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Buy this this booklet and the respective software under http://www.iabse.ethz.ch/publications/seddocuments/SED5.php
Copyright 1997 by International Association for Bridge and Structural Engineering Second Edition 2006 All rights reserved. No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher ISDN 3 85748 093 6 Publisher: IABSE-AIPC-IVBH ETH Hönggerberg CH-8093 Zürich, Switzerland Phone: Fax: E-mail: Web:
Int. + 41-44-633 2647 Int. + 41-44-633 1241
[email protected] www.iabse.org
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Preface Working Commission I of the International Association of Bridge and Structural Engineering (IABSE) has been looking for a short, informative, and more educational type of text on structural safety and reliability analysis to advance the use of reliability methods in structural engineering. The text should serve the interests of practising structural engineers who are not yet familiar with the subject. Working Commission I finally suggested that an existing textbook should be chosen and, if necessary, translated into English. The book you hold in your hand is the result of this undertaking. The text and figures are based on parts of the lecture course "Safety and Reliability of Structures" (Schneider, 1996) given (in German) to 3rd year students in the Civil Engineering Department of the Swiss Federal Institute of Technology, Zurich (ETHZ). This course was very much influenced by a short course given in Zurich by A. Nowak in 1987. This is gratefully acknowledged. The book is intended both for students and practising engineers. It aims to keep things understandable and to explain concepts and procedures by simple examples rather than by digging deep into the theory. Thus, almost no proofs are given in this book. It is hoped that this book serves its pur pose in furthering a topic which is gaining more and more attention and finding increasing application in practice. A first translation from the German was made by E.G. Prater, of ETHZ. The author wishes to thank Dr. Prater, as well as Dr. Hillary Hart , of the University of Texas at Austin, U.S.A., who both contributed to quite a number of improvements of the original text. A number of members of IABSE's Working Commission I and of the JCSS have carefully read the text pointing out mistakes and suggested shortening and amending here and there. Among those whose help is gratefully acknowledged are T. Vrouwenvelder and R. Rackwitz. Zurich, Spring 1997
Jörg Schneider
Second Edition This SED 5 was well received in 1997 and sold out in 2006. IABSE decided to print an essentially unchanged Second Edition. The author, in re-formatting the book, took the chance to correct a few misprints and errors and to add a few sentences and references. This Second Edition, grace to M. Petschacher, is supplemented with a free educational type of Variables Processor software, i.e., VaP 1.6, and a free one-year trial Software, VaP 2.2. Using this software may help in understanding the subjects treated. Zurich, Summer 2006
Jörg Schneider
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Table of Contents 1. Introduction 1.1 Main concepts 1.11 Safety 1.12 Reliability 1.13 Underlying concepts a) Probability and frequency b) Risk c) How safe is safe enough? d) Optimal design 1.2 Hazards in structural engineering 1.21 Findings from 800 failure cases 1.22 Hazard potential, safety, residual risks 1.23 Snow – an example 1.24 Strategies against human error 1.3 Dealing with hazards 1.31 Hazard recognition 1.32 Hazard scenarios 1.33 Categories of countermeasures 1.4 Basic documents 1.41 Hierarchical ordering 1.42 Service criteria agreement 1.43 Safety plan 1.44 Operational basic documents
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2. Information Processing 2.1 Elementary probability concepts 2.11 Events 2.12 Probabilities a) Classical probability b) Empirical probability c) Subjective probability 2.13 Axioms and computational rules 2.14 Determination of probabilities a) Estimating subjective probabilities b) Bayes's updating c) Empirical probabilities 2.2 Evaluation of samples 2.21 Basic notions 2.22 Histograms 2.23 Stochastic processes in time 2.24 Parameters from random samples 2.3 Distributions 2.31 Definitions 2.32 Important continuous distribution functions a) Symmetrical distributions b) Asymmetrical distributions
25 25 25 25 26 26 27 27 27 29 29 29 29 30 30 31 32 32 33 33 34
5 2.33 Probability paper 2.34 Discrete and mixed distribution functions 2.4 Parameter estimation and extrapolation 2.41 General 2.42 Parameter estimation 2.43 Distribution fitting using probability paper 2.44 Extrapolations 2.5 Observations in pairs and two-dimensional distributions 2.51 Problem description 2.52 Correlation 2.53 Regression 2.54 Bivariate distribution function 2.6 Functions of random variables 2.61 Computational rules 2.62 The central limit theorem 2.63 Further parameters of functions of variables
35 35 36 36 37 37 38 39 39 40 40 40 41 41 42 43
3. Basic Variables and Modelling 3.1 Introduction 3.2 State, components, basic variables 3.21 Basis of assessment 3.22 Basic variables 3.3 Resistance of structural elements 3.31 Resistance model 3.32 Model uncertainties 3.33 Material properties 3.34 Geometrical properties 3.4 Action effects in structural elements 3.41 Actions 3.42 Modelling of actions 3.43 Combination of action effects a) Turkstra's rule b) The Ferry Borges-Castanheta model 3.44 Model uncertainties 3.45 Some comments on actions 3.5 Other fields of engineering
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4. Reliability Analysis Methods 4.1 Preliminary remarks 4.2 The Monte-Carlo method 4.3 The problem G = R – S 4.31 Introduction and example 4.32 The classical solution 4.33 Basler , in the notation of Cornell 4.34 Representation as a joint probability density 4.35 The Method of Hasofer and Lind
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6 4.4 Extensions of the Hasofer/Lind method 4.41 Linear limit state functions with many variables 4.42 Non-linear limit state functions 4.43 Non-normally distributed variables a) Tail approximation b) Transformation into the standard-normal space 4.44 The use of computer programs 4.45 Remarks on correlated variables 4.5 Deriving partial safety factors 4.51 Design formats 4.52 Partial factors 4.53 Linearisation 4.6 Elementary approach to the reliability of systems 4.61 Definitions 4.62 Series systems 4.63 Parallel systems 4.64 Mixed systems
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5. Assessment, Judgement, and Quality Assurance 5.1 Target reliabilities 5.11 Calibration to existing practice 5.12 Reliability differentiation 5.13 The need for strategies against human error 5.2 Assessing existing structures 5.21 General considerations a) Responsibilities b) Basis of assessment c) Updating of information 5.22 Assessment phases a) Phase I: Preliminary assessment b) Phase II: Detailed investigations c) Phase III: Calling a team of experts 5.23 Activating reserves a) Preparing the basic documents b) Assessing the structure c) Loads and actions d) Material properties e) Structural system f) Methods of analysis and design 5.24 Reliability assessment 5.3 A case for Quality Assurance 5.31 Perceptions of the concept 5.32 Quantification of quality 5.33 The battle against errors 5.34 Does Quality Assurance pay dividends?
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6. Appendix 6.1 Frequently used distribution types 6.2 Standard-Normal distribution 6.3 Probability papers 6.31 Procedures a) Choosing the most appropriate paper b) Introducing the data c) Fitting the straight line d) Calculation of the distribution parameters 6.32 Normal probability paper 6.33 Log-Normal probability paper 6.34 Gumbel probability paper 6.4 Computer programs 6.41 STRUREL 6.42 VaP 6.43 SAPOS 6.5 Literature 6.51 References 6.52 Further reading
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