how to understand elastic displacement under seismic load 6

Hey mate,

I operate in NZ so our seismic codes are different and I don't know what AISC specifically says - however, I can guess that it is similar to what we do
Here, story drift is generally checked based off the actual displacement (including the effects of any plasticity) as that is representing the true building response - are you sure you've understood that clause correctly..?

The elastic displacement is estimated by just building a model and applying our relevant seismic loads
If it's a true 'elastic' design, these loads are higher and if we have a plastic system then the loads are lower (I think the US uses an R-factor as a reduction for ductility in this way?)
After running the model, look at the deflected shape and then multiply the maximum drift by the relevant code-prescribed factors to obtain the actual estimated deflection

+1 to Greenalleycat's response. We do essentially the same thing here in Australia - though designers like to design to mu = 1 a lot more here and end up avoiding the step of multiplying drifts by the code factors.

Image below illustrates the displacement relationship between forces and ductility factor, and I believe the line for elastic response is basically what software will output.

Hi Mates,

Thank you for sharing.
As per AISC 360. R factor(base on your structure system) will be used to reduce seismic load, we will get displacement under the reduced load. then multiply this number with Cd(normally same as R) to get the inelastic displacement.
my question is arising when computing elastic displacement with reduced load.

1.Is this still elastic displacement if some sections have plastic area?
2.i know some software(such as SAP2000) have option to consider plastic design or not, not sure we have to select this function or not?

looking forward some US designer sharing their experience.

Cheers

I think you're getting your wires a little crossed here
Be careful of your definitions of 'elastic' seismic loads, and 'elastic' structural analysis software

'Elastic' in seismic senses means that there is an assumption of no plasticity i.e. nothing yielded, nothing broken
You release the load and it goes back to zero displacement
'Elastic' structural modelling just means that the computer applies a load and does basic maths to give a deflection (like applying pl^3/3EI for a cantilever or whatever)
If you're starting with (say) a load of 100kips (look at me go with my US units) and reducing it to 50kips due to your R factor, your computer model will give you half the deflection
Base computer models are not smart enough to know whether anything went ductile, or how that ductility influenced the result - that's your job as a designer

In the case of SAP2000, there is an option to consider plastic design (other software does this too)
I'm familiar with the concept though not SAP specifically - basically, you can define complicated parameters for all your materials etc to inform the machine of how your elements perform as they start to yield (hysteresis loops, post-elastic behaviour, yield rotations of beams and whatever else)
The computer can then iterate its way through and produce a more realistic output of deflection, forces, etc, for your structure with plasticity occurring
However, this is highly complex and time consuming and should not be done unless you know what you are doing/have suitable oversight

To make it simple, codes have factors such as the Cd you mentioned to fudge your 50kips profile back up to represent the actual inelastic displacement
However, these are just fudges and do not necessarily reflect the true seismic performance - they allow us, as designers, to ballpark these effects in a cost-effective and timely way

ArcherC - some other wires are certainly crossed. "AISC 07-10"? Do you mean "ASCE 7-10"? Also, looks like you're in Ontario. Is this a US project? If not, why are you using US codes when Canada has their own? Just curious.

As for the question: I think Greenalleycat got it. I'm guessing you're looking at Equation 12.8-15 in ASCE 7-10, correct? delta_xe is defined as "the deflection at the location required by this section determined by elastic analysis." Elastic analysis operates on the basic assumption that everything remains linear and remains elastic. Most of our codes are "calibrated" to the results of linear elastic modeling, and this is an example of that. Can the sections become partially plastic? Yes. Will that affect the behavior in the real world? Yes. But we don't consider in the analysis. There's no need, really, unless you're doing a performance design where it is necessary. But your typical capacity design based on equivalent lateral force? Linear elastic is the way to go.

So you run that model (by hand, using software, however you choose to do it) and get the drift results from your linear elastic analysis assuming E is constant throughout the analysis but also considering P-Delta and P-delta as applicable. Then multiply by it the deflection amplification factor and divide by the importance factor and you have your design story drift (which is an approximation of the drift including plastification).

Hello Greenalleyca and phamENG,

Thank you so much for your further information and explanation, sorry for the typo. should be ASCE 07-10. I am in BC working on an offshore project which requires to follow US code.

I all agree and understand the concept of seismic design and pushover method... with Greenalleyca example.my question is what should i do if there are sections with plastic areas under 50kips load. what's the practice way to handle this situation and meet code requirement?

1. if we increase sections to delete all plastic sections, it will increase the cost of project and consider plastics sections for seismic design is a common practice ?
2. if we leave the plastic sections here, this won't be elastic displacement and how to check story drift as per chapter 12.8.6 AISC 07-10.

Thanks again your time and sharing

I think you're still misunderstanding - elastic analysis is NOT the same thing as maintaining fully elastic sections. So no, you don't keep sections fully elastic. But you do assume they are in the analysis. The reason for this is simple: under service loads, steel sections will generally remain elastic.

Consider AISC safety factors for ASD design. For flexure, you're looking at a safety factor of 1.67. So you're reducing the allowable capacity of a beam to to roughly 60% of it's theoretical capacity. The ratio of the plastic section modulus to the elastic section modulus for a wide flange beam varies, but it's typically in the 1.15 range. So assuming the beam is fully braced such that plastification is the controlling design criteria, we've already cut off our design load at 60% of the plastic capacity while plastification doesn't start until we get to about 87% of capacity. So under service loads, the chances of the structure plastifying at all is pretty slim. But even if it does happen, the results are still close enough to work for our purposes. Therefore, the use of a linear elastic model is still valid.

Do not overestimate the accuracy of your analysis. Especially when it comes to seismic, ASCE 7-10 is more of a best guest-imate of what might happen. When there's an earthquake, there's no lateral force acting on the building, there are forced displacements. That's why we call it equivalent lateral force. The goal is to determine a lateral force that would place similar strains on the structure as the internal inertia when the ground starts moving. So right off the bat you're dealing with plenty of inaccuracies in the loading itself.

Find your ELF, apply it to your structure. Size the members per AISC 341 (the seismic steel code) and AISC 360. Determine the story drifts through elastic analysis (NOT maintaining sections fully elastic - this isn't required nor expected) and multiply by the deflection amplification factor.

Hi phamENG,

you are right, i was not clear understand the difference between elastic and maintaining fully elastic sections. now I am clear.

Thank you for your further and detail explanation. Appreciate it so much.

Regards!