The doctoral thesis deals with the analysis of the dapped-end beam detail, in terms of theoretical modelling and practical design using the strut-and-tie method as well as experimental verification of the bearing capacity and the behaviour of the detail under load by means of load tests and subsequent numerical nonlinear analysis. A summary of known structural and static designs explored in the literature has been presented. In addition, the strut-and-tie method has been introduced as an appropriate tool for a consistent design of the detail, element or the whole structure. The theoretical basis for the method has been described, including the general methodology for design and analysis. Practical problems have been discussed, specifically those resulting from the known design of the analysed detail based on the German approach; its modification has been processed theoretically taking into account the practical mode of reinforcement. An experiment has been suggested with a view to verify the presented calculation procedure and the influence of the used ratio of vertical to inclined hanger reinforcement on the bearing capacity and behaviour of the detail under load. The experiment also included accompanying material tests of the concrete which were used along with the inspection certificates issued for the used reinforcement as a basis for the nonlinear finite element analysis. Based on the results, the presented design procedure can be considered safe. These results also imply that the chosen ratio of vertical and inclined hanger reinforcements has no influence on the ultimate bearing capacity within practical reinforcement, as it only influences the formation, development and final width of cracks. With the growing ratio of the inclined hanger reinforcement, the width and density of cracks decreases at all stages of loading. Owing to their limitations, primarily during the service state, it is recommended that the minimal inclined reinforcement should be used.

The main topic of this thesis concerns the behavior of concrete pile cap supported by four piles with two varying positions of longitudinal reinforcements. The positions include top of piles and bottom of the pile cap. For this purpose, non-linear finite element models of a pile cap are created using software ATENA 3D. The goal was to observe which position of reinforcement yields the higher bearing capacity and to observe the failure modes in the models. To achieve the above goals, a short review of theoretical background concerning shear phenomena is performed. This, in order to enhance the knowledge regarding shear stresses, shear transfer mechanism, factors affecting shear capacity, modes of shear failure and relate them to the behavior of pile cap. Furthermore, the calculation of shear resistance capacity based on Eurocode 2 using strut and tie method and sectional approach is presented. The numerical analysis started by creating four pile cap models in ATENA 3D. The difference between the models being the position and ratio of longitudinal reinforcement. The purpose behind two reinforcement ratios were to observe the behavior of pile cap model in two cases: a) when failure occurs prior to yielding of reinforcement; b) when failure occurs while reinforcement is yielding. The models are then analyzed using software ATENA Studio. The results revealed that placing the reinforcement on top of piles in case (a) increased the capacity of the model by 23.5 % and in case (b) increased the capacity by 18.5 %. This because the tensile stresses were found to be concentrated on top of piles rather than the bottom of the pile cap. The final failure mode in the model with top reinforcement position was crushing of the inclined compressive strut at the node beneath the column and in the model with bottom reinforcement position, the splitting of the compressive strut due to tensile stresses developed perpendicular to the inclined strut. The potential advantage of placing the reinforcement at the bottom were a better crack control in serviceability limit state and a slightly less fragile failure mode compared to the top position of reinforcement. A parametric study was performed in the model as well to observe the effects of various parameters on the results obtained. It was found that fracture energy had the most significant effect on the results obtained. Finally, a comparison between the results of numerical analysis and analytical design approaches based on strut and tie method and sectional approach was performed. The comparison reveals that the design values obtained based on strut and tie method for the model were very conservative. In particular, the equation for the strength of inclined compressive strut based on Eurocode 2 was very general. / Det huvudsakliga ämnet för den här avhandlingen handlar om beteendet hos pålfundament som stöds av fyra pålar med två olika positioner av längsgående armering. Positionerna inkluderar toppen av pålarna och botten av slagdynan. För detta ändamål skapas icke-linjära finita elementmodeller av en slagdyna med mjukvaran ATENA 3D. Målet var att observera vilket armeringsläge som ger den högre bärkapaciteten och att identifiera brottmekanismen i modellerna. För att uppnå ovanstående mål utförs en kort genomgång av teoretisk bakgrund rörande skjuvningsfenomen. Detta för att förbättra kunskapen om skjuvspänningar, skjuvöverföringsmekanism, faktorer som påverkar skjuvkapacitet, skjuvbrott och relaterar dem till beteendet hos slagdynan. Beräkningen av skjuvmotståndet baserad på Eurocode2 med hjälp av Srut and tie-metod och sektionsmetod. Den numeriska analysen började med att skapa fyra pålfundament i ATENA 3D. Skillnaden mellan modellerna är positionen och förhållandet mellan längsgående armering. Syftet bakom två armeringsförhållanden var att observera beteendet hos slagdynan i två fall: a) när brott inträffar innan armering plasticeras; b) när brott inträffar medan armeringen plasticeras. Modellerna analyseras sedan med hjälp av programvaran ATENA Studio. Resultaten visade att placering av armeringen ovanpå pålarna i fall a) ökade modellens kapacitet med 23,5% och i fall (b) ökade kapaciteten med 18,5%. Detta på grund av att dragspänningarna visade sig vara koncentrerade på toppen av pålarna snarare än på botten av slagdynan. Det slutliga brottet i modellen med topparmeringsposition var krossning av det lutande tryckstaget vid noden under pelaren. I modellen med bottenarmeringsposition delades kompressionsstaget på grund av dragspänningar vinkelrätt mot det lutande staget. The potential advantage of placing the reinforcement at the bottom were a better crack control and slightly less fragile failure mode compared to the top position of reinforcement. En parametrisk studie genomfördes också i modellen för att observera effekterna av olika parametrar på de erhållna resultaten. Det visade sig att brottenergi hade den mest signifikanta effekten på de erhållna resultaten. Slutligen genomfördes en jämförelse mellan resultaten från numerisk analys och analytiska designmetoder baserade på strut and tie-metoden och sektionsmetoden. Jämförelsen avslöjar att de designvärden som erhölls baserat på strut and tie-metoden för modellen var mycket konservativa. I synnerhet var ekvationen för kapaciteten hos det lutande tryckstag baserad på Eurocode 2 mycket generell.

O modelo de bielas e tirantes apresenta como uma de suas vantagens a generalidade, ou seja, é capaz de representar, de modo aproximado, porém realista e sistemático, grande parte dos elementos de concreto estrutural da atualidade. Além disso, permite ao engenheiro fácil visualização físico-intuitiva do comportamento do concreto estrutural. Por outro lado, o modelo ainda tem um enorme potencial não aproveitado. Ainda não se tem um critério exato para determinação dos nós e das seções transversais das bielas de alguns elementos. Apesar de haver certas incertezas no caso de vigas-parede e principalmente de blocos de fundação, nas vigas esses elementos do modelo podem ser determinados sem grandes dificuldades. Possivelmente, a solução seria variar as dimensões das bielas e as posições dos nós, ambas hipotéticas, a fim de confrontar várias situações com resultados experimentais. Daí a grande importância da difusão do modelo de bielas e tirantes: um maior número de análises de modelagens e de resultados de ensaios levará a um maior domínio sobre o modelo. Este trabalho consiste na análise de vigas de concreto armado utilizando modelos de bielas e tirantes. São apresentados os conceitos que levaram à concepção do modelo, desde a Analogia Clássica da Treliça, chegando aos critérios para verificação dos elementos da treliça e às recomendações atuais de normas e pesquisadores. Com o auxílio do programa computacional CAST (2000), foram modeladas quatro vigas, sendo as três primeiras biapoiadas sem descontinuidades e a quarta com balanço e descontinuidade geométrica (abertura na alma). A primeira viga biapoiada teve algumas de suas características iniciais alteradas a fim de gerar o segundo e o terceiro modelos, procurando-se estabelecer limites de carregamentos e análises comparativas. Os resultados das modelagens permitiram comparações com os resultados das verificações realizadas segundo os critérios da NBR 6118:2003 e do MC CEB-FIP (1990) e, permitiram também, identificar os aspectos de maior dificuldade na concepção de um modelo de bielas e tirantes e os pontos críticos dos mesmos, nos quais há maior possibilidade de falha nas verificações / One of the main advantages presented by the strut-and-tie model is generality. This model is able to approximately represent, in a realistic and systematic way, the majority of today’s reinforced concrete elements. Furthermore, it allows the physics-intuitive visualization of the behavior presented by structural concrete. On the other hand, its potentials are not fully explored yet. Up to date, there is no accurate criterion for the determination of nodes and transverse sections of some strut elements. Despite presenting some uncertainties related to the determination of wall-beams (and mainly of foundation blocks), the model can determine beams without major difficulties. Probably, the key is to vary the dimensions of the struts and the positions of the nodes, both hypothetical, in order to confront various situations with experimental data. Hence, it is very important to diffuse the strut-and-tie model: the bigger the number of modeling analysis and experimental data, the better the comprehension of the model. This work aims to analyze reinforced concrete beams employing the strut-and-tie model. Here are presented the concepts that led to the development of the model, ranging from the Truss Classic Analogy to the criteria employed to verify truss elements and the recommendations from researchers and established standards (rules or norms). Four examples of beams were modeled. Three of them were double-based and the fourth presented balance and no geometric discontinuity (with an opening). Some of the characteristics of the first double-based beam were altered in order to generate the second and the third model, thus establishing loading limits and comparative analysis. The modeling allowed comparisons between the verifications performed in accordance with the NBR 6118:2003 and MC CEB-FIP criteria. It also allowed the identification of major difficulties and critical aspects related to the development of struts and ties, the ones that are most prone to failure in the verification process

Este trabalho estuda o comportamento estrutural de blocos sobre estacas em concreto armado situados em divisas de terrenos. Foi feita revisão bibliográfica abordando os assuntos de blocos de coroamento, vigas de equilíbrio, modelo de bielas e tirantes e um breve comentário sobre o programa computacional Diana (2010). O trabalho apresenta um roteiro para análise estrutural e dimensionamento de vigas de equilíbrio sobre estacas com pilar excêntrico ao apoio. É apresentado um exemplo feito por Andrade (1989), comparado com o método proposto por Burke (1979) e com análise numérica. Além deste, foram analisados casos de projetos reais utilizando o método Burke (1979) adaptado neste trabalho. Alguns desses exemplos foram modelados em regime elástico e linear no programa computacional Diana (2010). São apresentadas comparações de resultados obtidos com o método Burke (1979) e análise numérica, comprovando a eficácia desse método. Em todos os exemplos estudados o método proposto por Burke (1979) indicou bons resultados quando comparados com os encontrados em análise computacional. A dissertação apresenta soluções para projetos de bloco sobre estacas, situados em divisas de terrenos e associados a vigas de equilíbrio. / This research investigates the structural behavior of reinforced concrete blocks piles located on the limit of land. Literature review was done about blocks piles, balance beams, strut and tie model and a short comment about the Diana computer program (2010). The dissertation presents a roadmap for structural analysis and sizing of balance beams on stakes with eccentric support pillar. An example, which was studied by Andrade (1989), is compared with the same example done using the method proposed by Burke (1979) and with numerical analysis. In addition to this, are analyzed real cases of projects using the method of Burke (1979). Some of these examples were modeled in linear and elastic characteristics using Diana program computer (2010). Here, it is presented comparisons between the method proposed by Burke (1979) and numerical analysis. It is presented comparisons between the method Burke (1979) and numerical analysis, proving the effectiveness of this method. In all examples studied the method proposed by Burke (1979) provided with good accuracy the results for computer analysis. The conclusion presents suggestions for projects of block piles located in limit of land associated with balance beams.

Este trabalho estuda o comportamento de blocos rígidos de concreto armado sobre uma, duas, três, quatro e cinco estacas, submetidos à ação de força centrada. Com o objetivo de contribuir para critérios de projeto, utilizaram-se resultados obtidos por meio de modelos analíticos e realizou-se análise numérica utilizando-se programa baseado no método dos elementos finitos. Foi desenvolvida, ainda, uma análise comparativa entre os processos de dimensionamento adotados em projeto, na qual se verificou grande variabilidade dos resultados. Para análise numérica adotou-se comportamento do material como elástico linear e os resultados de interesse foram os fluxos de tensões em suas direções principais. Nos modelos adotados variaram-se os diâmetros de estacas e dimensões de pilar, a fim de se verificar as diferenças na formação dos campos e trajetórias de tensões. Concluiu-se que o modelo de treliça utilizado em projetos é simplificado e foram feitas algumas sugestões para a utilização de um modelo de bielas e tirantes mais refinado. Foi possível a verificação da influência da variação da geometria de estacas e de pilares no projeto de blocos sobre e a revisão dos critérios para os arranjos das armaduras principais. Para os modelos de blocos sobre cinco estacas adotados concluiu-se que o comportamento não é exatamente como considerado na prática / This work describes the behavior of rigid reinforced concrete pile-caps with one, two, three, four and five piles subjected to patches of loading on the center top surfaces of the column. Programs based on finite elements method were used to obtain numerical results and results obtained by means of analytic models were used. A comparative analysis was developed among the processes adopted in design, which large variability of the results was verified. An elastic linear behavior of the material was adopted for numerical analysis and interest results were stress paths along main directions. Piles diameters and column dimensions of the models were been varied, in order to verify the differences in the formation of the regions and trajectories of stress. It is ended that used the truss model is simplified. Some suggestions were made for the use of a more refined strut-and-tie model than the one used in design and it was possible the verification of the variation geometry of piles and columns influence. It was still made a revision of the reinforcement layouts. The conclusion for adopted five-pile-caps was that the behavior is not exactly as considered in the practice

O projeto estrutural deve considerar as incertezas provenientes das variáveis envolvidas no dimensionamento dos elementos estruturais, tais como propriedades dos materiais, dimensões dos elementos estruturais e intensidade dos carregamentos atuantes. Existe também a variabilidade inerente aos métodos de análise estrutural, originária de imprecisões na idealização da distribuição das tensões e deformações dos elementos estruturais. Sendo assim, esta dissertação visa analisar a variabilidade dos desvios dos modelos de cálculo propostos por Blevot e Frémy (1967), Fusco (1994) e Santos (2013), todos baseados no método das bielas e tirantes, para blocos sobre duas, três e quatro estacas submetidos a carregamento centrado. Estes elementos estruturais possuem significativa importância, visto que atuam na transmissão dos esforços provenientes dos pilares às fundações profundas. Os modelos de cálculo foram confrontados entre si e com resultados experimentais de Blevot e Frémy (1967), Mautoni (1971), Clarke (1973), Miguel (2000) e Suzuki et al. (1998 / 1999 / 2000 / 2001) para determinação dos parâmetros estatísticos dos desvios desses modelos em relação aos ensaios. Os resultados apontaram desempenho satisfatório para os três modelos de cálculo. Em geral, todos os métodos se mostraram favoráveis à segurança nos casos avaliados para os três tipos de blocos de fundação. / Structural design must consider the uncertainties coming from the variables involved in dimensioning of the structural elements, such as material properties, dimensions of structural elements, and intensity of active loads. There is also inherent variability in structural analysis methods, originated from imprecision in idealization of the distribution of tensions and deformations of structural elements. Thus, this dissertation aims to analyze the variability of calculation models deviations proposed by Blevot and Frémy (1967), Fusco (1994) and Santos (2013), all based on strut and tie method, for two, three and four pile caps submitted to center load. These structural elements are of significant importance, since they act in transmission of loads from columns to deep foundations. Calculation models were compared with each other and with experimental results from Blevot and Frémy (1967), Mautoni (1971), Clarke (1973), Miguel (2000) and Suzuki et al. (1998 / 1999 / 2000 / 2001) to determine the statistical parameters of these model deviations in relation to the tests. Results indicated satisfactory performance for the three calculation models. In general, all methods were favorable to safety in cases evaluated for the three pile caps types.

Corrosion of reinforcing steel is a major problem facing infrastructures owners with billions of dollars spent in repairing our aging infrastructure. One of the first steps in the repair process is to quantify the strength degradation in a reinforced concrete element caused by the corrosion of reinforcing steel. An understanding of the forces involved in the load carrying mechanisms is imperative; the transfer of shear forces in reinforced concrete beams is one of these load carrying mechanisms. The shear transfer mechanism is different near the end of beams, adjacent to point loads, and near changes in cross section. These regions are known as disturbed regions. Structural engineers have a good understanding of the shear transfer mechanism in disturbed regions. However, the effects of corroded shear reinforcement in these regions have not been widely investigated. The current study is comprised of an experimental program and analytical strut and tie modeling aimed at quantifying the strength reduction that occurs in disturbed regions of reinforced concrete beams with corroded shear reinforcement. The feasibility of strengthening a beam with dry lay-up carbon fibre reinforced polymer (CFRP) to repair the damage caused by corrosion of the shear reinforcement was also investigated. In the experimental study, a total of 16 reinforced concrete beams were cast. The specimens were 350 mm deep, 125 mm wide and 1850 mm long. Three shear-span to depth ratios (1.0, 1.5, 2.0) were selected. Each specimen was reinforced in flexure with two 25M bars and the shear reinforcement was 10M spaced at 150 mm on centre. The specimens were corroded for 21 days, 60 days, and 120 days corresponding to low, medium, and high corrosion levels. In addition, three specimens were constructed without shear reinforcement in the shear-span in order to compare the results from the corroded specimens. One specimen was also corroded to a high level and repaired with dry lay-up CFRP. The specimens were corroded using an accelerated corrosion technique. There was evidence of cracking of the cover concrete in all specimens, and in the more severely corroded specimens delamination of the cover concrete was recorded. The stiffness of the corroded specimens was less than their corresponding control specimen, and a strength reduction was evident in most specimens. The maximum recorded strength reduction was 52% compared to the companion uncorroded specimen. It was revealed that a more critical case occurs when the corroded shear reinforcement was shifted during placement or was inclined closer to the direction of the compressive force flow. Also, it was observed that the corroded shear reinforcement still provides limited ductility in comparison to the un-corroded reinforcement. A strut and tie model was developed based on the experiments to explain the behaviour of disturbed regions with corroded shear reinforcement. The model consisted of direct and indirect struts. The effects of corrosion were expressed in terms of a reduction in the stirrup cross-section, a reduction of compressive strength due to corrosion cracking, and a reduction in the concrete cross section width. It was hypothesized that the corrosion crack width influences the concrete compressive strength in the strut; consequently, a mathematical model was developed that related the reduction in concrete compressive strength with corrosion crack width. Also, a relationship between reinforcing steel mass loss and corrosion crack width was utilized from the published literature. An effective cross section width was obtained by reducing the width by the damaged concrete cover. The results from these models were input into a strut and tie model as a reduction in concrete compressive strength. The output from the strut and tie model was the ultimate shear strength of the specimen. The developed models were compared with a model from the literature and compared with the experimental results. The major contribution of this research is to allow designers to analyze disturbed regions with corroded shear reinforcement and determine the strength degradation; subsequently, one can determine what strengthening procedure would be most appropriate.

Corrosion of reinforcing steel is a major problem facing infrastructures owners with billions of dollars spent in repairing our aging infrastructure. One of the first steps in the repair process is to quantify the strength degradation in a reinforced concrete element caused by the corrosion of reinforcing steel. An understanding of the forces involved in the load carrying mechanisms is imperative; the transfer of shear forces in reinforced concrete beams is one of these load carrying mechanisms. The shear transfer mechanism is different near the end of beams, adjacent to point loads, and near changes in cross section. These regions are known as disturbed regions. Structural engineers have a good understanding of the shear transfer mechanism in disturbed regions. However, the effects of corroded shear reinforcement in these regions have not been widely investigated. The current study is comprised of an experimental program and analytical strut and tie modeling aimed at quantifying the strength reduction that occurs in disturbed regions of reinforced concrete beams with corroded shear reinforcement. The feasibility of strengthening a beam with dry lay-up carbon fibre reinforced polymer (CFRP) to repair the damage caused by corrosion of the shear reinforcement was also investigated. In the experimental study, a total of 16 reinforced concrete beams were cast. The specimens were 350 mm deep, 125 mm wide and 1850 mm long. Three shear-span to depth ratios (1.0, 1.5, 2.0) were selected. Each specimen was reinforced in flexure with two 25M bars and the shear reinforcement was 10M spaced at 150 mm on centre. The specimens were corroded for 21 days, 60 days, and 120 days corresponding to low, medium, and high corrosion levels. In addition, three specimens were constructed without shear reinforcement in the shear-span in order to compare the results from the corroded specimens. One specimen was also corroded to a high level and repaired with dry lay-up CFRP. The specimens were corroded using an accelerated corrosion technique. There was evidence of cracking of the cover concrete in all specimens, and in the more severely corroded specimens delamination of the cover concrete was recorded. The stiffness of the corroded specimens was less than their corresponding control specimen, and a strength reduction was evident in most specimens. The maximum recorded strength reduction was 52% compared to the companion uncorroded specimen. It was revealed that a more critical case occurs when the corroded shear reinforcement was shifted during placement or was inclined closer to the direction of the compressive force flow. Also, it was observed that the corroded shear reinforcement still provides limited ductility in comparison to the un-corroded reinforcement. A strut and tie model was developed based on the experiments to explain the behaviour of disturbed regions with corroded shear reinforcement. The model consisted of direct and indirect struts. The effects of corrosion were expressed in terms of a reduction in the stirrup cross-section, a reduction of compressive strength due to corrosion cracking, and a reduction in the concrete cross section width. It was hypothesized that the corrosion crack width influences the concrete compressive strength in the strut; consequently, a mathematical model was developed that related the reduction in concrete compressive strength with corrosion crack width. Also, a relationship between reinforcing steel mass loss and corrosion crack width was utilized from the published literature. An effective cross section width was obtained by reducing the width by the damaged concrete cover. The results from these models were input into a strut and tie model as a reduction in concrete compressive strength. The output from the strut and tie model was the ultimate shear strength of the specimen. The developed models were compared with a model from the literature and compared with the experimental results. The major contribution of this research is to allow designers to analyze disturbed regions with corroded shear reinforcement and determine the strength degradation; subsequently, one can determine what strengthening procedure would be most appropriate.

A compatibility-based strut-and-tie model C-STM is proposed for analyzing deep beams and disturbed regions with particular emphasis on reinforced concrete bridge piers. In addition to the normal strut-and-tie force equilibrium requirements the model accounts for non-linear behavior through displacement compatibility using inelastic constitutive laws of cracked reinforced concrete. The model is implemented into widely used commercial structural analysis software and validated against results from previously conducted large scale experiments. A near full-scale experiment on a reinforced concrete sub-assemblage that represents cantilevered and straddle pier bents is conducted to investigate the shear-flexure performance of deep (disturbed) regions. Insights into the development of nonlinear behavior and the final collapse failure mechanism are then evaluated and accurately modeled using the C-STM. It is concluded that the proposed C-STM serves as an advanced method of analysis that can predict with suitable accuracy the force-deformation response of both D- and B- regions, deep beams, and beam-columns. This provides engineers with a supplementary analysis tool that can be used to assess the nonlinear behavior of bridge piers with stocky members and/or large disturbed regions.

Strut-and-tie modeling (STM) is a versatile, lower-bound (i.e. conservative) design method for reinforced concrete structural components. Uncertainty expressed by engineers related to the implementation of existing STM code specifications as well as a growing inventory of distressed in-service bent caps exhibiting diagonal cracking was the impetus for the Texas Department of Transportation (TxDOT) to fund research project 0-5253, D-Region Strength and Serviceability Design, and the current implementation project (5-5253-01). As part of these projects, simple, accurate STM specifications were developed. This thesis acts as a guidebook for application of the proposed specifications and is intended to clarify any remaining uncertainties associated with strut-and-tie modeling. A series of five detailed design examples feature the application of the STM specifications. A brief overview of each design example is provided below. The examples are prefaced with a review of the theoretical background and fundamental design process of STM (Chapter 2). • Example 1: Five-Column Bent Cap of a Skewed Bridge - This design example serves as an introduction to the application of STM. Challenges are introduced by the bridge’s skew and complicated loading pattern. A clear procedure for defining relatively complex nodal geometries is presented. • Example 2: Cantilever Bent Cap - A strut-and-tie model is developed to represent the flow of forces around a frame corner subjected to closing loads. The design and detailing of a curved-bar node at the outside of the frame corner is described. • Example 3a: Inverted-T Straddle Bent Cap (Moment Frame) - An inverted-T straddle bent cap is modeled as a component within a moment frame. Bottom-chord (ledge) loading of the inverted-T necessitates the use of local STMs to model the flow of forces through the bent cap’s cross section. • Example 3b: Inverted-T Straddle Bent Cap (Simply Supported) - The inverted-T bent cap of Example 3a is designed as a member that is simply supported at the columns. • Example 4: Drilled-Shaft Footing - Three-dimensional STMs are developed to properly model the flow of forces through a deep drilled-shaft footing. Two unique load cases are considered to familiarize the designer with the development of such models. / text