Probabilistic Assessment of Structures using Monte Carlo Simulations

Abstract

3R27. Probabilistic Assessment of Structures using Monte Carlo Simulations. - Edited by P Marek, J Brozzetti, M Gustar. Academy Sci Czech Rep, Prague, Czech Rep. 471 pp. CD-ROM included. Reviewed by I Elishakoff (Dept of Mech Eng, Florida Atlantic Univ, Boca Raton FL 33431-0991).This is a textbook, which was completed with the support of the European Commission under the Leonardo da Vinci program. It is an unusual book. It is composed by 33 authors, 11 of whom may be characterized as students. This reminds me of a Talmudic dictum stating that one can learn a lot from his teachers, even more from his colleagues, and the most from one’s students. This cooperation between the editors, university professors, and the PhD students is a most welcome one. The authors pose a rightful and timely question: “What is needed to be done in order to improve and to make progress in the use of full probabilistic reliability assessment?” Indeed, there are many research papers in this area by now (possibly several thousand), with attendant monographs, specialized regional and international conferences with multi-volume proceedings, contributed and keynote lectures. Yet the above-mentioned problem is seldom being addressed. This unfortunate situation makes an impression that the methods treating uncertainty constitute a second-order effect, or a curiosity that is unconnected with reality, for the designers and the deterministically minded engineers want to get some simple tools from the researchers engaged in the probabilistic mechanics. Returning to the authors’ question, their reply is as follows: “The attention should be focused to the qualitatively new reliability assessment methods considering the rapidly increasing potential of the computer and information technology.” Further that “The formation from the ‘pre-computer’ reliability assessment concepts to the new generation of ‘computer era technology’ which makes workable a fully probabilistic concept, will require education of designers and a ‘re-engineering’ of the whole assessment procedure of structural reliability.” The authors suggest massive utilization of the Monte Carlo method. The book has an attachment form of the software (CD-ROM) to demonstrate the feasibility of probabilistic reliability assessment. The textbook comprises 16 chapters and three appendices. Chapter 2 explains the Monte Carlo simulation technique. The authors explain: “Simulation is an experiment performed on a model rather than on a real system.” They note wisely that “There is not a generally accepted exact definition of the concept of randomness.” They discuss basic notions of probability theory and statistics, including random variables, histograms, and the Monte Carlo method, along with uncertainty of results, variance reduction techniques, and typical problems illustrating what can be calculated using Monte Carlo simulation. Then they proceed to the random number and pseudorandom generators, including testing of their quality, and a transformation method. They have developed simulation based reliability assessment (SBRA) programs. The load combination program (LoadCom) is a tool for loads effect combination analysis according to allowable stress design, partial safety factor design, and limit states design according to Canadian National Standards. They also describe response combination (ResCom) damage accumulation (DamAc), and an AntHill program allowing evaluation and display of multi-dimensional random variables. This permits a direct reliability assessment, as well as an iteration procedure for model parameter estimation. In Chapter 3, the authors present a problem of interpretation of the limit state philosophy, including serviceability limit states, static and dynamic models, and load effects. Chapter 4 is devoted to single component, load combinations; dead load effects for single-story buildings; analysis of principal stress at a point of a beam; combined dead, live, and snow load effects; and dependent load effects. Chapter 5 treats examples associated with resistance of structural elements and components. Ultimate bearing capacity of reinforced concrete cross-section subjected to bending and compression, resistance of short composite columns, variability of the strength of steel-concrete composite beams, post buckling resistance of compressed rectangular plates, tension resistance of a bolted beam to a beam connection, and shear resistance of a better beam are treated. Structural elements are discussed in the sixth chapter. The material includes pipes under internal pressure, nailed timber-to-timber joint, dowelled steel-to-timber joint, stability of a portion of a continuous girder exposed to several variable loads and to a moving variable load as many others. Chapters 7 and 8 are dedicated, respectively, to the first-order and second-order theories. The ninth chapter discusses reliability of retaining walls and slopes, whereas Chapter 10 deals with prestressed concrete examples. Accumulation of damage is discussed in Chapter 11; serviceability is treated in Chapter 12; and Chapter 13 deals with special situations. The title of Chapter 14 is “From Components to Systems.” It includes assessment of coupled steel beams, determination of the safety of a bolted lap joint, as well as that of the bolted web plate joint. Eurocodes are discussed in Chapter 15. Chapter 16 deals with the Bayesian approach. Numerous examples included in the text allow for a multifaceted education in a unified reliability context. It is an indispensable reference to those who want to see probabilistic methods in action. The Monte Carlo method is shown as a powerful technique for dealing with a large variety of engineering problems. Engineers may use it in order to contrast their own methodologies with the ones presented in the book in view of bringing some new aspects of the topics discussed. This reviewer would want to see the discussion of dependent random variables, correlations, as well as the sources of the assumptions of the adopted probabilistic densities. Probabilistic Assessment of Structures using Monte Carlo Simulations is an excellent text for educating practicing engineers. Some of the examples could also be adopted in various courses that have a deterministic flavor in order to demonstrate the philosophy of probabilistic design. This book, therefore, is a welcome new bird, telling us that possibly the probabilistic spring may still arrive for design purposes, not only for research.

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