Neste trabalho utiliza-se uma formulação do método dos elementos de contorno (MEC) para a análise de pavimentos de edifícios, dando-se particular ênfase à análise de lajes cogumelo feita com a incorporação da não-linearidade física. Nesta formulação são consideradas as tensões normais e cisalhantes possibilitando, assim, a determinação da resistência última da estrutura. A formulação é inicialmente desenvolvida para a análise de flexão de placas utilizando-se a teoria de Reissner. A seguir, a formulação é estendida de modo a considerar a interação da placa com outros elementos, como vigas e pilares. Na interação placa-viga, o enrijecimento produzido é computado através de uma combinação com o método dos elementos finitos. Este modelo permite uma avaliação precisa dos momentos e forças cortantes nas interfaces da placa com os elementos lineares. Admite-se a ocorrência de um campo de momentos iniciais, viabilizando, dentre outros, o estudo de pavimentos com não-linearidade física. Para a análise do comportamento não-linear, implementa-se um algoritmo incremental-iterativo baseado no método da rigidez inicial. Visando-se obter uma melhor representação do comportamento do concreto armado, a integração das tensões ao longo da espessura é feita por um esquema numérico tipo gaussiano; a contribuição da armadura é feita de modo discreto considerada concentrada em seu centro geométrico. Pode-se, assim, avaliar separadamente o processo de danificação do concreto e o escoamento das armaduras. Para o concreto adota-se o modelo de dano de Mazars e para as armaduras longitudinais, um modelo elastoplástico uniaxial com endurecimento isotrópico. Quanto à absorção dos esforços oriundos das tensões cisalhantes, adota-se um modelo semelhante à idealização da treliça clássica de Ritter e Mörsch para vigas de concreto armado. Admite-se ainda que, após o início da fissuração, as tensões cisalhantes sejam absorvidas apenas pelas armaduras transversais. Para estas, adotase comportamento elástico linear. Objetivando-se a comprovação da eficiência da formulação proposta, são analisados alguns exemplos cujos resultados são comparados com resultados experimentais ou resultados de outros métodos de análise / This work deals with a formulation of the boundary element method applied to slab floor analysis with special emphasis concrete flat slabs exhibiting physical non-linearities. In this formulation normal and shear components of the stress tensor are taken into account to capture more accurately the ultimate strength of the structural element. The boundary element formulation in the context of Reissner’s plate bending theory is initially studied. Then, the formulation is extended to deal with combinations of plate elements with other elements such as beams and columns and also to incorporate internal support effects, for which full contact is assumed over small areas. The plate-beam and plate-column interaction model is based on a combination with the finite element method. Thus, this model allows an accurate evaluation of the internal forces along the plate-linear element interfaces and also over its vicinity. The presence of possible initial moment fields is also taken into account, which enables us to consider physical non-linear behaviours. The solution of the nonlinear system of algebraic equations is based on an iterative algorithm with constant matrix. In order to obtain a better modelling of the reinforced concrete slabs, the stress integrals along the thickness are performed with an appropriate gauss scheme; the reinforcement contribution is computed by considering concentrated effects at its geometric centre. Thus, the concrete degradation and the steel yielding can be independently evaluated. To represent the concrete behaviour the Mazars’ damage model has been adopted, while the steel material is governed by a uniaxial elastoplastic criterion with isotropic hardening. After the initial cracking of the concrete the shear stresses are properly transferred to the shear reinforcement using the Mörsch truss concept. The accuracy of the proposed formulation is illustrated by the analysing some practical examples. The results obtained are compared with experimental results and other numerical technique solutions

This diploma thesis deals with the problems of revitalization of historical objects. The theoretical part describes the technologies for static reinforcing and rehabilitation of vertical and horizontal bearing structures for a purpose of increasing the general stiffness of the object. As the practical part a static design project is made for reinforcing of the bearing walls and also for the general reconstruction of the slab. The slab is designed as the composite timber-concrete structure. The design project of the slab is economically compared with other variants. The designs are made for an existing object of the old restaurant in the village Velichovky.

The usage of linear 3D FEA is widespread within the bridge design community, and although this tool provides substantial benefits in the design process, there are certain practical issues related to the application of this analysis tool. A situation in which such an issue prevails is when linear 3D FEA is used to analyze restraint forces due to thermal shrinkage or expansion in concrete slab frame bridges. Effects related to restraint forces in concrete are difficult to model and predict as these forces differ significantly in nature from external loads, and dealing with them in practical design situations is complicated. In this thesis, cracking due to restraint forces in concrete slab frame bridges was investigated using 3D non-linear FE-analyses in the software package ATENA 3D. Using volumetric finite elements, attempts were made to realistically capture the load response and cracking behavior of concrete slab frame bridges subjected to restraint forces induced by temperature differences among members. The initial parts of this thesis aims to find appropriate modelling techniques and material models for the prediction of cracks due to restraint forces in base restrained walls using a previously reported experimental research project as reference. Comparative simulations were performed, using crack widths and crack patterns as comparate. Overall good correspondence was obtained with an exception of deviation in cracks formed at locations near the restrained corners where crack widths were overestimated in the simulations. The technique used to model the restrained boundary proved to be highly influential in the context of obtaining realistic results. Subsequent to the comparative study, a parametric study was performed where the correlation between crack widths and selected attributes was investigated. The parameter which exhibited the most distinct influential effect on the results was the length-to-height (L/H) ratio of the wall. The applicability of a crack control approach intended for crack width estimation in liquid retaining and containment structures made of concrete exposed to thermally induced restraint forces, given in EN 1992-3, was then evaluated for use in design of concrete frame bridges. This approach proved to return conservative results for walls with low L/H-ratios when compared to results produced in the numerical simulations. Finally, a NLFE (non-linear finite element) model of a concrete slab frame bridge designed by the consultancy company Tyréns AB was composed and tested. Different procedures of applying temperature differences between front wall and bridge deck were evaluated. This study indicated that the width of cracks induced by lateral restraint forces decreased when temperature was modelled applying a discrete thermal gradient to members in contact with back filling material compared to using a uniform temperature in these members when temperature differences between bridge deck and wall was simulated. The interacting effects of permanent external load effects and restraint forces were also investigated. Crack widths from NLFE simulations were then compared with corresponding results calculated using linear FEA results as input for design equations given in EN 1992-1-1. The latter resulted in estimated cracks more than 10 times wider than that obtained in the simulations, while crack widths predicted using the EN 1992-3 approach showed better correspondence to the NLFE results.

Purpose: This study aims to identify three different types of house foundation. These house foundations are so called full basement foundation, crawlspace foundation and concrete slab foundation. When beginning a new construction, no matter if the house is small or large, there are many decisions that must be made. Including which foundation method is most suitable for the existing area. The house foundation must be able to stand firm for many years to come without suffering problems such as cracks and frost heave. It is important to choose at an early stage the foundation method that is most cost-effective and the ability to minimize the risks of frost heave. Method: The work is built up of two different methods; a literature study and a case study which contains several interviews with construction officials in Västerås region. Results: shows that concrete slab foundation is the primary construction that is chosen when choosing a house foundation for a new project aiming to build multiple single-family houses in Barkarö in Västerås city. All representatives decided that this construction has many advantages compared to the other house foundation methods, such as basement foundation and crawl space. It is the most proven basic method for this new construction of single-family houses. Conclusion: The conclusion of the thesis is that many of the representatives which works in the construction area choose concrete slab over other house foundations when there is no requirement for a specific house foundation from the customer.

The finite element method (FEM) is commonly used to design the reinforcement in concrete slabs. In order to simplify the analysis and to be able to utilize the superposition principle for evaluating the effect of load combinations, a linear analysis is generally adopted although concrete slabs normally have a pronounced non-linear response. This type of simplification in the modeling procedure will generally lead to unrealistic concentrations of cross-sectional moments and shear forces. Concrete cracks already at service loads, which leads to redistribution of moments and forces. The moment- and force-peaks, obtained through linear finite element analysis, can be redistributed to achieve a distribution more similar to what is seen in reality. The topic of redistribution is however poorly documented and design codes, such as the Eurocode for concrete structures, do not give descriptions of how to perform this in practice. In 2012, guidelines for finite element analysis for the design of reinforced concrete slabs were published in a joint effort between KTH Royal Institute of Technology, Chalmers University of Technology and ELU consulting engineers, which was financially supported by the Swedish Transport Administration. These guidelines aim to include the non-linear response of reinforced concrete into a linear analysis. In this thesis, the guidelines mentioned above are followed to obtain reinforcement plans based on crack control, for a fictitious case study bridge by means of a 3D finite element model. New models were then constructed for non-linear analyses, where the reinforcement plans were implemented into the models by means of both shell elements as well as a mixture of shell and solid elements. The results from the non-linear analyses have been compared to the assumptions given in the guidelines. The results from the non-linear analyses indicate that the recommendations given in the aforementioned guidelines are indeed reasonable when considering crack width control. The shell models yield crack widths equal to approximately half the design value. The solid models, however, yielded cracks widths that were 15 - 20$\%$ lower than the design value. The results show that many factors attribute to the structural behavior during cracking, most noticeably the fracture energy, a parameter not featured in the Eurocode for concrete structures. Some limitations of the models used in this thesis are mentioned as well as areas for further improvement.

Reinforced concrete slabs are a conventional type of foundation that is widely used in residential, commercial and industrial buildings. Most of the slab foundations are constructed directly on the ground without another structural medium in between and some of the slabs are therefore influenced by ground softening. A slab foundation is designed to transfer vertical loads and bridge imperfections in the ground, but excessive soil distortion may destroy the support conditions of the slab and through this influence the stability of the superstructures. The aim of this project is to study how ground softening and its further development influence a typical concrete slab. Furthermore, an approximate analytical method to evaluate the condition of a slab due to ground softening was studied. A practical case has been studied to capture the actual failure behaviours of a reinforced concrete slab, based on a previous project. For the case studied, possible future mining activities close to a high bay warehouse may cause damaging settlement in the underground. The fault that may appear softens the soils underneath the foundation, which may deteriorate and cause collapse of the concrete slab under the warehouse. Two types of failure scenarios were studied; subsoil softening and subsoil collapse. The Finite Element Method (FEM) was used to analyse the behaviour of the slab and the development of the failures in the subsoil. A commercial FEM software package, Abaqus, was used as the analytic tool, with a built-in Concrete Damaged Plasticity model (CDP) that for the concrete material model. Both linear and nonlinear material properties have been used in the analyses with same softening effect of the subsoil. A large number of models were analysed to simulate the development of the fault and capture the failure modes of the slab at different stages. Excessive tensile cracks and vertical deformations were found in both failure scenarios studied. A possible internal stability problem of the warehouse due to this was also found. The nonlinear behaviour of the concrete slab was captured through the failure scenarios before damage. It is shown that the serviceability of the reinforced concrete slab can be influenced by softening ground, and a more realistic description of the possible failures was here obtained based on the nonlinear model compared to previous elastic analyses. Keywords:     Reinforced concrete slab, Nonlinear, Ground softening, Finite Element Method (FEM), Abaqus, Concrete Damaged Plasticity (CDP). / Armerade betongplattor är en vanlig typ av fundament som ofta används för bostäder, kommersiella och industriella byggnader. De flesta av grundplattorna konstrueras direkt på marken utan andra strukturella medium emellan och vissa av plattorna påverkas därför av mjuknande undergrunder. En grundplatta är konstruerad för att överföra vertikala laster och överbrygga imperfektioner i marken, men stora sättningar i undergrunden kan förstöra plattans stödförhållanden och genom detta störa stabiliteten för överbyggnaderna. Syftet med projektet är att studera hur mjuknande undergrund och dess propagering påverkar en typisk betongplatta. Vidare används en approximativ analysmetod för att utvärdera tillståndet hos en platta på sådan mark. Ett praktiskt fall har studerats för att fånga det verkliga brottbeteendet hos en armerad betongplatta, vilket bygger på ett tidigare genomfört projekt. För det studerade fallet kan eventuell framtida gruvdrift nära ett höglager orsaka skadliga sättningar i undergrunden. Den förkastning som kan uppstå kan leda till uppmjukning av jordarna under fundamentet, vilket kan förvärras och orsaka kollaps av betongplattan under lagret. Två typer av brottscenarier studerades; uppmjuknande respektive full kollaps av undergrunden. Finita Element Metoden (FEM) användes för att analysera beteendet hos plattan och utvecklingen av fbrott och förskjutning i undergrunden. Ett kommersiellt FEM programpaket, Abaqus, användes som analytiskt verktyg, med en inbyggd plasticitets och skademodell (CDP) för att beskriva betongmaterialets egenskaper. Både linjärelastiska och icke-linjära materialegenskaper har använts i analyserna, för att simulera effekten av den mjukande undergrunnden. Ett stort antal modeller analyserades för att simulera skadepropageringen och fånga brottmoder i plattan genom olika skeden. Dragsprickor och vertikala deformationer uppstod i bägge de studerade scenariorna. Ett möjligt intern stabilitetsproblem hos lagret på grund av detta konstaterades också. Det olinjära beteendet hos betongplattan fångades fram tills allvarlig skada uppstod. Det visas att funktionen i bruksgränsstadiet hos den armerade betongplattan kan påverkas genom uppmjuknande undergrund, och att en mer realistisk beskrivning av möjliga brott här kunde erhållas genom den olinjära modellen, jämfört med tidigare elastiska analyser. Nyckelord:   Betongplatta , Icke-linjärt uppträdande, Finita Element Metoden (FEM), FE-modell, Abaqus, Plasticitets och skademodell för betong (CDP).

The presented thesis describes the development of an automation design procedure for structural design of concrete slab bridges and how it can be used to conduct a set-based structural design. The automation procedure integrated finite element modelling, analysis and structural related verification (verifications in geometry, ULS and SLS) together and realised automatic implementation of the two processes. By employing the automation design procedure and the set-based design methodology, a case study is performed based on an existed bridge. In contrast with a traditional point-based design process, the set-based structural design considers a wide range of possible design solutions, called design space, which are combinations of possible choices of different design parameters. In the case study, the design parameters like structural dimensions and reinforcement layout are considered and constitutes the design space. The design space is first narrowed by structural related constraints and further narrowed by multiple criteria which are material cost, material mass and global warming impact (equivalent CO2 emission) until reaching an optimal solution considering the three criteria. The results of the case study reveal the potential of set-based design by using the automation design procedure in obtaining optimal design solutions on the three mentioned criteria. Meanwhile, a rough time estimation shows the automatic procedure helps improve the design efficiency. It also suggests that the evaluation and decision of the finally chosen solution should be the trade-offs between material cost and environmental impact.

Fibre reinforced polymers (FRP’s) are considered an alternative to steel reinforcement in concrete structures because of their noncorrosive nature and nonmagnetic properties. FRP materials are, however, brittle and have a lower stiffness compared to steel. The latter property can lead to deflection and crack control problems in FRP-reinforced concrete flexural members under service loads. A considerable amount of information is available for short-term deflection of FRP-reinforced concrete members, but data on long-term deflections are scarce. This study presents the results of monotonic (short-term) and sustained (long-term) loading tests of 12 concrete shallow beams reinforced with either steel or glass FRP (GFRP) bars. The short-term load-deflection responses of the members are evaluated using existing deflection prediction models (Branson’s and Bischoff’s), and the long-term deflection results (monitored over a period of one year) are used to evaluate the existing ACI code and CSA standard approaches for estimating long-term deflection. The GFRP-reinforced concrete beams exhibited greater amounts of both immediate deflection (under sustained load) and long-term deflections over time, than the steel-reinforced concrete beams. The long-term deflections of both the steel- and GFRP-reinforced concrete beams are overestimated when using the ACI and CSA approaches. Although ACI Committee 440 recommends use of lower values of the long-term deflection multiplier for GFRP-reinforced concrete beams, results obtained from this study suggest that the same longterm multiplier values may be used for GFRP- and steel-reinforced concrete beams loaded at between 115 to 157 days of concrete age.

Between 1965 and 1974, the Swedish Parliament decided to build one million dwellings, called Million Program. The million program buildings were erected with new, untried design solutions, in a short range of time, and at low cost. The residential buildings from that time are now greatly in need of renovation. The municipal housing company, Gavlegårdarna, renovates and improves the energy efficiency at some of it’s apartment buildings in the district Sätra, Gävle. One problem is how to make the basic design of the slab on ground more energy efficiency and moisture proof. The study covers four representative flooring types in the Gavlegårdarnas million program area in Sätra. This study aims to investigate and evaluate proven methods for adding insulation in the four floor types. Also to look for solutions by designing additional insulation to treat damp problems and improve energy efficiency in an economical way. Existing flooring types are to be examined to check for new solutions as well. The aim is to produce a number of measures to provide property owners with different energy efficiency solutions. Results of calculations show that the perimeter area of the slab is exposed to moisture problems, while the centre of it does not have any notable problems. According to calculations, improved floor types have U-values reduced by 31% – 40% depending on the insulation thickness and design. However, investments have a long payback period and this is sometimes not economically viable. When a redevelopment project is performed, it is beneficial to simultaneously add insulation. If investors promote sustainable development, reduced energy consumption by the proposed measures is viable, as advocated by the environmental goals set by Sweden and the EU. / Sveriges riksdag beslutade att det skulle byggas en miljon bostäder, så kallade miljonprogramshus, mellan åren 1965 och 1974. Miljonprogramshusen uppfördes med nya och obeprövade konstruktionslösningar, på kort tid och till låga kostnader. Idag är bostadshusen från den tiden i stort behov av renovering. Det kommunalägda bostadsbolaget Gavlegårdarna håller på att renovera och energieffektivisera några av sina flerbostadshus i stadsdelen Sätra, Gävle. Ett problem är hur grundkonstruktionen, platta på mark i flerbostadshusen ska energieffektiviseras och fuktsäkras. Denna undersökning behandlar fyra representativa golvkonstruktioner som förekommer i Gavlegårdarnas miljonprogramsområde i Sätra. Syftet med undersökningen är att studera och utvärdera beprövade metoder för tilläggsisolering på de fyra utvalda golvtyperna. Lösningsförslagen på tilläggsisoleringsåtgärderna ska behandla fuktproblem, ekonomi och energieffektivisering. Resultaten från undersökningen visar att markplattans kantbalk är utsatt för fuktproblem medan plattans mitt inte har några anmärkningsvärda problem. Enligt U- värdesberäkningarna förbättras golvtypernas U-värde med 31 % - 40 % beroende på isoleringstjocklek och utförande, dock har investeringarna långa återbetalningstider. Utförs ett renoveringsarbete är det fördelaktigt att samtidigt tilläggsisolera. Satsar investerarna på en hållbar utveckling med minskad energianvändning rekommenderas förslagna åtgärderna, vilket förespråkas i miljömål uppsatta av Sverige och EU.

[pt] Neste trabalho apresenta-se ferramentas computacionais para o projeto de lajes maciças de concreto armado. O projeto de lajes é feito utilizando-se uma análise elástica, elasto- plástica perfeita, um dimensionamento ótimo utilizando programação matemática e um projeto pela análise plástica. O projeto convencional de lajes de concreto armado tem sido feito a partir de esforços solicitantes determinados pela hipótese de comportamento linear elástico do material. Utilizando-se as ferramentas computacionais desenvolvidas neste trabalho é proposto um procedimento de projeto de lajes maciças de concreto armado que utiliza esforços solicitantes obtidos através de uma análise elasto-plástica perfeita desenvolvida pelo método dos elementos finitos. O dimensionamento das armaduras ortogonais, positivas e negativas, em cada ponto da laje é feito de modo a atender aos critérios de resistência definidos em função dos momentos de flexão e de torção e de maneira a se ter o menor consumo de aço. Os estados limites de utilização correspondentes à flecha da laje e à abertura de fissuras também são considerados no projeto. A análise elástica e elasto-plástica perfeita das lajes, descritas pelo seu plano médio e discretizadas pelo método dos elementos finitos, são feitas em regime de pequenos deslocamentos com formulação consistente em deslocamentos. Na análise elasto- plástica perfeita é utilizado o algoritmo de Newton-Raphson para solução das equações de equilíbrio a nível global da estrutura. As relações da Teoria da Plasticidade são resolvidas a nível local, ou seja, para cada ponto de Gauss da estrutura discretizada. O problema de retorno das tensões na análise elasto-plástica perfeita é formulado como um problema de Programação Matemática (PM). O Método dos Pontos Interiores proposto por Herskovits (HERSKOVITS, 1995) é utilizado como algoritmo de retorno das tensões na análise elasto-plástica perfeita. / [en] In this work it is presented computational methodologies for the design of reinforced concrete massive slabs. The design of the slabs is made using an elastic and perfect elastoplastic analysis, an optimum design using mathematical programming and a plastic analysis project. The conventional project of reinforced concrete slabs has been made starting from efforts determined by the hypothesis of linear elastic behavior of the material. Using the computational methodologies developed in this work, it is proposed a procedure of design of reinforced concrete massive slabs that uses efforts obtained through a perfect elasto-plastic analysis developed by the finite element method. The design of the orthogonal reinforcements, positive and negative, in each point of the slab is made in order to assist the yield criteria defined in function of the bending and torsion moments and in order to obtain the lowest consumption of reinforcement. The limit states of serviceability corresponding to the slab deflection and crack opening are also considered in the design.The elastic and perfect elasto-plastic analyses of the slabs, described by their medium plan and discretized by the finite element method, are performed under the hypothesis of small displacements with consistent formulation in displacements. In the perfect elasto-plastic analysis, the Newton-Raphson algorithm is used to solve the equilibrium equations at global level of the structure. The relationships of the Plasticity Theory are resolved at local level,that is, for each Gauss point of the iscretized structure. The return mapping problem in the perfect elasto- plastic analysis is formulated as a problem of Mathematical Programming (PM). The Method of the Interior Points proposed by Herskovits (HERSKOVITS, 1995) is used as a return mapping algorithm in the perfect elasto-plastic analysis.