Questions about the period variation at each loading step

[Sangwook]

Hello, everyone.

I'm currently trying to analyze the change of the structural period at each time step based on nonlinear dynamic analysis.

I have two questions related to the study.

First question is.......

as for the fundamental period of the example (RC frame) is 1.5 s (verified), I've got the maximum period with 5.524 s.

And at the end step the period shows 1.5 s again.

Is this possible result? I just used the following script to check the period at each step.

--------------------------------script------------------------------------------
for {set i 1} {$i < $NumSteps} {incr i 1} {
analyze 1 $dt_analysis
set lambda [eigen 1]; # perform eigen analysis
set omega {}
set f {}
set T {}
set pi 3.141593
foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
# write the output file cosisting of periods
#-------------------------------------------
set period "eigenvalues.out";
set Periods [open $period "a+"]
foreach t $T {
puts $Periods " $t"
}
close $Periods
}
--------------------------------end------------------------------------------

Second question is.......

when I'm trying to apply the above process to other examples, I sometimes get this error.

--------------------------------error message------------------------------------------
Dynamic analysis complete
domain error: argument not in valid range
while executing
"expr pow($lambdaI,0.5)"
("for" body line 11)
invoked from within
"for {set i 1} {$i < $NumSteps} {incr i 1} {
analyze 1 $dt_analysis
# perform eigen analysis
set pi [expr 2.0*asin(1.0)..."
--------------------------------end------------------------------------------

I have no idea why the program gave such comments to me.

Would you please share your opinion?

Thank you for your time and concern.

Sangwook

[selimgunay]

Increase of the period from 1.5s to 5.524s looks reasonable. Which materials are you using? If your materials don't have stiffness degradation, it also makes sense to arrive at the same period at the end.

For the case of "argument not in valid range", the eigenvalues for those particular time steps should be negative.

[Sangwook]

Dear selimgunay,

Thank you for your comments!

First of all,
I actually used Bilin material to define the behavior of beam and column in the modeling, and I applied the verified parameters to the material.
Then, can I understand the results as that the intensity of the earthquake was not sufficient to cause some damage? But, the maximum inter-story drift ratio was more than 0.04 corresponding to CP level, so I judged that there must be some damage on the structure.

Secondly,
if the eigenvalues are negative, what kind of things should I check?

[selimgunay]

This means that the initial stiffness and the stiffness at the end of the analysis are same. If the eigenvalues are negative, it indicates severely degraded response. Are you using the eigenvalues for any particular purpose?

[Sangwook]

Yes, I just wanted to check the period of the damaged structure compared to the initial statement before earthquake. Do you think that this is a proper approach for it?

Thank you for your concern.

[selimgunay]

Yes that is a proper approach, but I don't know how to quantify that. I don't know any studies which correlate the levels of damage to period elongation.

[Sangwook]

Yes, I agree with your statement. Thank you for your help and advice!