Time dependent deformations in concrete, both creep and shrinkage, play a critical role in prestressed concrete structures, such as bridge girders, nuclear containment vessels, etc. These strains result in lossess, through release of prestress, and thereby influence the safety of these structures. The present study comprises of an experimental and analytical program to assess the levels of creep and shrinkage in normal and heavy density concrete. The experimental program includes tests on creep using standard cylinder specimen, while shrinkage studies have been conducted using prism specimen, both under controlled environmental conditions. The experimental results suggest that creep and shrinkage strains are higher in heavy density concrete than in normal concrete. This may be attributed to the relatively smaller pore structure of heavy density concrete, that results in larger availability of free water and a relatively slower hydration process in comparison to normal concrete. While there is some scatter in the results, creep strains decrease with age of loading and both creep and shrinkage strains are smaller when the relative humidity is higher. Statistical model reported in the literature for normal concrete is able to predict the test results for both normal and heavy density concrete quite well. Long term predictions of creep and shrinkage using this model, accounting for uncertainties, is also projected and shown to predict some long term measured results not used in the model calibration. The long term predictions are sensitive to the initial data used in model calibration.

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Predicting the long-term behavior of steel-concrete composite structures is a very complex systems problem, both because obtaining reliable information on material properties related to creep and shrinkage is not straightforward and because it is not easy to clearly determine the correlation between the effects of creep and shrinkage and the resultant structural response. Slip occurring at the interface between the steel and concrete may also make prediction more complicated. While the short-term deflection of composite beams may be easily predicted from fundamental theories of structural mechanics, calculating the long-term deflection is complicated by creep and shrinkage effects on the concrete deck varying over time. There are as yet no comprehensive ways for engineers to reliably deal with these issues, and the development of a set of justifiable numerical standards and equations for composite structures that goes beyond a simple commentary is well overdue. As the first step towards meeting this objective, this research is designed to identify a simple method for calculating the long-term deformations of steel-concrete composite members based on existing models to predict concrete creep and shrinkage and to estimate the time-varying deflection of steel-composite beams for design purposes. A brief reexamination of four existing models to predict creep and shrinkage was first conducted, after which an analytical approach using the age-adjusted effective modulus method (AEMM) was used to calculate the long-term deflection of a simply-supported steel-concrete composite beam. The ACI 209R-92 and CEB MC90-99 models, which adopt the concept of an ultimate coefficient, formed the basis of the models developed and examples of the application of the two models are included to provide a better understanding of the process involved. For the analytical approach using the AEMM, the entire process of calculating the long-term deflections with respect to both full and partial shear interactions is presented here, and the accuracy of the calculation validated by comparing the model predictions with experimental data. Lastly, the way the time-dependent deflection varies with various combinations of creep coefficient, shrinkage strain, the size of the beam, and the span length, was analyzed in a parametric study. The results indicate that the long-term deflection due to creep and shrinkage is generally 1.5 ~ 2.5 times its short-term deflection, and the effects of shrinkage may contribute much more to the time-dependent deformation than the effect of creep for cases where the sustained live load is quite small. In addition, the composite beam with a partial interaction exhibits a larger mid-span deflection for both the short- and long-term deflections than a beam with a full shear interaction. When it comes to the deflection limitations, it turned out that although the short-term deflections due to immediate design live load satisfy the deflection criteria well, its long-term deflections can exceed the deflection limitations. / Master of Science

Estimating the delayed strains in concrete, namely creep and shrinkage is very important to asses the condition of the structure. Time dependent deformations in concrete, both creep and shrinkage, play a critical role in prestressed concrete structures, such as bridge girders, nuclear containment vessels, etc. These strains result in lossess, through release of prestress, and thereby influence the safety of these structures. Recognizing the role of free and bound moisture movement is the primary ingredient responsible for the development of both creep and shrinkage stains as well as the degradation of concrete under high temperature, the present study has also examined the effects of high temperature on concrete degradation, experimentally and also analytically in the same modelling framework. Fire in concretes deteriorates mechanical properties of the material and lead to col-lapse under loads. Two types of spalling occur in concrete when exposed to high temperature, namely explosive and thermal spalling. Explosive spalling occurs once the hydrostatic stress (developed due to pore pressure) exceeds the tensile strength of the concrete. Where as thermal spalling of concrete happens due to degradation of material properties (elastic modulus, compressive and tensile strength) when exposed to high temperature due to decomposition of chemical bonds that release the bound water. The present study comprises of an experimental and analytical program to assess the levels of creep and shrinkage in different concrete under various loads and environmental conditions. Deformations due to high temperature in di erent concretes forms another component of the present study. Total six concrete mixes has been studied to investigate and asses the extent of creep and shrinkage taking place in the concretes under different environmental conditions, load level and age at loading. In total six mixes, three that are self compacted concrete mixes (35MPa, 55MPa and SCC70MPa), a high volume y ash concrete mix ( 45 MPa) and two normal concrete mixes (35 MPa and 45 MPa) have been considered in this study. To study the high temperature effects, the same mixes considered in the creep and shrinkage study and in addition a heavy density concrete mix (25 MPa) is used. A normal concrete having a 28 day uniaxial compressive strength of 45 MPa after proper curing, referred to as M45 concrete, was one of the six mixes. Likewise a heavy density concrete designated as H25, corresponding to a 28 day uniaxial compressive strength of 25 MPa was another mix that was studied and was made using iron ore aggregate and iron ore sand. A concrete having high volume y ash replacing cement designated as F45 offered a 28 day strength of 45MPa. Three self-compacting concretes with uniaxial compressive strengths of 35, 55 and 70 MPa were designated as SCC35 SCC55 and SCC70, respectively is studied for creep, shrinkage and high temperature effects. F45 concrete shows lower creep strain when compared to normal M45 concrete, under similar casting, curing and testing condtions. This is due to increase in stiffness of y ash based concretes with time. Where as in shrinkage it is observed that a little higher strain takes place in F45 at initial ages than in M45 concrete mix for the same conditions. But in the later age, F45 concrete shows a decreasing rate of shrinkage strain. This is because, water to cement ratio of y ash concrete is higher than the M45 concrete. The SCC35 concrete shows higher creep and shrinkage than M35 concrete even though both the concretes have the same water cement ratio. This difference comes from the aggregate cement ratio (a/c). The lower the aggregate cement ratio, the higher the creep and shrinkage. M35 concrete has a higher aggregate cement ratio than the SCC35. Concretes exposed to higher temperature and lower humidity shows higher creep and shrinkage due to its higher rate of drying. An analytical model has been developed to simulate the drying phenomena in concrete based on poromechanics. The hydration effects of blended cements is considered while developing the model. This models prediction of degree of hydration, temperature and relative humidity is used to model creep and shrinkage in concrete. To model creep and shrinkage, micro prestress solidi cation theory is implemented and validated with the present experimental results. The model is able to predict the drying phenomena of concrete realistically. Further, a benchmark problem reported in the literature is solved through this model and validated through a comparison with the experimental results (beam detection due to creep and shrinkage). Under high temperature tests, H25 concrete shows better resistance for all the ranges of temperatures. This may be because of the hematite aggregate having a high melting point and strong interfacial transition zone (ITZ) properties between aggregate and cement mortar. The SCC70 shows poor performance against explosive spalling at both the ages (28 and 365 days) due to its lower permeability when exposed to high temperature. The intensity of explosive spalling is higher in SCC70 concrete tested at 28 days than at 365 days of age. This is because of variation in moisture content. SCC70 concrete failed due to explosive spalling at temperature of 398oC when tested at 28 days and failed at 575oC when tested at 365 days. This indicates the amount of moisture content in the concrete plays an important role while causing explosive spalling. F45 concrete shows a poor resistance against temperature beyond 500oC in its residual properties. SCC55 contains cement and y ash and shows higher residual properties when compared to normal vibrated M45 mix under similar high temperature conditions. Two geopolymers pastes prepared with y ash and metakaolin as a complete cement replacement were studied for passive re protection capability. The study shows MF70 mix (containing 70% y ash and 30% metakaolin) gives better resistance against heating than MF50 mix (50% each of metakaolin and y ash). Hence y ash geopolmer is a choice of material for passive re protection. An analytical model has been developed based on poromechanics to simulate high temperature e ects in concrete. Two type of spalling is considered while modelling the high temperature e ects of concrete, namely explosive and thermal spalling. Explosive spalling is estimated based on the hydro static stress (Biotech efficient times the pore pressure). If the hydrostatic stress increases beyond the tensile strength of concrete then explosive spalling occurs. Where as the thermal spalling is estimated based on the stresses developed due to applied mechanical and thermal loading. To validate this model, two benchmark problems from the literature have been solved and validated with the reported results. This model is able to predict pore pressure and temperatures gradients accurately, and this in turn helps to predict explosive and thermal spalling realistically in concrete under elevated temperature conditions.

This study is based on an analysis of a foundation slab where calculations are done to find the minimum amount of reinforcement needed. The purpose of this thesis is to find a balance between time-cost, carbon dioxide emissions and the working environment. One way to minimize time-cost is by using FEM-software. In some cases, FEM-software is more exact than manual calculations, since manual calculations usually approximate. For this reason, manual calculations are compared to FEM-Design. FEM-software is commonly used for other parts of construction, which saves time-cost and materials compared to manual calculations. The use of FEM-software for foundation slabs could improve the dimensioning process in the same manner. The slab that is analysed in this thesis is part of an industrial building. The slab has two parts with different prerequisites in forms of area, thickness and point loads. Shrinkage- and creep-deformations are common causes for cracks in concrete. The results show that FEM-Design saves time for both parts of the slab but requires more reinforcement for the bigger of the two dimensions, which entails higher carbon dioxide emissions. Both calculation-methods met the maximum distance of 150 mm between the reinforcement bars which is the requirement for the workplace environment. / Detta examensarbete handlar om att analysera en grundplatta genom att hitta en balans mellan tid, arbetsmiljö och minimering av koldioxidutsläpp. Sweco presenterade utmaningen att beräkna den optimala ameringsmängden med hänsyn till dessa aspekter och erbjöd resurser för analysen. Plattan som analyseras är en del av en industribyggnad. Den är uppdelad i två delplattor som har olika förutsättningar för tjocklek och laststorlek. Ett sätt att minimera tid kan vara att använda sig av FEM-beräkningsprogram. I vissa fall är FEM-beräkningsprogram mer säkra än handberäkningar då handberäkningar approximerar. Av dessa anledningar jämförs handberäkningar med FEM-Design. Grundplattor är intressanta konstruktionsdelar som utsätts för krymp- samt krypdeformationer utöver externa laster. Dessa deformationer kan orsaka sprickbildning i armerade grundplattor. Momentfördelningen för grundplattor skiljer sig avsevärt jämfört med betongplattor som vilar på stöd. Resultaten visar att FEM-Design tar mindre tid, men utifrån avgränsningar kräver större armeringsmängd för större dimensioner av grundplattor. Större mängdarmering innebär negativ miljöpåverkan, eftersom större koldioxidutsläpp uppstår vid tillverkning. Båda metoderna klarar arbetsmiljökravet på maximalt 150 mm i centrumavstånd.

Balanced cantilever bridges have historically experienced excessive deformations. Previous researchsuggeststhat the cause may be due to differential thickness in the box girder cross-section and underestimation of creep and shrinkage.In this project, the long-term deformationof balanced cantilever bridges due tonon-uniformcreep and shrinkage have been investigated. The non-uniformcreep and shrinkage arecaused by variations in drying rates for the different parts of the box-girder cross-sections.A finite element model was createdintheprogram Abaqusas a case study of the Alvik bridge.The finite element model was used to evaluate the difference betweennon-uniform and uniform creep and shrinkage with Eurocode 2.Further, a comparison between Eurocode 2 and Bažant’sB4 modelwas conductedfor non-uniform creep and shrinkage. The comparison aimedto evaluate the difference between industry and research specific calculation models, forthe effect of creep and shrinkage on deformations.A parameter study was alsoconducted to discern theeffect of parameters: ballast load, water-cementratio and conditions related to drying of concrete (relative humidity and perimeter exposed to air).Acomparison withthe deformationmeasurementsof theAlvik bridge was conductedto validate the resultsfrom the model.The results showed that there was a significant difference in the calculateddeformationof the bridge during the first ten years between analyses based onnon-uniform and uniformdistribution of creepand shrinkage,respectively.The non-uniformanalysis gave largerdeformations.However, only minor differences between the two approachescould be detected in the final deformation after 120 years. The main reason for the differences in the early behaviour is primarily caused by the differences in shrinkage rate between the top and bottom flanges. In these analyses, the top flange was assumed tonotdry out from the top. Thereby, the shrinkage rate of the top flange caused by one-way drying was similar to the bottom flange that was assumed to be exposed for two-waydrying.TheB4 model gave larger deformations compared to Eurocode2.This may be due to difference in the definition ofperimeter and surface. Eurocode 2 considers the perimeter exposed to air. The B4 model instead considers the entire surface area of the part.TheB4 model and Eurocode 2 show similar results asthe measurements. However, the B4 model gaveresults more consistent with the measurements.In the parameter study,lowerrelative humidity gave smaller deformations, since concrete shrinksquicker in dry ambient air.Varying the water-cement ratiodid not affect the deformationsnoticeably.Higher ballastheight gave significantly larger deformations. The height of the ballast was an uncertainfactor due to varying heights in the structural drawings of the case study. Accurate height of ballast is therefore important. / Freivorbau broar har historiskt sett haft problem med kraftiga deformationer. Tidigare forskning föreslår att detta har orsakats av tjockleksskillnader i lådtvärsnitt och underskattning av krypning och krympning. Denna studie har undersökteffektenav ojämn krypningoch krympning på freivorbau broars långtidsdeformationer.Den ojämna krypningen och krympningen orsakas av skillnader i uttorkningshastigheterför lådtvärsnittets olika delar. En finitaelementmodell definieradesi programmet Abaqus som en fallstudie på Alviksbron.Modellen användes för att utvärdera skillnaden mellan ojämn och jämn krypning och krympning med Eurokod 2. En jämförelsemellan Eurokod 2 och Bažant’s B4 modellgenomfördes med hänsyn till ojämn krypningoch krympning.Syftet med jämförelsen var att utvärdera skillnadermellan byggnormeroch forskningmodeller med hänsyn till deformationer orsakade av ojämnkrypningoch krympning.Vidare genomfördes enparameterstudie för att urskilja effekten av parametrarna: ballast last, vatten-cement-tal och förhållanden relaterade till betongensuttorkning(relativ fuktighet och omkrets utsatt för luft).Deformationerna från finita elementmodellen jämfördes med uppmätta deformationer av Alviksbron.Resultaten visade att det fanns en signifikant skillnad i beräknad deformationunder de första tio årenmellan ojämn och jämn krypning och krympning.Ojämn krypning och krympning gav större deformationer.Mindre deformationsskillnad gavs dock i slutgiltig deformationefter 120 år. Den främsta anledningentill skillnaderna i deformation under de första tio årenär orsakat av skillnaderi krympningens hastighet mellan övre-och undre fläns.I analyserna antogs det att övre flänsen inte torkade ut från dess övre del.Därmed varkrympningens hastighetlikartad för övre flänsen som torkade ut åt ett håll, och undre flänsen som torkade ut åttvå håll.B4 modellen gav större deformationerjämfört med Eurokod 2.En möjlig förklaring för detta är definieringen av omkrets gentemot ytans area.Eurokod 2 definierar en omkrets utsatt för luft. B4 modellen definierar i stället arean av en yta, utan att ta hänsyn till om den är utsatt för luft.Även om B4 modellen och Eurokod 2 ger likartade deformationer, ger B4 modellen oftare deformationer som stämmer bättre överens med deformationsmätningarna av Alviksbron.Lägre relativ fuktighet gav mindre deformationer, eftersom betong krymper fortare i torrt klimat. Ändring av vattencementtal gav inte någon märkbar ändring i deformationer.Högre ballasthöjd gav betydligt större deformationer. Höjden på ballast var en osäker faktorpå grund av varierandehöjder i Alviksbrons konstruktionsritningar.Noggrann höjdbestämmelse av ballasten är därför viktigt.