FE model validity

Back in the day I used to do a bunch of modeling using the same sort of models that TF engineers use (I think)(finite difference and element models). The problem with those models is whether they are valid or not, that is whether they can match 'real world data.' There are generally a lot of assumptions within these models, the simplest often being the most problematic. That is, that the materials are homogeneous and isotropic, and in the case of TF that all of the connections are hinged (is that right??).

The reason that I bring this up, is that in another post it was mentioned that heavy wind loading was pushing the post in bending. It wasn't mentioned whether or not the post will actually break or not, which is a fairly important point. My initial reaction was, that I just can't see a post breaking in half from a brace pushing on it from wind loading (in a frame based on traditional designs, that is without all kinds of weird stuff).

Which finally gets to the point, I'm sure that the models used in structural engineering have been validated on bridges made of steel and concrete (both homogeneous and isotropic) and so on, but are they really valid on timber frames. Has anyone ever plugged a bunch of European cathedrals, English barns, American colonials, or Japanese temples (with no diagonal bracing by the way!) and found that the model shows all of those buildings should be lying in heaps on the ground. If the models haven't been validated by confirming and trying to understand how the model explains (or doesn't) buildings that we know work, then perhaps the industry needs to take a step back. FE analysis can certainly be a very valuable tool, I'm just asking how well we understand it in our world of traditional joinery.

I'd love to hear back some from engineers, as I have no experience on this other than looking at Ed Levin's pictures of wiggly timber frames.

Thanks,
Brad

Hi Timber Wrestler & Derek,

I agree Derek's comments and now find myself trying to answer two questions inside two days.

One of the reasons that I got into 2D and 3D timber frame CAD, plane frame (2D) and space frame (3D) structural modelling was to be able to provide quantified answers to the very question raised by TW.

Observations made on old buildings that have failed in a particular way led me to survey and record old buildings and then to try and better understand the processes at work. As mentioned elsewhere on this forum the timber frame frame is the primary structure and usually its structural performance is suplemented by other building materials and in some cases even by adjacent buildings so it can be difficult to prove positive the actual loads and moments being experienced on any given component. That said, the plane frame (2D) structural model can and does provide a quick and dirty indication on how any particular frame is likely to behave. By measuring actual historic timber dimensions from a building and then entering these into the model and then applying loads as per today's standard building design codes it is then possible to establish a set of outcomes for each component that provide a historic and empirical benchmark set of acceptable (or not) design load and stress levels that might help a designer to be more confident with his (or her) predictions for new buildings. That's what I do !

Most building failures and especially those related to the timber frame elements rarely lead to the immediate collapse of a building. This is more likely to be a long drawn out affair progressing until the point of no return is reached with a partial or full collapse then happening. This type of extreme event would most likely be be occassioned by a very heavy snow storm or hurricane wind.

Having said all that the the problem still remains for the designer / engineer to demonstrate to all concerned that a building is likely to be able to safely perform its intended function and hence the plane and space frame structural programmes go a long way toward convincing others of the appropriateness or otherwise of design configurations and timber sizing.

This week I have been working inside the scissor braced roof of the Bishop's Camera in Farnham, Surrey. This roof is about 600 - 700 years old and comes with more than its fair share of problems. We took the unusual step of performing dendro testing on the roof timbers and found that the wall plates and primary tie beams were likely to date to 1306 (A. Moir, 2007) but rather surprisingly we then discovered that the rafters and scissor braces above dated to 1381 (A, Moir, 2007), so it would appear for whatever reason that this roof has been subject to a major rebuild from wall plate up. Why ? Did the first roof not perform adequately ? Did the black death that hit Farnham in 1349 resulting in the death of between one third and one half of the population have some kind of impact on the roof ? Did the Bishop just decide to remodel his roof ? Though it is important to try and understand the events that have ocurred over the life of a timber frame structure it may prove almost impossible to establish proof positive as to why exactly why some historic buildings fail or are replaced.

This topic would certainly provide a fantastic scope of work for a Masters dissertation or Doctoral thesis.

Sounds like you are up for it TW.

Regards

Ken Hume P.Eng.
http://www.kfhume.freeserve.co.uk

First, let me just say "hello". I'm a practicing strucutral engineer, and TFs got me into the building side of engineering a decade ago.

Yes, FEM really works, but only if you do it right, and it's very easy to do it wrong. I've been doing this kind of work for about 15 years, first for shuttle and low eath orbit payloads, then for military/black project gear, now for buildings. Analysis ALWAYS gets followed by at least a rule-of-thumb check, and often by a supplemetal (but simplified) hand check. While there's no magic to it, the complexity with which you can model something can easily outstrip any closed form solution.

Wood is a special beast. It has the worst properties of any engineering material I can imagine, except possibly soil. The designs for wood are less "exact answers" and more "relatively safe envelopes" since the properties will vary quite a bit within grades and species.

What you may be thinking of is the theory by which FEM works - the stiffness matrix. A strucutre is broken down into degress of freedom and a stiffness matrix is generated. It is then inverted and multiplied by the force to get displacements. Derivatives are taken to get the rest of the "stuff". That's a gross oversimplification of modern solvers - but I'll take it one step further. A simple spring is governed by:

F = k * x

where F is the force, k is the stiffness, and x is the displacement. A timber beam is a spring. Push on it in the middle and it defelcts. if you know the force and measure the deflection, you can get the stiffness. So 1000lbs in the middle of an 8x10 creating a 1/4" deflection is 4000lbs/inch. Piece of cake right?

So if you can calculate the k, and you know the F, you get the x...

F / k = x

Simple! For FEM and frames, all those simple values become matrices, with thousands and thousands of terms. Those terms are interdependant (push on a knee brace and it deflects a column).

Here's the kicker - with the material stiffness within a grade possibly varying by a factor of 2 or 3 over the 5%-95% range, you introduce an effective error in your model.

It turns out that it doesn't matter too much. The averages tend to work in our favor, and the factors of safety used are conservative enough to catch most of the funny business. That, and while you can get lumber to vary wildly, you still end up with mostly the middle of the road values.

So, yeah, it's not quite like entering 6061T6 aluminum with +/-0.0005 tolerances, but it really does work.

Now if I could just figure out how to take a solid model from ADT and collapse the memebers to line elements for importing into my FEA software, I'd be dancing a jig.

Welcome Jordan.
Isn't is possible to draw the frame using the central axis line of the timbers for input into the FEA software?
Jim Rogers

It could be done - but there are no convenient snap points to use when we looked at it last time, and our 3d capabilities are somewhat knowledge-limited - we don't make 3d drawings, so we are not efficient in working with them. We're effectively doing that with the frames in 2D at this point.

The data may exist, but haven't the faintest clue how to get it out. For the number of frames we process, the cost of training doesn't justify the work. We might be able to save $200-$300 per structure; training would likely cost in the $3000-5000 range in direct and indirect costs. We've done 4 timber frames in the past year. If I split the savings with the TFer, it would take 5-8 years to pay that back at our rate.

thanks Ken and Jordan for writing these posts.... more, please.
Ken: would you have an example of this process on your website, or know of a web accessible historic building that has been measured and engineered?
Jordan: I often build timberframes using center snap lines and the shop drawings are done with centerlines as the dominant feature, would these drawings therefore work as a basis for the FEA software?

Hi Mark,

You can check out a link to Hume & Son Engineering where you can download a composite stress *.pdf file that shows typical deflections on a simple queen post truss frame, axial stress diagram for a hammer beam roof, shear stress diagram for a typical big American barn frame and bending moment diagream for a lattice truss frame.

I have toyed with the idea of producing either an article or short book on the recording and analysis of historic timber framed structures but have wondered just how many people would actually be interested in this type of thing.

I will be recording a lovely 3 bay Wealden town house in Farnham at the beginning of May specifically to produce a 3D CAD model of same. It might be appropriate to follow this project through and publish the actual timber sizes employed together with typical stress, moment and deflections predicted by present day structural analysis for this 600 year old building. It is a particularly good example of a solidly built and fairly complete survival of this important traditional frame type.

Regards

Ken Hume P.Eng.

Hi Derek,

The Town Wealden was duly recorded last weekend with the layout and timber sizes all now noted. Some of the timbers are surprisingly large with the full height rear post head jowls weighing in at 15.5" x 9". It is a three bay building with two open bays at ground level and upper floors at both ends projecting to form a jettied front with recessed centre bay resulting in a 16 x 32 ft footprint. Quite a small but perfectly formed hall house.

I shall in due course produce a cross section and analysis of same to see what level of stress, bending moment, shear and deflections that this frame has been subject to for the past 550 years.

I now need to figure out how to make this information available and I like your book suggestion and title but with all this information technology available to us I wonder if we couldn't do this more easily.

Ideas please ?

Regards

Ken Hume
http://www.kfhume.freeserve.co.uk

I think you touched on it already Ken...

It's a niche market kind of thing, so why not self publish in some kind of multi-media format and market directly ?

I'd buy a disk !

Hi Will,

Your support and interest is encouraging.

I wonder if you and others would care to share with us typically what kind of vernacular building and design / engineering information it is that would be of interest to you.

Regards

Ken Hume

Make this one a group project?
I could see it as a sketchup plan published in 3d so the "reader" can walk through and see joinery details. The fea could be a "movie" of typical loading scenarios. I'd bet it could be interactice allowing the user to input other loadings.
I think as something like that evolves within a large group ideas might start popping up? Then follow the parts that seem to work as a template.

Ken –

My own biased interest in modeling historic framing schemes would be in typical English-tieing. ( if there can be said to be such a thing ) As you know here in New England we are surrounded by this typology, it was the dominate form for just over two hundred years. I can be in a half dozen examples within a ten minute ride. Though here in NNE common purlins, again are dominate, to a degree that could be described as universal, and from early on, the first period through to the late Federal, when English-tieing was finally abandoned, though CP’s survived this transition. I’ve long puzzled and have tried to research as to why CP’s are the dominate roof framing pattern here, having at one time assumed it to be like language and accent patterns on this side, tied to county of origin and migration patterns from your side. Yet as far as I’ve been able to determine it is not tied to any regional framing variation, or migration pattern from one. I do believe it is a successful and symbiotic combination, that redirecting thrust away from the plate makes for an excellent English-tieing frame, and would be interested in how they model in comparison to other historical English roof framing variations

I looked at a potential restoration yesterday, exceptionally fine pre-revolutionary example. ( now I’m really regretting forgetting my camera ) I have restored more than a few and build in this form more often than not.

If you would like to represent a colonial sampling in your project, I’d be happy to provide a survey and photographic / video documentation of an example or two from this corner of the former colonies.

Hi Will & Don,

I think that an idea might be emerging that is worth pursuing and a cross pond design comparison would be an interesting undertaking.

Re common purlin versus Common Rafter

I would surmise that this might have much to do with snow load and I also understand that (Northern) New England can be subject to hurricane force winds that can and does flatten forests.

All of the above and in particular the standard width of a frame might have some significant effect on the roof pitch.

A standard house frame in SE England is one pole wide (16' 6") and I would hazard a guess that a typical standard New England frame like a cape or the like would be much wider. With a steep roof pitch this would push up the ridge height exposing the frame to quite a bit more wind load.

We would need a frame cross section with timber sizes and species. Joint details are not really required at this stage.

Re 3D Models

Producing a Sketchup 3D model is fairly simple. Sketchup will import perfectly from heavyweight CAD programmes such as AutoCAD allowing non CAD users to view and manipulate a model with relative ease.

The demonstration of FEA that is interactive is a bit more problematic and I need to think about how this could be achieved when a recipient is not equipped with the same analysis programmes. I have prepared this kind of thing before for windmills i.e. how they perform in different wind speed and directions but this was done on the basis of preparing a whole series of outputs for a series of fixed inputs and then animating same in a screen show so that variable inputs / outputs could be demonstrated.

It would be nice to hear from the rest of the regular contributors and also some of the TFEC members who do not seem to regularly frequent these haunts.

A digi pic of the two contender buildings chosen to square up in this cross pond match would usefull.

How would we judge the winner ?

Regards

ken Hume

I wrote a reply quite a while ago when the server was getting switched, so it has been lost in the ether. I'm not sure what I wrote, but it was surely poetic and profound.

Ken and Jordan, thanks for the replies.

Ken, so your models do show the buildings surviving? Do you have to tweak the model much to make things work? I don't know how tweakable these particular models are. The models I used to work on were crazy tweakable. Actually in my modeling class we took a real world problem, split the class into two groups and each group produced a perfectly valid model, with two very different conclusions. Hence my initial question and skepticism. And thanks for the enticement on the graduate work, but my previous graduate work burnt me out on homework.

Jordan, as a matter of fact the modeling I used to do was with soil, or really the stuff under the soil. And while the properties of wood may vary by a factor of 2 or 3, the properties of sand may vary by 12 orders of magnitude (like 1 to 1 billion). In general, the geologists would just say this way too complicated, and the engineers would say just take the median and call it in an assumption. The compromise would be stochastic modeling, which could probably be applied to structural FE models pretty easily.

I also like the idea of our cross-cultural tying joint exchange, and would definately support you Ken in your work. What about contacting the Guild or your Fellowship to see if they would be interested in publishing a series of articles or book or something. The SU models would be great as well.

It would be great to hear from more engineers on this subject. It seems as though the Guild is slowly getting through studying and analyzing trusses, chuches, and bridges (the articles seen in the past few years in Timberframing). But I don't know whether those lowly capes and colonials and Dutch barns and so on have been looked at by engineers.

On an entirely separate note...Will, I haven't seen too many English barns in western Mass (although they are certainly around), but the ones that I've seen all have common rafters, and often principal purlins. Again, I'm not sure whether these are just later examples of English barns, or if it's a regional thing. I'll ask Jack. I did ask him whether he had ever seen a historic example of a principal rafter bearing on the end grain of a post (dropped plates I guess you'd call it, as most frames are today), and he said no. Those thing scare me.

Brad