the first two, and then remove one of the first two (you didn't define the structure or the location/direction of the load)

1) Analyze the original beam, find the displacement of the beam at the point of the new support.
2) Add the support. Since the beam is already carrying the full load and you said we're not unloading the original structure, the load on the new support is zero and the deflected shape remains unchanged.
3) When the support at one end is removed, the beam will find a new equilibrium and, since it's a determinate structure, you won't get any "locked in" stresses (unless you want to go deep in the weeds an look at steel residual stresses, creep in wood/concrete, etc.). What you will have is a slightly sloped beam - because you do have a locked in displacement where the support was added.

 

[Danielsp]

Yes, phamENG. Youe are absolutely right, that is the case for isostatic structures - only for those, though.
But as I stated in my 3 Aug 22 12:45 post, hiperstatic structures will keep some locked in stresses. That is the whole point.

 

[rb1957]

redundancy (and it's hyperstatic) doesn't matter. If you change the structure (subtractive or additive) you change the internal loadpaths.

Of course, if you have a determinate structure and remove a support (or the loadpath to a support) then you have a mechanism (and not a structure).

If you have a redundant structure, then you can remove internal components and still (maybe) have a structure. As I said above this is "Fail Safe" analysis.

But you need to run each of your structures.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[phamENG]

Hiperstatic? I'm guessing you mean hyperstatic? Or maybe it's spelled different where you are. Don't know. It's a bit esoteric...I've never met anyone who actually uses that term. Everyone I've ever met or worked with calls it 'indeterminate.'

You'd still find the stresses the same way, but you have to use indeterminate analysis techniques. You'll account for any 'locked in' stresses with the displacement at the new support location.

Next time, post a sketch.

 

[Danielsp]

Yes, phamENG... I'm sorry for my misspelling.

 

[Brad805]

It takes 5min in bluebeam or some other software to draw a proper sketch.