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El. knyga: Structural Reliability Analysis and Prediction

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(University of Sćo Paulo, Brazil), (The University of Newcastle, Australia)
  • Formatas: EPUB+DRM
  • Išleidimo metai: 02-Nov-2017
  • Leidėjas: John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9781119266068
Kitos knygos pagal šią temą:
Structural Reliability Analysis and PredictionDidesnis paveikslėlis
  • Formatas: EPUB+DRM
  • Išleidimo metai: 02-Nov-2017
  • Leidėjas: John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9781119266068
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Structural Reliability Analysis and Prediction, Third Edition is a textbook which addresses the important issue of predicting the safety of structures at the design stage and also the safety of existing, perhaps deteriorating structures. Attention is focused on the development and definition of limit states such as serviceability and ultimate strength, the definition of failure and the various models which might be used to describe strength and loading. This book emphasises concepts and applications, built up from basic principles and avoids undue mathematical rigour. It presents an accessible and unified account of the theory and techniques for the analysis of the reliability of engineering structures using probability theory.

This new edition has been updated to cover new developments and applications and a new chapter is included which covers structural optimization in the context of reliability analysis. New examples and end of chapter problems are also now included.

Preface xv
Preface to the Second Edition xvii
Preface to the First Edition xviii
Acknowledgements xx
1 Measures of Structural Reliability 1(30)
1.1 Introduction
1(1)
1.2 Deterministic Measures of Limit State Violation
2(6)
1.2.1 Factor of Safety
2(1)
1.2.2 Load Factor
3(1)
1.2.3 Partial Factor ('Limit State Design')
4(1)
1.2.4 A Deficiency in Some Safety Measures: Lack of Invariance
5(3)
1.2.5 Invariant Safety Measures
8(1)
1.3 A Partial Probabilistic Safety Measure of Limit State Violation-The Return Period
8(4)
1.4 Probabilistic Measure of Limit State Violation
12(12)
1.4.1 Introduction
12(2)
1.4.2 The Basic Reliability Problem
14(3)
1.4.3 Special Case: Normal Random Variables
17(2)
1.4.4 Safety Factors and Characteristic Values
19(4)
1.4.5 Numerical Integration of the Convolution Integral
23(1)
1.5 Generalized Reliability Problem
24(5)
1.5.1 Basic Variables
24(1)
1.5.2 Generalized Limit State Equations
25(1)
1.5.3 Generalized Reliability Problem Formulation
26(1)
1.5.4 Conditional Reliability Problems
27(2)
1.6 Conclusion
29(2)
2 Structural Reliability Assessment 31(32)
2.1 Introduction
31(2)
2.2 Uncertainties in Reliability Assessment
33(12)
2.2.1 Identification of Uncertainties
33(1)
2.2.2 Phenomenological Uncertainty
34(1)
2.2.3 Decision Uncertainty
34(1)
2.2.4 Modelling Uncertainty
34(1)
2.2.5 Prediction Uncertainty
35(1)
2.2.6 Physical Uncertainty
36(1)
2.2.7 Statistical Uncertainty
36(1)
2.2.8 Uncertainties Due to Human Factors
37(8)
2.2.8.1 Human Error
37(3)
2.2.8.2 Human Intervention
40(3)
2.2.8.3 Modelling of Human Error and Intervention
43(1)
2.2.8.4 Quality Assurance
44(1)
2.2.8.5 Hazard Management
45(1)
2.3 Integrated Risk Assessment
45(6)
2.3.1 Calculation of the Probability of Failure
45(2)
2.3.2 Analysis and Prediction
47(1)
2.3.3 Comparison to Failure Data
48(2)
2.3.4 Validation-a Philosophical Issue
50(1)
2.3.5 The Tail Sensitivity 'Problem'
50(1)
2.4 Criteria for Risk Acceptability
51(5)
2.4.1 Acceptable Risk Criterion
51(3)
2.4.1.1 Risks in Society
51(2)
2.4.1.2 Acceptable or Tolerable Risk Levels
53(1)
2.4.2 Socio-economic Criterion
54(2)
2.5 Nominal Probability of Failure
56(4)
2.5.1 General
56(1)
2.5.2 Axiomatic Definition
56(1)
2.5.3 Influence of Gross and Other Errors
57(1)
2.5.4 Practical Implications
58(1)
2.5.5 Target Values for Nominal Failure Probability
59(1)
2.6 Hierarchy of Structural Reliability Measures
60(1)
2.7 Conclusion
61(2)
3 Integration and Simulation Methods 63(32)
3.1 Introduction
63(1)
3.2 Direct and Numerical Integration
63(2)
3.3 Monte Carlo Simulation
65(8)
3.3.1 Introduction
65(1)
3.3.2 Generation of Uniformly Distributed Random Numbers
65(1)
3.3.3 Generation of Random Variates
66(2)
3.3.4 Direct Sampling ('Crude' Monte Carlo)
68(1)
3.3.5 Number of Samples Required
69(3)
3.3.6 Variance Reduction
72(1)
3.3.7 Stratified and Latin Hypercube Sampling
73(1)
3.4 Importance Sampling
73(9)
3.4.1 Theory of Importance Sampling
73(2)
3.4.2 Importance Sampling Functions
75(1)
3.4.3 Observations About Importance Sampling Functions
76(3)
3.4.4 Improved Sampling Functions
79(1)
3.4.5 Search or Adaptive Techniques
80(1)
3.4.6 Sensitivity
81(1)
3.5 Directional Simulation
82(8)
3.5.1 Basic Notions
82(2)
3.5.2 Directional Simulation with Importance Sampling
84(1)
3.5.3 Generalized Directional Simulation
85(2)
3.5.4 Directional Simulation in the Load Space
87(3)
3.5.4.1 Basic Concept
87(2)
3.5.4.2 Variation of Strength with Radial Direction
89(1)
3.5.4.3 Line Sampling
90(1)
3.6 Practical Aspects of Monte Carlo Simulation
90(3)
3.6.1 Conditional Expectation
90(1)
3.6.2 Generalized Limit State Function - Response Surfaces
91(1)
3.6.3 Systematic Selection of Random Variables
92(1)
3.6.4 Applications
92(1)
3.7 Conclusion
93(2)
4 Second-Moment and Transformation Methods 95(36)
4.1 Introduction
95(1)
4.2 Second-Moment Concepts
95(2)
4.3 First-Order Second-Moment (FOSM) Theory
97(15)
4.3.1 The Hasofer-Lind Transformation
97(1)
4.3.2 Linear Limit State Function
98(3)
4.3.3 Sensitivity Factors and Gradient Projection
101(1)
4.3.4 Non-Linear Limit State Function-General Case
102(4)
4.3.5 Non-Linear Limit State Function-Numerical Solution
106(1)
4.3.6 Non-Linear Limit State Function-HLRF Algorithm
106(3)
4.3.7 Geometric Interpretation of Iterative Solution Scheme
109(1)
4.3.8 Interpretation of First-Order Second-Moment (FOSM) Theory
110(2)
4.3.9 General Limit State Functions-Probability Bounds
112(1)
4.4 The First-Order Reliability (FOR) Method
112(14)
4.4.1 Simple Transformations
112(2)
4.4.2 The Normal Tail Transformation
114(2)
4.4.3 Transformations to Independent Normal Basic Variables
116(5)
4.4.3.1 Rosenblatt Transformation
117(1)
4.4.3.2 Nataf Transformation
118(3)
4.4.4 Algorithm for First-Order Reliability (FOR) Method
121(3)
4.4.5 Observations
124(1)
4.4.6 Asymptotic Formulation
125(1)
4.5 Second-Order Reliability (SOR) Methods
126(2)
4.5.1 Basic Concept
126(1)
4.5.2 Evaluation Through Sampling
126(1)
4.5.3 Evaluation Through Asymptotic Approximation
127(1)
4.6 Application of FOSM/FOR/SOR Methods
128(1)
4.7 Mean Value Methods
129(1)
4.8 Conclusion
130(1)
5 Reliability of Structural Systems 131(48)
5.1 Introduction
131(1)
5.2 Systems Reliability Fundamentals
132(15)
5.2.1 Structural System Modelling
132(4)
5.2.1.1 Load Modelling
132(1)
5.2.1.2 Material Modelling
133(2)
5.2.1.3 System Modelling
135(1)
5.2.2 Solution Approaches
136(3)
5.2.2.1 Failure Mode Approach
136(1)
5.2.2.2 Survival Mode Approach
137(1)
5.2.2.3 Upper and Lower Bounds-Plastic Theory
138(1)
5.2.3 Idealizations of Structural Systems
139(8)
5.2.3.1 Series Systems
139(2)
5.2.3.2 Parallel Systems-General
141(2)
5.2.3.3 Parallel Systems-Ideal Plastic
143(3)
5.2.3.4 Combined and Conditional Systems
146(1)
5.3 Monte Carlo Techniques for Systems
147(6)
5.3.1 General Remarks
147(1)
5.3.2 Importance Sampling
147(4)
5.3.2.1 Series Systems
147(2)
5.3.2.2 Parallel Systems
149(1)
5.3.2.3 Search-Type Approaches in Importance Sampling
150(1)
5.3.2.4 Failure Modes Identification in Importance Sampling
151(1)
5.3.3 Directional Simulation
151(1)
5.3.4 Directional Simulation in the Load Space
151(2)
5.4 System Reliability Bounds
153(15)
5.4.1 First-Order Series Bounds
153(1)
5.4.2 Second-Order Series Bounds
154(3)
5.4.3 Second-Order Series Bounds by Loading Sequences
157(1)
5.4.4 Series Bounds by Modes and Loading Sequences
158(1)
5.4.5 Improved Series Bounds and Parallel System Bounds
158(1)
5.4.6 First-Order Second-Moment Method in Systems Reliability
159(5)
5.4.7 Correlation Effects
164(1)
5.4.8 Bounds by Matrix Operations and Linear Programming
164(4)
5.5 Implicit Limit States
168(5)
5.5.1 Introduction
168(1)
5.5.2 Response Surfaces
169(3)
5.5.2.1 Basics of Response Surfaces
169(1)
5.5.2.2 Fitting the Response Surface
170(2)
5.5.3 Applications of Response Surfaces
172(1)
5.5.4 Other Techniques for Obtaining Surrogate Limit States
173(1)
5.6 Functionally Dependent Limit States
173(4)
5.6.1 Effect of Order of Loading
173(1)
5.6.2 Failure Mode Enumeration and Reduction
174(1)
5.6.3 Reduction of Number of Limit States-Truncation
175(1)
5.6.4 Applications
176(1)
5.7 Conclusion
177(2)
6 Time-Dependent Reliability 179(68)
6.1 Introduction
179(3)
6.2 Time-Integrated Approach
182(3)
6.2.1 Basic Notions
182(2)
6.2.2 Conversion to a Time-Independent Format
184(1)
6.3 Discretized Approach
185(6)
6.3.1 Known Number of Discrete Events
185(2)
6.3.2 Random Number of Discrete Events
187(1)
6.3.3 Return Period
188(1)
6.3.4 Hazard Function
189(2)
6.4 Stochastic Process Theory
191(5)
6.4.1 Stochastic Process
191(1)
6.4.2 Stationary Processes
192(1)
6.4.3 Derivative Process
193(1)
6.4.4 Ergodic Processes
194(1)
6.4.5 First-Passage Probability
194(2)
6.4.6 Distribution of Local Maxima
196(1)
6.5 Stochastic Processes and Outcrossings
196(19)
6.5.1 Discrete Processes
196(6)
6.5.1.1 Borges Processes
196(1)
6.5.1.2 Poisson Counting Process
197(1)
6.5.1.3 Filtered Poisson process
198(1)
6.5.1.4 Poisson Spike Process
199(1)
6.5.1.5 Poisson Square Wave Process
200(1)
6.5.1.6 Renewal Processes
201(1)
6.5.2 Continuous Processes
202(1)
6.5.3 Barrier (or Level) Uperossing Rate
202(3)
6.5.4 Outcrossing Rate
205(9)
6.5.4.1 Generalization from Barrier Crossing Rate
205(2)
6.5.4.2 Outcrossings for Discrete Processes
207(2)
6.5.4.3 Outcrossings for Continuous Gaussian Processes
209(4)
6.5.4.4 General Regions and Processes
213(1)
6.5.5 Numerical Evaluation of Outcrossing Rates
214(1)
6.6 Time-Dependent Reliability
215(11)
6.6.1 Introduction
215(1)
6.6.2 Sampling Methods for Unconditional Failure Probability
216(2)
6.6.2.1 Importance and Conditional Sampling
216(1)
6.6.2.2 Directional Simulation in the Load Process Space
217(1)
6.6.3 FOSM/FOR Methods for Unconditional Failure Probability
218(7)
6.6.4 Summary for Time-Dependent Reliability Estimation
225(1)
6.7 Load Combinations
226(8)
6.7.1 Introduction
226(1)
6.7.2 General Formulation
226(2)
6.7.3 Discrete Processes
228(2)
6.7.4 Simplifications
230(4)
6.7.4.1 Load Coincidence Method
230(1)
6.7.4.2 Borges Processes
231(2)
6.7.4.3 Deterministic Load Combination-Turkstra's Rule
233(1)
6.8 Ensemble Crossing Rate and Barrier Failure Dominance
234(3)
6.8.1 Introduction
234(1)
6.8.2 Ensemble Crossing Rate Approximation
234(1)
6.8.3 Application to Turkstra's Rule and the Point Crossing Formula
235(1)
6.8.4 Barrier Failure Dominance
236(1)
6.8.5 Validity
237(1)
6.9 Dynamic Analysis of Structures
237(4)
6.9.1 Introduction
237(1)
6.9.2 Frequency Domain Analysis
238(2)
6.9.3 Reliability Analysis
240(1)
6.10 Fatigue Analysis
241(3)
6.10.1 General Formulation
241(1)
6.10.2 The S-N Model
242(1)
6.10.3 Fracture Mechanics Models
243(1)
6.11 Conclusion
244(3)
7 Load and Load Effect Modelling 247(26)
7.1 Introduction
247(1)
7.2 Wind Loading
248(4)
7.3 Wave Loading
252(3)
7.4 Floor Loading
255(16)
7.4.1 General
255(1)
7.4.2 Sustained Load Representation
256(4)
7.4.3 Equivalent Uniformly Distributed Load
260(3)
7.4.4 Distribution of Equivalent Uniformly Distributed Load
263(2)
7.4.5 Maximum (Lifetime) Sustained Load
265(2)
7.4.6 Extraordinary Live Loads
267(1)
7.4.7 Total Live Load
268(1)
7.4.8 Permanent and Construction Loads
269(2)
7.5 Conclusion
271(2)
8 Resistance Modelling 273(20)
8.1 Introduction
273(1)
8.2 Basic Properties of Hot-Rolled Steel Members
273(7)
8.2.1 Steel Material Properties
273(1)
8.2.2 Yield Strength
274(3)
8.2.3 Moduli of Elasticity
277(1)
8.2.4 Strain-Hardening Properties
278(1)
8.2.5 Size Variation
278(1)
8.2.6 Properties for Reliability Assessment
279(1)
8.3 Properties of Steel Reinforcing Bars
280(1)
8.4 Concrete Statistical Properties
281(3)
8.5 Statistical Properties of Structural Members
284(6)
8.5.1 Introduction
284(1)
8.5.2 Methods of Analysis
284(1)
8.5.3 Second-moment Analysis
284(3)
8.5.4 Simulation
287(3)
8.6 Connections
290(1)
8.7 Incorporation of Member Strength in Design
290(2)
8.8 Conclusion
292(1)
9 Codes and Structural Reliability 293(28)
9.1 Introduction
293(1)
9.2 Structural Design Codes
294(2)
9.3 Safety-Checking Formats
296(5)
9.3.1 Probability-Based Code Rules
296(1)
9.3.2 Partial Factors Code Format
297(2)
9.3.3 Simplified Partial Factors Code Format
299(1)
9.3.4 Load and Resistance Factor Code Format
300(1)
9.3.5 Some Observations
300(1)
9.4 Relationship Between Level 1 and Level 2 Safety Measures
301(3)
9.4.1 Derivation from FOSM/FOR Theory
302(1)
9.4.2 Special Case: Linear Limit State Function
303(1)
9.5 Selection of Code Safety Levels
304(1)
9.6 Code Calibration Procedure
305(5)
9.7 Example of Code Calibration
310(5)
9.8 Observations
315(2)
9.8.1 Applications
315(1)
9.8.2 Some Theoretical Issues
316(1)
9.9 Performance-Based Design
317(2)
9.10 Conclusion
319(2)
10 Probabilistic Evaluation of Existing Structures 321(24)
10.1 Introduction
321(2)
10.2 Assessment Procedures
323(4)
10.2.1 Overall Procedure
323(2)
10.2.2 Service-Proven Structures
325(1)
10.2.3 Proof Loading
326(1)
10.3 Updating Probabilistic Information
327(6)
10.3.1 Bayes Theorem
327(1)
10.3.2 Updating Failure Probabilities for Proof Loads
328(1)
10.3.3 Updating Probability Density Functions
328(4)
10.3.4 Pre-Posterior Analysis
332(1)
10.4 Analytical Assessment
333(5)
10.4.1 General
333(1)
10.4.2 Models for Deterioration
334(4)
10.5 Acceptance Criteria for Existing Structures
338(5)
10.5.1 Nominal Probabilities
338(1)
10.5.2 Semi-Probabilistic Safety Checking Formats
339(1)
10.5.3 Probabilistic Criteria
340(1)
10.5.4 Decision-Theory-Based Criteria
340(2)
10.5.5 Life-Cycle Decision Approach
342(1)
10.6 Conclusion
343(2)
11 Structural Optimization and Reliability 345(26)
11.1 Introduction
345(1)
11.2 Types of Reliability-based Optimization Problems
346(8)
11.2.1 Introduction
346(1)
11.2.2 Deterministic Design Optimization (DDO)
347(2)
11.2.2.1 Formulation
347(1)
11.2.2.2 Example of DDO Using FOSM
348(1)
11.2.3 Reliability-Based Design Optimization (RBDO)
349(2)
11.2.3.1 Formulation
349(1)
11.2.3.2 Example of RBDO using FOSM
350(1)
11.2.4 Life-Cycle Cost and Risk Optimization (LCRO)
351(2)
11.2.4.1 Formulation
351(1)
11.2.4.2 Example of LCRO using FOSM
352(1)
11.2.5 Comparison, Summary and Outlook
353(1)
11.3 Reliability Based Design Optimization (RBDO) Using First Order Reliability (FOR)
354(8)
11.3.1 Introduction
354(1)
11.3.2 Alternative Robust Solutions Schemes
354(3)
11.3.3 Comparison Between RIA and PMA Solution Schemes
357(1)
11.3.4 Solution of Nested Optimization Problems
358(1)
11.3.5 Example of RBDO Using RIA and PMA
358(3)
11.3.6 Decoupling Techniques for Solving RBDO Problems
361(1)
11.3.6.1 Decoupling: Serial Single Loop Methods
361(1)
11.3.6.2 Decoupling: Uni-level Methods
361(1)
11.3.6.3 Sequential Approximate Programming (SAP)
361(1)
11.4 RBDO with System Reliability Constraints
362(1)
11.4.1 Formulation of System RBDO
362(1)
11.4.2 Structural Systems RBDO with Component Reliability Constraints
363(1)
11.4.3 Structural System RBDO-solution Schemes
363(1)
11.5 Simulation-based Design Optimization
363(4)
11.5.1 Introduction
363(1)
11.5.2 Problem Formulation
364(1)
11.5.3 Remarks About Solutions
365(2)
11.6 Life-cycle Cost and Risk Optimization
367(1)
11.6.1 Introduction
367(1)
11.6.2 Optimal Structural Design Under Stochastic Loads
367(1)
11.6.3 Optimal Structural Design Considering Inspections and Maintenance
368(3)
11.7 Discussion and Conclusion
368(3)
A Summary of Probability Theory 371(32)
A.1 Probability
371(1)
A.2 Mathematics of Probability
371(2)
A.2.1 Axioms
371(1)
A.2.2 Derived Results
372(1)
A.2.2.1 Multiplication Rule
372(1)
A.2.2.2 Complementary Probability
372(1)
A.2.2.3 Conditional Probability
372(1)
A.2.2.4 Total Probability Theorem
372(1)
A.2.2.5 Bayes' Theoremx
372(1)
A.3 Description of Random Variables
373(1)
A.4 Moments of Random Variables
373(2)
A.4.1 Mean or Expected Value (First Moment)
373(1)
A.4.2 Variance and Standard Deviation (Second Moment)
374(1)
A.4.3 Bounds on the Deviations from the Mean
374(1)
A.4.4 Skewness gamma1 (Third Moment)
374(1)
A.4.5 Coefficient gamma2 of Kurtosis (Fourth Moment)
375(1)
A.4.6 Higher Moments
375(1)
A.5 Common Univariate Probability Distributions
375(15)
A.5.1 Binomial B(n, p)
375(1)
A.5.2 Geometric G(p)
376(1)
A.5.3 Negative Binomial NB(k, p)
376(1)
A.5.4 Poisson PN (vt)
377(1)
A.5.5 Exponential EX(v)
377(1)
A.5.6 Gamma GM(k, v) [ and Chi-squared x2(n)]
378(1)
A.5.7 Normal (Gaussian) N(µ, sigma)
379(2)
A.5.8 Central Limit Theorem
381(1)
A.5.9 Lognormal LN(lambda, epsilon)
381(2)
A.5.10 Beta BT (a, b, q, r)
383(2)
A.5.11 Extreme Value Distribution Type I EV - I(mu, alpha [ Gumbel distribution]
385(1)
A.5.12 Extreme Value Distribution Type II EV - II(u, k) [ Frechet Distribution]
386(2)
A.5.13 Extreme Value Distribution Type III EV - III(epsilon, u, k) [ Weibull]
388(2)
A.5.14 Generalized Extreme Value distribution GEV
390(1)
A.6 Jointly Distributed Random Variables
390(2)
A.6.1 Joint Probability Distribution
390(1)
A.6.2 Conditional Probability Distributions
391(1)
A.6.3 Marginal Probability Distributions
391(1)
A.7 Moments of Jointly Distributed Random Variables
392(1)
A.7.1 Mean
392(1)
A.7.2 Variance
393(1)
A.7.3 Covariance and Correlation
393(1)
A.8 Bivariate Normal Distribution
393(4)
A.9 Transformation of Random Variables
397(1)
A.9.1 Transformation of a Single Random Variable
397(1)
A.9.2 Transformation of Two or More Random Variables
397(1)
A.9.3 Linear and Orthogonal Transformations
398(1)
A.10 Functions of Random Variables
398(2)
A.10.1 Function of a Single Random Variable
398(1)
A.10.2 Function of Two or More Random Variables
398(1)
A.10.3 Some Special Results
399(1)
A.10.3.1 Y = X1 + X2
399(1)
A.10.3.2 Y = X1 X2
399(1)
A.11 Moments of Functions of Random Variables
400(2)
A.11.1 Linear Functions
400(1)
A.11.2 Product of Variates
400(1)
A.11.3 Division of Variates
401(1)
A.11.4 Moments of a Square Root [ Haugen, 1968]
401(1)
A.11.5 Moments of a Quadratic Form [ Haugen, 1968]
402(1)
A.12 Approximate Moments for General Functions
402(1)
B Rosenblatt and Other Transformations 403(12)
B.1 Rosenblatt Transformation
403(2)
B.2 Nataf Transformation
405(2)
B.3 Orthogonal Transformation of Normal Random Variables
407(3)
B.4 Generation of Dependent Random Vectors
410(5)
C Bivariate and Multivariate Normal Integrals 415(14)
C.1 Bivariate Normal Integral
415(4)
C.1.1 Format
415(2)
C.1.2 Reductions of Form
417(1)
C.1.3 Bounds
417(2)
C.2 Multivariate Normal Integral
419(10)
C.2.1 Format
419(1)
C.2.2 Numerical Integration of Multi-Normal Integrals
419(1)
C.2.3 Reduction to a Single Integral
420(1)
C.2.4 Bounds on the Multivariate Normal Integral
420(1)
C.2.5 First-Order Multi-Normal (FOMN) Approach
421(5)
C.2.5.1 Basic Method: B-FOMN
421(3)
C.2.5.2 Improved Method: I-FOMN
424(1)
C.2.5.3 Generalized Method: G-FOMN
425(1)
C.2.6 Product of Conditional Marginals (PCM) Approach
426(3)
D Complementary Standard Normal Table 429(4)
D.1 Standard Normal Probability Density Function q(x)
432(1)
E Random Numbers 433(2)
F Selected Problems 435(22)
References 457(40)
Index 497
ROBERT E. MELCHERS, PhD, is a Professor in the Department of Civil Engineering at The University of Newcastle, Australia. His main areas of research expertise are in structural engineering risk and reliability analyses, probabilistic modelling of engineering systems, corrosion and deterioration modeling, and investigation of structural failures.

ANDRÉ T. BECK, PhD, is an Associate Professor in the Department of Structural Engineering at the University of Sćo Paulo, Brazil. His research interests include structural mechanics and structural safety.
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