P-delta + Modal Spectral Analysis 1

[vaquers]

Is there any way to take into account the p-delta effect when you are working with load combinations which have a Response Spectrum load case? I mean in the comercial softwares.

I know that it makes no sense to combine p-delta with a response spectrum result because it loose the sign. But how can I have this amplification into account?

Currently I'm scaling up the drifts and forces by the ASCE 7-05 Section 12.8.7 coefficient. Is there another way? Regards,

Sebastian

 

[JoshPlumSE]

Sebastian -

Well, there are two basic ways of doing this.

1) From within the program itself:
Some programs will use a Geometric P-Delta adjustment to their stiffness matrix. Every program will have variations on how their implementation works. But, they should all have to solve a static case first to use as the basis for the stiffness adjustment. One limitation would be that this is only capable of capturing the P-Big Delta effect. Though that should be reasonable enough for most normal structures.

2) Based on hand calcs:
Not all programs will use a geometric stiffness adjustment for P-Delta. Or, their geometric stiffness implementation may not work for dynamic analysis. In that case, a hand calculation should work fine.

Your method of using the ASCE theta coefficient is perfectly reasonable. Other similar calculations would be the B2 factor that AISC uses, or the Q factor that ACI uses. These are all very similar concepts.

I would probably calculate these values story by story and then just apply the maximum value as an amplification on the response spectra results.

One last thing to keep in mind is that the deflections used as the basis for the P-Delta amplification should be the reduced elastic deflection (based on 1/R as your forces and NOT amplified by the Cd value). If you apply your Cd factor, then you'll start getting very large P-Delta amplification.

 

[vaquers]

I´m agree, actually I've computed the value story by story, and then I used the max. value exactly as you said. It's nice to find similar opinions. Thanks! Regards,

Sebastian

 

[trainguy]

Josh,

Don't you have to account for plasticity when evaluating (big) P-delta effects for seismic loading? I don't see why this wouldn't be used for a response spectrum analysis, unless the amplified deflections are used later in the workflow.

tg

 

[WillisV]

Not using the amplified deflections is how its been done for quite a while - mainly based on experience that in actual earthquakes the kind of damage associated with that kind of huge P-delta effect is not observed, primarily due to dynamic stability effects (as soon as the building reaches that big a delta it swings the other way in an earthquake thus now allowing for the p-delta effect to really kick in).

 

[JoshPlumSE]

TG -

WillisV is basically right. This is just how it has been done. And, it is certainly how the ASCE code reads.

There is some good discussion in the NEHRP commentary about this. As I recall, it said something along the lines of:

1) Using the inelastic displacements would result in a significant increase in design forces for moment frames that does not appear to be justified based on the observance of past seismic events.

2) I think they recommended that the issue be investigated further using a 2nd order, nonlinear time history analysis for past earthquakes. The idea being that this may show basically what Willis is suggesting... that effect of momentum or impedence of the structure tends to mean that the full P-Delta effects do not have time to be "felt" by the structure as it is swaying back and forth.