FORM of 2D RC frame

[amadeus]

Dear Scott,

I would like to conduct a FORM analysis of the 2D RC frame given in http://opensees.berkeley.edu/wiki/index ... excitation. All the eight gradient parameters have been assigned with normal distributed random variables. There are two problems in my analysis:
1) how can i conduct a static pushover reliability simulation as in the paper "OpenSees-SNOPT Framework for Finite-Element-Based Optimization of Structural and Geotechnical Systems" (Gu et al. 2012). When i tried to continue the sensitivity study in example3_input.tcl, I found that "integrator LoadControl" cannot give convergent results. If i switched to use "integrator DisplacementControl", the simulation would not stop at the loading defined in the load pattern. Instead, it could only stop when the controlling displacement has been reached, which would make the displacement-based performance function meaningless. How can I solve this problem?
2) how could i get the time history of reliability indices of the frame, if time series have been given as load pattern. It seems that "runFORMAnalysis" can only give one single reliability index, which is, in my opinion, corresponding to the reliability index at the end of the dynamic analysis.

Thanks a lot!
David

[mhscott]

> 1) how can i conduct a static pushover reliability simulation as in the paper "OpenSees-SNOPT
> Framework for Finite-Element-Based Optimization of Structural and Geotechnical Systems"
> (Gu et al. 2012). When i tried to continue the sensitivity study in example3_input.tcl,
> I found that "integrator LoadControl" cannot give convergent results. If i switched
> to use "integrator DisplacementControl", the simulation would not stop at the loading
> defined in the load pattern. Instead, it could only stop when the controlling displacement
> has been reached, which would make the displacement-based performance function meaningless.
> How can I solve this problem?

I'm not familiar with the examples in the paper you mention, but you are correct, a displacement controlled solution will give meaningless results when the performance function is defined in terms of the nodal displacement that is controlled. Can you instead define a performance function in terms of an internal section force when using displacement control for the analysis?

> 2) how could i get the time history of reliability indices of the frame, if time
> series have been given as load pattern. It seems that "runFORMAnalysis" can only
> give one single reliability index, which is, in my opinion, corresponding to the
> reliability index at the end of the dynamic analysis.

You can do a FORM analysis inside an analysis loop and dump the results to unique output files named by the loop variable, e.g., $i shown below

for {set i 1} {$i <= $numSteps} {incr i} {
analyze 1 $dt
runFORMAnalysis output$i.out
}

*However*, path-dependency is a real problem here, as the FORM analysis at one time step will not be consistent with that at a subsequent time step when materials yield and changes states. You should really do a full time history analysis ending with a FORM analysis for each time step.

Time step 1 - analyze, run FORM
reset
Time step 2 - analyze, analyze, run FORM
reset
Time step 3 - analyze, analyze, analyze, run FORM
reset
......

This can easily be accomplished with nested loops, but will require much more computational time. It would be interesting to compare this approach with the results from doing FORM at every time step.

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