One of the most common building materials is concrete and it has been for a long time. To overcome its low tensile capacity concrete structures are normally reinforced with steel rebars. The use of FRP (Fibers Reinforced Polymers) bars in concrete structures has emerged as an alternative to conventional steel reinforcement, due to the corrosion of steel in aggressive environments. FRP has been used as internal reinforcement for more than 30 years, bridges and parking garages are examples of structures in harsh environments where FRP is a good replacement for steel reinforcement. This due to the higher strength of FRP compared to steel and non-corrosive properties, however FRP as internal reinforcement is not commonly used in Scandinavia. This work has been divided into four parts, a Literature survey, a Literature study on durability, structural behaviour in the serviceability limit state and a FE analysis of previously carried out laboratory tests. In the literature survey the material FPR is described with its components, manufacturing process, history and various applications. A literature study was done to determent the long-term durability of GFRP by accelerated laboratory tests for durability, then compared to field tests on durability of GFRP rebars. The accuracy of FRP design international standards has been evaluated in terms of serviceability limit stat, such as ACI 440.1R-15, ISIS and a variant of Eurocode 2 (EC2). The design models for deflection available for these standards were compared to a database of experimental studies collected by the author. The stiffness of structures reinforced with FRP is such an important parameter so a non-linear calculation using ATENA software was conducted. Results were compared to laboratory tests performed at Denmark Technical University (DTU). In several accelerated laboratory experiments where bare FRP bars were exposed to different harsh environments the degradation of strength was significant, where an alkaline solution at elevated temperature was the harshest environment for the GFRP bars. When GFRP rebars are embedded in concrete the degradation was significantly lower (around 40 percentage points), the concrete protects the GFRP rebars considerably. The largest rate of degradation on GFRP rebars is in the initial state, in comparison to steel which starts to corrode when carbonation and/or chloride penetration critical levels reaches the reinforcement. In field studies there were small signs of degradation of the GFRP rebars, mainly in tropical climates. De-icing salts have a limited effect on the degradation. Laboratory experiments are very conservative with unrealistic harsh environments compared to the natural harsh environments. Therefore, after 20 years of service in harsh environment there were no or small signs of degradation on the GFRP rebars which indicates the validity of GFRP. All three standards evaluated had a large spread on the predicted deflection compared to the experiments, with ACI 440.1R-15 as the most conservative standard with a mean value of the deflection ratio at 0.81. The mean value of the deflection ratio when using ISIS was 0.87, slightly less conservative but with the same spread as ACI 440.1R-15. The calculation using a variant of EC2 had the most spread of results, but with a mean value of the deflection ratio at 0.93, this excluding 11 beams that had an unrealistic prediction due to the wrong prediction of the crack moment. The FEM model created had a similar stiffness as compared to the experiment from DTU, which indicates that the use of Atena was accurate for calculating the deflection of the beams. Although the ultimate load was not well predicted, probably due to the failure mode crushing of concrete in the compressive zone. Despite this, there are many structural parts where FRP could be beneficial, for example in splash zones, in edge beams and slabs etc. This could bring down the costs for maintenance and also prolong the life span of the structure.

Com o avanço tecnológico dos computadores e o desenvolvimento de soluções para problemas não lineares através do método dos elementos finitos, hoje é possível fazer uma análise mais complexa e mais próxima da realidade. É de extrema importância à verificação dos resultados obtidos pelos programas com a realidade e saber em quais casos esses modelos podem ser aplicados. Assim, o objetivo deste trabalho é discutir as vantagens e desvantagens da modelagem de estruturas de concreto armado em duas e três dimensões, através dos modelos de fissuras distribuídas. Foram escolhidos três experimentos para a modelagem numérica: o primeiro trata-se de um experimento com uma viga de concreto armado (LEONHARDT; WALTHER, 1962), o segundo experimento também é realizado com uma viga de concreto armado (BRESLER; SCORDELIS, 1963) e o terceiro experimento utiliza vigas de concreto armado em escala reduzida, fabricadas com microconcreto e arame, simulando uma barra de aço lisa (ALMEIDA et al, 2006). Para a modelagem numérica, utilizando-se o modelo de fissuras distribuídas com fissura rotacional e a análise das estruturas de concreto foi escolhido o programa comercial ATENA - \"Advanced Tool Engineering Non-linear Analysis\". / The technological advancement of computers and the development of solutions for nonlinear problems by finite element method are now possible to make more complex the analysis and closer to reality. It is extremely important to verify the results obtained by programs with reality and know which cases these models can be applied. So the objective is to discuss the advantages and disadvantages of modeling reinforced concrete structures in two and three dimensions, through the smeared cracking models. Three experiments were chosen to make the numerical modeling: the first is an experiment with a reinforced concrete beam (LEONHARDT; WALTHER, 1962), the second experiment is also a reinforced concrete beam (BRESLER; SCORDELIS, 1963) and the third experiment is reinforced concrete beams with small-scale and made of wire microconcrete simulating flat steel bar (ALMEIDA et al, 2006). For numerical modeling, using the smeared crack model with rotational crack, and analysis of concrete structures was chosen the commercial program ATENA - Advanced Tool Engineering Non-linear Analysis.

Com o avanço tecnológico dos computadores e o desenvolvimento de soluções para problemas não lineares através do método dos elementos finitos, hoje é possível fazer uma análise mais complexa e mais próxima da realidade. É de extrema importância à verificação dos resultados obtidos pelos programas com a realidade e saber em quais casos esses modelos podem ser aplicados. Assim, o objetivo deste trabalho é discutir as vantagens e desvantagens da modelagem de estruturas de concreto armado em duas e três dimensões, através dos modelos de fissuras distribuídas. Foram escolhidos três experimentos para a modelagem numérica: o primeiro trata-se de um experimento com uma viga de concreto armado (LEONHARDT; WALTHER, 1962), o segundo experimento também é realizado com uma viga de concreto armado (BRESLER; SCORDELIS, 1963) e o terceiro experimento utiliza vigas de concreto armado em escala reduzida, fabricadas com microconcreto e arame, simulando uma barra de aço lisa (ALMEIDA et al, 2006). Para a modelagem numérica, utilizando-se o modelo de fissuras distribuídas com fissura rotacional e a análise das estruturas de concreto foi escolhido o programa comercial ATENA - \"Advanced Tool Engineering Non-linear Analysis\". / The technological advancement of computers and the development of solutions for nonlinear problems by finite element method are now possible to make more complex the analysis and closer to reality. It is extremely important to verify the results obtained by programs with reality and know which cases these models can be applied. So the objective is to discuss the advantages and disadvantages of modeling reinforced concrete structures in two and three dimensions, through the smeared cracking models. Three experiments were chosen to make the numerical modeling: the first is an experiment with a reinforced concrete beam (LEONHARDT; WALTHER, 1962), the second experiment is also a reinforced concrete beam (BRESLER; SCORDELIS, 1963) and the third experiment is reinforced concrete beams with small-scale and made of wire microconcrete simulating flat steel bar (ALMEIDA et al, 2006). For numerical modeling, using the smeared crack model with rotational crack, and analysis of concrete structures was chosen the commercial program ATENA - Advanced Tool Engineering Non-linear Analysis.

This study will compare two prominent goddesses from the ancient Greek and Roman worlds, Athena and Minerva. The purpose is to explore what differences and likenesses the two goddesses have with each other, to see if a major distinction can be made between the two using mythological descriptions. The reason for the study is to show to what extent the Roman goddess Minerva had her own mythological background, attributes and character as distinct from that of Athena.  In academia the difference between Athena’s and Minerva’s characteristics are vague and unclear. Minerva’s Roman mythological background is often hard to point out since the Romans borrowed several mythological views of the gods and goddesses from the Greek perspective of the gods. With this comparison one will be able to more clearly know how the Romans viewed Athena’s counterpart by comparing the main Greek and Roman mythical description of the two. The materials used to compare the two will comprise of the Iliad, and the Aeneid. The fact that the ancient religions of Greece and Rome were different concerning their gods' character and place in the mythology of each culture is at times overlooked, albeit recognized. At instances they are simply lumped together as one and the same even though major differences might exist between them and the way they were viewed in their respective cultures. This habit of treating the gods in the respective sphere of Greek and Roman as the same is problematic because it takes away our understanding of them as gods from different religious cultures. This is particularly the case in our unconscious mind when we study Greek and Roman religion. The goal of this study is to identify what differences can be found and thereby get a clearer understanding of the similarities or differences between Athena and Minerva.

No description available.

Betong är ett av våra idag absolut viktigaste och vanligaste byggnadsmaterial. Betong har väldigt låg draghållfasthet och på grund av detta spricker betongkonstruktioner oftast. Att helt förhindra att betong spricker är svårt och ofta kostsamt istället ställs krav för hur vida sprickorna får vara. Sprickviddsbegränsning görs genom att konstruktionerna armeras. Detta examensarbete granskar uppkomsten av sprickor i ung betong (ålder lägre än 28 dygn) som orsakas av förhindrad rörelse. Rörelser som förhindras kallas för tvång. När betongkonstruktioner utsätts för tvång uppstår spänningar i betongen. Dessa spänningar kan leda till sprickor. Tvångsfallet som studerats är när en ny betongvägg gjuts mot en platta av betong som redan uppnått dimensionerad hållfasthet. Examensarbetet fokuserar på tvångsspänningar som uppstår på grund av den värmeutveckling som sker när betong hårdnar samt uttorkningen som sker efter formrivning. I arbetet har 3D modeller i FE-programmet Atena arbetats fram. Dessa modeller simulerar fuktutvecklingen, värmeutvecklingen och avkylningen som sker under betongens hårdnande. De beräknar även de spänningar och sprickor som uppstår på grund av tvånget som uppstår mellan den nygjutna väggen och den befintliga plattan. Det finns sedan tidigare arbeten som studerat dessa fenomen men de har enbart modellerats som 2D problem. Ett antal fall med olika randvillkor har upprättats för att jämföras och nå en sprickbild som stämmer med verkligheten. Att begränsa sprickvidder är viktigt eftersom de påverkar betongens hållfasthet och livslängd. Hur breda sprickor blir är extra viktigt i täta konstruktioner, som exempelvis vattenmagasin. Vida sprickor leder till läckage, försämrad hållfasthet och livslängd. Rapporten tar upp regler från Eurokod gällande hur täta konstruktioner ska konstrueras. En handberäkningsmall för beräkning av sprickvidder orsakade av tvång har skapats. Denna mall har baserats på Eurokods regelverk. Då Eurokod saknar metod för att beräkna värmeutveckling har detta gjorts separat i FE-programmet ConTeSt R&D, som är utvecklat för att specifikt beräkna värme i ett 2D-tvärsnitt. Syftet med arbetet är att ta fram en fungerande metod för att modellera uppkomsten av sprickbildning orsakad av tvångsspänningar. Resultaten från FE-modelleringen ska jämföras med de resultat som fås från handberäkningar enligt eurokodmetoden. Rapporten visar att det är möjligt att simulera en förväntad utveckling i spänningar och sprickor, men åstadkommer ingen generell modell då rapportens lösningen är fallspecifik. Eftersom vi enbart nått fallspecifika lösningar och inga generella metoder har det inte gått att göra någon jämförelse mellan handberäkningar och sprickmodellering i Atena. / Concrete is one of the most important and common building materials today. Concrete has very low tensile strength and because of this some amount of cracking is to be expected. Completely preventing cracking in concrete is complicated and costly. This report examines cracks in concrete caused by restraint. When the natural movement in a construction is restrained this will cause stress. This stress might lead to cracking. This report examines cracks that appear in concrete that has yet to reach its full tensile strength. The case that is being studied is that of a new wall that is cast on a slab that has reached full maturity. The report focuses on stresses that appear because of the heat production during hardening, as well as the drying that occurs after the cast is removed. For this purpose 3D models in the finite element software application Atena have been developed. These models simulate the heat and moisture development as well as the cooling that will occur during the hardening of the concrete. These models are also used to simulate the stress and cracking that will occur because of the relationship between the newly cast wall and the slab in place. Studies have previously been published based on this subject, but only in a 2D context where the shrinkage is applied as a boundary condition. A number of cases with varying boundary conditions have been compared in order to reach a crack pattern that corresponds to actual behavior. Reducing crack widths is important as they affect the strength as well as the lifetime of the concrete. The width of cracks that appear is even more important in constructions that need to be impermeable, for example water containers. Wide cracks are a cause of leakage, as well as reduced strength and longevity. The study looks at rules from Eurocode for designing impermeable structures. A template for calculating crack widths has been produced. This template is based on the Eurocode rule set. Since Eurocode is lacking any formulas to calculate heat development this has been done in the FE-software ConTeSt R&D, which is specifically designed to calculate heat development in a 2D section. The purpose of the study is to achieve a working model for the simulation of crack widths due to restraint. These results are to be compared to the results of the Eurocode calculations. The study shows that we are able to simulate an expected development in stresses and cracks, but does not result in a general model as the solution becomes specific to the case. As we have only achieved case specific solutions and no general method we have been unable to compare modelled results with manually calculated results.

Detta examensarbete vid Luleå tekniska universitet har utförts i samarbete med avdelningen för byggkonstruktionvid det nordiska konsultföretaget Norconsult AB. Arbetet bygger på en önskan från Norconsultatt ta fram en beräkningsmodell för höga balkar i överensstämmelse med Eurokod 2 motsvarande densom finns i BBK 04. Eurokod 2 har endast en knapphändig beskrivning av hur höga balkar bör dimensioneras.Detta skapar frustration och osäkerhet hos konstruktörer. Den tidigare svenska betongnormen,BBK 04, innehöll en tydlig och enkel mer empirisk beräkningsmetod för höga balkar, vilket gav en störresäkerhet vid projekteringen. Arbetet begränsas till att studera enkelt upplagda och kontinuerliga balkar i två spann belastade med enpunktlast mitt i vartdera spannet. Geometrin är densamma för samtliga balkar och armeringsmängdenvarieras tillsammans med brottlasten. Initialt utfördes en litteraturstudie för att erhålla en fördjupad kunskap om området samt att bygga uppen förståelse för teorin för höga balkar och den fackverksmodell som används i Eurokod 2. Vidare presenterasen försöksrapport, Rogowsky et al. (1983), som redovisar en experimentell laboratoriestudie därhöga balkar belastas till brott. Resultaten som presenteras är brottlast, töjning i betong och armering,sprickmönster samt nedböjning. Fyra enkelt upplagda och fyra kontinuerliga balkar väljs ut för vidarejämförelse och analys. Härvid används det ickelinjära beräkningsprogrammet ATENA 2D, där studeradebalkar modelleras. Handberäkningar enligt EK2 och BBK 04 utförs för respektive balk och tillhörandearmeringsmängd beräknas. En maximal brottlast itereras fram för respektive balk och beräkningsmetod (EK2 eller BBK 04). Armeringsmängdensom ges av denna beräkning modelleras i ATENA 2D och motsvarande balk analyseras.Resultaten jämförs sedan. Erhållna resultat sammanställs och jämförs med varandra: Rogowsky et al. (1983), ATENA 2D och handberäkningarnaenligt både Eurokod 2 och BBK 04. Jämförelsen visar att det finns få likheter mellan EK2och BKK 04, med avseende på erhållen armeringsmängd. BBK kräver generellt större armeringsmängdän Eurokod 2. Studien visar att beräkningarna med ATENA 2D stämmer väl överens med laboratorieförsöken.Resultaten visar även att antaganden enligt Eurokod 2 stämmer väl överens med hur de studeradebalkarna beter sig i verkligheten. En enkel beräkningsmodell som motsvarar BBKs konservativa modell är inte möjlig att ta fram inom deramar och begränsningar som finns för detta examensarbete. Istället sammanställs en modell i form av enpunktlista som förtydligar, sammanfattar och exemplifierar den mer verklighetstrogna beräkningsgångenför höga balkar enligt Eurokod 2.

Punching shear is a failure mechanism caused by concentrated loads, creating a crack pattern that resembles a cone shape or piece of pie starting from the top surface of the slab and prolongs downwards. When the total shear force is greater than the shear resistance of the slab, it may eventually lead to punching shear failure. It can be visualized as the column punches through the slab. Punching shear is very brittle and occurs all of a sudden. It is believed that the slab is subjected to hogging moments over the column in both directions, i.e. parallel and perpendicular to the free edge. Non-linear finite element analyses (NLFEA) has been used to study the cracking and failure mechanism for the reinforced slab. It is a slab over the edge support without clamping stiffness, therefore simulating the slab shear mechanism over a slender steel column is carried out in this study. The analyses has been performed using the software ATENA 3D Engineering developed by Červenka Consulting. Since the symmetry has been taken into account over an edge column, only one half of the cross-section has been modeled, with a symmetry line passing vertically through the slab and column. It can be summarized that the failure encountered around the column has a conical shape crack pattern similar to the ones encountered when punching shear occurs. However, it is important to note that this failure is not due to classic punching shear, but instead due to shear cracks developing around the column in both directions, both parallel and perpendicular to the free-edge. Three models (C1, C2, and C3) are studied to evaluate the impact that the length of the lower leg of the c-bar reinforcement has during failure. As mentioned earlier above, the crack propagation during punching shear begins from the upper surface of the slab and prolongs downwards diagonally towards the bottom of the slab and adjacent to the column. However, the crack propagation in the strip perpendicular to the free edge in all three models initiate from the bottom and propagate upwards. It can be concluded that the length reduction of the lower leg of the c-bars as a consequence reduced the shear strength capacity of the slab around the steel-plate. The reason for this is due to a reduction in maximum peak load when the lower leg of the c-bars were reduced. Consequently, this leads to a decrease in shear strength capacity of the slab and an earlier failure, where the inner-span was not able to take additional loads which could have led to greater deflections. / Genomstansning är en brottmekanism orsakad av koncentrerade laster, vilket skapar ett sprickmönster i likhet med en konfrom ellet en bit av paj som börjar från den övre ytan av plattan och förlängs nedåt. När den totala skjuvkraften är större än skjuvmotståndet i plattan , kan det så småningom leda till ett genomstansningsbrott. Det kan visualiseras som att pelaren stansar eller slår igenom plattan. Genomstansning är ett mycket sprött brott och inträffar helt plötsligt. Det antas att plattan utsätts för negativt moment ovanför pelaren i båda riktningarna, d.v.s såväl parallellt som vinkelrät mot den fria kanten. Icke-linjära finita elementanalyser (NLFEA) har använts för att studera sprickbildnings och brottmekanismen för den förstärkta plattan. Det är en platta över kantstödet utan någon fast inspänd styvhet, därför simuleras skjuvmekanismen för plattan över en slank stålpelare i denna studie. Analyserna har utförts med programvaran ATENA 3D Engineering som utvecklats av Červenka Consulting. Eftersom hänsyn har tagits till symmetrin över en kantpelare har endast halva tvärsnittet modellerats, med en symmetrilinje som går vertikalt genom plattan och pelaren. Det kan sammanfattas att brottet som påträffas runt pelaren har en konisk form med ett sprickamönster som liknar de som påträffas vid genomstansning. Det är dock viktigt att notera att detta brott inte orsakats av klassisk genomstansning, utan istället på grund av skjuvsprickor som utvecklast runt pelaren i båda riktningarna, såväl parallellt som vinkelrät mot den fria kanten. Som det tidigare nämnts ovanför börjar sprickan vid genomstansning från plattans övre yta och förlängs nedåt diagonalt mot bottenplattan och intill pelaren. Sprickmönstret i remsan vinkelrät mot den fria kanten i alla tre modellerna (C1, C2 och C3) initierar dock från botten och sprids uppåt. Slutsatsen kan dras att längdminskningen av c-stängernas underben minskade skjuvhållfastheten hos betongplattan runt pelaren. Anledningen till detta beror på en minskning av maximal toppbelastning när c-stängernas underben reducerades. Följaktligen leder detta till en minskning av skjuvhållfastheten och ett tidigare brott, där den inre spännvidden inte kunda ta ytterligare belastningar som kunde ha lett till större nedböjningar.

In Sweden, prefabrication in the construction industry is a very common system. In prefabricated structures, there are various kinds of connections and generally many hinged connections. Therefore, it is of high interest to study the behavior of the prefabricated buildings in relation to the connections. Two main theories that can be used to evaluate our structures are the non-linear finite element analysis (NLFEA) and the second order effects. These two theories help to study the real behavior of the structures. Software that can apply these two theories is the ATENA-GiD. Therefore, it was very interesting to explore this software and find out how it can be used for prefabricated buildings. For this reason, a simplified ten-storey building was studied which had been also used in Lindwall’s and Wester’s (2016) master thesis. Various cases were chosen for this building. The building was studied either with monolithic walls or with vertical slip connection between the prefabricated walls. Also, the hollow core (HC) slabs were modelled in two ways and the supports of the columns were modelled in three ways. Even when each slab was modelled with two materials (solid concrete for the upper and lower layer with smeared reinforcement for the lower layer and modified concrete in order to compensate for the voids), the increase in the time for analysis was not important. Also, the cracking was not extensive thanks to the relatively low wind load. The slip joint between the walls didn’t lead to the different displacement between the walls. It was found that the hinged support in the columns was modelled by using the upwind line of the base. In non-linear analysis cases, the model of the structure gave 20% larger displacements than in linear analysis cases which means that the cracking had an important influence on the second order effects despite that the cracking was not extensive. The reduction of the stiffness of the walls to 40% accounting for cracked sections in additional linear analyses to according to the Eurocode 2 was a conservative choice for this building. The most remarkable result was that when the supports of the columns were modelled with hinges there was smaller displacement than when the supports were fixed. The reason for this was the negative displacements due to the buckling of the columns of the first storey. Moreover, for the linear cases, there was a much smaller displacement (5mm) than Lindwall and Wester (2016) (17mm) and this was possibly due to the way that the hinges were modelled in my building. It is interesting to investigate other ways to model the hinges in ATENA-GiD as well as other ways to model the connections between the HC slabs and the perimetric beams. Also, the effect of creep through the modulus of elasticity could be analyzed. Finally, it would be interesting to include foundations in the model to study the possible need for anchorages.

Reinforced concrete deep beams are vital structural members serving as load transferring elements. The behavior of reinforced concrete deep beams is complex. Nonlinear distribution of strain and stress must be considered. Prior to 1999, ACI 318 Codes included an empirical design equation for reinforced concrete deep beams. Since 2002, the strut and tie model and nonlinear analysis have been required. However, both methods have disadvantages of complexity or lack of transparency. The objective of this study is to produce a simple, reliable design equation for reinforced concrete deep beams. A nonlinear finite element program, ATENA, was used for analyzing and predicting the behavior of concrete and reinforced concrete structures. First, applicability of ATENA was verified by developing the computer models of simply supported and two span continuous deep beams based on Birrcher’s tests of simply supported deep beams. Tests by Rogowsky and Macgregor and by Ashour are the basis for the models of continuous two span deep beams. Those tests were selected because the researchers reported adequate details of the experimental program and on specimen behavior. Then a series of simply supported and two span continuous deep beam models were developed based on the details and geometry of Birrcher's beams. The computer models were used to investigate the following parameters: the compressive strength of concrete, shear span to depth ratios, longitudinal reinforcement ratios, web reinforcement, effect of member depth, and loading conditions. Finally, a proposed design equation for shear strength of reinforced concrete deep beams was derived based on the observed the behavior of reinforced concrete deep beam tests, the results of the analytical study, and a plastic truss model. The proposed equations were in good agreement with test values and provide an alternate approach to current design procedures for deep beams. / text