## Methods of Structural Reliability Analysis

le Lecture: Methods of Structural Reliability Analysis The aim of the present lecture is to introduce the most common techniques of structural reliability analysis, namely, First Order Reliability Methods (FORM) and Monte-Carlo simulation. First the concept of limit state equations and basic random variables is introduced. Thereafter the problem of error propagation is considered and it is shown that FORM provides a generalization of the classical solution to this problem. Different cases of limit state functions and probabilistic characteristics of basic random variables are then introduced with increasing generality. Furthermore, FORM results are related to partial safety factors used in common design codes. Subsequently, crude Monte-Carlo and Importance sampling is introduced as an alternative to FORM methods. The introduced methods of structural reliability theory provide strong tools for the calculation of failure probabilities for individual failure modes or components. On the basis of the present lecture, it is expected that the students should acquire knowledge and skills in regard to:
• What is a basic random variable and what is a limit state function? • What is the graphical interpretation of the reliability index? • What is the principle for the linearization of non-linear limit state functions? • How to transform non-normal distributed random variables into normal distributed variables? • How to consider dependent random variables? • How are FORM results related to partial safety factors? • What is the principle of Monte-Carlo simulation methods? • Why is importance sampling effective and what does it require in terms of information additional to crude Monte-Carlo methods?

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