Richard-Abbott Modified

[massimolatour]

I am trying to apply the modified Richard-Abbott model first developed by Della Corte and then employed by Nogueiro and Da Silva to describe the cyclic behavior of composite and simple steel beam-to-column joints. I am defining the coefficients of the modified RA model which best fit the experimental behavior. I am developing a routine that is able to give the response of the joints according to the model described in the paper "NUMERICAL IMPLEMENTATION AND CALIBRATION OF A HYSTERETIC MODEL WITH PINCHING FOR THE CYCLIC RESPONSE OF STEEL AND COMPOSITE JOINTS".

At the present time I am making a comparison between my routine and the results given by the software Seismostruct. I obtained good results applying the strength degradation but I encountered some problems in applying the stiffness degradation. Probably I have not understood well how to apply this degradation and, if possible, I would like to ask you some questions about this part of the model.

I would be really grate to you if you would help me in understanding what is wrong with my application of the model.


QUESTION 1


Stiffness degradation and strength degradation are defined as reported in Nogueiro work but, while the coefficient defining the strength degradation is non-dimensional, the parameter defining the stiffness degradation seems to be dimensional. In fact, in case of force-displacement spring the energy [kNm] is divided by the stiffness [kN/m] and the ultimate displacement [m] resulting in a coefficinet ik that should have a dimension [1/m]. In case of moment-rotation spring the energy [kNm rad] is divided by the stiffness [kNm/rad] and the ultimate rotation [rad] resulting in a coefficient ik that should have a dimension [1/rad]. Is this right?


QUESTION 2


Concening the energy Eh I found that the energy used in seismostruct to compute the strength degradation is the energy cumulated up to the previous cycle. [For instance: First monotonic semi-cycle you have no degradation, Second semi-cycle you have no degradation, Third Semi-cycle you have strength degradation calculated using the energy up to the first semi-cycle, Fourth semi-cycle you have strength degradation using the energy up to the second semi-cycle.... and so on). Is this hypotesis right?


QUESTION 3


I applied stiffness degradation both to K0t and Kht, is this right?



QUESTION 4


Dealing with the extension of the elastic part at unloading it is not clear to me if varies during the loading process . In particular I found that, using only strength degradation, my results match those obtained by Seismostruct (i.e. using an extension of the unloading branch equal to My) but, when I introduce also stiffness degradation it looks like that the extension of the unloading branch is not anymore equal to My. What is the procedure to determine this extension?


QUESTION 5


Dealing with the line passing through the origin with slope equal to Kh it is not clear to me if varies during the loading process as the stiffness degradation increase. Does it change during the loading history or it is fixed?

Thanking you in advance,

Sincerely

Eng.Massimo Latour

[seismosoft]

Dear Massimo Latour,

Apologies for the very long delay with which we address this query of yours. We have contacted the authors of this model's implementation in SeismoStruct (Nogueiro and Da Silva), and we believe that they have now provided you with an answer to your questions. For the benefit of others, we try to reproduce such answers below:

1) the authors note that ik is a non-dimensional parameter (this may not necessarily be in contradiction with your dimensional analysis)

2) yes, correct

3) the authors response seems indeed to imply your assumption to be correcty

4-5) the source code that the authors have now provided you with will hopefully clarify these two final queries

Renewed apologies for the delay.

Seismosoft Support