Probabilistic Methods in Structural Engineering

Augusti, Giuliano; Baratta, Alessandro; Casciati, Fabio; Epstein, Howard I.

doi:10.4324/9780203215449

Cited by 200 publications

(32 citation statements)

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“…By retaining the first-order terms, the failure surface is replaced with a hyperplane at the linearization point. This level of analysis is referred to as a first-order reliability analysis [5][6][7][8][9]. Generally, in practical situations, the information available on the resistance and load effects is only sufficient to estimate the first and second moments, i.e.…”

Section: Approximate Methodsmentioning

confidence: 99%

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Reliability analysis of wind-sensitive structures

Kareem

1990

Journal of Wind Engineering and Industrial Aerodynamics

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SummaryThe theoretical background of practical structural reliability methods encompassing numerical integration, approximate methods and simulation techniques is reviewed in the context of windexcited structures. Their relative merits, shortcomings and limitations are addressed from the standpoint of their accuracy and computational efficiency. Quantitative reliability estimates of a concrete chimney are made, using different analysis procedures. Multiple potential failure modes are represented by the exceeding of the ultimate moment capacity at any level of the chimney height. The general bounds on the system failure probability are expressed in terms of the failure probability of the individual modes. The narrower bounds are established based on the existing theory by taking into account not only the failure probability of the individual modes, but also the joint failure probabilities in any two modes. Based on the findings of this study, it is suggested that the advanced first-order second-moment approximation and the simulation methods, which combine the Monte Carlo technique with variance reduction techniques, may provide accurate results for practical reliability analysis of wind-excited structures.

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Section: Approximate Methodsmentioning

confidence: 99%

“…For better approximation, one must retain some higher-order terms in addition to the first two terms in the Taylor series expansion of the limit state function. The formulation which retains secondorder terms is referred to as a second-order reliability analysis (SOR) procedure [5][6][7][8][9][10][11][12][13].…”

Section: Approximate Methodsmentioning

confidence: 99%

Reliability analysis of wind-sensitive structures

Kareem

1990

Journal of Wind Engineering and Industrial Aerodynamics

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“…Hence, in the present case of "multiple loadings" caused by the random variations of R=R(w), the survival of the structure, i.e. the existence of certain arrangements F(w) of internal member forces/bending-moments not overwhelming the strength of the structure, can be evaluated by the probability of survival Ps:= P(There is F=F(w) such that CF(w) -R(w) (8) and FL(w) oS F(w) oS FU(w», see [2], [10], assuming that, cf. …”

Section: Analysis and Design Of Structures In Case Of Random Datamentioning

confidence: 99%

“…In the plastic design of trusses, frames [5] having no members, the n-vectors FL,F U of lower and upper bounds (2) for the n-vector F of internal member forces and bending-moments Fj' j-l, ..…”

Section: Plastic and Elastic Design Of Structuresmentioning

confidence: 99%

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Stochastic optimization methods in engineering

Marti

1996

System Modelling and Optimization

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Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors are not given fixed quantities in practice, but have to be modelled as random variables with a certain joint probability distribution. Hence, problems from limit (collapse) load analysis or plastic analysis and from plastic and elastic design of structures are treated in the framework of stochastic optimization. Using especially reliabilityoriented optimization methods, the behavioral constraints are quantified by means of the corresponding probability P. of survival. Lower bounds for p. are obtained by selecting certain redundants in the vector of internal forces; moreover, upper bounds for p. are constructed by considering a pair of dual linear programs for the optimizational representation of the yield or safety conditions. Whereas P. can be computed e.g. by sampling methods or by asymptotic expansion techniques based on Laplace integral representations of certain multiple integrals, efficient techniques for the computation of the sensitivities (of various orders) of P. with respect to input or design variables have yet to be developed. Hence several new techniques are suggested for the numerical computation of derivatives of P •.

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Corrections to B-models for fatigue life prediction of metals during crack propagation

Bea

Doblaré

Villanueva

et al. 1999

Int. J. Numer. Meth. Engng.

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SUMMARYIn this paper a new model for the prediction of the Cumulative Distribution Function (CDF) of fatigue life of structural elements during the crack propagation stage is described. This problem is considered as a cumulative damage process following the probabilistic approach of Bogdano! and Kozin [1] (B-models). The initial and "nal crack lengths, the crack propagation angle, the material fracture and elastic parameters and the external loads may be considered as random variables. In this initial approach, a linear approximation of the random variable &fatigue life' and a truncated uniform distribution for the crack length variable are considered. Two corrections to this model are discussed: a second-order approximation of the fatigue life to compute its variance, and a modi"cation of the Probability Density Distribution (PDD) of the crack length, which is now derived from the truncated uniform distributions of the initial and "nal crack lengths. Some examples for mode I are compared to the ones obtained using a Monte Carlo scheme with 400 000 samples, showing a good agreement and a much better performance of the corrected version of the model, specially for big standard deviations.

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Probabilistic Methods in Structural Engineering

Cited by 200 publications

References 0 publications

Reliability analysis of wind-sensitive structures

Reliability analysis of wind-sensitive structures

Stochastic optimization methods in engineering

Corrections to B-models for fatigue life prediction of metals during crack propagation

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