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2004 | Buch

Safety Factors and Reliability: Friends or Foes?

verfasst von: Isaac Elishakoff

Verlag: Springer Netherlands

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Über dieses Buch

Have you ever wondered where the safety factors come from? Why is it that deterministic analysis has reached a very sophisticated level, but in the end empirical factors are still needed? Is there a way to select them, rather than assigning them arbitrarily as is often done?
This book clearly shows that safety factors are closely related with the reliability of structures, giving yet another demonstration of Albert Einstein's maxim that "It is incomprehensible that Nature is comprehensible". The book shows that the safety factors are much more comprehensible if they are seen in a probabilistic context. Several definitions of the safety factors are given, analytical results on insightful numbers are presented, nonprobabilistic safety factors are shown, as well as their estimates derived by the inequalities of Bienayme, Markov, Chebushev and Camp-Meidell. A special chapter is devoted to important contributions by Japanese experts.
This volume will help to critically re-think the issue of safety factors, which can create a false feeling of security. The deterministic paradigm can be enhanced by incorporating probabilistic concepts wisely where they are needed without treating all variables as probabilistic ones. The book shows that there is a need of their integration rather than separation.
This book is intended for engineers, graduate students, lecturers and researchers.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Prologue
Abstract
It is a conventional wisdom to maintain that the scientists and engineers, who earn a living by being engaged in applied mechanics, are divided into two groups: those in the first, traditional group deal with deterministic mechanics, whereas the representatives of the second, more recent, group devote themselves to non-deterministic mechanics. The traditionalists neglect uncertainties in the loading conditions, in the mechanical properties of structures, in boundary conditions, in geometric characteristics and in other parameters entering into the description of the problem at hand.
Isaac Elishakoff
Chapter 2. Reliability of Structures
Abstract
This chapter represents a brief review of the concepts of the reliability of structures. Some closed form solutions, as well as approximate methods are elucidated. Different attempts to describe probabilistically the so-called “safety factor” are provided as well as and some instructive counter-examples are given.
Isaac Elishakoff
Chapter 3. Safety Factors and Reliability: Random Actual Stress & Deterministic Yield Stress
Abstract
In this chapter we will deal with the simplest possible case, when the yield stress constitutes a deterministic quantity but the actual stress is random, due to the randomness of the distribution or concentrated loads, or the randomness of distributed or the concentrated moments. It becomes possible to express the safety factor via the structural reliability.
Isaac Elishakoff
Chapter 4. Safety Factors and Reliability: Deterministic Actual Stress & Random Yield Stress
Abstract
In the previous chapter we studied the case in which the actual stress was treated as a random variable, while the yield stress was considered as a deterministic quantity. In this report we investigate the reverse case, namely, when the actual stress is deterministic, while the yield stress is treated as a random variable. Various probability densities to model the actual behavior of the structural element in question are considered.
Isaac Elishakoff
Chapter 5. Safety Factor and Reliability: Both Actual Stress and Yield Stress Are Random
Abstract
In this chapter both stress and strength are treated as random variables. Thus, this is the most general case within the context of random variables theory. The connection between the reliability and safety factors will be demonstrated for various possible distributions.
Isaac Elishakoff
Chapter 6. Non-Probabilistic Factor of Safety
Abstract
In this chapter we first illustrate some difficulties associated with probabilistic calculations of the reliability. It appears that these and other difficulties are either overlooked or pushed under the rug, as it were, by the probabilistic analysts. Then the alternative approach called ‘convex modeling’ is presented, and the safety factor’s associated definition is suggested.
Isaac Elishakoff
Chapter 7. Stochastic Safety Factor by Birger and Maymon
Abstract
In this chapter we will discuss, at some detail, the concept of stochastic safety factor, independently introduced by Birger (1970) and Maymon (2002). It differs for the central safety factor, extensively discussed in Chapters 3–5, and constitutes one of the four possible definitions of the safety factor in the probabilistic context, as briefly exposed in Section 3.2.
Isaac Elishakoff
Chapter 8. Safety Factor in Light of the Bienaymé-Markov and Chebychev Inequalities
Abstract
We have amply seen in previous chapters that in order to relate the reliability and the safety factor, one needs the knowledge of the probability densities of the involved random variables. Often, such information is missing. It is shown in this chapter that the celebrated inequalities by Irenée-Jules Bienaymé (1796–1878), Andrei Andreevich Markov (1856–1922) and Pafnutii Lvovich Chebychev (1821–1894) may come to help in finding bounds on the desired probabilities and safety factors. Short biographical notes about Bienayme and Chebychev are given in the Appendix B.
Isaac Elishakoff
Chapter 9. Japanese Contributions to the Interrelating Safety Factor and Reliability
Abstract
As it was shown in Chapter 6 the probability of failure is a very sensitive to the exact shapes of the probability density function of the stress and strength, respectively. This gave rise to a non-probabilistic safety factor, proposed in the Chapter 6. Another, alternative approach is the use of the estimates of the safety factors that do not depend on particular shape of the probability densities of the stress and strength. Such approaches have been advanced by various investigators, notably by Mischke (1970), Dao-Thien and Massoud (1974) and Ichikawa (1983). We will be mostly following Ichikawa’s (1983) and Reiser’s (1985) works in exposition of this subject.
Isaac Elishakoff
Chapter 10. Epilogue
Abstract
The natural question arises: “Probabilistic methods have been around quite for some time. When will they be introduced into design?” In their careful review Roësset and Yao (2002) write:
“Risk analyses have started to become standard requirements in these fields [earthquake engineering; nuclear engineering; offshore engineering].Yet the introduction in practice of probability concepts has been slow. Even when the probability-based load and resistance factors design (LRFD) specifications were introduced in design codes, they were used without explicit mention of probabilities. The load and resistance factors were selected through calibration, in order to obtain results similar to those of the working stress design and past experience, rather than on the basis of existing uncertainties.”
Isaac Elishakoff
Backmatter
Metadaten
Titel
Safety Factors and Reliability: Friends or Foes?
verfasst von
Isaac Elishakoff
Copyright-Jahr
2004
Verlag
Springer Netherlands
Electronic ISBN
978-1-4020-2131-2
Print ISBN
978-90-481-6500-1
DOI
https://doi.org/10.1007/978-1-4020-2131-2