abstract: Most engineers may agree that an optimum design of a particular structure is a proposal that minimizes costs without compromising resistance, serviceability and aesthetics. Additionally to these conditions, the theory and application of the method that produces such an efficient design must be easy and fast to apply at the structural engineering offices. A considerable amount of studies have been conducted for the past four decades. Most researchers have used constraints and tried to minimize the cost of the structure by reducing the weight of it [8]. Although this approach may be true for steel structures, it is not accurate for composite structures such as reinforced and prestressed concrete. Maximizing the amount of reinforcing steel to minimize the weight of the overall structure can produce an increase of the cost if the price of steel is too high compared to concrete [8]. A better approach is to reduce the total cost of the structure instead of weight. However, some structures such as Prestressed Concrete AASHTO Girders have been standardized with the purpose of simplifying production, design and construction. Optimizing a bridge girder requires good judgment at an early stage of the design and some studies have provided guides for preliminary design that will generate a final economical solution [17] [18]. Therefore, no calculations or optimization procedure is required to select the appropriate Standard AASHTO Girder. This simplifies the optimization problem of a bridge girder to reducing the amount of prestressing and mild steel only. This study will address the problem of optimizing the prestressing force of a PC AASHTO girder by using linear programming and feasibility domain of working stresses. A computer program will be presented to apply the optimization technique effectively. / Dissertation/Thesis / Masters Thesis Civil Engineering 2016

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The manufacturing process ‘long line method’ has shown many advantages when producing prestressed concrete sleepers, such as rapid production and low cost. However, there have been certain difficulties when cutting the 100 m long concrete blocks into sleepers. The sleepers tend to crack when the diamond cutting blade cuts through the last strands. Moreover, the shape and size of the cracks varies from one sleeper to another. Although these cracks may not affect the load carrying capacity, they will not be aesthetically pleasing. No earlier studies within the area have been found, i.e. diamond cutting of prestressed concrete blocks. As a result, there have been certain difficulties when approaching the problem. Finite element analysis has been proven to be a useful tool when analyzing stress variation. Throughout this project, the cutting simulation has been analyzed using the finite element analysis software ABAQUS. To summarize, stress variation has been examined during different cutting depths. The results from the FE model shows that no critical values were reached in the areas expected to have cracks. The true cause of the problem could not be specified. Therefore, further studies are needed yet this thesis could be a good foundation.

The goal of the project is a static provision design of Drnovice castle. This castle (today a municipal office and a restaurant) is violated by vertical cracks. There is a significant horizontal displacement vector. That’s why horizontal prestress redevelopment (using prestressed cables) was chosen. A drawing documentation is an integral part of the project.

Uncertainties are present in the inverse analysis of damage identification with respect to the given measurements, mainly the modelling uncertainties and the measurement uncertainties. Modelling uncertainties occur due to constructing a representative model of the real structure through finite element modelling, and representing damage in the real structures through changes in material parameters of the finite element model (assuming smeared crack approach). Measurement uncertainties are always present in the measurements despite the accuracy with which the measurements are measured or the precision of the instruments used for the measurement. The modelling errors in the finite element model are assumed to be encompassed in the updated uncertain parameters of the finite element model, given the uncertainties in the measurements and in the prior uncertainties of the parameters. The uncertainties in the direct measurement data are propagated to the estimated output data. Empirical models from codal provisions and standard recommendations are normally used for prediction of long-time deformations in concrete structures. Uncertainties are also present in the creep and shrinkage models, in the parameters of these models, in the shrinkage and creep mechanisms, in the environmental conditions, and in the in-situ measurements. All these uncertainties are needed to be considered in the damage identification and prediction of long-time deformations in concrete structures. In the context of modelling uncertainty, uncertainties can be categorized into aleatory or epistemic uncertainty. Aleatory uncertainty deals with the irresolvable indeterminacy about how the uncertain variable will evolve over time, whereas epistemic uncertainty deals with lack of knowledge. In the field of damage detection and prediction of long time deformations, aleatory uncertainty is modeled through probabilistic analysis, whereas epistemic uncertainty can be modeled through (1) Interval analysis (2) Ellipsoidal modeling (3) Fuzzy analysis (4) Dempster-Shafer evidence theory or (5) Imprecise probability. Many a times it is di cult to determine whether a particular uncertainty is to be considered as an aleatory or as an epistemic uncertainty, and the model builder makes the distinction. The model builder makes the choice based on the general state of scientific knowledge, on the practical need for limiting the model sophistication to a significant engineering importance, and on the errors associated with the measurements. Measurement uncertainty can be stated as the dispersion of real data resulting from systematic error (instrumental error, environmental error, observational error, human error, drift in measurement, measurement of wrong quantity) and random error (all errors apart from systematic errors). Most of instrumental errors given by the manufacturers are in terms of plus minus ranges and can be better represented through interval bounds. The vagueness involved in the representation of human error, observational error, and drift in measurement can be represented through interval bounds. Deliberate measurement of wrong quantity through cheaper and more convenient measurement units can lead to bad quality data. Quality of data can be better handled through interval analysis, with good quality data having narrow width of interval bounds and bad quality data having wide interval bounds. The environmental error, the electronic noise coming from transmitting the data and the random errors can be represented through probability distribution functions. A major part of the measurement uncertainties is better represented through interval bounds and the other part, is better represented through probability distributions. The uncertainties in the direct measurement data are propagated to the estimated output data (in damage identification techniques, the damaged parameters, and in the long-time deformation, the uncertain parameters of the deformation models, which are then used for the prediction of long-time deformations). Uncertainty based damage identification techniques and long-time deformations in concrete structures require further studies, when the measurement uncertainties are expressed through interval bounds only, or through both interval and probability using imprecise techniques. The thesis is divided into six chapters. Chapter 1 provides a review of existing literature on uncertainty based techniques for damage identification and prediction of long-time deformations in concrete structures. A brief review of uncertainty based methods for engineering applications is made, with special highlight to the need of interval analysis and imprecise probability for modeling uncertainties in the damage identification techniques. The review identifies that the available techniques for damage identification, where the uncertainties in the measurements and in the structural and material parameters are expressed in terms of interval bounds, lack e ciency, when the size of the damaged parameter vector is large. Studies on estimating the uncertainties in the damage parameters when the uncertainties in the measurements are expressed through imprecise probability analysis, are also identified as problems that will be considered in this thesis. Also the need for estimating the short-term time period, which in turn helps in accurate prediction of long-time deformations in concrete structures, along with a cost effective and easy to use system of measuring the existing prestress forces at various time instances in the short-time period is noted. The review identifies that most of modelers and analysts have been inclined to select a single simulation model for the long-time deformations resulted from creep, shrinkage and relaxation, rather than take all the possibilities into consideration, where the model selection is made based on the hardly realistic assumption that we can certainly select a correct, and the lack of confidence associated with model selection brings about the uncertainty that resides in a given model set. The need for a single best model out of all the available deformation models is needed to be developed, when uncertainties are present in the models, in the measurements and in the parameters of each models is also identified as a problem that will be considered in this thesis. In Chapter 2, an algorithm is proposed adapting the existing modified Metropolis Hastings algorithm for estimating the posterior probability of the damage indices as well as the posterior probability of the bounds of the interval parameters, when the measurements are given in terms of interval bounds. A damage index is defined for each element of the finite element model considering the parameters of each element are intervals. Methods are developed for evaluating response bounds in the finite element software ABAQUS, when the parameters of the finite element model are intervals. Illustrative examples include reinforced concrete beams with three damage scenarios mainly (i) loss of stiffness, (ii) loss of mass, and (iii) loss of bond between concrete and reinforcement steel, that have been tested in our laboratory. Comparison of the prediction from the proposed method with those obtained from Bayesian analysis and interval optimization technique show improved accuracy and computational efficiency, in addition to better representation of measurement uncertainties through interval bounds. Imprecise probability based methods are developed in Chapter 3, for damage identifi cation using finite element model updating in concrete structures, when the uncertainties in the measurements and parameters are imprecisely defined. Bayesian analysis using Metropolis Hastings algorithm for parameter estimation is generalized to incorporate the imprecision present in the prior distribution, in the likelihood function, and in the measured responses. Three different cases are considered (i) imprecision is present in the prior distribution and in the measurements only, (ii) imprecision is present in the parameters of the finite element model and in the measurement only, and (iii) imprecision is present in the prior distribution, in the parameters of the finite element model, and in the measurements. Illustrative examples include reinforced concrete beams and prestressed concrete beams tested in our laboratory. In Chapter 4, a steel frame is designed to measure the existing prestressing force in the concrete beams and slabs when embedded inside the concrete members. The steel frame is designed to work on the principles of a vibrating wire strain gauge and is referred to as a vibrating beam strain gauge (VBSG). The existing strain in the VBSG is evaluated using both frequency data on the stretched member and static strain corresponding to a fixed static load, measured using electrical strain gauges. The crack reopening load method is used to compute the existing prestressing force in the concrete members and is then compared with the existing prestressing force obtained from the VBSG at that section. Digital image correlation based surface deformation and change in neutral axis monitored by putting electrical strain gauges across the cross section, are used to compute the crack reopening load accurately. Long-time deformations in concrete structures are estimated in Chapter 5, using short-time measurements of deformation responses when uncertainties are present in the measurements, in the deformation models and in the parameters of the deformation models. The short-time period is defined as the least time up to which if measurements are made available, the measurements will be enough for estimating the parameters of the deformation models in predicting the long time deformations. The short-time period is evaluated using stochastic simulations where all the parameters of the deformation models are defined as random variables. The existing deformation models are empirical in nature and are developed based on an arbitrary selection of experimental data sets among all the available data sets, and each model contains some information about the deformation patterns in concrete structures. Uncertainty based model averaging is performed for obtaining the single best model for predicting the long-time deformation in concrete structures. Three types of uncertainty models are considered namely, probability models, interval models and imprecise probability models. Illustrative examples consider experiments in the Northwestern University database available in the literature and prestressed concrete beams and slabs cast in our laboratory for prediction of long-time prestress losses. A summary of contributions made in this thesis, together with a few suggestions for future research, are presented in Chapter 6. Finally the references that were studies are listed.

The diploma thesis is focused on design and assessment of mounted storage hall. I have designed prestressed truss, reinforced truss, beam, column and foundation pad. I have made calculations for consideration of ultimated limit state as well. I have made analysis of internal forces for beams just with manual calculations. Analyses of internal forces for column and foundation pad were found with Scia Engeneer. All calculations are following the Eurocode 2. All designed elements have formwork drawing and reinforcement drawing.

The diploma thesis is focused on the design and review of selected load-bearing elements of the precast hall. Girder is dimensioned in two variants: reinforced and prestressed concrete. Design and assessment of prestressed girder was carried out using the simplified method and the IDEA statica. Column and footing was also dimensioned. All calculations are done in accordance with Eurocode 2.