Well, i ask prof. Bozorgnia himself and he was not so sure about his index and also ask one his colleagues who is close to him (Dr. Farzin Zarei who is associate proffessor in Irvine California) and his oponion was, not to use Bozorgnia and Bertero indices.
Anyway thanks mr Goran Jekic
Mr. Kamalzadeh, do you know how to obtain the betha coeff. in Park & Ang damage index?
Dear Mr.Jekic this coefficient varies for each frame type and as i know there is no certain theoritical way to obtain beta but there are several papers that gain this coeff. from experimental work and some others from these type of data's fit an equation for obtaining this beta as an instance for RC frames see "Investigation of Park–Ang damage index model for flexural behavior of reinforced concrete columns" by R.Rajabi, M.Barghi, R.Rajabi
I think for steel structures the most appropriate damage indices may be derived using aviation fatigue damage concept
I believe the best damage index is the developed level of strain.
In the case of steel elements, principal strain should be well bellow rupture strain of the used steel. In this technique the used steel must have some minimum strain hardening or else your model would experience some unrealistic strain localization.
For concrete elements, principal compressive strain should be smaller than crushing strain of the concrete and the principal tensile strain should be limited by rupture strain of the reinforcement. Note that by this technique reinforcement bucklings are also considered as they wouldn't buckle before concrete crushing.
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