By Palle Thoft-Christensen Ph. D., Michael J. Baker B.Sc. (Eng) (auth.)
Structural reliability concept is worried with the rational remedy of uncertainties in struc tural engineering and with the equipment for assessing the protection and serviceability of civil en gineering and different buildings. it's a topic which has grown speedily over the last decade and has developed from being an issue for tutorial study to a collection of well-developed or enhance ing methodologies with quite a lot of sensible purposes. Uncertainties exist in so much components of civil and structural engineeri'1.g and rational layout judgements can't be made with out modelling them and taking them into consideration. Many structural en gineers are protected from having to contemplate such difficulties, a minimum of while designing basic buildings, as a result of the prescriptive and basically deterministic nature of such a lot codes of perform. this is often an bad state of affairs. so much so much and different structural layout parameters are hardly recognized with sure bet and will be considered as random variables or stochastic strategies, whether in layout calculations they're ultimately taken care of as deterministic. a few difficulties reminiscent of the research of load mixtures can't also be formulated with no recourse to probabilistic reasoning.
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33)). Admittedly this approach can be adopted only when such information is available_ Expressing this problem in another way, it is important that the statistical analysis of data should be restricted to samples which are homogeneous (or more precisely - for which there is no evidence of non-homogeneity). A further aspect of modelling must now be introduced. Models do not represent reality, they only approximate it. g. finite-element versus finite-difference approaches. The same is true of probabilistic models.
Let X be log-normally distributed with the parameters Ily and ay . Note that Ily and ay are not equal to IlX and ax. 53) . 8. Let X be log-normally distributed with the parameters Ily and ay . ;;; x) Qnx -Ily . ) = ( a y is the standard normal distribution function. 9. 12. 2 MPa). Then /lx 1 = exp(3 + 2". 4 . 10-4 An important distribution is the so-called Weibull distribution with 3 parameters (3, e and k. , e and (3 If e > 1, k > e. 10. 57) 28 2. 0 .. 7 RANDOM VECTORS Until now, the concept of a random variable has been used only in a one-dimensional sense.
11 are such that a logarithmic normal distribution plots as a straight line. 50 3. 1 /. 4 ~ ( /. / V Mill »Y. 10. Cumulative frequency diagram for yield stress of mild steel plates. 1 ..... ,-:::: ~ rt" •. 11. Combined cumulative frequency diagram for 12 mm mild steel plates from three mills. 4 MODELLING OF RESISTANCE VARIABLES - MODEL SELECTION We now return to the question of selecting a suitable probability distribution to model the uncertainty in the strength variable X. It should be clear from the preceding arguments that a procedure of random sampling and testing of, say, reinforcing bars at a construction site and attempts to fit a standard probability distribution to the data will not lead to a sensible outcome.