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Arch building stiffness - calibrate model with reality

Arch building stiffness - calibrate model with reality

Arch building stiffness - calibrate model with reality

(OP)
Well I've got a real interesting problem at work. Some testing was done on arches in an existing wood storage building (see attached sketch) to determine deflections under load, and I've been asked to make a FEM model that can match these and thereafter be used for reliable analysis (knocking out some conservative assumptions we'd make in design). I've matched deflections reasonably well for interior arches, modelling arch connections as pinned, and adding in the 5/8" plywood roof and 2x10 purlins @ 20" o/c. When I get to the arch with rod bracing on either side though, I'm getting deflections ~60% in excess of what was measured (measured deflections here are much smaller than for interior arches). I've modelled the bracing with pre tension (this does very little in the model and hand checks I did suggested that would be the case) and I've modelled the end wall as roller supports free in the long direction of the building. Curious to see what other people think of this problem. Deflections in the order of 1-3 inches all around FYI.

RE: Arch building stiffness - calibrate model with reality

I would expect the truss with the bracing on either side to deflect roughly the same as the remaining interior ones. The rod bracing doesn't do much (anything) for vertical resistance.

Actually, the more I think about it, I guess whichever arch would be acting as the top chord of your horizontal truss would be in compression and might push that arch up giving the appearance of less deflection.

But I could just be talking out of my ass.

RE: Arch building stiffness - calibrate model with reality

(OP)
I think these braces don't actually do anything, and that plywood acting as shear panels over the whole roof is probably stiff enough to take all the lateral load. But I doubt that's how it was designed originally. It can't hurt to throw some compression into the arch and see what happens though.

RE: Arch building stiffness - calibrate model with reality

So what are your results for the arch with rods, both analysis and testing values?

As I said I would have assumed the deflection was the same for all interior arches. I can only guess that the testing numbers revealed it deflected less than expected.

The other thing you need to keep in mind, old wood was super strong and highly variable. It is entirely possible that the one arch is made out of stiffer material than the rest or that perhaps the connections at the base are performing better.

RE: Arch building stiffness - calibrate model with reality

(OP)
Deflection in the interior arches is around 2.3 inches (11 measured, ranges from 2 1/8" to 2 5/8"), and the two braced arches deflect only 1 1/4" to 1 3/8". Should note we have no data on the arches immediately beside the arches in between bracing. Everything else seems too consistent to be explained away by stronger wood. In my model these arches are 20% stiffer due to end wall effects, but I need to see increases of roughly 100%.

RE: Arch building stiffness - calibrate model with reality

It sounds like your model is causing your braces to transfer vertical loads to the arch in a way that's not happening with the structure. Can you make the rods "tension-only" members and see what that does?

RE: Arch building stiffness - calibrate model with reality

(OP)
The rods are tension only, with 500 pounds pre tension. I'm worried what's happening is the exact opposite of what you described - because the rods don't significantly affect stiffness in the model but in reality these arches are much stiffer.

RE: Arch building stiffness - calibrate model with reality

Hmm...well, can you make the rods "compression only" members?bigsmile

Probably not as I've never heard of a modeling package with that as an option but what happens if you remove the pre-tension?

In any case it sounds to me like the rods are pulling down the arch in the model but not in reality.

RE: Arch building stiffness - calibrate model with reality

That's an astute point archie. Have you made your rods density near zero. You don't want them bending due to self weight and skewing the results.

RE: Arch building stiffness - calibrate model with reality

(OP)
In STAAD, the tension only command prevents any bending in the member. I should clarify that the test load was ~36 kip applied to a single arch, so it looks like the bracing would be pulling up on the loaded arch in reality and this isn't happening in the model, nor can I get any meaningful pull up from rods when I do hand calcs.

RE: Arch building stiffness - calibrate model with reality

Will your support detail on the other end really let it behave like that (translate laterally)? Even if it does, you may want to check the reactions: sometimes the thrust load is very high and it will move; sometimes not (due to the resistance of sliding friction; it depends on the arch geometry). In any case, if the support is laterally displacing, that can facilitate deflections at the crown.

RE: Arch building stiffness - calibrate model with reality

(OP)
For reactions, I've assumed pinned on both ends with no lateral displacement. Each end of the arch sits on piled foundations, I think this is more than reasonable.

As far pre tension goes, an increase to 50kip of pre tenstion stiffens the arch ~11%. Obviously this is not realistic and probably not where I'll be able to account for the measured deflection.

RE: Arch building stiffness - calibrate model with reality

Firstly, ignore the wheels in my sketch below. There should be no wheels.

This is an interesting problem. I've got a theory to submit. KootK confidence level = 7%.

You can think of your deflection as two separate components:

1) The component associated with arch action resistance. This should be very stiff.
2) The component associated with arch flexure. I'm guessing that this is where most of the action is.

I think (7%) that the tension rods, in combination with accidental compression struts formed by the plywood and the purlins, is creating "mini-arches" within the larger arch. And that is resulting in a stiffening because a greater portion of your load will be resisted via arch action as opposed to flexural bending.

It would be relatively easy to test this theory. Just model the accidental struts as such in your FEM model and see what happens. If you do that, I would love to see an axial load plot of the members of concern.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

RE: Arch building stiffness - calibrate model with reality

Ok, your OP (and sketch) made it look like a roller on one end. I'd still be a little careful with that assumption (i.e. pinned) because piles are not that stiff laterally (unless driven in at a angle; i.e. batter).

RE: Arch building stiffness - calibrate model with reality

(OP)
WArose: Two piles per arch base - one vertical and one battered at the angle of the arch. The foundations are quite stiff.

Kootk: Interesting theory. I've already modelled the purlins, the purlin nearest to the peak has 2.5 kip of compression in it. I've made a quick 2D model to test out these mini arches, they're actually in compression for the hinged arch I have (makes sense when you look at the deflected shape of the arch). I'll continue exploring the concept.

RE: Arch building stiffness - calibrate model with reality

Koot,

Based on your recommendation on another thread I bought the book "The Stone Skeleton" and have begun reading it. Your arch-with-a-hinge-sketch looks like it could have come right out of it.

RE: Arch building stiffness - calibrate model with reality

Thanks for trying out my idea.

Does the same thing happen at the other end of the building?

The rod braces are really tension AND compression members until the pretension is overcome. That means that the cross bracing can form its own arch capable of supporting a few kips.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

RE: Arch building stiffness - calibrate model with reality

(OP)
Kootk
Agreed - I'm fine tuning my model to try and capture some of these effects. My 2D simulations done just for proof of concept show a much stiffer hinged arch system with mini arches, just a matter of trying to capture these effects in the more complex building model

RE: Arch building stiffness - calibrate model with reality

@Archie: just noticed your comment. I'm still reading stone skeleton so I may well be channeling that. Have you read the fictional book "Pillars of the Earth"? Firstly, all SE's should read it on account of it being awesome and related to our work in a way that no other fiction book that I know of is. Secondly, if could go back in time, I would have read Pillars right after Stone Skeleton.
 

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

RE: Arch building stiffness - calibrate model with reality

No, never heard of "Pillars of the Earth"...I'll have to check it out. Thanks.

The last (only other?) work of fiction that I know of that involved structural engineers in any way was that tv show "Prison Break" from a few years back.

RE: Arch building stiffness - calibrate model with reality

If the end arches have about half the measured deflection of the internal arches, isn't that what you would expect, since they are carrying about half the load?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Arch building stiffness - calibrate model with reality

(OP)
Not the end arches, the arches two bays away from the end. And deflection is being measured against load we apply to the arch, so they'd all take the same load. Not related to the problem, but the end arches would be expected to deflect a lot less because of the end walls below.

Update on my progress - I've got deflections only 25% greater than those measured by basically making sure the bracing more closely resembles what's on site in terms of location and placement, through better member offsets. I think this might be close enough.

RE: Arch building stiffness - calibrate model with reality

@IDS: Doug, I think the OP has effectively three conditions: 1) interior arches withOUT bracing (2.3" deflection), 2) interior arches WITH adjacent rod-bracing (1.3" deflection), and 3) end arches. The OP's question relates to condition 2) NOT 3).

RE: Arch building stiffness - calibrate model with reality

We had a similar project 15yrs ago and I had the same problem. Our arches were site built so we even ended up x-raying the members too. Strain gauges and all sorts of other tech gadgets. It was great fun. In our case they used a thick decking without any 2x_ stock. I recall my initial 2D arch analysis was magnitudes greater than the actual measurements. I also had to model a region of the roof as the stiffness of the arch led to a greater load re-distribution than I thought. In your case the decking stiffness might not be as great as a thick deck, but how many arches did you model in your interior analysis?

RE: Arch building stiffness - calibrate model with reality

(OP)
I ended up with 7 modelled for an interior arch

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