Dear Reza

I myself have worked on the subject of seismic damage indices for my thesis. To this day, the only registered example of damage indices in OprnSees forum that I'm aware of, was a syntax written for Park-Ang damage model, which I didn't find useful because of some ambiguities. Generally said, the procedure for calculation of damage indices using OpenSees, is to first extract force-deformation outputs from OpenSees and then post-process it with a programming software (Matlab can be really helpful). If you specify which damage index (or indices) you are working on, I may have some suggestions that can be helpful.

Dear Behnam,

Warmly thanks for your response.

I have seen the syntax that you mentioned, but as you know there is no manual how to set it or how to record it. I have tried to apply it but no result was gained.

anyway, at first step I'm really interested to set a procedure for extracting popular damage index, i.e. the one by Park and Ang.

I will be extremely appreciate if you introduce me a reference or a code which enables me to reach desired aim.

Bests

Dear Reza,

First a point about syntax: as I can remember, it is only usable with previous versions of OpenSees (if not mistaken ver. 1.7.3). Anyway as I said using this syntax may not be a good idea, at least I and some of my colleagues didn't find it helpful.

But I guess I can help you with some problems in coding Park and Ang damage index. First I have to know the modeling assumption for members of your structure, did you use spread plasticity (Fibers) or did you use concentrated plasticity (Beam with Hinges)?

Dear Behnam,

thanks for your kind help.

I have used concentrated method.

Dear Reza,

Sadjad has already explained the solution well. I just didn't get what he meant by "do not follow PADI in openSEES", I just can say that I personally found OpenSees really powerful and also easy to use for damage index calculation.

Just in addition to what sadjad mentioned, remember that energy term of Park-Ang damage index should be calculated at the end of time history (i.e. maximum energy dissipated during loading) and then add it to ductility term at each step of loading.

Dear Sadjad and Behnam,

Thanks in advance for your kind help and following this question.

I didn't understand the same as Behnam mentioned too.

But is it possible to clear how you calculate Plastic energy dissipation (for example a simple way is multiplying moment and plastic rotation to each other) . and the other question is, when it must be calculated?

Behnam said that, it must be cumulative and gained at the end of process, then it could be understood that it's maximum dissipated energy due to ground motion. is it correct?

Dear Reza,

Yes, that is what I meant. You will need to calculate maximum dissipated energy due to ground motion. But regarding how to do so, the procedure you can use is:

Extract moment-rotation values of a hinge for all steps of seismic loading using related recorders that exists in OpenSees. you will have a vector of rotation values and a vector of moment values with number of elements equal to analysis steps. Now using a simple method like trapezoidal, you can calculate the total area under the moment-rotation hysteresis curve which represents absorbed energy. A very important thing: there is difference between absorbed energy and dissipated energy. If you want to calculate dissipated energy, then you will have to deduct the parts of area that relate to unloading branches of moment-rotation hysteresis (this will give you confined area of moment-rotation that equals to dissipated energy).

Dear Behnam,

Sorry for my late answer. but I have another doubt too.

How you will know that you are calculation is correct. since as I know there are lots of suggestions for beta. Do you know any way to calibrate the method or not?

Personally I compared results from my code with an article in field of seismic damage indices. It's a really strong and helpful article that presents some equations to calculate park-ang damage index based on some input variables. Only unfortunate point is that this article is restricted to steel structures but nevertheless it can help you in many ways. This is the article that I mean:

"Seismic damage estimation of in-plane regular steel

moment resisting and x-braced frames", George S. Kamaris, Yasemi-Maria Vallianatou, Dimitri E. Beskos. Bull Earthquake Eng (2012) (check Springer website).

Good luck

Dear Behnam and Sadjad,

I learned a lot from both of you. thanks in advance for your kind help and I wish the bests.

check my asce, journal of structural engineering 2011, 137(3):456-467 paper entitled damage-based design earthquake loads for inelastic structures. you will find a good literature review and common used mathematical expressions to quantify damage of structures under earthquake loads.

Dear Professor Moustafa,

Warmly thanks for consideration and help.

Dear Behnam Ordoubadi and Reza Allahvirdizadeh

In your comments, a person has said that Beta = 0.1 or 0.15 are suitable values depending the ductility of the steel frames. Do you know the article that used these values?

In this article (abstract in English)

Determination of the ultimate EBF shear link rotations by taking into account the low cycle fatigue under different seismic records

there is an example for calibration of damage law (fatigue constants) in OpenSees based on experimental testing of EBF shear links.

Dear Chavdar Penelov

Thanks a lot

OpenSees uses Coffin-Manson relationship in order to calculate the damage index. In this relationship there are two constants that you have to calibrate based on your own material. You should take two important issues under consideration:

1- You have to perform cyclic tests on the material of interest (at least twice with two different strain amplitudes) and then plot the N-Eps curve in a log-log space. N is the number of cycles to fatigue and Eps is the plastic strain. You can find the two constants of the Coffin relationship from this curve.

2- Coffin-Manson relationship is only valid for low cycle fatigue and if your material undergoes large plastic strains and the number of cycles to fatigue is less than 100, this model is not acceptable since it overestimates the fatigue life drastically.

All in all, you cannot simply use the damage model with the default coefficients, it will not give you the correct results and you will be challenged.