Table Of Contenti
Philosophies of Structural
Safety and Reliability
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Philosophies of Structural
Safety and Reliability
Vladimir Raizer and Isaac Elishakoff
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First edition published 2022
by CRC Press
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© 2022 Vladimir Raizer and Isaac Elishakoff
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ISBN: 9781032209302 (hbk)
ISBN: 9781032209340 (pbk)
ISBN: 9781003265993 (ebk)
DOI: 10.1201/ 9781003265993
Typeset in Times
by Newgen Publishing UK
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Contents
Authors ...................................................................................................................ix
Preface .................................................................................................................xiii
Introduction .........................................................................................................xvii
Chapter 1 Introduction .......................................................................................1
Chapter 2 Historical Notes .................................................................................7
2.1 History of Safety Factors ........................................................7
2.2 Development of the Theory of Structural Reliability ...........16
2.3 The Connection between Ancient Sparta and the
Failure Rate ...........................................................................18
Chapter 3 Safety Factor and Reliability Index .................................................19
3.1 Features of Failure and Principles of Design ........................20
3.2 Safety Factor .........................................................................22
3.3 Reliability Index and Partial Factors Method .......................24
3.4 Importance Factor .................................................................28
3.5 Concept of Equal Reliability .................................................30
3.5a Calibration of Model Partial Factor ..........................30
3.5b Reliability of Transmission Lines .............................33
3.6 Development of Reliability- Based Design Approach ...........36
Chapter 4 Evaluation of Failure Probability ....................................................39
4.1 General Comments ................................................................39
4.2 “Hot Point” Method ..............................................................42
4.3 Monte- Carlo Method ............................................................49
4.3a Monte- Carlo Technique ............................................49
4.3b Monte- Carlo Method for Stratified Modeling
Samples .....................................................................51
4.4 Simulation Method................................................................53
4.5 Direct Integration of Distribution Function ..........................58
4.6 Influence of Failure Boundary Curvature on Reliability ......63
4.7 Implementation of Reliability Theory in
Structural Design ..................................................................66
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Chapter 5 Alternative Definitions of the Fuzzy Safety Factor .........................73
5.1 Introductory Comments ........................................................73
5.2 Safety Factor in the Probabilistic Framework .......................74
5.3 Safety Factor in the Fuzzy Theory Framework .....................76
5.4 Fundamental Problem in the Strength of Materials ..............78
5.5 Numerical Examples .............................................................83
5.6 Stability Problem ..................................................................84
5.7 Bending Failure of the Beam ................................................85
5.8 Stability Analysis of the Column ..........................................86
5.9 Fuzzy Sets- Based Approach .................................................86
Chapter 6 Convex Models of Uncertainty ........................................................89
6.1 Introductory Comments ........................................................89
6.2 Sensitivity of Failure Probability ..........................................91
6.3 Remarks on Convex Modeling of Uncertainty .....................98
6.4 “Worst- Case” Probabilistic Safety Factor ...........................105
6.5 Which Concept Is More Feasible: Non- Probabilistic
Reliability or Convex Safety Factor? ..................................112
6.6 Concluding Comments on How to Treat
Uncertainty in a Given Situation .........................................116
Chapter 7 Systems and Components ..............................................................119
7.1 Conditionality of Concept ...................................................119
7.2 Connection of Components in Series ..................................120
7.3 Parallel Connection of Brittle Components ........................123
7.4 Dynamic Effects in Brittle Systems ....................................125
7.5 Parallel Connection of Plastic Components ........................129
7.6 Failure Probability of Multi- Element Systems ...................130
7.7 Probabilistic Limit Equilibrium Method .............................131
Chapter 8 Loads and Their Combinations .....................................................139
8.1 Classification .......................................................................139
8.2 Statistical Models of Variable Actions ................................141
8.3 Climatic Actions on Structures ...........................................145
8.4 Consideration of Random Wind Speed Directions .............148
8.5 Loads on Building Floors....................................................151
8.6 Combination of Loads as Random Values ..........................156
8.7 Combination of Extreme Values of Loads ..........................158
8.8 Combination of Loads in the Form of Markov Process ......160
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Chapter 9 Properties of Materials and Structural Deterioration ....................165
9.1 General Comments ..............................................................165
9.2 Bayesian Treatment in Analysis of Mechanical
Properties ............................................................................166
9.3 Smoothing of Experimental Data ........................................169
9.4 Reliability of Corroding Structures .....................................173
Chapter 10 Risk Evaluation and Optimal Probabilistic Design .......................179
10.1 Acceptable Risk ..................................................................179
10.2 Optimization of Reliability Index .......................................183
10.3 Optimization of Protected Structures ..................................187
10.4 Optimization of Multiplex Systems ....................................191
10.5 Optimal Allocation of Protective Resources of
Structures ............................................................................195
10.6 Mathematical Model of Public Opinion .............................204
Chapter 11 Natural Disasters and Structural Survivability ..............................207
11.1 Disaster Prediction Problems ..............................................207
11.2 Statistical Evaluation of Natural Disasters..........................208
11.3 Safety Criteria of Unique Structures ...................................209
11.4 Survivability of Structural Systems ....................................210
11.5 Stochastic Analysis of Dynamic Instability ........................220
11.6 Effects of Uneven Footing Settlement ................................228
Chapter 12 Conclusion .....................................................................................235
Appendix. Definitions for Terms Used in the Book ........................................243
Bibliography ......................................................................................................247
Author Index......................................................................................................261
Subject Index .....................................................................................................265
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Authors
Vladimir Raizer, DSc, PhD has dedicated his entire professional life to strength
analysis of civil structures, mainly risk and reliability assessment and probabilistic
methods.
During the four decades of his career in Russia, Dr. Raizer served as a fellow in
the most prestigious civil engineering establishments in the country – the Central
Research Institute of Building Structures, Moscow (1959–1999) – and for 25 years
as the head of the Department of Strength and Reliability of Structures. His experi-
ence includes analysis of strength, stability, and design on static and dynamic
action space structures, domes, reservoirs, pipelines, power transmission lines,
masts, probabilistic modeling loads and actions, and processes of failure in multi-
element structures, application of the theory of reliability to the problem of risk,
safety, and structural survivability, and COD procedures, among others.
Simultaneously, he was also a full professor in the Department of Structural
Mechanics, Moscow State University of Civil Engineering (1982–1999). Along
with a course of lectures on the problems of strength, stability, and reliability of
structures, he led the research of graduate students, of whom more than 30 earned
their PhDs.
From 1976–1999, he chaired the Coordinated Council on Structural Safety
responsible for developing the National Codes of Practice.
Between 1978 and 1991, he represented his country at the ISO, Technical
Committee 98 “Bases for Design of Structures,” and chaired ISO TC98, SC3
“Loads, Forces and Other Actions.”
Upon immigrating to the US in 1999, Dr. Raizer worked as a consultant at
FC&T Corp. in San Diego, CA (1999–2003) and then as an independent consultant
providing scientific support for a number of engineering projects.
Dr. Raizer has authored and coauthored more than 150 technical publications
and 11 books in Russian and English.
In 1996, Dr. Raizer was appointed as Honorary Scientist of Russia and in 1998
he was elected as Honorary Member of the Russian Academy of Architecture and
Construction Science.
Isaac Elishakoff, PhD serves as the Distinguished Research Professor in the
Department of Ocean and Mechanical Engineering at Florida Atlantic University.
He also holds a courtesy appointment as a Professor in the Department of
Mathematical Sciences. He was born in Kutaisi, Republic of Georgia, Europe.
Professor Elishakoff holds a master’s and Candidate of Sciences Degree (latter
being equivalent to the PhD degree in the US) in dynamics and strength of machines
from the Power Engineering Institute and Technical University in Moscow, Russia.
Prior to joining Florida Atlantic University, he taught 1 year at the Abkhazian
University, Sukhumi, Republic of Georgia, and 18 years at the Technion-Israel
Institute of Technology in Haifa (1972–1989). He also occupied several visiting
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