Reliability-based Structural Design - download pdf or read online

By Seung-Kyum Choi

ISBN-10: 1846284449

ISBN-13: 9781846284441

ISBN-10: 1846284457

ISBN-13: 9781846284458

This publication offers readers with an figuring out of the basics and purposes of structural reliability, stochastic finite aspect strategy, reliability research through stochastic enlargement, and optimization below uncertainty. It examines using stochastic expansions, together with polynomial chaos enlargement and Karhunen-Loeve growth for the reliability research of useful engineering difficulties.

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Hasofer and Lind [15] provide a geographic interpretation of the safety index and improve the FOSM method by introducing the Hasofer and Lind (HL) transformation. In the transformation procedure, the design vector X is transformed into the vector of standardized, independent Gaussian variables, U. 2. Because it makes the most significant contribution to the nominal failure probability Pf ) ( E ) , this design point is called the Most Probable failure Point (MPP).

5. 4 If ln X has a Gaussian distribution, what is the distribution of X ? Solution: This problem is the proof of the derived density of the lognormal distribution. Let Y = ln X. Then X e Y . 45. 4, ª 1 § ln x P Y exp« ¨¨ «¬ 2 © V Y 2S xV Y 1 f X ( x) · ¸¸ ¹ 2 º » »¼ Therefore, if ln X is normal, the random variable X has a lognormal distribution. 6) consists of the gamma function, a mathematical function defined in terms of an integral. This distribution is important because it allows us to define two families of random variables, the exponential and chi-square, which are used extensively in applied engineering and statistics.

16a). 16b). The current section discusses the fitting of polynomials to data in some detail, and the next section presents statistical tests to help determine the appropriate regression model to use. An understanding of polynomial approximation provides the foundation for most numerical analysis since polynomials are frequently used to approximate numerical solutions. In addition, solutions of many physical problems resemble polynomials, and in turn, polynomial approximation sometimes produces exact answers.

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