Because forcing thousands of engineers who have been doing elastic analysis for 10 to 40 years to suddenly switch to plastic analysis is impractical. And using the elastic analysis coupled with limit states/LRFD is sufficiently conservative to produce safe and reliable designs.
An elastic analysis is appropriate for reviewing and controlling serviceability concerns. I'd think the ultimate limit state is more for forensic engineers.
In the case of a beam, Mn = Zx*Fy, is a plastic hinge, which is failure. Considering the use of the minimum Fy instead of expected strength, and a factor of safety, the beam behavior is elastic.
In the case of earthquake design, plastic hinges are not failure. Connection failures are a failure.
One simple situation is when the ULS limitation is stability. Then a plastic analysis is often not applicable. Another thought, SLS analysis for concrete can include the cracking of the concrete which is not an elastic analysis. I would say that difference between elastic and plastic analysis is usually not only depending on if it is SLS or ULS, it is more complex.
Forensic engineering, in my experience, deals with structures not functioning as intended. And a structure can fail both for SLS and ULS criteria. However, ULS is often more dramatic.
About 80% of the steel warehouses where there is repetitive continuity that I've done in the last 40 years have used plastic design. There is a real economy to it. It's easy, doesn't require the same consideration for alternating loads, fewer pieces, etc. The only issue I've found is the selection of a Class 1 section.
An elastic analysis is appropriate for reviewing and controlling serviceability concerns. I'd think the ultimate limit state is more for forensic engineers.
When designing for strength using LRFD, that's an ultimate limit state design, whether US codes choose to use that term or not.
The main reasons that elastic analysis is allowed are:
1) With appropriate adjustment of stiffness properties, limited redistribution of moments, and appropriate checks for buckling it is conservative and much simpler than carrying out a plastic analysis.
2) When the first codes using current methodologies were developed ('60s and '70s) doing a plastic analysis for routine design was not practicable. Changing the approach now would require a complete re-write from scratch.
Some codes do allow non-linear and plastic design methods however, without giving detailed requirements on how it should be carried out.
Thats a very good question and something I ponded on for a while now.
Technically a plastic limit state design would be the appropriate analysis technique and doing an elastic analysis with the load factors would not guarantee that parts of the structure are still elastic.
But it is still analysed elastically according to the codes for the (not very rational) reasons above IMO.
I'll make a different argument.... An economic one.
What's the opportunity cost? Or, put another way, what's the benefit vs cost? Elastic analysis is easy to perform, and relatively inexpensive. It has proven reliable for design.
Analysis that includes plasticity is much more expensive to perform. Meaning it takes a lot more engineering hours to perform and to get it right. Therefore, it is really only used for cases (performance based design) where the extra cost can be justified by significant cost savings to the project as a whole.
Why would a client (owner or architect or such) want to hire a much more expensive engineer to provide a service that offered little demonstrable benefit? The don't, which is why this type of analysis isn't performed nearly as often as elastic analysis.
"What's the opportunity cost? Or, put another way, what's the benefit vs cost? Elastic analysis is easy to perform, and relatively inexpensive. It has proven reliable for design.
Analysis that includes plasticity is much more expensive to perform. Meaning it takes a lot more engineering hours to perform and to get it right. Therefore, it is really only used for cases (performance based design) where the extra cost can be justified by significant cost savings to the project as a whole."
What basis are you making this statement. I've often found plastic analysis is easier and faster? There are a few issues that you need to check, but, this is fairly straight forward and easy once you get the hang of it; I've not used plastic design for high rise... shakedown analysis can be tricky and difficult, but for single storey structures, it's not hard and is surprisingly easy.
I'm not aware of any design programs that automatically accommodate redistribution... determining the mechanism may be beyond many software packages...
This was one of my postings on Eng-Tips from about 10 years back...
"I've used plastic design for nearly 40 years and it generally results in minimal weight and cost (I've not used it for seismic areas and shakedown and reversals may mess with the economy)
The general provision for designing the moment connections for 25% of the strength usually accommodates moment generated from unbalanced loading. Unbalanced loading, other than the connection has no effect on the member size, hence a general reduction in weight. Also the use of the plastic modulus instead of the section modulus gives approximately a 15% increase in member strength. The continuity also minimises deflections. There are generally fewer pieces to handle further reducing costs. The beams can often span the long cantilever distance."
Try it, you'll like it, specially for warehouses... and something to remember is that it only behaves plastically for the first overloading... from there on, once it has yielded, it behaves elastically. <G>
Are you talking seismic design or non-seismic design?
I was specifically thinking of multi-story structures in a high seismic region. The kind of effort you have to put to modeling plastic hinges, demonstrating post hinging rotational ductility and such is pretty darn significant. You've got to create backbone curves for all your non-linear elements. Probably do some more complex modeling for the panel zones (for steel moment frames), et cetera, et cetera.
But, even for single story structures in California, I have trouble imagining most building departments letting you get away with plastic design without demonstrating a ridiculous amount of effort to show exactly what you did and how it's allowed by code.
Agree, that with strength requirements plastic analysis and design is more economical than elastic analysis, however with serviceability requirements sections generally increase in size particularly with large span portal frames and plastic analysis becomes less relevant.
Josh:
I've not used it for seismic or for multistorey buildings... I've done a couple of two storey buildings and not for seismic. For single storey buildings seismic would be fairly easy. Problems with AHJ is another issue... they should leave engineering to 'real' engineers... Your taxpayers money hard at work. Plastic design has its uses... There are frame programs that model shakedown, but, I've not used them; I don't know how good they are... You likely get a more uniform model... like a rigid frame for a pre-engineered building... ideally it becomes fully plastic at failure. Plastic designed buildings only enter into plastic mode on full loading. Afterwards, they reach the same load conditions and are elastic, albeit, with residual stresses (This is what causes shakedown.)
CivEng80:
My experience is that with the continuity usually found in multi span beams for warehouse type construction that servicebility is not an issue. Deflection is approx 1/3 of the simple span construction as opposed to 1/5 for elastic design. When I first started I was told that connections and erection difficulties made plastic design uneconomical... I quickly learned that this was a myth. Consider... lighter members, fewer pieces, and fewer connections. Connections with stiffened end plates at approx L/7 splice points... Try doing your next warehouse using it and do it elastically... compare costs... you may be surprised.
I don't usually use plastic design for portals... occasionally to get a member that is a tad undersized to work. Just had a rectangular 'waler' using W24 beams that was about 100 'K shy, and by redistributing the moments, I could get the W24 to work. I usually use plastic design for warehouse roof beams... plastic design really comes to the forefront.
At the end of the day, the steel quantities were about 3 psf less than estimated and there was over 1000 design hours saved. 400,000 ft2 and 40' clear height for most of it.
