I want to drive (draw) a seismic fragility curve for the four damage states (Slight, Moderate, Extensive, and Complete) for an existing building. I performed a nonlinear static pushover analysis (NSP) and I got the spectral capacity curve (spectral acceleration vs spectral displacement curve). As the last step to draw the fragility cure, I need to determine the lognormal mean modal displacement and lognormal standard deviation of modal displacement values from the capacity curve. How can I do that according to FEMA (or HAZUS)? pictures for Base shear-Displacement and spectral acceleration-displacement curves are attached. I appreciate your help.
After you got Base shear-displacement, you will convert them to relation of acceleration and displacement. Herein, you determine the position of damage states (slight, Moderate, Extensive, and Complete). Finally, using fragility function in HAZUS-MH Software - MH MR1 to plot fragility curves.
The lognormal mean and lognormal standard deviation are used for incremental dynamic method.
Dear Ngo Thuyet
thank you so much for your respond. If I want to draw the fragility curve in excel (HAZUS-MH Software - MH MR1 didn't work on my computer). HAZUS Technical Manual provided tables with values of median and Beta for different types of buildings as shown in the IMAGE below (the highlighted building is my type building). But if I use these values, then why do I need to establish my pushover curve and convert it to the spectral capacity curve. I didn't understand your say: "Finally, using fragility function in HAZUS-MH Software - MH MR1 to plot fragility curves". Can you explain how can I get these functions please?
Again thank you so much for your help.
Best regards,
Note: my pushover and spectral capacity curves are established by ETABS 2013 and attached in the question.
Dear Ngo Thuyet
thank you so much for your respond. If I want to draw the fragility curve in excel (HAZUS-MH Software - MH MR1 didn't work on my computer). HAZUS Technical Manual provided tables with values of median and Beta for different types of buildings as shown in the IMAGE below (the highlighted building is my type building). But if I use these values, then why do I need to establish my pushover curve and convert it to the spectral capacity curve. I didn't understand your say: "Finally, using fragility function in HAZUS-MH Software - MH MR1 to plot fragility curves". Can you explain how can I get these functions please?
Again thank you so much for your help.
Best regards,
Note: my pushover and spectral capacity curves are established by ETABS 2013 and attached in the question.
You can plot by NORMSDIST command in Excel or CDF command in MathLab.
According to the attached file, authors divided damage states to 4 level and calculated the mean and standard deviation of them, you only plot fragility curves.
If you model the structure by Sap or ETab and estimate vulnerability by nonlinear static pushover analysis, you can click Display > Show Static pushover Curve > Choose type of picture > Sa-Sd (Using FEMA, ATC) or using fomula in attached file.
Nog Thuyet
Yes, NORMDIST command in excel determines the distribution function. But I need mean and standard deviation, the command in excel: =NORMDIST(x, mean, standard deviation, cumulative), so I should enter mean & Std. Dev. inside the command. How can I calculate (determine) mean and standard deviation from spectral capacity curve (Sa - Sd curve)? I mean how can I get the mean & Std. Dev. from the capacity curve so that they represent my building when I draw the fragility curve?
Thanks for your time and help.
If you used the nonlinear static pushover analysis, you can plot Base shear-displacement -> convert to Sa-Sd -> plot fragility curves.
However, using nonlinear dynamic analysis with input of some ground motions, for each ground motion we can plot each curve of Sa-drift ratio. So the curves is different for every ground motion. Therefore, we can determine mean and standard deviation of them.
Ngo Thuyet
"If you used the Base shear-displacement -> convert to Sa-Sd -> plot fragility curves". You mean I don't need to determine mean & Std. Dev. from Sa - Sd curve to plot the fragility curves for pushover analysis? How can I plot the fragility curves of the four damage states without determining mean & Std. Dev. of them ? I converted Base shear-displacement curve to Sa-Sd curve and waiting to plot fragility curves for the four damage states. Can you please tell thecsteps to do that ? And If it is required to determine mean & Std. Dev., how can I determine them from Sa-Sd curve?
Thank you for your help.
Best regards,
Yes.
For medians of the four damage states I adopted the values proposed by Milutinovic Z.V., Trendafiloski G.S in "RISK-UE, an Advanced Approach to Earthquake
Risk Scenarios with Applications to Different European Towns", 2003 and adopted by IOANA OLTEANU et al. 2011 in their paper titled: "VULNERABILITY AND RISK EVALUATION FOR A REINFORCED CONCRETE FRAME" then for the log-standard deviation (beta), I used the values proposed by Hazus®-MH MR5 Technical and User’s Manual as shown in the attachments. for median you need to establish your own static pushover curve and convert it to Sa-Sd curve then you can determine your medians based on an approximate method like the one mentioned above. for betas you can use the values proposed by HAZUS since the value of Beta is not quantified by structural analysis but approximately established based on statistical analysis of field observation data of building damage.
Hope that helps
Regards,
Dear Abdulelah Al-Ahdal,
I would like calculte fragility parameters (mean and standard deviation) of intake tower height 62.5m from push over analysis. How can i calculate the fragility parameters?
try this paper
Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...
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