Euro-SiBRAM’2002 Prague, June 24 to 26, 2002, Czech Republic
Session 4 – Discussion
Reference Function and Reference Values in SBRA
In the current interpretations of the Limit States Philosophy, in so called Partial Factors Design (see, e.g., LRFD in the U.S. and Eurocode in Europe), it can be understood that the resistance of structural components and systems is in the limit states of carrying capacity defined by the “ultimate” plastic behaviour. In case of a steel beam, for example, the resistance is expressed by a bending moment corresponding to the formation of a plastic hinge. The safety assessment is based on comparing the maximum “design” load effects combinations and the “ultimate” resistance.
Such approach is not applied in the fully probabilistic SBRA method. The probability of failure expresses the probability of exceedance of a “use-ability” limit (and not the limit expressed, e.g., by plastic collapse mechanism).
In order to make clear the difference between the “ultimate values” applied in the Partial Factors Design concept and the “limit values” applied in a probabilistic approach, the authors of SBRA introduced the term Reference Value, which expresses the substance of the limit in the calculation of the probability of exceedance. For example, if a limit of the use-ability of a steel beam steel beam is defined by onset of yielding, the “Reference Function” is defined by a yield stress histogram. In each simulation step one random selected yield stress “Reference Value” is applied. In such way the Reliability Function RF = (RV – S) is evaluated, where RV defines the limit of “use-fulness”, and S represents the load effects combination.
The textbook [1] contains basic definitions, comments and examples of the application of Reference Values, RV, considering safety assessment as well as serviceability and durabilitz assessment.
Reference function in reliability conditions according to SBRA constitute variable limitations on resistance and serviceability requirements. They are expressed in various forms according to the character of the individual reliability conditions and may be expressed by elementary values or by compound values. Examples of elementary RV are either blurred, such as yield stress expressed by histogram, or sharp expressed, for example, by “tolerable” strain and/or deformation, and “tolerable” acceleration, as requested by the user or as specified in standards. Compound RV values might be resistance of a cross-section of a beam exposed to bending, resistance of a column, or fatigue life of a structural element expressed by Palmgren- Miner’s rule. RV values for particular problems and applications are related to the types of transformation models used, the character of the particular reliability condition and the way in which it is expressed.
The determination of RV may be based on such factors as: available statistics of relevant data, estimates, calibration, and agreement among the designer, user, and the institution having jurisdiction. It should be emphasized that RV are only one component of a complex procedure. RV values, therefore, should be determined and applied in reliability assessment only in harmony with the principles of individual reliability conditions (see [1]).
The RV values are generally random variables expressed by parametric frequency distributions or by bounded histograms. In special situations the RV values may be expressed by a particular values. The survey of RV in [1], although far from complete, provides an idea of the diversity and character of these variables and their application in probabilistic simulation-based reliability assessment of structures and emphasizes the creative role of the designer.
Using probabilistic simulation-based reliability assessment method (such as SBRA), in individual design situation the correct and complete definition, explanation and justification of the selected Reliability Function/Values are needed. The probability of failure cannot be properly determined without specifying an adequate Reference Function/Value.
The interaction of the Design Target Probabilities (contained in codes) and Reference Values is to be considered. According to the “rules of the game” of the probabilistic structural reliability assessment, the complete definition of the Reference Values in individual cases is as important as a correct evaluation of the Load Effects.
Numerous examples in the textbook [1] can serve for illustration of the application of the Reference Values in the safety, serviceability and durability assessment of structures. All Authors of examples contained in the book were asked to make very clear the selection and definition of the Reference Values applied in their text.
In the development of codes and databases for structural design based on probabilistic reliability assessment method, special attention must be given to the definitions of the Reference Values.
[1] Marek P., Brozzetti J. and Guštar M. (edit.) Probabilistic Reliability Assessment of Structures using Monte Carlo Simulation. Basics, Exercises, Software. (2001).Published by ITAM Academy of Sciences of Czech Republic, Prague.