yes / This paper presents an analytical method for estimating the flexural strength of reinforced concrete beams strengthened with externally bonded fibre reinforced polymer (FRP) laminates. The method is developed from the strain compatibility and equilibrium of forces. Based on the size of external FRP laminates, several flexural failure modes may be identified, namely tensile rupture of FRP laminates and concrete crushing before or after yielding of internal steel reinforcement. Upper and lower limits to the size of FRP laminates used are suggested to maintain ductile behaviour of strengthened reinforced concrete sections. Comparisons between the flexural strength obtained from the current method and experiments show good agreement. Design equations for calculating the size of FRP laminates externally bonded to reinforced concrete sections to enhance their flexural strength are proposed.

The full text will be available at the end of the embargo: 26th April 2025

Inledning: Kantbalkar på broar är en utsatt konstruktionsdel som ofta har beständighetsproblem och betongkantbalkar är svåra att utföra till den kvalitet som krävs. I denna studie undersöks möjligheten att byta ut den traditionella betongkantbalken till en fiberförstärkt polymerkomposit (FRP-komposit) med avseende på trafiksäkerhet, beständighet och lönsamhet. Studien omfattar endast brokantbalkar och inte hela brokonstruktioner. Metod: Studien omfattar litteraturstudie och beräkningar. Insamling av information till litteraturstudien sker genom sökning i forskningsdatabaser. Beräkningar utförs genom handberäkningar och med hjälp av programvara. FEM Design 17 används för att ta fram inre spänningar i konstruktionen och Granta EduPack används för att hitta material som uppfyller kraven. Beräkningar utförs i enlighet med Eurokoderna. Resultat: Spänningar i konstruktionen uppgick som högst till 151 MPa. De karakteristiska hållfasthetsvärdena i materialet behövde som högst motsvara minst 240 MPa när reduktionsfaktorer bestämts. Av totalt 782 tillgängliga FRP-kompositer i Granta EduPack fanns 18 som klarade samtliga krav på bärförmåga. Litteraturstudien fann flera tidigare studier där FRP-kompositer använts i brokonstruktioner med goda resultat angående beständighet och långsiktig lönsamhet.Diskussion och slutsatser: Flera antaganden gjordes i beräkningarna, vilka förenklar modellen och påverkar resultatets pålitlighet. Vidare påverkas resultatet av både konstruktionens design och profilers tjocklek. Resultatet av beräkningarna skulle dock kunna användas som en uppskattning av de hållfasthetsvärden som FRP-kompositer behöver uppnå i en kantbalkskonstruktion. Resultatet av litteraturstudien indikerar att en brokantbalk i FRPkomposit skulle vara fördelaktigt beständighetsmässigt, samt att det skulle kunna vara ekonomiskt lönsamt i längden, men det behövs vidare studier för att bekräfta detta. / Introduction: Edge girders on bridges are an exposed structural part that often has durability problems and concrete edge girders are difficult to produce to the required quality. In this study, the possibility of replacing the traditional concrete edge girder with a fibre reinforced polymer composite (FRP-composite) is investigated regarding traffic safety, durability, and profitability.The study covers only bridge edge girders and not entire bridge structures. Method: The study includes literature study and calculations. Collection of information for the literature study is done by searching in research databases. Calculations are performed by hand calculations and with the help of software. FEM Design 17 is used to produce internal stresses in the construction and Granta EduPack is used to find materials that meet the requirements. Calculations are conducted in accordance with the Eurocodes. Results: Stresses in the construction amounted to a maximum of 151 MPa. The characteristic strength values in the material had to correspond at most to at least 240 MPa when reduction factors were determined. Out of a total of 782 available FRP-composites in Granta EduPack, there were 18 that met all the load-bearing capacity requirements. The literature study found several previous studies where FRP-composites were used in bridge structures with good results regarding durability and long-term profitability. Discussion and conclusions: Several assumptions were made in the calculations, which simplify the model and affect the reliability of the results. Furthermore, the result if affected by both the design of the construction and the thickness of the profiles. However, the result of the calculations could be used as an estimate of the strength values that FRP-composites need to achieve in an edge girder construction. The results of the literature study indicate that a bridge edge girder in FRP-composite could be advantageous in terms of durability, and that it could be economically profitable in the long run, but further studies are needed to confirm this

Ce travail porte sur la mise en forme des matériaux composites à matrice polymère renforcée par des fibres courtes dont les performances physiques et mécaniques sont directement reliées à la distribution spatiale et à l’orientation des renforts employés. Il se focalise sur l’étude des mécanismes de déformation se produisant au cours de l’écoulement de ces systèmes qui se comportent comme des suspensions de fibres non-newtoniennes. Le problème est abordé par une procédure originale combinant images 3D acquises en temps réel et simulations numériques avancées, réalisées à l’échelle des fibres. Dans le premier cas, des suspensions modèles avec fluide suspensif non-newtonien ont été déformées en compression dans des conditions confinées dans un microtomographe à rayons X synchrotron. Cette technique a permis l’acquisition en temps réel de clichés 3D à forte résolution spatiale de l’écoulement des suspensions. Dans le deuxième cas, un code de calculs éléments finis 3D a été utilisé, celui-ci étant capable de décrire finement des objets immergés dans des fluides non-newtoniens, par des level-sets et des techniques de remaillage anisotrope. La pertinence des simulations numériques dans les régimes de concentration dilués à semi-dilués a été jaugée par une comparaison expériences-simulations avancée.De là, dans le régime de concentration dilué, nous montrons que le confinement de l’écoulement et le comportement rhéofluidifiant du fluide suspensif ont une influence mineure sur la cinématique des fibres, si ces dernières sont suffisamment éloignées des plateaux de compression. Si ce prérequis n’est pas respecté, l’effet du confinement devient important. Des modifications au modèle heuristique d’haltère de la littérature ont été proposées pour corriger la cinématique de fibres. Dans le régime semi-dilué, des déviations de la cinématique de fibres sont également observées au cœur des suspensions. Ces déviations sont principalement liées aux interactions hydrodynamiques entre fibres suffisamment voisines. La cinématique des fibres prédite par le modèle de Jeffery et les approximations de champ affine sont mises en défaut. Dans le régime concentré, si l’évolution de l’orientation globale de la suspension est étonnamment bien décrite par l’équation de Jeffery, de très importantes fluctuations des champs de translation et de rotation des fibres sont observées à l’échelle des fibres. Celles-ci sont induites par les nombreux contacts entre fibres qui peuvent par ailleurs être correctement prédits par le modèle de tube. / This study focuses on the processing of short fibre-reinforced polymer composites. The physical and mechanical properties of these materials are mainly affected by the position and orientation distribution of fibres induced during their forming. Thus, we analysed the flow-induced micro-mechanisms that arose at the fibre scale during the forming stage of these complex systems which behave as non-Newtonian fibre suspensions. For that purpose, an original approach was developed by combining 3D imaging technique and direct numerical simulation, both performed at the fibre scale. Hence, several model fibre suspensions with a non-Newtonian suspending fluid and with a concentration regime that ranged from dilute to concentrated were prepared . They were subjected to confined lubricated compression loadings using a rheometer mounted on a synchrotron X-ray microtomograph. Thanks to very short scanning times, 3D images of the evolving fibrous microstructures at high spatial resolution were recorded in real-time. These experiments were also simulated using a dedicated Finite Element library enabling an accurate description of fibre kinematics in complex suspending fluids thanks to high performance computation, level sets and adaptive anisotropic meshing. The efficiency of the numerical simulation from the dilute to semi-dilute concentration regimes was assessed through experimental and numerical comparisons.Then, we showed that the confinement effect and the non-Newtonian rheology of the suspending fluid had a weak effect on the fibre kinematics, if the fibres were sufficiently far from the compression platens, typically the fibre-platen distance should be larger than twice the fibre diameter. Otherwise, confinement effects occurred. Some extensions of the dumbbell model were proposed to correct the fibre kinematics in this flow conditions. In semi-dilute concentration, deviations of the fibre kinematics compared to the Jeffery’s predictions were also observed and related to hydrodynamic interactions between fibres. In this case, the predictions of Jeffery’s model and the related assumption of affine fibre motions are less relevant. In the concentrated regime, even if the overall orientation of fibre suspension could be astonishingly well described by using the Jeffery’s model, strong fluctuations on each fibre motion and rotation were observed. These deviations were induced by the numerous fibre-fibre contacts, which could be correctly predicted by the tube model.

The strive for lower fuel consumption and downsizing in the automotive industry has led to the use of alternative high performance materials, such as fibre composites. Designing chassis components with composite materials require accurate simulation models in order to capture the behaviour in car crashes. By simplifying the development process of a B-pillar with a new dynamic test method, composite material products could reach the market faster. The setup has to predict a cars side impact crash performance by only testing the B-pillar in a component based environment. The new dynamic test method with more realistic behaviour gives a better estimation of how the B-pillar, and therefore the car, will perform in a full-scale car side impact test. With the new improved tool for the development process, the search for a lighter product with better crash worthiness is done by optimising a steel carbon fibre hybrid structure in the B-pillar. The optimisation includes different carbon fibre materials, composite laminate lay-up and stiffness analysis. By upgrading simulation models with new material and adhesive representation physical prototypes could be built to verify the results. Finally the manufactured steel carbon fibre hybrid B-pillar prototypes were tested in the developed dynamic test method for a comparison to the steel B-pillar. The hybrid B-pillars perform better than the reference steel B-pillar in the dynamic tests also being considerably lighter. As a final result a hybrid B-pillar is developed that will decrease fuel consumption and meet the requirements of any standardized side impact crash test. / Strävan efter lägre bränsleförbrukning och minimalistiskt tänkande inom bilindustrin har lett till användning av alternativa högpresterande material, såsom fiberkompositer. Vid design av chassi-komponenter utav kompositer krävs noggranna simuleringsmodeller för att fånga upp bilens beteende vid en krock. Genom att förenkla utvecklingsprocessen för en B-stolpe med en ny dynamisk testmetod kan produkter bestående av fiberkompositer nå marknaden snabbare. Provuppställningen skall förutse bilens prestanda vid ett sidokrocktest genom att endast testa B-stolpen i en komponentbaserad miljö. Den nya dynamiska testmetoden med ett mer realistiskt beteende skall ge en bättre uppskattning om hur B-stolpen, och därmed bilen, kommer att prestera i ett fullskaligt sidokrocktest. Med utvecklingsprocessens nya förbättrade verktyg kan strävan mot lättare produkter med bättre krocksäkerhet utvecklas genom optimering av en hybrid B-stolpe i stål och kolfiber. Optimeringen innefattar olika kolfibermaterial, laminatvarianter och styvhetsanalyser. Genom att uppgradera simuleringsmodeller med nya material och adhesiva metoder kunde fysiska prototyper tillverkas för att verifiera resultaten. Slutligen testades de tillverkade prototyperna utav stål och kolfiber i den nyutvecklade dynamiska testmetoden för jämförelse mot den ursprungliga stål B-stolpen. Hybrid B-stolparna presterade bättre än referensstolpen utav stål i de dynamiska provningarna och är samtidigt betydligt lättare. Det slutgiltigt resultatet är en utvecklad hybrid B-stolpe som både ger minskad bränsleförbrukningen och uppfyller kraven för ett standardiserat sidokrocktest.

This research aims to investigate the behaviour of glass fibre reinforced polymer bars (GFRP) reinforced continuous concrete deep beams. For this purpose, experimental, analytical and numerical studies were conducted. Nine continuous concrete deep beams reinforced with GFRP bars and one specimen reinforced with steel bars were experimentally tested to failure. The investigated parameters included shear span-to-overall depth ratio (𝑎/ℎ), size effect and web reinforcement ratio. Two 𝑎/ℎ ratios of 1.0 and 1.7 and three section heights of 300 mm, 600 mm and 800 mm as well as two web reinforcement ratios of 0% and 0.4% were used. The longitudinal reinforcement, compressive strength and beam width were kept constant at 1.2%, ≈55 MPa and 175 mm, respectively. The web reinforcement ratio achieved the minimum requirements of the CSA S806-12. The experimental results highlighted that the web reinforcement ratio improved the load capacities by about 10% and 18% for specimens having 𝑎/ℎ ratios of 1.0 and 1.7, respectively. For specimens with web reinforcement, the increase of 𝑎/ℎ ratio from 1.0 to 1.7 led to reductions in the load carrying capacity by about 33% and 29% for beams with overall depths of 300 mm and 600 mm, respectively. Additionally, a considerable reduction occurred in the shear strength due to the increase of the section depth from 300 mm to 600 mm. The experimental results confirmed the impacts of web reinforcement and size effect that were not considered by the strut-and-tie method (STM) of the only code provision, the Canadian S806-12, that addressed such elements. In this study, the STM was illustrated and simplified to be adopted for GFRP RC continuous deep beams, and then, the experimental results obtained from this study were employed to assess the performance of the effectiveness factors suggested by the STMs of the American (ACI 318-2014), European (EC2-04) and Canadian (S806-12) codes as well as those factors recommended by the previous studies to predict the load capacities. It was found that these methods were unable to reflect the influences of member size and/or web reinforcement reasonably, the impact of which has been confirmed by the current experimental investigation. Therefore, a new effectiveness factor was recommended to be used with the STM. Additionally, an upper bound analysis was developed to predict the load capacities of the tested specimens considering a reduced bond strength of GFRP bars after assessing the old version recommended for steel RC continuous deep beams. A good agreement between the predicted results and the measured ones was obtained with the mean and coefficient of variation values for experimental/calculated results of 1.02 and 5.9%, respectively, for the STM and 1.03 and 8.6%, respectively, for the upper-bound analysis. A 2D finite element analysis using ABAQUS/Explicit approach was carried out to introduce a model able to estimate the response of GFRP RC continuous deep beams. Based on the experimental results extracted from the pullout tests, the interface between the longitudinal reinforcement and concrete surface was modelled using a cohesive element (COH2D4) tool available in ABAQUS. Furthermore, a perfect bond between the longitudinal reinforcement and surrounding concrete was also modelled to evaluate the validity of this assumption introduced by many previous FE studies. To achieve a reasonable agreement with the test results, a sensitivity analysis was implemented to select the proper mesh size and concrete model variables. The suitability and capability of the developed FE model were demonstrated by comparing its predictions with the test results of beams tested experimentally. Model validation showed a reasonable agreement with the experiments in terms of the failure mode, total failure load and the load-deflection responses. The perfect bond model has overestimated the predicted results in terms of stiffness behaviour and failure load, while the cohesive element model was more suitable to reflect the behaviour of those specimens. The validated FE model was then employed to implement a parametric study for the key parameters that govern the behaviour of beams tested and to achieve an in depth understanding of such elements. The parametric study showed that the higher the 𝑎/ℎ ratio the more pronounced the effect of web and the longitudinal reinforcements and the lower the effect of concrete compressive strength; and vice versa when 𝑎/ℎ ratio reduces.

The search and research for high performance materials for aerospace applications is a continuous evolving process. Among several fibre reinforced polymers, carbon fibre reinforced polymer (CFRP) is well known for its high specific stiffness and strength. Though high modulus and high strength carbon fibre with structural resin systems have currently been established reasonably well and are catering to a wide variety of aerospace structural applications, these properties are generally directional with very high properties along the fibre direction dominated by fibres and low in other directions depending mainly on the resin properties. Thus, there is a need to enhance the mechanical properties of the resin systems for better load transfer and to improve the resin dominated properties like shear strength and properties in directions other than along the fibre. Use of carbon nanotubes (CNTs) with their extraordinary specific stiffness and strength apparently has great potential as an additional reinforcement in resin for development of CNT-CFRP nanocomposites. However, there are several issues that need to be addressed such as compatibility of a particular resin with CNTs, amount of CNTs that can be added, uniform dispersion of these nanotubes, surface treatment and curing process etc., for optimal enhancement of the required properties. Epoxy and cyanate ester resin systems are finding applications in aerospace structures owing to their desirable set of properties. Of these, bisphenol E cyanate ester (BECy) resin of low viscosity with its low moisture absorption, better dimensional stability, and superior mechanical properties can establish itself as potential structural resin system for these applications. BECy in particular has the advantage of being more suitable for out of autoclave manufacturing process such as Vacuum Assisted Resin Transfer Molding (VARTM). Literature shows that, significant work has been carried out by various researchers reporting improvements using CNTs in epoxy resins along with various associated problems. However, studies on effects of addition of CNTs /fCNTs to BECy-CFRP composite system are not well reported. Thus, objective of this work is to study the effects of adding pristine and functionalized CNTs to low viscosity cyanate ester as well as epoxy resin systems. Further, to study the effects on mechanical properties of nanocomposites with carbon fibre reinforcement in these CNT dispersed resin system through a combination of experimental and computational approaches. Multiwall carbon nanotubes (CNTs) without and with different chemical functionalization are chosen to be added to epoxy and BECy resins. The quantity of these CNTs /fCNTs is varied in steps up to 1% by weight. Different methods of mixing such as shear mixing, ultrasonication and combined mixing cycles are implemented to achieve uniform dispersion of these nanotubes in the resin system. Standard test samples are prepared from these mixtures of nanotubes in resin systems to study the variation in mechanical properties. Further, these nanotubes added resin systems are used in fabricating CFRP laminates by VARTM process. Both uni-directional and bi-directional laminates are made with the above modified resin systems with CNTs/fCNTs. Series of experimental investigations are carried out to study various aspects involved in making of nanocomposites and the effects of the same on different mechanical properties of the nanocomposites. Standard specimens are cut out from these laminates to evaluate them for tension, compression, flexure, shear and interlaminar shear strength. The main parameters investigated are the effects of varied quantity of CNTs and functionalized CNTs in the resin mix and in CFRP nanocomposites, effect of different mixing / curing cycles etc. on the mechanical properties of the nanocomposites. The investigations have yielded very interesting and encouraging results to arrive at optimum quantity of CNTs to be added and also the effects of functionalization to achieve enhanced mechanical properties. In addition, correlation of mechanical property enhancements with failure mechanisms, dispersion behaviour and participation of CNTs / fCNTs in load transfer are explained with the aid of scanning electron microscope images. Computational studies are carried out through atomistic models using computational tools to estimate the mechanical properties, understand and validate the effects of various parameters studied through series of experimental investigations. An atomistic model is built taking into consideration the nanoscale effects of the single wall carbon nanotubes (SWCNTs) and its reinforcement in the BECy resin. Using these atomistic models, mechanical properties of individual SWCNT, BECy polymer resin, polymer with different quantities of added SWCNT, and the CFRP laminates with improved resin are computed. As the interaction of CNT with the polymer is only at the outermost layer and the mechanical properties of either MWCNTs or SWCNTs are too high compared to resin systems, it is not expected to have any difference in the final outcome whether it is MWCNT or SWCNT. Hence, only SWCNTs are considered in computational studies as it helps in reducing the complexity of atomistic models and computational time when coupled with polymer resin. This is valid even for functionalized CNT as functionalization is also a surface phenomenon. To start with, the mechanical behaviour of SWCNT is studied using molecular mechanics approach. Molecular mechanics based finite element analysis is adopted to evaluate the mechanical properties of armchair, zigzag and chiral SWCNT of different diameters. Three different types of atomic bonds, i.e., carbon-carbon covalent bond and two types of carbon-carbon van der Waals bonds are considered in the carbon nanotube system. The stiffness values of these bonds are calculated using the molecular potentials, namely Morse potential function and Lennard-Jones interaction potential function respectively and these stiffness values are assigned to spring elements in the finite element model of the SWCNT. The importance of inclusion of Lennard-Jones interactions is highlighted in this study. Effect of these non-bonded interactions is studied by making the numerical stiffness of these bonds to negligible levels and found that they significantly reduce the mechanical properties. The effect of non-bonded Lennard-Jones atomic interactions (van der Waal interactions) considered here is a novelty in this work which has not been considered in previous research works. The finite element model of the SWCNT is constructed, appropriate boundary conditions are applied and the behaviour of mechanical properties of SWCNT is studied. It is found that the longitudinal tensile strength and maximum tensile strain of armchair SWCNTs is greater than that of zigzag and chiral SWCNTs and its value increases with increasing SWCNT diameter. The estimated values of the mechanical properties obtained agree well with the published literature data determined using other techniques. As the systems become more complicated with the inclusion of polymers, molecular dynamics (MD) method using well established codes is more adoptable to study the effect of SWCNTs on BECy. Hence, it is used to model and solve the nanosystems to generate their stress-strain behavior. Further, MD approach followed here can effectively include interfacial interaction between polymer and the CNTs as well. Mechanical properties of SWCNT functionalized SWCNT (fSWCNT), pure BECy resin and that of the CNT nanocomposite consisting of specific quantity of SWCNT / fSWCNT in BECy are estimated using MD method. Atomistic models of SWCNT, fSWCNT, BECy, BECy with specific quantities of CNT / fSWCNT are constructed. A monomer of BECy is modelled and stabilized before its usage as a building block for modelling of BECy resin and to compute its properties. A cell of specific size containing monomers of BECy and another cell of same size with SWCNT at centre surrounded by BECy monomer molecules are built. The appropriate quantity of SWCNT in resin is modelled. This model captures the required density of the composite resin. The models so constructed are subjected to geometric optimization satisfying the convergence criteria and equilibrated through molecular dynamics to obtain a stable structure. The minimized structure is subjected to small strain in different directions to calculate the Young’s modulus and other moduli of the CNT-BECy resin composite. The process is repeated for different quantities of SWCNT in BECy resin to obtain their moduli. Further, tensile and shear strengths of CNT-BECy are obtained by subjecting the equilibrated structure to a series of applied strains from 0 to 10% in steps of 1%. The stress values corresponding to each strain are obtained and a stress – strain curve is plotted. From the stress- strain curve, the strengths of the CNT -BECy which is the stress corresponding to the modulus after which the material starts to soften are determined. Effects of functionalization on mechanical properties of SWCNT are observed. Further, effects of functionalization of SWCNT are studied with a specific quantity of fSWCNT on different moduli and strengths of BECy are investigated. The properties of enhanced CNT–BECy nanocomposite resin with different quantities of added CNT obtained through MD are used to estimate the mechanical properties of the CNT-BECy-CFRP nanocomposite using micromechanics model. Further, validation with experimental results is attempted comparing the trends in enhancement of properties of the CNT-BECy resin and CNT-BECy-CFRP nanocomposite system. The outcome of this research work has been significantly positive in terms of i) Development of an appropriate process establishing different parameters for dispersing CNTs in the resin system, mixing, curing cycle for making of nanocomposites demonstrating significant and consistent enhancement of mechanical properties of BECy based resin system and CFRP nanocomposites using optimum quantity of CNTs /fCNTs through a series of well planned and executed experimental investigations. Evaluation of mechanical properties for each of the cases has been carried out experimentally. ii) Establishing a computational methodology involving intricate atomistic modelling and molecular dynamics of nanosystems for estimation of mechanical properties of BECy polymer resin and to study the effects by addition of SWCNT / functionalized SWCNT on the properties. Results obtained through series of experimental investigations have been validated through this computational study. This could be an important step towards realising the potential of this resin system for high performance aerospace applications. Thus, in brief, detailed experimental work combined with computational studies performed as presented in this thesis resulted in achieving structurally efficient cyanate ester based nanocomposites which is unique and not reported in open literature.

This diploma thesis deals with the design of FRP reinforced concrete structures. The theoretical part is focused mainly on the punching shear of a flat two way slab according to ACI, fib Bulletin, CSA, and JSCE standards. This thesis also includes a description of the punching shear resistance according to Eurocode 2. FRP reinforcement, its mechanical properties, and their behaviour in time are also described. Next, a parametric study was performed that examines the effects of various parameters on the punching shear resistance according to the standards mentioned above. At the end a non-linear analysis using the ATENA software was performed. The practical part includes a structural design of a flat two way slab. The slab uses a steel reinforcement at the bottom, while the top is reinforced with FRP reinforcement. The punching shear design is also included. In the last chapter the serviceability limit state is checked, specifically the slab long-term deflection. The thesis also includes drawings. All calculations were performed in accordance with Eurocode 2 and fib Bulletin No. 40.