Following the answers

can you mention about type of structure you are studying how you are applying multi support excitation(depth in-variant or horizontal spatial in-variant), then maybe it's easy to understand your question.

Hi, bridge, horizontal

That means, you are conducting spring beam approach,? Do you have site specific ground any bed rock inclination (that will influence the delay time)? Are you considering the kinematic and inertial interaction effects to modify the seismic demand?

Or you may consider the this paper to estimate the horizontal spatial incoherence and delay time to define the multi support excitation.

https://hal-brgm.archives-ouvertes.fr/hal-01226818/document

Dear, Sadiq, I simulated required arrays based on a paper by Konakli 2011. the procedure consider wave-passage, incoherency and local site effects. i used OpenSEES to simulate a reinforced concrete bridge. then imposed simulated arrays on the supports. now i am going to extract pseudo components of non-uniform excitation. generally it is possible to consider the deck mass=0 and do an multiple support excitation. the outcomes must be pseudo static components. but i am looking for an analytical way to verify the results. for example, consider you did uniform and non-uniform analysis, now you have two different outputs. where is the pseudo components considering two results?! certainly the results are different, how is possible to calculate pseudo components?

I could not understand. 2 type of interactions modify the component of seismic demand in SSI. Kinematic and inertial interaction (mass=0, means you are not considering inertial interaction), and the kinematic interaction is defined in terms of base slab averaging and embedment depth. Now it is typical in code guidelines to perform psedostaic analysis ignoring these interactions when we define the seismic demand. If you read this report it has empirical and analytical procedures to account for such interactions to modify the psedostatic sesimic demand

https://peer.berkeley.edu/sites/default/files/2017-08_turner_9.10.18.pdf

Good document, the basic question is, the differences in responses caused by uniform and non uniform excitation. It is customary in multiple support excitation to separate pseudu static responses from total response. Now we have a multiple support analysis results, how to extract the pseudo static responses from total response?

I could not understand.

Can you please sketch the numerical model, computational domain? corresponding to " the differences in responses caused by uniform and non uniform excitation "

1. Uniform excitation

2. Multisupport excitation

Sure, I added a photo and explined the multiple support and uniform excitation for a portal frame. Frame 3 show the pseudo static response due to multiple support excitation. Actully the main difference between uniform and non uniform excitation is the mentioned response. In some cases the total response considering pseudo static components maybe more than result from uniform excitation. Now the problem is, how to caculate it when a multiple support analysis conducted and the cosequent results prepared. Especially under ground motions.

I reckon if mass and damping are considered zero in an additional analysis, you will dirctly calculate the pseudo static part of responses.

Thank you for your response. i do agree.