Empirical Limit State Modelling in Reliability Analysis

  • Gunnar Mohr
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


Carrying capacity interaction diagrams are often established by using regression analysis on a given, usually small, set of interaction data. From a structural reliability point of view such regression analyses are not completely satisfactory. In this paper a different approach is followed.

First,a suitable (and preferably mechanically based) analytical expression of the failure function is formulated. The expression typically contains a number of unknown parameters. These are modelled as random variables whose joint distributional properties are obtained by use of Bayesian methods. Thus, a random set of failure functions is established. This set can be used directly in a modern reliability analysis. For the communication of the results of the analysis,it is often convenient not to have parameters without mechanical relevance in the interaction diagram expression. Therefore, special attention is given to the problems of eliminating these parameter random variables from the interaction diagram equation and transforming their randomness into model uncertainty randomness.

The ideas are exemplified by the examination of a small sample of interaction data related to the moment-normal force failure condition of a specific type of wall element.


Reliability Index Limit State Function Structural Reliability Moment Capacity Interaction Diagram 
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  1. 1.
    Madsen, H.O., Krenk, S. & Lind, N.C.,Methods of Structural Safety. Prentice Hall, Inc. New Jersey. 1986.Google Scholar
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    Ditlevsen, O., Uncertainty Modeling. McGraw-Hill Inc. New York. 1981.MATHGoogle Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1994

Authors and Affiliations

  • Gunnar Mohr
    • 1
  1. 1.Department of Civil EngineeringEngineering Academy of DenmarkLyngbyDenmark

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