Structural Reliability Analysis and Prediction

by Melchers, Robert E.

• ISBN13: 9780471987710
• ISBN10: 0471987719
• Edition: 2nd
• Format: Paperback
• Copyright: 1999-05-04
• Publisher: WILEY

Summary

Structural reliability has become a discipline of international interest, addressing issues such as the safety of buildings, bridges, towers and other structures. This book 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.Much consideration is given to problem formulation and to the various techniques which can be applied to problem solution. These include the First Order Second Moment method and their derivatives, as well as various Monte Carlo tchniques. Each of these are described in considerable detail and example applications are given. Structural systems are also described, as is the effect of time on reliability estimation, and on the development of design code rules on the basis of limit state principles as under-pinned by probability theory. Furthermore, procedures for the reliability estimation of existing structures are also included.The book emphasises concepts and applications, built up from basic principles and avoids undue mathematical rigour. It presents an accesible and unified account of the theory and techniques for the analysis of the reliability of engineering structures using probability theory. A balanced view of the subject is offered here not only for newcomers, but also for the more specialist reader, such as senior undergraduate and post-graduate students and practising engineers in civil, structural, geotechnical and mechanical engineering.

Table of Contents

Preface	xv
Measures of Structural Reliability	1	(31)
Introduction	1	(1)
Deterministic measures of limit state violation	2	(7)
Factor of safety	2	(1)
Load factor	3	(1)
Partial factor (`limit state design')	4	(1)
A deficiency in some safety measures: lack of invariance	5	(3)
Invariant safety measures	8	(1)
A partial probabilistic safety measure---the return period	9	(4)
Probabilistic measure of limit state violation	13	(12)
Introduction	13	(2)
The basic reliability problem	15	(3)
Special case: normal random variables	18	(2)
Safety factors and characteristic values	20	(5)
Numerical integration of the convolution integral	25	(1)
Generalized reliability problem	25	(6)
Basic variables	26	(1)
Generalized limit state equations	27	(1)
Generalized reliability problem formulation	28	(1)
Conditional reliability problems	29	(2)
Conclusion	31	(1)
Structural Reliability Assessment	32	(32)
Introduction	32	(2)
Uncertainties in reliability assessment	34	(12)
Identification of uncertainties	34	(1)
Phenomenological uncertainty	34	(1)
Decision uncertainty	35	(1)
Modelling uncertainty	35	(1)
Prediction uncertainty	36	(1)
Physical uncertainty	36	(1)
Statistical uncertainty	37
Uncertainties due to human factors	27	(11)
Human error	38	(3)
Human intervention	41	(3)
Modelling of human error and intervention	44	(1)
Quality assurance	45	(1)
Hazard management	46	(1)
Integrated risk assessment	46	(6)
Calculation of the probability of failure	46	(2)
Analysis and prediction	48	(1)
Comparison to failure data	49	(2)
Validation---a philosophical issue	51	(1)
The tail sensitivity `problem'	51	(1)
Criteria for risk acceptability	52	(5)
Acceptable risk criterion	52	(1)
Risks in society	52	(3)
Acceptable or tolerable risk levels	55	(1)
Socio-economic criterion	55	(2)
Nominal probability of failure	57	(4)
General	57	(1)
Axiomatic definition	58	(1)
Influence of gross and other errors	58	(2)
Practical implications	60	(1)
Target values for nominal failure probability	60	(1)
Hierarchy of structural reliability measures	61	(1)
Conclusion	62	(2)
Integration and Simulation Methods	64	(30)
Introduction	64	(1)
Direct and numerical integration	64	(2)
Monte Carlo simulation	66	(7)
Introduction	66	(1)
Generation of uniformly distributed random numbers	66	(1)
Generation of random variates	67	(1)
Direct sampling (`crude' Monte Carlo)	68	(2)
Number of samples required	70	(3)
Variance reduction	73	(1)
Importance sampling	73	(10)
Theory of importance sampling	73	(2)
Importance sampling functions	75	(2)
Observations about importance sampling functions	77	(2)
Improved sampling functions	79	(2)
Search or adaptive techniques	81	(1)
Sensitivity	82	(1)
Directional simulation	83	(8)
Basic notions	83	(2)
Directional simulation with importance sampling	85	(1)
Generalized directional simulation	86	(2)
Directional simulation in the load space	88	(1)
Basic concept	88	(2)
Variation of strength with radial direction	90	(1)
Practical aspects of Monte Carlo simulation	91	(2)
Conditional expectation	91	(1)
Generalized limit state function---response surfaces	92	(1)
Systematic selection of random variables	92	(1)
Applications	92	(1)
Conclusion	93	(1)
Second-Moment and Transformation Methods	94	(38)
Introduction	94	(1)
Second-moment concepts	94	(3)
First-Order Second-Moment (FOSM) theory	97	(16)
The Hasofer-Lind transformation	97	(1)
Linear limit state function	97	(3)
Sensitivity factors	100	(2)
Non-linear limit state function---general case	102	(4)
Non-linear limit state function---numerical solution	106	(1)
Non-linear limit state function---iterative solution scheme	106	(3)
Geometric interpretation of iterative solution scheme	109	(2)
Interpretation of First-Order Second-Moment (FOSM) theory	111	(1)
General limit state functions---probability bounds	112	(1)
The First-Order Reliability (FOR) method	113	(15)
Simple transformations	113	(1)
The normal tail transformation	114	(3)
Transformations to independent normal basic variables	117	(1)
Rosenblatt transformation	118	(2)
Nataf transformation	120	(2)
Algorithm for First-Order Reliability (FOR) method	122	(4)
Observations	126	(1)
Asymptotic formulation	127	(1)
Second-order methods	128	(2)
Basic concept	128	(1)
Evaluation through sampling	129	(1)
Evaluation through asymptotic approximation	129	(1)
Application of FOSM/FOR/SOR methods	130	(1)
Conclusion	131	(1)
Reliability of Structural Systems	132	(52)
Introduction	132	(1)
Systems reliability fundamentals	133	(16)
Structural system modelling	133	(1)
Load modelling	133	(1)
Material modelling	134	(1)
System modelling	135	(2)
Solution approaches	137	(1)
Failure mode approach	137	(1)
Survival mode approach	138	(1)
Upper and lower bounds---plastic theory	139	(1)
Idealizations of structural systems	140	(1)
Series systems	140	(3)
Parallel systems---general	143	(2)
Parallel systems---ideal plastic	145	(3)
Combined and conditional systems	148	(1)
Monte Carlo techniques for systems	149	(6)
General remarks	149	(1)
Importance sampling	149	(1)
Series systems	149	(2)
Parallel systems	151	(1)
Search-type approaches in importance sampling	152	(1)
Failure modes identification in importance sampling	153	(1)
Directional simulation	153	(1)
Directional simulation in the load space	153	(2)
System reliability bounds	155	(13)
First-order series bounds	156	(1)
Second-order series bounds	157	(3)
Second-order series bounds by loading sequences	160	(1)
Series bounds by modes and loading sequences	160	(1)
Improved series bounds and parallel system bounds	161	(1)
First-order second-moment methods in systems reliability	162	(5)
Correlation effects	167	(1)
Implicit limit states---response surfaces	168	(4)
Introduction	168	(1)
Basic concept	169	(1)
Simplifications for large systems	170	(1)
Iterative solution scheme	171	(1)
Response surfaces and finite element analysis	171	(1)
Applications and observations	172	(1)
Complex structural systems	172	(10)
Description	172	(2)
Truncated enumeration	174	(4)
Limit state formulation	178	(1)
Node replacement (`artificial load') technique	178	(1)
Incremental load technique	178	(3)
System probability evaluation	181	(1)
Applications	182	(1)
Conclusion	182	(2)
Time Dependent Reliability	184	(67)
Introduction	184	(3)
Time-integrated approach	187	(3)
Basic notions	187	(2)
Conversion to a time-independent format	189	(1)
Discretized approach	190	(6)
Known number of discrete events	191	(1)
Random number of discrete events	192	(2)
Return period	194	(1)
Hazard function	195	(1)
Stochastic process theory	196	(7)
Stochastic process	197	(1)
Stationary processes	198	(1)
Derivative process	199	(1)
Ergodic processes	200	(1)
First-passage probability	201	(1)
Distribution of local maxima	202	(1)
Stochastic processes and outcrossings	203	(19)
Discrete processes	203	(1)
Borges processes	203	(1)
Poisson counting process	204	(1)
Filtered Poisson process	205	(1)
Poisson spike process	206	(1)
Poisson square wave process	207	(1)
Renewal processes	208	(1)
Continuous processes	209	(1)
Barrier (or level) upcrossing rate	209	(3)
Outcrossing rate	212	(1)
Generalization from barrier crossing rate	212	(2)
Outcrossing for discrete processes	214	(2)
Outcrossing for continuous Gaussian processes	216	(5)
General regions and processes	221	(1)
Numerical evaluation of outcrossing rates	222	(1)
Time dependent reliability	222	(12)
Introduction	222	(2)
Sampling methods for unconditional failure probability	224	(1)
Importance and conditional sampling	224	(1)
Directional simulation in the load process space	225	(1)
FOSM/FOR methods for unconditional failure probability	226	(8)
Summary	234	(1)
Load combinations	234	(9)
Introduction	234	(1)
General formulation	235	(2)
Discrete processes	237	(2)
Simplifications	239	(1)
Load coincidence method	239	(1)
Borges processes	240	(2)
Deterministic load combination---Turkstra's rule	242	(1)
Dynamic analysis of structures	243	(4)
Fatigue analysis	247	(3)
General formulation	247	(1)
The S-N model	247	(2)
Fracture mechanics models	249	(1)
Conclusion	250	(1)
Load and Load Effect Modelling	251	(25)
Introduction	251	(1)
Wind loading	252	(3)
Wave loading	255	(4)
Floor loading	259	(15)
General	259	(2)
Sustained load representation	261	(3)
Equivalent uniformly distributed load	264	(2)
Distribution of equivalent uniformly distributed load	266	(3)
Maximum (lifetime) sustained load	269	(2)
Extraordinary live loads	271	(1)
Total live load	272	(1)
Permanent and construction loads	273	(1)
Conclusion	274	(2)
Resistance Modelling	276	(19)
Introduction	276	(1)
Basic properties of hot-rolled steel members	276	(6)
Steel material properties	276	(1)
Yield strength	277	(3)
Moduli of elasticity	280	(1)
Strain-hardening properties	280	(1)
Size variation	280	(2)
Properties for reliability assessment	282	(1)
Properties of steel reinforcing bars	282	(1)
Concrete statistical properties	283	(2)
Statistical properties of structural members	285	(6)
Introduction	285	(1)
Methods of analysis	286	(1)
Second-moment analysis	286	(2)
Simulation	288	(3)
Connections	291	(1)
Incorporation of member strength in design	292	(2)
Conclusion	294	(1)
Codes and Structural Reliability	295	(25)
Introduction	295	(1)
Structural design codes	296	(1)
Improved safety-checking formats	297	(5)
Probabilistic and probability-based codes	297	(1)
Unified rules of the Comite European du Beton and others	298	(2)
National Building Code, Canada	300	(1)
Load and Resistance Factor Design [LRFD]	301	(1)
Some observations	302	(1)
Relationship between level 1 and level 2 safety measures	302	(4)
Derivation from FOSM/FOR theory	303	(2)
Special case: linear limit state function	305	(1)
Selection of code safety levels	306	(1)
Code calibration procedure	307	(5)
Example of code calibration	312	(5)
Observations	317	(2)
Applications	317	(1)
Some theoretical issues	318	(1)
Conclusion	319	(1)
Probabilistic Evaluation of Existing Structures	320	(20)
Introduction	320	(2)
Assessment procedures	322	(2)
Updating probabilistic information	324	(4)
Bayes theorem	324	(1)
Application to inspection data	325	(3)
Proof and service load information	328	(4)
Proof loading	328	(2)
Effect of proof loads	330	(1)
Service-proven structures	331	(1)
Analytical techniques	332	(2)
General	332	(1)
Deterioration	333	(1)
Acceptance criteria for existing structures	334	(5)
Nominal probabilities	334	(1)
Semi-probabilistic safety checking formats	335	(1)
Decision-theory based criteria	336	(2)
Life-cycle decision approach	338	(1)
Conclusion	339	(1)
Appendix A: Summary of Probability Theory	340	(30)
A.1 Probability	340	(1)
A.2 Mathematics of probability	340	(1)
A.2.1 Axioms	340	(1)
A.2.2 Derived results	341	(1)
A.3 Description of random variables	341	(1)
A.4 Moments of random variables	342	(2)
A.4.1 Mean or expected value (First Moment)	342	(1)
A.4.2 Variance and standard deviation (Second Moment)	342	(1)
A.4.3 Bounds on the deviations from the mean	343	(1)
A.4.4 Skewness γ1 (Third Moment)	343	(1)
A.4.5 Coefficient of kurtosis γ2 (Fourth Moment)	344	(1)
A.4.6 Higher moments	344	(1)
A.5 Common univariate probability distributions	344	(16)
A.5.1 Binomial	344	(1)
A.5.2 Geometric	345	(1)
A.5.3 Negative Binomial	345	(1)
A.5.4 Poisson	346	(1)
A.5.5 Exponential	347	(1)
A.5.6 Gamma	347	(1)
A.5.7 Normal (Gaussian)	348	(3)
A.5.8 Central limit theorem	351	(1)
A.5.9 Lognormal	351	(1)
A.5.10 Beta	352	(2)
A.5.11 Extreme value distribution type I	354	(2)
A.5.12 Extreme value distribution type II	356	(2)
A.5.13 Extreme value distribution type III	358	(2)
A.6 Jointly distributed random variables	360	(2)
A.6.1 Joint probability distribution	360	(1)
A.6.2 Conditional probability distributions	361	(1)
A.6.3 Marginal probability distributions	361	(1)
A.7 Moments of jointly distributed random variables	362	(2)
A.7.1 Mean	362	(1)
A.7.2 Variance	362	(1)
A.7.3 Covariance and correlation	363	(1)
A.8 Bivariate normal distribution	364	(3)
A.9 Transformation of random variables	367	(1)
A.9.1 Transformation of a single random variable	367	(1)
A.9.2 Transformation of two or more random variables	367	(1)
A.9.3 Linear and orthogonal transformations	368	(1)
A.10 Functions of random variables	368	(2)
A.10.1 Functions of a single random variable	368	(1)
A.10.2 Functions of two or more random variables	369	(1)
A.10.3 Some special results	369	(1)
A.11 Moments of functions of random variables	370	(38)
A.11.1 Linear functions	370	(1)
A.11.2 Product of variates	371	(1)
A.11.3 Division of variates	371	(1)
A.11.4 Moments of a square root	372	(1)
A.11.5 Moments of a quadratic form	372	(1)
A.12 Approximate moments for general functions	372	(2)
Appendix B: Rosenblatt and Other Transformations	374	(12)
B.1 Rosenblatt transformation	374	(2)
B.2 Nataf transformation	376	(3)
B.3 Orthogonal transformation of normal random variables	379	(3)
B.4 Generation of dependent random vectors	382	(4)
Appendix C: Bivariate and Multivariate Normal Integrals	386	(15)
C.1 Bivariate normal integral	386	(4)
C.1.1 Format	386	(2)
C.1.2 Reductions of form	388	(1)
C.1.3 Bounds	388	(2)
C.2 Multivariate normal integral	390	(11)
C.2.1 Format	390	(1)
C.2.2 Numerical integration of multi-normal integrals	391	(1)
C.2.3 Reduction to a single integral	391	(1)
C.2.4 Bounds on the multivariate normal integral	392	(1)
C.2.5 First Order Multinormal (FOMN) approach	392	(6)
C.2.5.1 Basic method: B-FOMN	392	(3)
C.2.5.2 Improved method: I-FOMN	395	(2)
C.2.5.3 Generalized method: G-FOMN	397	(1)
C.2.6 Product of Conditional Marginals (PCM) approach	398	(3)
Appendix D: Complementary Standard Normal Table	401	(4)
Appendix E: Random Numbers	405	(1)
Appendix F: Computer Programs	406	(2)
References	408	(23)
Index	431