One critical consideration in the design of buildings constructed in the western United States is the weight of settled snow on the roof of the structure. Engineers are tasked with selecting a design snow load that ensures that the building is safe and reliable, without making the construction overly expensive. Western states use historical snow records at weather stations scattered throughout the region to estimate appropriate design snow loads. Various mapping techniques are then used to predict design snow loads between the weather stations. Each state uses different mapping techniques to create their snow load requirements, yet these different techniques have never been compared. In addition, none of the current mapping techniques can account for the uncertainty in the design snow load estimates. We address both issues by formally comparing the existing mapping techniques, as well as creating a new mapping technique that allows the estimated design snow loads to be represented as an interval of values, rather than a single value. In the process, we have improved upon existing methods for creating design snow load requirements and have produced a new tool capable of handling uncertain climate data.

The reliability of structures subjected to time-invariant or time-variant random loads is considered herein. This is an important field of engineering, as it provides the framework for assessing whether newly designed or existing structural systems meet their design requirements in a given lifetime, or whether they experience what is termed “structural failure”. An important aspect of reliability analysis is the study of structures subjected to multiple time-varying loads. For this class of systems, it is well-known that by modelling the loads as (time-variant) random processes, the reliability may be evaluated by considering the outcrossing of a vector process out of a safe domain. However, due to the possibility that the loads may not be fully-dependent, all loads may not necessarily contribute to structural failure. To account for this the treatment of vector-outcrossings may need to allow for the possibility of outcrossings being caused by individual loads, as distinct from combinations of all loads. The procedure used to analyse combinations of loads depends on the stochastic process model used to represent the loads. Two well-known load models have been presented in the literature—they are referred to herein as the ‘on-off’ model and the ‘standard’ model. The ‘on-off’ model typically assumes loads are non-negative, and are either ‘on’ (eg their value is non-zero) or ‘off’ (eg their value is strictly zero). They can contribute to failure only when they are ‘on’. This model is represented by a somewhat artificial ‘composite’ probability distribution, obtained by modifying the original load probability density function (pdf) so that a ‘finite’ non-zero probability represents explicitly the possibility that the load is ‘off’. To implement this model in time-variant analysis, it is necessary to consider all possible combinations of loads being ‘on’ and ‘off’. In contrast, the ‘standard’ model (which is the more commonly used) typically allows loads to be negative; it is also typically represented solely by the original load pdf, and therefore effectively assumes each load is always ‘on’. To allow for the possibility of one or more loads not to cause failure, herein the value of such loads is held ‘constant’ at the time of failure, when the value of all loads actually causing failure is allowed to change. Use of the ‘standard’ model is examined herein. The “Directional Simulation in the Load Space (DS-LS)” approach is a tool used to perform reliability analysis. It is particularly suitable for time-variant analysis, as it allows loads to be represented as random processes, and to be modelled properly. DS-LS has so far been shown to work well for relatively simple structures subjected to one or more time-invariant random loads, and has been used to examine vector outcrossings in systems comprising either discrete or continuous loads. To enable the proper consideration of load combinations, and to provide some improvements in the formulation of the technique, a generalisation of the DS-LS approach is proposed herein. The generalisation is achieved in two stages. The first involves modifying the time-invariant and time-variant DS-LS formulation to allow for the possibility of positioning the origin of DS-LS not only in the ‘safe’ region of the load space (which the formulation currently requires) but in the ‘failure’ region, or even ‘exactly’ on the boundary separating the safe and failure regions. The modifications are necessary because for even simple structures, the ‘exact’ location of the safe and failure region is not always known explicitly ‘a priori’. The second involves developing the time-variant DS-LS formulation to consider explicitly outcrossings caused by combinations of one or more loads, during analysis of systems comprising stationary continuous gaussian loads. To do this, the direction of the load process vector is ‘fixed’ at each point of outcrossing, to physically represent the particular combination of loads causing the outcrossing. By considering each possible load combination, all loads not causing an outcrossing are then held constant during radial integration, thereby modelling those that do not contribute to each outcrossing. The proposed formulation differs from most load combination analysis techniques (which, evidently, simplify the analysis) as it is analytically ‘exact’, and it considers explicitly all possible combinations of loads. The concepts and formulations proposed herein may provide further understanding of reliability analysis performed by DS-LS (or other techniques) and may aid their future development. / PhD Doctorate

A practical engineering design problem is used to examine the over-conservativeness of designs obtained using deterministic optimization with worst-case parameter assumptions and a safety factor. Additionally, an attempted application of reliability-based design optimization (RBDO) demonstrates the limits of RBDO for practical problems. The design problem considered here is TESCO's Internal Casing Drive System (ICDS), which is used in feeding pipeline, or casing, into predrilled holes. After developing a finite element model of the ICDS, experimental data is used to successfully validate modeling methods and assumptions. The validated model is then subjected to multiple analyses to determine an appropriate design configuration to be used as the starting point for optimization. Worst-case, safety factor-based design optimization (SFBDO) is then applied considering two and three design variables, and is successful in increasing the critical load of the ICDS, Pcrit, by 35% and 45%, respectively. An efficient and recognized RBDO method, Sequential Optimization and Reliability Assessment, is selected for application to the design problem to determine an optimum design based on reliability. Due to the optimization formulation, however, SORA cannot be applied. The ICDS design problem represents a practical example that demonstrates the difficulties and limits in applying RBDO to practical engineering design problems. To evaluate the over-conservativeness of worst-case SFBDO, structural reliability analysis is performed on the deterministic optimum designs. It is found that the value of Pcrit for both the two and three variable optimum designs can be increased by 53% while maintaining acceptable probability of failure, demonstrating the over-conservativeness of the worst-case SFBDO. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2008-09-05 10:51:26.273

Overheight vehicle impact to bridge decks is a major problem in the transportation networks in the United States. An important factor that causes this problem is inadequate vertical clearance of bridges. Using steel pedestals to elevate bridge decks is an efficient and cost-effective solution for this problem. So far, steel pedestals have been used in the low seismic regions of the United States and therefore, their design has been based on providing enough strength to carry vertical loads and the lateral behavior of bridges elevated with pedestals have not been a major concern. But even in low seismic zones the seismic hazard should not be completely ignored. Also there might be some bridges in medium or high seismic regions that need to be elevated because of the lack of enough vertical clearance and using steel pedestals can be considered as an option for elevating those bridges. To address the mentioned needs, this dissertation proposes a framework to determine the structural reliability of bridges elevated with steel pedestals by developing probabilistic capacity and demand models for the slab-on-girder bridges subjected to lateral loads. This study first compares the behavior of previously tested pedestals with the behavior of elastomeric bearings in low seismic regions using statistical tests. Then, to provide a general framework, which can be applied to all bridges that are elevated with steel pedestals, this dissertation develops probabilistic capacity and demand models for steel pedestals considering all the aleatory and epistemic uncertainties of the problem. Using the developed probabilistic models along with the available models for other components of bridges, seismic fragility curves for elevated bridges are obtained and used to determine the structural reliability. Finally, this study uses the developed framework in a decision analysis that helps the engineering community and decision makers to check if the installation of steel pedestals on a specific bridge has financial justification or not. Results show that for a typical two-span slab-on-girder bridge, the use of steel pedestals has financial justification only in low seismic regions and if the societal benefits of elevating the bridge can at least cover the installation cost of pedestals.

Hurricanes and earthquakes have caused extensive property damage to wood-frame residential construction in the past two decades in the United States. In order to improve residential building performance and mitigate losses from hurricane and earthquake hazards, there is an urgent need for better understanding of building performance and improvements in design and evaluation tools. In this study, a fragility analysis methodology is developed for assessing the response of light-frame wood construction exposed to extreme hurricane winds and earthquakes. The fragility is a conditional limit state probability, presented as a function of the 3-second gust wind speed (hurricanes) or spectral acceleration at the fundamental period of the building (earthquakes), leading to a relation between damage state probability and the hazard stipulated in ASCE Standard 7. A fully coupled probabilistic framework is proposed to assess reliability of the residential construction through convolution of the structural fragility model with hazard models. Finally, a comparative risk assessment addresses the similarities and differences in competing hurricane and earthquake hazards. The tools above can be used to evaluate new and existing building products, model the uncertainties that are inherent to the prediction of building performance, and manage the risk that is consequent to these uncertainties economically

No description available.

Este trabalho de pesquisa visa apresentar um processo de avaliação probabilística de integridade mecânica de elementos estruturais, e ilustra sua aplicação em situações de otimização dimensional de tais elementos. O processo apresentado é baseado na análise de confiabilidade por métodos analíticos, utilizando o diagrama de avaliação de falha (FAD) como critério de falha. A escolha da curva FAD como critério de falha visa padronizar a análise de confiabilidade estrutural, permitindo a sua aplicação tanto em simulações numéricas quanto em mapas utilizados para rápidas tomadas de decisão. Os métodos de análise e o processo apresentado são aplicados em casos de estudo para mostrar a influência da percepção probabilística nas tomadas de decisão de projeto e a importância da análise de risco no dimensionamento de sistemas estruturais. / This work intends to present a process for probabilistic assessment of mechanical integrity of structural elements, and illustrates its application in situations of dimensional optimization of such elements. The presented process is based on the reliability analysis by analytical methods, using the failure assessment diagram (FAD) as failure criteria. The choice of FAD curve as a failure criteria aims to standardize the structural reliability analysis, allowing its application both in numerical simulations and in chart maps used for fast decision making. The methods of analysis and the presented process are applied in case studies to show the influence of probabilistic perception on project decision making and the importance of risk analysis in the design of structural systems.

[pt] Neste trabalho apresenta-se a avaliação do desempenho de ferramentas de inspeção em linha (ILI) ou pig instrumentado na medição de defeitos causados por corrosão e estudam-se diferentes métodos para o cálculo da confiabilidade estrutural ou cálculo da probabilidade de falha (POF) de um duto corroído, baseada na análise do relatório do pig. O relatório de inspeção do pig é avaliado através de comparações de seus resultados com as medições dos defeitos feitas por ferramentas de referência (medições em campo). Os erros associados a cada sistema de medição podem ser encontrados a partir de métodos estatísticos como os métodos da raiz do erro quadrático médio, dos estimadores de Grubbs, de Thompson e de Jaech. As medições das duas ferramentas são também avaliadas através de testes estatísticos para a linha de tendência e o coeficiente de correlação linear (r). O número mínimo de medições de campo necessárias para verificar o desempenho do pig no dimensionamento dos defeitos de corrosão é determinado pela implementação de um teste baseado na análise seqüencial. Uma vez que o relatório do pig é avaliado e aceito, a POF de um duto corroído é calculada usando os métodos analíticos de primeira ordem (FORM) e propagação de incertezas, e o método de simulação de Monte Carlo. A POF do duto é calculada em função de modelos de pressão de falha onde suas variáveis são definidas como funções de probabilidade (fdp). No caso das dimensões do defeito, a fdp e seus parâmetros estatísticos são obtidos a partir da exatidão do pig. A comparação entre a POF calculada e a POF admissível permite determinar quando será necessário fazer uma nova re-inspeção. Quando a POF calculada atinge um valor maior que a POF admissível, antes de se completar um tempo desejado para a próxima inspeção, o procedimento desenvolvido permite decidir qual o número de reparos que deverá ser feito para que este tempo seja alcançado. / [en] This work presents: i) the assessment of in line inspection (ILI) tools performance in the measurement of defects caused by corrosion; ii) differents methods to calculate structural reliability and probability of failure (POF) of corroded pipeline based in the ILI report. The inspection report of the ILI (or instrumented pig) is compared with the the geometry of defects measured by a reference tool (field measurements) and the erros associated to each measurement system are analyzed and assessed from statistical methods. The statistical analysis emploies methods such as the root mean square error/diffrential, and the Grubbs s, Thompson s and Jaech s estimators. The measurements taken by both tools (pig and field) are compared and analyzed through statistical tests that consider the tendency line and the coefficient of linear correlation (r). The minimum number of field measurements necessary to verify the performance of the ILI in sizing of corrosion defects is determined by the implementation of a test based on the sequential analysis. POF of a pipeline is calculated using three different methods: i) first order reliability methods (FORM); ii) propagation of uncertainties and iii) the method Monte Carlo. The POF of the pipeline is calculated as a function of different failure models whose variables (such as pressure, geometric and material parameters) are defined by their probability functions (pdf). The pdf and statistical parameters of the defect dimensions are determined from the accuracy of the pig measurements. The comparison between calculated and acceptable POF allows the determination of next reinspection period. When the calculated POF exceeds the acceptable POF before completing the amount of time desired for the next inspection, the developed procedure allows to know the number of repairs that must be made to reach the desired time when the next ILI will be carried out.

O evento do colapso progressivo começou a ser estudado, principalmente, após o acidente do edifício Ronan Point, em 1968, na cidade de Londres. Esse acidente fez o meio técnico rever as considerações normativas, sobretudo de maneira a adicionar recomendações que visem minimizar os danos causados à estrutura quando sujeita a um dano acidental.Entretanto, tais recomendações não realizam a análise do risco da estrutura colapsar. Essas também não conseguem analisar medidas de robustez e vulnerabilidade, e nem determinar qual é o elemento chave para a estrutura. Desse modo, partindo desses questionamentos, o presente trabalho desenvolveu uma nova metodologia nomeada aqui de Risk Analysis of the Progressive Collapse (RAPC). Este procedimento fornece uma medida mais precisa dos riscos, através de uma abordagem que utiliza a Teoria da Confiabilidade Estrutural. Assim, é deduzida uma expressão para a determinação da probabilidade de colapso progressivo, bem como são definidos os coeficientes de importância e vulnerabilidade para identificar o(s) elemento(s) chave. O elemento chave é definido como o que apresenta a maior interseção entre vulnerabilidade e importância para o colapso estrutural. Essas formulações desenvolvidas na metodologia do RAPC são implementadas em Fortran. Para isso, a modelagem do edifício de alvenaria estrutural é feita utilizando o software DIANA®, no qual os esforços solicitantes são obtidos e utilizados como dados de entrada na análise de confiabilidade. Valores de probabilidades de falha individual por elemento, condicional e condicional dupla são calculados pelo First Order Reliability Method (FORM) e Importance Sampling Monte Carlo (ISMC) com auxílio do programa StRAnD. Um algoritmo em Fortran é implementado para acoplamento do DIANA® e StRAnD, além de mapear a probabilidade de falha dos elementos estruturais. Portanto, torna-se evidente que a identificação dos elementos mais vulneráveis, e do elemento chave em particular, é útil para abordagens diretas de concepção estrutural, tais como a melhoria da resistência local. Contudo, os coeficientes propostos também medem os efeitos dos procedimentos de projeto que conduzem à continuidade, ductilidade e redundância. Quando essas medidas trabalham para reduzir as probabilidades de propagação de dano ou colapso, isso se reflete nas vulnerabilidades de elementos eventualmente iniciando esses caminhos de falha. Sendo assim, conclui-se que a formulação do RAPC se mostra como uma ferramenta na determinação do risco do colapso progressivo nas estruturas. / The progressive collapse event began to be studied, mainly, after the accident of the Ronan Point building, at 1968, in the city of London. This accident caused the engineers review their normative considerations, mainly in order to add recommendations aimed at minimizing the damage to structure when subjected to abnormal loading. However, such recommendations do not perform the risk analysis of the structure to collapse. These also fail to analyze measures of robustness and vulnerability, and either determine which is the key element of the structure. Thus, leaving of these questions, the present work to develop a new methodology named here of Risk Analysis of the Progressive Collapse (RAPC). This procedure provides a more accurate measure of risks through an approach that uses Structural Reliability Theory. Thus, an expression is deduced for the determination of the probability of progressive collapse, as well as the importance and vulnerability coefficients are defined to identify the key element (or key elements). The key element is identified as the one presenting the largest intersection between vulnerability and importance to collapse.These formulations developed in the RAPC methodology are implemented in Fortran.For this, the structural masonry building modeling is done using the DIANA® software, in which the requesting efforts are obtained and used as input data in the reliability analysis. Probabilities values individual, conditional, and double conditional are calculated by the First Order Reliability Method (FORM) and Importance Sampling Monte Carlo (ISMC) using the StRAnD software. A Fortran algorithm is implemented for DIANA® and StRAnD coupling, besides mapping the probability of failure of the structural elements. Therefore, it is clear that identification of the most vulnerable elements, and of the key element in particular, is useful for direct design approaches to structural design, such as local resistance enhancements. However, the coefficients proposed herein also measure the effects of design procedures leading to continuity, ductility or redundancy. When these measures work to reduce probabilities of damage propagation or collapse, this is reflected in the vulnerabilities of elements eventually initiating these failure paths. Therefore, it is concluded that the formulation of RAPC is shown as an tool in determining the risk of progressive collapse in structures.

As demandas do mercado da construção civil têm exigido vãos cada vez maiores e ao mesmo tempo alturas cada vez menores das vigas. Isto tem levado muitos projetistas à adoção da solução do pavimento em laje lisa em concreto armado ou protendido. No entanto, a ausência das vigas torna possível a ruptura das lajes por puncionamento junto aos pilares. A norma NBR-6118:2014 prescreve as disposições para o projeto de lajes sob punção. O trabalho proposto teve como objetivo principal a análise da confiabilidade da ligação laje-pilar interno sob o efeito da punção em lajes que se apoiam diretamente sobre pilares de acordo com a NBR-6118:2014. Primeiramente, com o intuito de se entender melhor o fenômeno da punção, realizou-se uma breve revisão bibliográfica, identificando os principais parâmetros que influenciam na resistência da ligação, assim como os principais métodos de análise e trabalhos realizados na área. Em seguida, estudou-se o software de análise em elementos finitos ANSYS (Analysis Systems Incorporated), especificamente a ferramenta UPF (User Programmable Features), que foi utilizada para adoção de um modelo constitutivo para o concreto. Utilizando o software, foram modeladas lajes estudadas por outros autores, visando a validação do modelo numérico. Para o estudo da confiabilidade foi dimensionado um conjunto de lajes lisas seguindo as prescrições da NBR 6118:2014. A análise da confiabilidade foi realizada utilizando a ferramenta PDS (Probabilistic Design System), empregando o método de simulação numérica de Monte Carlo com amostragem por Latin Hypercube. Por fim, determinou-se o índice de confiabilidade em cada projeto e realizaram-se análises paramétricas com as variáveis adotadas no trabalho. Os resultados obtidos mostraram que as lajes lisas sem armadura de cisalhamento projetadas segundo a NBR 6118:2014 obtiveram, em sua maioria, índices de confiabilidade adequados. Porém, para as lajes lisas com armadura de cisalhamento, o índice de confiabilidade foi, em grande parte, menor que o índice de confiabilidade alvo adotado. / The demands of the construction market have required increasingly large spans while diminishing of the beam heights. This has led many designers to adopt the pavement solucion of reinforced or prestressed concrete flat slab. However, the absence of the beams makes it possible to slabs failure by punching shear. The Standard NBR-6118: 2014 prescribes the requirements for the design of slabs under punching. The aim of this work was to analyze the reliability of the internal slab-column intersection under punching in slabs supported directly on columns according to NBR-6118: 2014. Firstly, in order to better understand the punching phenomenon, a brief bibliographic review was carried out, identifying the main parameters that influence the connection strength, as well as the main methods of analysis and published in the area. Then, the finite element analysis software ANSYS (Analysis Systems Incorporated), specifically the UPF (User Programmable Features) tool, was used to adopt a concrete constitutive model. Using the software, slabs studied by other authors were modeled, aiming at the validation of the numerical model. For the reliability study, a set of flat slabs was designed following the requirements of NBR 6118: 2014. The reliability analysis was performed using the PDS (Probabilistic Design System) tool, using the Monte Carlo numerical simulation method with Latin Hypercube sampling. Finally, the reliability index was determined in each project and parametric analyzes were performed with the variables adopted in the study. The results from this study show that the flat slabs without shear reinforcement designed according to NBR Standarts obtained appropriate reliability index. However, for the flat slabs with shear reinforcement, the reliability index, in most cases, did not achieve the target reliability index.