Equipment behavior is often discussed in terms of age and use. For example, an automobile is frequently referred to 3 years old with 30,000 miles. Bivariate failure modeling provides a framework for studying system behavior as a function of two variables. This is meaningful when studying the reliability/availability of systems and equipment. This thesis extends work done in the area of bivariate failure modeling. Four bivariate failure models are selected for analysis. The study includes exploration of bivariate random number generation. The random data is utilized in estimating the bivariate renewal function and bivariate availability function. The two measures provide insight on system behavior characterized by multiple variables. A method for generating bivariate failure and repair data is developed for each model. Of the four models, two represent correlated random variables; the other two, stochastic functionally dependent variables. Also, methods of estimating the bivariate renewals function and bivariate availability function are constructed. The bivariate failure and repair data from the four failure models is incorporated into the estimation processes to study various failure scenarios. / Master of Science

Same types of systems with the same age usually have different amounts of cumulated usage. These systems when in operation usually have different performance and effectiveness. In this case the existing models of the univariate measures of system effectiveness are inadequate and incomplete. For example, the univariate availability measures for these same-aged systems are all the same even though with different amounts of usage. This is the motivation for this research to pursue a bivariate approach in reliability and maintenance modeling. This research presents a framework for bivariate modeling of a single-unit system. Five key efforts are identified and organized as: (i) bivariate failure modeling, (ii) bivariate renewal modeling, (iii) bivariate corrective maintenance (CM) modeling, (iv) bivariate preventive maintenance (PM) modeling, and (v) bivariate availability modeling. The results provide a foundation for further study of bivariate and multivariate models. For bivariate failure modeling, several bivariate failure models are constructed to represent the possible correlation structures of the two system aging variables, time and usage. The behavior of these models is examined under various correlation structures. The developed models are used to analyze example maintenance problems. Models for bivariate renewal, bivariate CM, and bivariate PM are derived based on the constructed bivariate failure models and the developed bivariate renewal theory. For bivariate CM modeling, corrective maintenance is modeled as an alternating bivariate renewal process or simply an ordinary bivariate renewal process. For bivariate PM modeling, PM models are examined under a bivariate age replacement preventive maintenance policy. The Laplace transforms of the renewal functions (and densities) for these models are obtained. Definitions for bivariate availability functions are developed. Based on the derived CM and PM models, the Laplace transforms for their corresponding bivariate availability models are constructed. The idea of the quality of availability measure is also defined in terms of bivariate availability models. The most significant observation is that this framework provides a new way to study the reliability and maintenance of equipment for which univariate measures are incomplete. Therefore, a new area of reliability research is identified. The definitions offered may be modified and the approach to model formulation presented may be used to define other models. / Ph. D.

This paper presents an analytical method for estimating the flexural strength of reinforced concrete (RC) beams strengthened with externally bonded fibre-reinforced polymer (FRP) laminates. The method is developed from the strain compatibility and equilibrium of forces. Based on the size of external FRP laminates, several flexural failure modes may be identified, namely tensile rupture of FRP laminates and concrete crushing before or after yielding of internal steel reinforcement. Upper and lower limits to the size of FRP laminates used are suggested to maintain ductile behaviour of strengthened RC sections. Comparisons between the flexural strength obtained from the current method and from experiments show good agreement. Design equations for calculating the size of FRP laminates externally bonded to RC sections to enhance their flexural strength are proposed.

Esta pesquisa teve como principal objetivo analisar o comportamento de lajes alveolares protendidas de uso corrente no Brasil (pequenas espessuras e alta protensão) quanto ao cisalhamento em região fissurada por ação do momento fletor, para diferentes situações: sem e com capa e com preenchimento parcial de alvéolos. Foi desenvolvido um estudo teórico com o emprego de equacionamentos analíticos disponíveis na literatura técnica, envolvendo as recomendações da norma brasileira NBR 6118:2003 (Projeto de Estruturas de Concreto), do ACI-318:2008 (Building code requirements for structural concrete) e da EN 1992-1-1 (2004) (Eurocode 2- Projeto de estruturas de betão Parte 1-1: Regras gerais e regras para edifícios). Foram feitas comparações com resultados experimentais obtidos a partir de inúmeros ensaios de lajes alveolares protendidas. As unidades ensaiadas nesta pesquisa foram disponibilizadas por quatro empresas brasileiras de intensa atividade no mercado, sendo analisadas as capacidades resistentes de diferentes tipos. Assim, foram realizados 96 ensaios, 31 para a determinação da capacidade resistente à flexão e 65, ao cisalhamento, sendo selecionados modelos de lajes com grande emprego no mercado brasileiro. A partir desses ensaios, foi possível entender melhor o comportamento das lajes alveolares protendidas produzidas no Brasil. Com as diversas análises, considerando os ensaios experimentais e um vasto estudo teórico quanto ao dimensionamento dessas lajes, verificou-se a adequabilidade de equações de diferentes normas. Assim, foi possível identificar o equacionamento que melhor representa o comportamento das peças produzidas no Brasil, considerando inclusive peculiaridades de comportamento, que apresentam diferenças constratantes com relação a unidades produzidas em outros países. A partir desses estudos, produziu-se um amplo memorial de cálculo, considerando as diversas tipologias de lajes estudadas, com o objetivo de contribuir de modo didático com os engenheiros de estrururas. Logo, com esta pesquisa, foi possível não somente melhorar o entendimento do comportamento de tais lajes alveolares, como também fornecer subsídios para a avaliação desses elementos, considerando as características específicas das lajes produzidas no Brasil e, assim, contribuir para a padronização do dimensionamento junto à norma brasileira NBR 14861 (Laje pré-fabricada - Painel alveolar de concreto protendido). / This work had as major objective to analyze the behavior of Brazilian prestressed hollow core slabs - small thickness and high level of prestressing - considering shear in a cracked region due to bending moment, for different design situations: without concrete topping, with concrete topping and with filling the voids. A theoretical study was developed with the use of analytical equations available in the technical literature, involving the recommendations of the Brazilian code NBR 6118:2003 (Design of concrete structures), ACI-318: 2008 (Building code requirements for structural concrete) and EN 1992-1-1 (2004) (Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings), comparing experimental results from many prestressed hollow core slabs tests. The slabs tested in this study were provided by four different Brazilian companies with intense activity in the market, and the resistant capacity of different typologies was analyzed. Thus 96 tests were made, 31 to determine the bending capacity and 64 for the determination of shear strength, and were selected slab models from the Brazilian market that are highly employed. From these tests, it was possible a better understanding of the prestressed hollow core slabs behavior produced in Brazil. With several analysis considering the experimental tests and an ample theoretical study about the design of these slabs, the adequacy of different codes equations were verified. Thus, it was possible to identify the equations that best represent the behavior of elements produced in Brazil, also considering the behaviour peculiarities of these slabs that have contrasting differences, if compared with units produced in other countries. From these studies it was produced a large design manual, considering the various types of studied slabs, aiming to contribute in a didactic way to the structural engineers. So, with this research, it was possible not only to improve comprehension of the behavior of such prestressed hollow core slabs, as well as provide information for evaluation of these elements, considering the specific characteristics of the slabs fabricated in Brazil and thus to contribute with the standardization of the design in the Brazilian code NBR 14861 (Prefabricated slab - Prestressed concrete hollow core panel).

Esta pesquisa teve como principal objetivo analisar o comportamento de lajes alveolares protendidas de uso corrente no Brasil (pequenas espessuras e alta protensão) quanto ao cisalhamento em região fissurada por ação do momento fletor, para diferentes situações: sem e com capa e com preenchimento parcial de alvéolos. Foi desenvolvido um estudo teórico com o emprego de equacionamentos analíticos disponíveis na literatura técnica, envolvendo as recomendações da norma brasileira NBR 6118:2003 (Projeto de Estruturas de Concreto), do ACI-318:2008 (Building code requirements for structural concrete) e da EN 1992-1-1 (2004) (Eurocode 2- Projeto de estruturas de betão Parte 1-1: Regras gerais e regras para edifícios). Foram feitas comparações com resultados experimentais obtidos a partir de inúmeros ensaios de lajes alveolares protendidas. As unidades ensaiadas nesta pesquisa foram disponibilizadas por quatro empresas brasileiras de intensa atividade no mercado, sendo analisadas as capacidades resistentes de diferentes tipos. Assim, foram realizados 96 ensaios, 31 para a determinação da capacidade resistente à flexão e 65, ao cisalhamento, sendo selecionados modelos de lajes com grande emprego no mercado brasileiro. A partir desses ensaios, foi possível entender melhor o comportamento das lajes alveolares protendidas produzidas no Brasil. Com as diversas análises, considerando os ensaios experimentais e um vasto estudo teórico quanto ao dimensionamento dessas lajes, verificou-se a adequabilidade de equações de diferentes normas. Assim, foi possível identificar o equacionamento que melhor representa o comportamento das peças produzidas no Brasil, considerando inclusive peculiaridades de comportamento, que apresentam diferenças constratantes com relação a unidades produzidas em outros países. A partir desses estudos, produziu-se um amplo memorial de cálculo, considerando as diversas tipologias de lajes estudadas, com o objetivo de contribuir de modo didático com os engenheiros de estrururas. Logo, com esta pesquisa, foi possível não somente melhorar o entendimento do comportamento de tais lajes alveolares, como também fornecer subsídios para a avaliação desses elementos, considerando as características específicas das lajes produzidas no Brasil e, assim, contribuir para a padronização do dimensionamento junto à norma brasileira NBR 14861 (Laje pré-fabricada - Painel alveolar de concreto protendido). / This work had as major objective to analyze the behavior of Brazilian prestressed hollow core slabs - small thickness and high level of prestressing - considering shear in a cracked region due to bending moment, for different design situations: without concrete topping, with concrete topping and with filling the voids. A theoretical study was developed with the use of analytical equations available in the technical literature, involving the recommendations of the Brazilian code NBR 6118:2003 (Design of concrete structures), ACI-318: 2008 (Building code requirements for structural concrete) and EN 1992-1-1 (2004) (Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings), comparing experimental results from many prestressed hollow core slabs tests. The slabs tested in this study were provided by four different Brazilian companies with intense activity in the market, and the resistant capacity of different typologies was analyzed. Thus 96 tests were made, 31 to determine the bending capacity and 64 for the determination of shear strength, and were selected slab models from the Brazilian market that are highly employed. From these tests, it was possible a better understanding of the prestressed hollow core slabs behavior produced in Brazil. With several analysis considering the experimental tests and an ample theoretical study about the design of these slabs, the adequacy of different codes equations were verified. Thus, it was possible to identify the equations that best represent the behavior of elements produced in Brazil, also considering the behaviour peculiarities of these slabs that have contrasting differences, if compared with units produced in other countries. From these studies it was produced a large design manual, considering the various types of studied slabs, aiming to contribute in a didactic way to the structural engineers. So, with this research, it was possible not only to improve comprehension of the behavior of such prestressed hollow core slabs, as well as provide information for evaluation of these elements, considering the specific characteristics of the slabs fabricated in Brazil and thus to contribute with the standardization of the design in the Brazilian code NBR 14861 (Prefabricated slab - Prestressed concrete hollow core panel).

Today's automotive requirements have resulted in complex Sheet Metal Forming (SMF) processes of Sheet Metal (SM) with reduced formability, and thus it is crucial to be able to predict formability accurately to prevent material failure during SMF. Formability predictions today utilize Forming Limit Curves (FLC)s in Finite Element Analysis (FEA), but  FLCs are not valid for the Non-Linear Strain Paths (NLSP)s generated during SMF. One purpose of this thesis is thus to increase the knowledge on FP handling NLSP,  which was obtained through providing suggestions of failure models for handling NLSP effects, based upon literature on the subject. Generating NLSP experimentally is both time and material costly with the conventional method, thus the second purpose of this thesis was to increase the knowledge on test procedures for generating NLSP in SM. Based upon the findings of Chandramohan \cite{chandramohan_study_2021} five test procedures for generating NLSP were put forward, and the Nakajima test with modified punch geometry was chosen for further study.   In this thesis, the NLSP characteristics of two modified punch geometries were evaluated by FEA performed using LS-DYNA. For the FEA three specimens with blank width of 50, 100 and 200 mm was used, and the anisotropic Barlat yld2000  was used as the material model. This material model was calibrated to material data of Mild steel CR4, Aluminium alloy AA6016, and Dual-phase steel DP800. The results for all materials showcased similar reacquiring general NLSP characteristics at the corners of the punch features, which are unfavorable positions when failure by necking is evaluated, and thus it was concluded that the tested punch geometries are not favorable and more development of the punch geometry is needed. / Dagens fordonskrav, har lett till komplexa plåtformnings processer av plåtmaterial med reducerad formbarhet, och det är därför väsenligt att kunna förutsäga formbarhet noggrant för att förhindra materialbrott under plåtformning. Försträckning och brott förutses idag genom Formgränskurvor (FGK) i finita element analyser (FEA), men dessa gäller inte för icke-linjära töjningsvägar som uppkommer under plåtformning. Ett syfte av denna avhandling är därför att öka kunskapen kring modeller för att förutsäga formbarhet under icke-linjära töjningsbanors effekter, vilket uppnådes genom att  presenteras  förslag på brott modeller för att hantera de icke-linjära töjningsvägar baserade på  literatur inom området. Att generera icke-linjära töjningsvägar experimentellt är både tids och materialkrävande med den konventionella metoden, således är det andra syftet av denna avhandling att öka kunskapen kring test metoder för att generera icke-linjär töjningsbvägar i plåt. Baserat på Chandramohans \cite{chandramohan_study_2021} resultat diskuteras fem test procedurer för att generera icke-linjära töjningsvägar, och Nakajima test med modifierad stämpelgeometri valdes för vidare studie.  I denna avhandling studerades töjningsignaturen av två stämpelgeometrier med FEA i LS-DYNA. Till FEA:n användes tre ämnen med bredd av 50, 100 och 200mm, och anisotropiska Barlat yld2000 användes som materialmodell. Denna materialmodell kalibrerades mot experimentella mätvärden för mjukt stål CR4, Aluminiumlegering AA6016 och Stål DP800. Resultaten visade för alla material återkommande generella icke-linjära töjningsbanor enbart för hörnorna på stansgeometrierna, vilket är icke önskvärda positioner då brott pga. midjebildning utvärderas, och således drogs slutsatsen att nuvarande stansgeometri inte är gynnsam och ytterligare utveckling behövs.