Safety is a necessity, and for the assessment of structures, getting a reliability index is interesting and helpful, but how can we calculate it, and which code gives the best index?
The Eurocode 1990 is the standard giving the the acceptable level of failure probability. It contains also a brief survey on methods applicable to calculate the failure probability or the reliability index in practical application.
The Eurocode 1990 is the standard giving the the acceptable level of failure probability. It contains also a brief survey on methods applicable to calculate the failure probability or the reliability index in practical application.
If you can canculate the probability of construction failure, you can calculate the reliability index from normalized Normal (Gauss) distribution. But in my opinion using the sole probability is a better idea. The probability density function of random function describing reliability can have different form than Normal distribution. I use Monte Carlo simulation method and the resulting function often has quite high skewness. Equating probability od failure with reliability index in such case can be erroneous.
The Eurocode 0 provides target reliability indexes for serviceability and ultimate limit states
In order to calculate reliability (safety) index of systems like structures, it could be followed two different approaches:
1- Extract performance or failure functions as:
g = Capacity - Demand
and then performing FORM, SORM or simulation techniques such as Monte-Carlo and 2k+1. but it must be considered that extracting this close form failure function will not be easy and most times only for linear elastic system will be available.
2- In cases which you expect structure to undergo nonlinear branch of behavior, like earthquake excitation, it would be practical to conduct nonlinear time-history or incremental dynamic analysis (IDA) and then plot fragility curve to each desired performance level or failure. then safety index could be calculated using approximate relation as below:
beta = -1*inverse_standard normal (probability of failure)
In the case of fatitgue design you can use a probabilistic approach to be applied to the Miner number as proposed in our Publication
Fernández-Canteli A., Blasón S., Correia J.A.F.O., de Jesus A.M.P.
“A probabilistic interpretation of the Miner number for fatigue life prediction”
Frattura ed Integrità Strutturale/Fracture and Structural Integrity Journal, 30, 325-339, 2014.
The Eurocode 4 is in this respect painful
Best regards.
Alfonso
Thank You so much Sir Alfonso for the answer, helpful as well.
Best Regards,
Hi
I advice you to see the books " Structural Reliability Analysis " and " Uncertainty Modeling and Analysis in Civil Engineering ".
You will find what you need.
Best regards
https://books.google.fr/books?id=1yxtNSrrfoMC&pg=PA35&lpg=PA35&dq=reliability+index+for+civil+engineering+structures&source=bl&ots=KRbg68Enet&sig=yln8CITzhXmTy1sB55wVt0XKcT0&hl=fr&sa=X&ei=q6NjVbqqGYfjUZKjgLAI&ved=0CDoQ6AEwAw#v=onepage&q=reliability%20index%20for%20civil%20engineering%20structures&f=false
https://books.google.fr/books?id=c4ttTMnqswAC&pg=PA311&lpg=PA311&dq=reliability+index+for+civil+engineering+structures&source=bl&ots=FBR-iie27B&sig=_gakv8tIHK6v97S-_k3Z-NIDQG8&hl=fr&sa=X&ei=q6NjVbqqGYfjUZKjgLAI&ved=0CFgQ6AEwBw#v=onepage&q=reliability%20index%20for%20civil%20engineering%20structures&f=false
Hi all, can you suggest me, how I can calculate reliability index, β from seismic fragility curve?
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