The Texas Department of Transportation (TxDOT) uses precast, prestressed concrete panels (PCPs) as stay-in-place formwork for most bridges built in Texas. The PCPs are placed on the top flanges of adjacent girders and topped with a 4-in. cast-in-place (CIP) slab. This thesis is directed towards identifying and quantifying the serviceability implications of reducing the deck reinforcement across the interior spans of CIP-PCP decks. The goal of this research is to understand how the PCPs influence cracking and crack control in the CIP slab and to make recommendations to optimize the top mat reinforcement accordingly. Several tests were conducted to evaluate the performance of different top mat reinforcement arrangements for ability to control crack widths across PCP joints. The longitudinal reinforcement was tested using a constant bending moment test, a point load test, and several direct tension tests. Because of difficulty with the CIP-PCP interface during the longitudinal tests, direct tension tests of the CIP slab only were used to compare the transverse reinforcement alternatives. Prior to testing, various top mat design alternatives were evaluated through pre-test calculations for crack widths. Standard reinforcing bars and welded wire reinforcement were considered for the design alternatives. During this study, it was found that the tensile strength of the CIP slab is critical to controlling transverse crack widths. The CIP-PCP interface is difficult to simulate in the laboratory because of inherent eccentricities that result from the test specimen geometry and loading conditions. Furthermore, the constraint and boundary conditions of CIP-PCP bridge decks are difficult to simulate in the laboratory. Based on the results of this testing program, it seems imprudent to reduce the longitudinal reinforcement across the interior spans of CIP-PCP decks. The transverse reinforcement, however, may be reduced using welded wire reinforcement across the interior spans of CIP-PCP decks without compromising longitudinal crack width control. A reduced standard reinforcing bar option may also be considered, but a slight increase in longitudinal crack widths should be expected. / text

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No description available.

Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Strain Hardening Cement-based Composite (SHCC) is part of the High Performance Fibre Reinforced Cement-based Composite (HPFRCC) family and is a relative new concrete composite. This Fibre Reinforced Cement-based Composite (FRCC) contains randomly distributed short fibres and when subjected to a uni-axial tensile load multiple cracking occurs. The multiple cracking generates fine cracks which are normally smaller than 100 μm and achieve a strain capacity of more than 5 %. There are limited publications regarding the research of sustained tensile tests on SHCC and especially the cracking behaviour of SHCC under quasi-static uni-axial as well as sustained tensile loads. The cracking behaviour is described as the average crack width, number of cracks and descriptive statistical properties which could be used to represent the distribution of the multiple fine cracks under uni-axial tension. There are two types of tests that were under consideration to determine the cracking behaviour of SHCC. The first is quasi-static uniaxial tensile tests and the second is sustained tensile tests. The latter was dependant on the uni-axial tensile tests in terms of the sustained load applied. The sustained loads ranged from 40 % to 80 % of the ultimate tensile resistance recorded from the uni-axial tensile tests that correspond with a strain rate of 0.001 /s. Different strain rates were used for the uni-axial tensile tests to determine the effect on the cracking behaviour. The cracking behaviour was determined with the aid of a non-contact optical 3D digital deformation measuring device called ARAMIS. The content of this thesis gives a background study of the cracking behaviour and relevant research performed on SHCC under certain loads as well as some literature about the timedependant effects of a cement-based composite. The functioning of the device called ARAMIS is explained as well as the resulting effects of this device on the preparation of the test specimens. The experimental framework for the uni-axial and sustained tensile tests is discussed. Thereafter, the experimental results of the tests are depicted and discussed. The results shed some light on the basic material properties such as the average ultimate stress and average ultimate strain, Young’s modulus, etc. for the quasi-static tensile tests as well as shrinkage and creep of SHCC. The cracking behaviour such as the average crack width, number of cracks, the variance and skewness of the distribution of the crack widths in the test specimens for the quasi-static uni-axial and sustained tensile tests are depicted and discussed. The cracking behaviour when subjected to uni-axial tensile tests with different strain rates is significantly governed by the formation of new cracks and the average crack width remains small with increase in strain. There is no significant difference for the cracking behaviour found when subjected to different strain rates. However, when SHCC is subjected to a sustained load then the average crack width is dependant on the number of cracks that form over time as well as the load level. The formation of fewer and wider cracks was observed for specimens loaded at average 40 % of the ultimate tensile resistance stress, however at loading percentages of higher than 65 % more cracks developed which resulted in a smaller average crack width. / AFRIKAANSE OPSOMMING: Vervorming Verharding Sement gebaseerde samestelling “Strain Hardening Cement-based Composite” (SHCC) is deel van die familie van “High Performance Fibre Reinforced Cement-based Composite” (HPFRCC) en is ʼn relatiewe nuwe beton samestelling. Hierdie vesel versterkte sement gebaseerde beton bevat willekeurig verspreide kort vesels en veelvoudige klein krake vorm onder monotoniese trekkragte. Hierdie veelvoudige klein krake is minder as 100 μm wyd en lei tot ʼn vervorming van meer as 5 %. Daar is ʼn tekort aan navorsing oor die kruip van SHCC sowel as die kraak gedrag van hierdie sement gebaseerde samestelling onderhewig aan trek. Die kraak gedrag word beskryf as die gemiddelde kraakwydte, aantal krake en ʼn paar beskrywende statistiese parameters. Hierdie kraak gedrag parameters kan gebruik word om ʼn verdeling te kan weergee van die veelvoudige klein krake onder ʼn trek belasting. Twee tipes toetse was uitgevoer om die kraak gedrag te beskryf. Die eerste tipe toets was monotoniese trek toetse en die tweede tipe was kruip toetse. Die tweede toets was afhanklik van die monotoniese trek toetse in terme van die belasting wat gebruik was vir die kruip toetse. Die belasting was gevarieer vanaf 40 % tot 80 % van die breekbelasting wat bepaal is met die monotoniese trektoetse wat ooreenstem met ʼn vervorming tempo van 0.001 /s. Verskillende vervorming tempo’s vir die monotoniese trektoetse was uitgevoer om te bepaal wat die effek is op die kraak gedrag. Die kraak gedrag was bepaal met behulp van ʼn geen-kontak optiese 3D digitale deformasie meet instrument genoem ARAMIS. Die inhoud van die tesis bevat ʼn kort opsoming oor ʼn agtergrond studie van die kraak gedrag en relevante navorsing oor vesel versterkte sement gebaseerde beton, sowel as literatuur oor die tydafhanklike effekte van ʼn sement gebaseerde samestelling. Die beheer en gebruik van die meet instrument ARAMIS word verduidelik, sowel as die effek van hierdie masjien op die voorbereiding vir die eksperimente. Die eksperimentele uiteensetting vir die monotoniese en kruip toetse word beskryf. Daarvolgens is die resultate van die eksperimentele toetse getoon en verduidelik. Die resultate verduidelik die basiese materiaal eienskappe, byvoorbeeld die gemiddelde breekspanning met die ooreenkomstige breekvervorming, Young’s modulus en so voorts vir die monotoniese trektoetse, sowel as eienskappe met betrekking tot krimp en kruip van SHCC. Die kraak gedrag naamlik die gemiddelde kraakwydte, aantal krake per meter, variansie en die skuinsheid van die ontwikkelde krake met die toets proefstukke vir die monotoniese en kruip trek toetse word weergegee en verduidelik. Die kraak gedrag van SHCC wanneer getoets word met verskillende monotoniese trektoets tempo’s word beheer deur die ontwikkeling van nuwe krake en die gemiddelde kraakwydte is beduidend laag met toenemende vervorming. Daar is geen beduidende verskil in die kraak gedrag ten opsigte van die verskillende monotoniese trek tempo’s nie. In teendeel, wanneer SHCC belas word met ʼn konstante las oor tyd word die gemiddelde kraakwydte beheer deur die ontwikkeling van nuwe krake sowel as die belasting wat aangewend is. Onder ʼn belasting van so laag as 40 % van die breekbelasting vorm daar minder krake, maar met ʼn groter gemiddelde kraakwydte. Wanneer belas word met meer as 65 % van die breekbelasting vorm meer krake wat lei tot ʼn kleiner gemiddelde kraakwydte.

Efter introduktionen av Eurokoderna har mängden minimiarmering i betongkonstruktioner ökat. Denna ökning beror på skillnader i metoderna som nu används för att beräkna mängden minimiarmering i olika typer av betongkonstruktioner och de som användes tidigare då BKR var den gällande normen. Minimiarmering används i betongkonstruktioner för att omfördela tvångsdeformationer. I detta arbete undersöks om mängden minimiarmering kan minskas utan att dess huvudsakliga funktion går förlorad. I arbetet har ett antal metoder för att beräkna minimiarmering jämförts för att se hur stora skillnaderna i armeringsmängd blir, varför dessa uppkommer och vilka för- och nackdelar som finns med metoderna. De undersökta metoderna inkluderar den som anges i Eurokod 2, förändringar som gjorts i den tyska nationella bilagan till Eurokod 2 och ett förslag till ändring som presenterats av Hallgren i ett preliminärt arbete.   Resultaten bygger på simuleringar utförda i FEM-programmet Atena där olika typfall undersökts. I typfallen har betongens hållfasthetsklass, tvärsnittsdimension, armeringsdimension, täckande betongskikt och vidhäftningsförutsättning varierats. Armeringsmängden varierades för att motsvara den mängd som krävs vid beräkning enligt de tidigare nämnda metoderna. I alla undersökta fall antas tvärsnittet vara utsatt för ren dragbelastning, vilket är fallet vid krympning. Resultaten från de numeriska simuleringarna visade att en större armeringsmängd ger minskade sprickbredder och ökade möjligheter att omfördela tvångsdeformationer till nya sprickor. Bildandet av nya sprickor sker också vid en mindre krympning. Skillnaderna jämfört med om en mindre armeringsmängd används blir dock i de flesta fall små och mängden armering kan reduceras utan att minimiarmeringens sprickfördelande funktion äventyras. Resultaten från de numeriska simuleringarna användes också för att ta fram ett alternativ som ger en mindre mängd minimiarmering utan att armeringens huvudsakliga funktion försvinner. I detta arbete föreslås en förändring rörande koefficienten k i Eurokod. Förändringen av värdet på koefficienten k gör att mängden erforderlig minimiarmering minskar betydligt vid beräkningar, speciellt för tvärsnitt med en större tvärsnittshöjd. Fler numeriska simuleringar utfördes och det kunde säkerställas att en armeringsmängd motsvarande den som ges med den föreslagna ändringen fungerar för alla undersökta typfall. Endast en liten ökning av sprickbredderna sker.   En undersökning av sprickproblematiken under betongens hållfasthetstillväxtfas har gjorts, och resultaten visar att problem med sprickbildning inte beror på den autogena krympningen eller på uttorkningskrympningen. Endast en liten andel av denna krympning hinner uppnås under de första veckorna, samtidigt som hållfasthetstillväxten sker relativt snabbt. Problem med sprickbildning under denna tidsperiod beror istället på andra faktorer såsom en stor värmeutveckling i betongen, en ojämn uttorkning eller en ojämn temperaturfördelning över tvärsnittet i kombination med tvång. Efter den värmeutveckling som skett i betongen under det första dygnet efter gjutning påbörjas en avsvalningsfas. Under denna kan sprickbildning uppstå i betongen, och denna sprickbildning finns kvar när uttorkningskrympningen senare fortskrider. En jämförelse har även gjorts mellan handberäkningar av karaktäristiska sprickbredder enligt Betongföreningens handbok till Eurokod 2 och sprickbredder utlästa ur resultaten från de numeriska simuleringarna. Resultaten visar att metoden överlag fungerar bra, men att vissa justeringar skulle kunna göras för att anpassa den till mindre värden på betongens krympning. / After the introduction of the Eurocodes, the minimum amount of reinforcement for crack control in concrete structures has increased. This is due to differences in themethods for calculating the minimum amount of reinforcement used in the Eurocodes and in BKR, a standard which was used in Sweden before the Eurocodes. Minimum reinforcement for crack control is used in concrete structures to redistribute the tensile stresses caused by restraint during the shrinkage. This thesis examines if the amount of minimum reinforcement can be reduced without compromising the main functions of the reinforcement. In this thesis a number of methods for calculating the minimum reinforcement has been compared to see how large the differences in the amount of reinforcement are, why they occur and what are the advantages and disadvantages of the different methods. The different methods revised in this thesis are the method in Eurocode 2, the changes made in the German National Annex to the Eurocode 2 method and a method proposed by Hallgren in a preliminary work.   The results are based on simulations performed in the FEM-application Atena where different scenarios were examined. In the investigated scenarios, the strength classes of the concrete, the cross-sectional dimensions, the size of the reinforcement bars, the size of the concrete cover and the bond strength has been varied. The amount of reinforcement in each case has been varied to correspond to the required minimum amount according to the different methods for calculating minimum reinforcement. In all investigated cases, the cross section is assumed to be exposed to pure tensile load, which is the case for shrinkage. The results of the simulations showed that a larger amount of reinforcement reduces the width of the cracks, that a larger amount of small cracks are formed, and that new cracks are formed earlier at a lower shrinkage value. The differences are however in most cases small compared to when a lower amount of reinforcement is used. In other words, a lower amount of reinforcement could be used without compromising the main functions of the minimum reinforcement. The results from the simulations have also been used to obtain an alternative method for calculating the minimum reinforcement that gives a lower amount of reinforcement without compromising the main functions. The proposed change in Eurocode is a modification in the value of the coefficient k. By changing the value of the coefficient k, the amount of required minimum reinforcement is decreased significantly, especially for large crosssection heights. More numerical simulations were performed to ensure that the reinforcement amount according to the proposed change works for all scenarios considered in this thesis. The results showed that the reinforcement were capable of redistributing the tensile stresses caused by restraint. Only a small increase in the crack widths could be observed.   An investigation was conducted to find an explanation to why cracks occur during the first weeks after casting of the concrete. The results show that the problem with cracks occurring during this period is neither due to the autogenous shrinkage nor the drying shrinkage. Only a small share of those types of shrinkage are achieved during the first weeks, and at the same time the concrete strength growth is relatively fast. Instead, the problems with cracks seem to be caused by other factors, such as a large heat development in the concrete during the first day, uneven drying shrinkage or an uneven temperature distribution over the cross section in combination with restraint. Cracks can develop during the first days after casting of the concrete due to the shrinkage that occur when the concrete cools off after the large heat development the first day. These cracks remain when the drying shrinkage continues. A comparison was also made between hand calculations of the characteristic crack widths according to “Betongföreningens handbok till Eurokod 2” and the crack widths read out of the results from the numerical simulations. The results showed that the method generally works well, but some minor adjustments could be made to adapt the method to smaller values of concrete shrinkage.

Reinforced concrete deep beams are known for applications in tall buildings, foundations and offshore structures. Deep beams are structural elements with length and height within the same magnitude and have significantly smaller thickness compared to a conventional concrete beam. Deep beams in bending have non-linear strain distribution compared to conventional beams where Bernoulli’s hypothesis is valid. Crack formation is a common problem in reinforced concrete structures, which reduce the durability of the structure. Once the concrete cracks the tension reinforcement carry the tensile forces instead of the concrete. Therefore, the design of tension reinforcement is important since the serviceability should be retained even after the structure cracks. The crack widths can be limited by using proper reinforcement and one alternative is to combine tensile reinforcement with crack reinforcement.  The function of the reinforcement is to distribute the cracks over the cross section which leads to that many smaller cracks occur instead of fewer, wider cracks. Small cracks are seen as less of a problem compared to large cracks since larger cracks reduce the durability significantly. For deep beams, there is at the present no well-substantiated analysis model for how crack widths shall be calculated when having reinforcement in multiple layers with different diameters. The use of crack reinforcement in the outer bottom layer has by tradition been considered as a cost efficient way to achieve small crack widths. In this work the crack width in deep beams have been analysed using the finite element program Atena 2D. The numerical results have been verified by analytical calculations based on Eurocode 2. The aim is to achieve reduced crack widths  by analysing the combination of crack- and tensile reinforcement compared to the case with tensile reinforcement only. Tensile reinforcement has a larger diameter, for example ø25 mm, and crack reinforcement has smaller diameters, often between ø10 and ø16 mm. The result from the calculations with Atena showed that there was an improvement regarding the reduction of crack widths when using crack reinforcement in combination with tensile reinforcement compared to using tensile reinforcement only. However, this improvement decreased by using reinforcement in multiple layers since a tensile reinforcement bar 1ø25 mm needed to be replaced by approximately six crack reinforcement bars 6ø10 mm in order to achieve the same total reinforcement area. The main disadvantage was that more space was required to place all reinforcement bars in the cross section, which reduced the lever arm. The reduction of the lever arm resulted in a reduced capacity for the reinforcement and the cracks might unintentionally become wider than expected. Furthermore, significant reduction of both crack widths and reinforcement stresses were obtained when the total area for a case with 7ø25 mm was increased to 9ø25 mm. The increased total area of only tensile reinforcement ø25 mm reduced the crack width more compared to using a combination of crack- and tensile reinforcement, which could simplify the construction work at building sites and minimize time consumption. / Armerade höga betongbalkar är kända för tillämpningar i höga byggnader, grundsulor och offshore konstruktioner. Höga balkar är konstruktionselement med längd och höjd i samma storleksordning och har betydligt mindre tjocklek jämfört med en konventionell betongbalk. Höga balkar i böjning har en icke-linjär töjningsfördelning jämfört med konventionella balkar där Bernoullis hypotes gäller. Sprickbildning är ett vanligt problem i armerade betongkonstruktioner, vilket minskar beständigheten hos konstruktionen. När betongbalken spricker kommer armeringen att ta upp dragkraften istället för betongen därför är utformningen av böjarmering viktig eftersom bruksgränstillståndet bör behållas även efter att konstruktionen spricker. Sprickvidderna kan begränsas genom att använda korrekt armering och ett alternativ är att kombinera kraftarmering med sprickarmering. Armeringens funktion är att sprida ut sprickorna över tvärsnittet vilket leder till att många små sprickor uppkommer i stället för färre, bredare sprickor. Små sprickor ses som ett mindre problem jämfört med stora sprickor eftersom större sprickor minskar beständigheten avsevärt. För höga balkar finns det för närvarande ingen välunderbyggd analysmodell för hur sprickvidder ska beräknas när de har armering i flera lager och med olika diametrar. Användningen av sprickarmering har traditionellt ansetts vara ett kostnadseffektivt sätt att uppnå små sprickvidder. I detta arbete har sprickvidden i höga balkar analyserats med hjälp av finita elementprogrammet Atena 2D. De numeriska resultaten har verifierats med analytiska beräkningar baserade på Eurokod 2. Syftet är att uppnå reducerade sprickvidder genom att analysera kombinationen av sprick- och kraftarmering jämfört med fallet med endast kraftarmering. Kraftarmeringen har en större diameter, till exempel ø25 mm och sprickarmering har mindre diametrar, ofta mellan ø10 och ø16 mm. Resultaten från beräkningarna i Atena visade att sprickvidderna minskade vid användning av sprickarmering i kombination med kraftarmering jämfört med användning av endast kraftarmering. Denna förbättring minskade emellertid i och med användning av armering i flera lager. En kraftarmeringsstång 1ø25 mm behöver ersättas med ungefär sex sprickarmeringsstänger, 6ø10 mm, för att uppnå samma totala armeringsarea. Den största nackdelen var att det krävdes mer utrymme för att placera alla sprickarmeringsstänger i tvärsnittet, vilket minskade hävarmen. Minskningen av hävarmen medförde en reducerad kapacitet i armeringen och sprickorna blev bredare än förväntat. Vidare erhölls signifikant reduktion av både sprickvidder och armeringsspänningar när den totala arean för ett fall med 7ø25 mm ökades till 9ø25 mm. Den ökade totalarean av endast kraftarmeringsstänger ø25 mm minskade sprickvidden mer jämfört med att använda en kombination av sprick- och kraftarmering vilket skulle kunna förenkla byggarbetet på byggarbetsplatser och minimera tidsförbrukningen.

The main purpose of thesis is a static solution of load bearing reinforced concrete structure of flat house. The work contains an assessment of waterproof concrete building. The object is built under the groundwater level. Supporting structures are concrete slab, walls and columns. An assessment of these structures is realized in terms of first critical state- carrying capacity and second limit state- limitation of crack widths.