Corrosion of reinforcing bars is the major cause of deterioration of reinforced concrete (RC) structures in North America, Europe, the Middle East, and many coastal regions around the world. This deterioration leads to a loss of serviceability and functionality and ultimately affects the structural safety. The objective of this research is to formulate and implement a general stochastic finite element analysis (SFEA) framework for the time-dependent reliability analysis of RC beams with corroding flexural reinforcement. The framework is based on the integration of nonlinear finite element and reliability analyses through an iterative response surface methodology (RSM). Corrosion-induced damage is modelled through the combined effects of gradual loss of the cross-sectional area of the steel reinforcement and the reduction bond between steel and concrete for increasing levels of corrosion. Uncertainties in corrosion rate, material properties, and imposed actions are modelled as random variables. Effective implementation of the framework is achieved by the coupling of commercial finite element and reliability software. Application of the software is demonstrated through a case study of a simply-supported RC girder with tension reinforcement subjected to the effects of uniform (general) corrosion, in which two limit states are considered: (i) a deflection serviceability limit state and (ii) flexural strength ultimate limit state. The results of the case study show that general corrosion leads to a very significant decrease in the reliability of the RC beam both in terms of flexural strength and maximum deflections. The loss of strength and serviceability was shown to be predominantly caused by the loss of bond strength, whereas the gradual reduction of the cross-sectional area of tension reinforcement was found to be insignificant. The load-deflection response is also significantly affected by the deterioration of bond strength (flexural strength and stiffness). The probability of failure at the end of service life, due to the effects of uniform corrosion-induced degradation, is observed to be approximately an order of magnitude higher than in the absence of corrosion. Furthermore, the results suggest that flexural resistance of corroded RC beams is controlled by the anchorage (bond) of the bars and not by the yielding of fully bonded tensile reinforcement at failure. This is significant since the end regions can be severely corroded due to chloride, moisture, and oxygen access at connections and expansion joints. The research strongly suggests that bond damage must be considered in the assessment of the time-dependent reliability of RC beams subjected to general corrosion.

This thesis discusses a methodology for probabilistic design optimization of aircraft structures subject to a multidisciplinary set of requirements originating from the desire to minimize structural weight while fulfilling the demands for quality, safety, producibility, and affordability. With this design methodology as the framework, a software is developed, which is capable of performing design optimization of metallic built-up beam structures where the material properties, external load, as well as the structural dimensions are treated as probabilistic random variables. The structural and failure analyses are based on analytical and semi-empirical methods whereas the component reliability analysis is based on advanced first-order second moment method. Metrics-based analytical models are used for the manufacturability analysis of individual parts with the total manufacturing cost estimated using models derived from the manufacturing cost / design guide developed by the Battelle¡¯s Columbus Laboratories. The resulting optimization problem is solved using the method of sequential quadratic programming. A wing spar design optimization problem is used as a demonstrative example including a comparison between non-buckling and buckling web design concepts. A sensitivity analysis is performed and the optimization results are used to highlight the tradeoffs among weight, reliability, and manufacturing cost.

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This research investigates if the LRFD strength reduction factor for cold-formed steel compression members can be increased above its current value of Ï c = 0.85, which was established by the LRFD Cold-Formed Steel Design Manual (1991) on the basis of 264 column tests. The resistance factor in the Canadian code for cold-formed steel compression members is also evaluated. A total of 675 concentrically loaded plain and lipped C-section columns, plain and lipped Z-section columns, hat and angle columns, including members with holes, are considered in the study. The predicted strengths are calculated with the AISI-S100-07 Main Specification and the AISI Direct Strength Method. The test-to-predicted strength statistics are employed with the first order second moment reliability approach in AISI-S100-07 Chapter F as well as a higher order method to calculate the resistance factor per cross-section type, ultimate limit state, and considering partially and fully effective columns. The observed trends support a higher resistance factor for columns buckling in a distortional buckling limit state and an expansion of the current DSM prequalified limits. The results also show that DSM predicts the column capacity more accurately than the Main Specification. The test-to-predicted ratios for plain and lipped angle columns exhibit a high coefficient of variation and become more and more conservative as global slenderness increases. It is concluded that fundamental research on the mechanics of angle compression members is needed to improve existing design methods. / Master of Science

This dissertation addresses the ultimate strength analysis of nonlinear beam-columns under axial compression, the sensitivity of the ultimate strength, structural optimization and reliability analysis using ultimate strength analysis, and Reliability-Based Design Optimization (RBDO) of the nonlinear beam-columns. The ultimate strength analysis is based on nonlinear beam theory with material and geometric nonlinearities. Nonlinear constitutive law is developed for elastic-perfectly-plastic beam cross-section consisting of base plate and T-bar stiffener. The analysis method is validated using commercial nonlinear finite element analysis. A new direct solving method is developed, which combines the original governing equations with their derivatives with respect to deformation matric and solves for the ultimate strength directly. Structural optimization and reliability analysis use a gradient-based algorithm and need accurate sensitivities of the ultimate strength to design variables. Semi-analytic sensitivity of the ultimate strength is calculated from a linear set of analytical sensitivity equations which use the Jacobian matrix of the direct solving method. The derivatives of the structural residual equations in the sensitivity equation set are calculated using complex step method. The semi-analytic sensitivity is more robust and efficient as compared to finite difference sensitivity. The design variables are the cross-sectional geometric parameters. Random variables include material properties, geometric parameters, initial deflection and nondeterministic load. Failure probabilities calculated by ultimate strength reliability analysis are validated by Monte Carlo Simulation. Double-loop RBDO minimizes structural weight with reliability index constraint. The sensitivity of reliability index with respect to design variables is calculated from the gradient of limit state function at the solution of reliability analysis. By using the ultimate strength direct solving method, semi-analytic sensitivity and gradient-based optimization algorithm, the RBDO method is found to be robust and efficient for nonlinear beam-columns. The ultimate strength direct solving method, semi-analytic sensitivity, structural optimization, reliability analysis, and RBDO method can be applied to more complicated engineering structures including stiffened panels and aerospace/ocean structures. / Ph. D.

Today, in structural design, a structure is verified against failure by using the partial coefficient method provided by the Eurocodes. The verification method is, in its nature, a deterministic method where the input variables for load and resistance are assigned partial coefficients to ensure that the resistance is exceeded by the load effect. Since these coefficients are calibrated by using probabilistic methods, the partial coefficient method is also called a semi-probabilistic method. As an alternative, the verification is possible by using probabilistic methods. Instead of assigning partial coefficients to load- and resistance variables, they are treated as stochastic variables considering any physical- and statistical uncertainties associated with the same. For a complete probabilistic analysis, however, the model uncertainty must be considered. This uncertainty is associated with the mathematical models that are used to transform load- and material values into load effects and resistance and also uncertainties due to variations and simplifications of e.g. geometrical quantities and failure modes. There is another uncertainty not explicitly dealt with in the Eurocodes and the background material to the codes, that is the uncertainties related to the designers’ choice. That is, how the designer interprets given design conditions and existing codes and also due to the assumptions- and simplifications that takes place when the designer, based on a realistically given design task, must presume e.g. geometrical dimensions, loads and other necessary parameters when designing a structural element. As a basis for this study is a large statistical material, were a number of structural engineers have solved the exact same task which includes the calculation of loads- and load effects and to design a number of elements in an industrial single-storey building in steel. Statistical parameters, associated with the load effect variations due to the designers’ choice, has been estimated using mathematical statistics. Based on this results, a probabilistic level 2 method has been carried out in order to assess how the failure probability is affected when this model uncertainty is varied. It was found in the study that, using a 95% confidence interval, the coefficient of variance of the calculated load effects, defined herein as the model uncertainty due to the designers’ choice and denoted VθS, varies somewhat between 0 – 0,3 depending on the load combination- and type. By using simple examples, including only one variable load, it was shown that the variations in the model uncertainty VθS increases the failure probability thus decrease the reliability index β. The magnitude of these effects depends on the ratio φ between the permanent- and variable load. As an example, when φ = 0,75 (75% of the total load is variable thus 25% is permanent) and VθS = 0,3 then β ≈ 3,24 as compared to the target reliability index βt = 4,75 of safety class 3, which is a 32% reduction. Moreover, it was shown in the examples that the negative effects of increasing VθS, in terms of a decreased reliability index β, is more eminent in the case when the permanent load dominates the variable load, i.e. as φ = 0,25. Thus, increasing VθS from 0,1 to 0,2 decreases the reliability index by 30% (as compared to a 16% reduction when φ = 0,75). / Det vanligaste sättet att, i dagsläget, verifiera en byggnads säkerhet mot brott är med hjälp av partialkoefficientmetoden enligt Eurokoderna. Verifikationsmetoden är till sin form en deterministisk metod där de ingående variablerna som last och bärförmåga tillskrivs partialkoefficienter som verifierar att bärförmågan inte understiger lasteffekten. Då dessa koefficienter är kalibrerade med sannolikhetsteoretiska metoder brukar man kalla partialkoefficientmetoden för semi-probabilistisk.   Alternativt, kan verifieringen ske med hjälp av sannolikhetsteoretiska metoder. Istället för att tillskriva last- och bärförmågeparametrar partialkoefficienter så behandlas dessa som stokastiska variabler och inkluderar fysiska- såväl som statistiska osäkerheter. En korrekt sannolikhetsteoretisk analys måste även inkludera modellosäkerheter. Denna osäkerhet är förknippad med de matematiska modeller som används för att översätta last- och materialvärden till lasteffekt och bärförmåga samt osäkerheter på grund av variationer och förenklingar i exempelvis val av geometriska storheter och brottyp. Det finns en annan typ av osäkerhet som inte explicit behandlas av Eurokoderna samt bakgrundsdokumenten till dessa, och det är de osäkerheter som svarar mot ingenjörens val. Det vill säga, hur denne tolkar givna dimensioneringsunderlag och aktuella regelverk samt de antaganden och förenklingar som uppkommer då ingenjören, utifrån ett realistiskt konstruktionsuppdrag, förutsätter exempelvis geometriska mått, laster och andra nödvändiga parametrar som krävs för att dimensionera en byggnadsdel. Som underlag till detta arbete finns ett omfattande statistiskt material, där ett stort antal byggnadskonstruktörer har tillhandahållits exakt samma uppgift som handlar om att ta fram laster, beräkna lasteffekter och dimensionera ett antal komponenter i en mindre hallbyggnad i stål. Statistiska parametrar, kopplade till variationerna i beräknade lasteffekter på grund av ingenjörens val, har skattats med hjälp av matematisk statistik. Utifrån detta resultat, har en sannolikhetsteoretisk nivå 2 metod använts för att analysera hur brottsannolikheten påverkas då denna modellosäkerhet varieras. I studien konstaterades, utifrån ett 95% konfidensintervall, att variationskoefficienten för de beräknade lasteffekterna, härvid definierad som modellosäkerheten på grund av ingenjörens val med beteckningen VθS, varierar någonstans mellan 0 – 0,3 beroende på aktuell lastkombination och lasttyp. Med hjälp av enkla exempel, innehållandes endast en variabel last, påvisades att variationerna hos modellosäkerheten VθS medför en ökning av brottsannolikheten och därmed en minskning av säkerhetsindexet β. Storleken på dessa effekter beror av fördelningen φ mellan den permanenta- och variabla lasten. Som ett exempel konstaterades att då φ = 0,75 (75% av den totala lasten är variabel och 25% är permanent) samt VθS = 0,3 så reducerades målvärdet för säkerhetsindexet βt = 4,75 i säkerhetsklass 3, med 32% till β ≈ 3,24. Vidare så konstaterades att de negativa effekterna av att öka VθS, beträffande en minskning av säkerhetsindexet β, är mer påtagliga då den permanenta lasten är den dominerande lasten, det vill säga då φ = 0,25. Genom att exempelvis öka VθS från 0,1 till 0,2 så minskas säkerhetsindexet med 30% (jämfört med en minskning på 16% då φ = 0,75).

O método construtivo com painéis portantes de concreto é economicamente viável, porém relativamente novo no cenário nacional, sobretudo no caso dos pré-moldados. As incertezas referentes às peculiaridades desse método, bem como a nova norma brasileira de painéis pré-moldados, ainda em elaboração, vem a motivar uma análise probabilística dos critérios de projeto disponíveis. Utilizando-se a técnica da confiabilidade estrutural, é possível propagar as incertezas referentes às variáveis a uma resposta final no índice de confiabilidade, sendo um cálculo totalmente probabilístico. Neste trabalho, emprega-se tal técnica com informações estatísticas referentes a lajes de concreto moldadas in loco para verificar, de maneira mais verossímil, a segurança dos critérios de projeto impostos pelo Precast Concrete Institute Design Handbook - Precast and Prestressed Concrete - 7th Edition (2010) às fases transitórias (desforma, transporte e içamento) e pela Norma Brasileira ABNT NBR 6118: 2014 - Projeto de estruturas de concreto, à fase em uso. Prossegue-se a uma análise crítica dos resultados bem como sugestões para diminuir a variação dos resultados, sobretudo pela calibração de novos coeficientes parciais de segurança, processo para o qual este trabalho pode servir de base. / The shear wall building method is economicaly viable, but relatively new in the brazillian scene, that is specially true for precast members. The uncertainty pertaining this method, and the new brazillian design code for precast shear walls, still in development, serve as motivation for a probabilistic analysis of available project criteria. Using the structural reliability technique, it is possible to forward the variables uncertainties to a final answer in the form of the reliability index, being that this method is entirely probabilistic. In this study, this technique is used with statistical data pertaining cast-in-place concrete slabs to ascertain, with a higher degree of verisimilitude, the safety of the design criteria imposed by the Precast Concrete Institute Handbook - Precast and Prestressed Concrete - 7th Edition (2010) to the temporary states (stripping, transit and lifting) and by the Brazillian Code ABNT NBR 6118: 2014 - Concrete structures design, to the working state. The study then proceeds to a critical analysis of the results and to suggestions to reduce their variability, specially through calibration of new partial safety factors, a procedure to which this study might serve as a basis.

Apresentam-se neste trabalho formulações do método dos elementos de contorno (MEC), visando sua utilização em problemas de fratura e também de modelos de confiabilidade e otimização aplicados na análise de problemas de fadiga. Com relação aos progressos e avanços nas formulações do MEC, apresentam-se modelos que representam o processo de crescimento de fissuras em domínios planos constituídos por materiais frágeis, quase-frágeis e dúcteis. Considerando esses diferentes tipos de materiais, a formulação numérica adotada na análise descreve o comportamento estrutural não linear decorrente do processo de propagação das fissuras e conseqüente degradação estrutural. Nos modelos de fratura é empregada a formulação MEC dual, a qual é mais adequada para a análise da propagação aleatória de fissuras. São também apresentadas as expressões dos operadores tangente para as formulações não lineares que tratam os problemas de fratura elástico linear e coesiva, problemas de contato e os problemas de domínios enrijecidos. Com relação às análises de confiabilidade estrutural, o modelo mecânico de fadiga é acoplado a algoritmos de confiabilidade para a determinação do índice de confiabilidade e do conjunto de valores aleatórios com maior probabilidade de ocorrência. São testados alguns algoritmos de confiabilidade, podendo-se claramente definir um deles como mais eficiente para a análise de problemas de fadiga. A esse modelo é acoplado um algoritmo de otimização para a determinação das dimensões do elemento estrutural e dos intervalos para os procedimentos de manutenção e inspeção, que levam ao mínimo custo estrutural com base nas incertezas determinadas pelo modelo de confiabilidade. São apresentados vários exemplos validando e mostrando a eficiência das formulações desenvolvidas. / This work deals with the development of boundary element method (BEM) formulations to be used in engineering problems. Particular attention is given to using these formulations in development of reliability and optimization models applied to fatigue problems. Contributions to BEM formulations are developed, particularly, models that deal with crack growth in plane domains composed by brittle, quasi-brittle and ductile materials. Taking into account these different types of materials, the proposed formulation properly represents the nonlinear structural behaviour induced by crack growth and the resulting structural damage. The dual BEM formulation is adopted here for the proposed crack model and to analyse random crack propagation. In this thesis tangent operators are used in the non-linear BEM formulations, in order to deal with cohesive crack, contact problems and debonding problems in reinforced domains. Regarding structural reliability analysis, the fatigue mechanical model was coupled with appropriate reliability algorithms to compute the reliability index and other important random values. Several reliability algorithms were tested for this coupled model, in order to find the most efficient in the analysis of fatigue problems. An optimization model was also coupled with the fatigue reliability model, in order to evaluate the optimal structural element dimensions and also to schedule the intervals for maintenance and inspection procedures, taking into account the minimum cost and problem uncertainties. Many examples are presented in order to show the efficiency and accuracy of the proposed formulations in dealing with crack propagation, fatigue reliability analysis and optimization problems.

O trabalho propõe avaliação das respostas de esforços e deslocamentos de edifícios 3D considerando a interação solo-fundação-estrutura usando o conceito de Confiabilidade Estrutural. Para isso, empregam-se os Métodos dos Elementos Finitos (MEF) para a análise de estruturas e os métodos de Monte Carlo Simples (MCS) e First Order Second Moment (FOSM) para calcular sua segurança perante a inserção de variabilidade em certos parâmetros significativos no projeto, como as incertezas dos dados de rigidez do solo e a velocidade de vento. A formulação do edifício é baseada no MEF com elementos de barra e de casca, sendo as vigas, pilares e estacas elementos de barra e as sapatas em elementos de casca. Essa formulação é elastostática, mas permitindo a analise não-linear geométrica para os pilares. O solo é representado pelo modelo discreto de Winkler, o qual substitui sua influência contínua por molas pontuais com rigidezes equivalentes, tanto para a fundação rasa (sapatas isoladas) como para profunda (estacas). Com os resultados obtidos pelos modelos gerados, são feitas discussões e comparações com os métodos tradicionais de avaliação do fenômeno de recalque diferencial confrontando limites de índices de confiabilidade apresentados no Joint Committee on Structural Safety (JCSS, 2001) e os valores absolutos propostos pela literatura com base na Associação Brasileira de Normas Técnicas, ABNT, NBR6122: Projeto e execução de fundações (2010). Realiza-se também a análise de Estado Limite Último de pilares submetidos a flexo-compressão oblíqua com não linearidade física, de modo a avaliar o dimensionamento com fatores de segurança parciais da NBR 8681: Ações e segurança nas estruturas - Procedimento (2004) e Métodos de Confiabilidade Estrutural. / This work proposes the evaluation for the effects of forces and displacements about 3D buildings considering the soil-foundation-structure interaction using the concept of Structural Reliability. To do so, it is applied the Finite Elements Method (FEM) for the structural analysis and Simple Monte Carlo Method (SMC) and the First Order Second Moment (FOSM) to calculate its safety towards the application of variability at certain significant parameters of the project, as the uncertainness about the data of soil stiffness and wind speed. The building\'s formulation is based on the FEM with framed bars and shell elements, being beams, columns and piles as beam elements and the footings as shell elements. That formulation is elastostatic, although permits a non-linear geometric analysis for the columns. The soil is represented by the discrete Winkler\'s model, in which substitutes its continuum influence by nodal springs with equivalent stiffness, such as for shallow foundations (isolated footings), as for deep foundations (piles). With the results obtained by the generated models, discussions are done and comparisons about traditional method to evaluate the phenomenon of the differential settlement confronting the limits of the reliability presents in the Joint Committee on Structural Safety (JCSS,2001) and the absolute values proposed by the literature based on the Brazilian Association of Technical Standards, ABNT, NBR6122: Project and execution of foundations (2010). An analysis about the Ultimate Limit State of columns submitted by flexo-compression with physical non-linearity it is also performed, so that to compare the design with partial safety factors of the NBR 8681: Action and safety on structures - Proceedings (2004) and structural reliability methods.

A aplicação de simulações numéricas em problemas de confiabilidade estrutural costuma estar associada a grandes custos computacionais, dada a pequena probabilidade de falha inerente às estruturas. Ainda que diversos casos possam ser endereçados através de técnicas de redução da variância das amostras, a solução de problemas envolvendo grande número de graus de liberdade, respostas dinâmicas, não lineares e problemas de otimização na presença de incertezas são comumente ainda inviáveis de se resolver por esta abordagem. Tais problemas, porém, podem ser resolvidos através de representações analíticas que aproximam a resposta que seria obtida com a utilização de modelos computacionais mais complexos, chamadas chamados meta-modelos. O presente trabalho trata da compilação, assimilação, programação em computador e comparação de técnicas modernas de meta-modelagem no contexto da confiabilidade estrutural, utilizando representações construídas a partir de redes neurais artificiais, expansões em polinômios de caos e através de krigagem. Estas técnicas foram implementadas no programa computacional StRAnD - Structural Reliability Analysis and Design, desenvolvido junto ao Departamento de Engenharia de Estruturas, USP, resultando assim em um benefício permanente para a análise de confiabilidade estrutural junto à Universidade de São Paulo. / The application of numerical simulations to structural reliability problems is often associated with high computational costs, given the small probability of failure inherent to the structures. Although many cases can be addressed using variance reduction techniques, solving problems involving large number of degrees of freedom, nonlinear and dynamic responses, and problems of optimization in the presence of uncertainties are sometimes still infeasible to solve by this approach. Such problems, however, can be solved by analytical representations that approximate the response that would be obtained with the use of more complex computational models, called meta-models. This work deals with the collection, assimilation, computer programming and comparison of modern meta-modeling techniques in the context of structural reliability, using representations constructed from artificial neural networks, polynomial chaos expansions and Kriging. These techniques are implemented in the computer program StRAnD - Structural Reliability Analysis and Design, developed at the Department of Structural Engineering, USP; thus resulting in a permanent benefit to structural reliability analysis at the University of São Paulo.