<p>The strut-and-tie method (STM) is a powerful tool used for the design of D-regions (disturbed regions) of reinforced concrete structures. Many typical bridge substructure components consist of D-regions and require the use of the STM for design. Implementation of the STM is more complex than typical design methods, and engineers are often unfamiliar with the design process. As a result, designing using the STM is more time consuming than traditional design methods. The Indiana Department of Transportation (INDOT) identified a need for a tool that assists with the design of typical bridge substructure components using the STM. STEP (Strut-and-Tie Evaluation Program) is a computer program created to fulfill this role. To use the computer program, engineers input geometric conditions, material properties, and reinforcement information for a structural component. STEP uses this information to develop a strut-and-tie model and perform STM design procedures. A graphical representation of the model and a summary of the design results are provided as program outputs for the user.</p> <p> </p> <p>STEP, created using Excel VBA, is intended to aid in the design of multi-column bent caps and integral and semi-integral end bent caps. Within this thesis, an overview of the STM is provided, including the basic procedures for designing using the STM. An introduction to Excel VBA is also presented. The document describes the layout and formatting of the computer program, required user inputs, and program outputs. Furthermore, limitations and assumptions within the computer program for the substructure components are also included. Finally, design examples focused on the use of STEP for the design of a five-column bent cap and an integral end bent cap are presented. This document can be used as a resource for engineers when designing bridge substructure components using STEP. </p>

Reinforced concrete frame corners (that is, knee joints) subjected to closing moments plays an important role of transmitting stress between the two adjoining members. Being categorized as geometric discontinuity regions (D-regions), knee joints cannot be correctly analyzed and designed using traditional sectional analysis procedures. Instead, the strut-and-tie method is particularly suitable for such joints. Although strut-and-tie models provide the means to represent the distribution of stresses within a closing knee joint, questions arise when a curved-bar node is used to model the bar bend of the longitudinal reinforcement at the outer corner. The code-specified design expressions for curved-bar nodes have not been experimentally verified; therefore, the accuracy and conservativeness of the expressions remain unknown. This research project is aimed to provide insights to the proper application of the strut-and-tie method, through the concept of curved-bar nodes, to knee joints under closing moments.<br><br>An experimental program consisting of 24 specimens was conducted to investigate the effect of curved-bar nodes on knee joints under closing moments. An evaluation of the code-specified design expressions was included. The results demonstrate that the minimum code-specified bend radius is appropriate. The current requirements related to bond along the bar bend and clear side cover are shown to be conservative. Based on the test results, a procedure for constructing proper strut-and-tie models for closing knee joints is proposed and verified using an evaluation database consisting of 116 knee joint tests from the literature. Compared to other strength predictive methods and the code-specified strut-and-tie method, the proposed strut-and-tie method mitigates unconservativeness and delivers improved accuracy.<br>In addition to the experimental program and the proposed procedure, non-linear finite element analysis (FEA) using the software ATENA-3D was employed to conduct a parametric analysis as a supplement to the experimental data. Seventy-two numerical models were analyzed to further evaluate the code-specified expressions and the proposed strut-and-tie method. The FEA results are in a good agreement with the experimental observations and corroborate the conclusions from the experimental program regarding current code requirements. Moreover, the parametric analysis further supports the application of the proposed strut-and-tie methodology to knee joints under closing moments.

The strut-and-tie method (STM) is a simple and conservative method for designing concrete structures, especially deep beams. This method expresses complicated stress patterns as a simple truss or kinematic model made up of compression elements (struts), tension elements (ties), and the joints between elements (nodes). STM is based on lowerbound plasticity theorem, so using it properly will lead to a conservative design. Although the concepts of STM have been around in concrete design since the late 19th century, STM was first introduced in AASHTO LRFD in 1994 and ACI 318-02 in 2002. ACI 318 defines two different types of struts (prismatic and bottle-shaped) based on whether compression stress can spread transversely along the length of the strut. Recent work has brought into question whether these two types of struts do exist and whether current design provisions conservatively estimate failure loads for all members. The performance of struts and nodes were investigated experimentally by testing six fullscale concrete deep beams. The specimens had two different shapes (rectangular and trusslike), two different shear span-to-depth ratio (1 and 1.6), and three different types of development (externally unbonded bars, internally bonded hooked bars, and internally bonded bars with welded external plates). All the specimens were supported vertically and vii tested under a three-point load setup. Based on the results, the truss-like specimen failed at higher loads than rectangular specimens with the same shear span-to-depth ratio. According to these results and recent debate in the literature, bottle-shaped struts are not weaker than prismatic struts because of their shape. They are weaker due to shear failure where struts cross a diagonal tension field. Therefore, the structures should be separately checked for shear strength when they are designed with STM. In this dissertation, the development of the design equation for shear strength of discontinuity regions was introduced, and the procedure is under consideration for adoption in ACI 318-19. This research was expanded numerically by studying the effect of development type and length, strut type, and strut angle on the behavior of concrete deep beams. The crack patterns and load-displacement curves, which were obtained from experimental tests, were used to validate numerical models. The strength of concrete deep beams was assessed by modeling thirty-five specimens in a nonlinear finite element software. According to the results, development length and development types influenced the presence of tensile stress in the support nodes. Additionally, the effect of the tensile stresses from reinforcement development and diagonal tension were not additive in rectangular specimens.

Made available in DSpace on 2014-12-17T14:48:13Z (GMT). No. of bitstreams: 1 JulioCCD_DISSERT.pdf: 5293520 bytes, checksum: 35065f2bef6951ad4ce1b2b752aa3b02 (MD5) Previous issue date: 2012-02-28 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The main objective of this thesis was the study of bracing panels of structural masonry, by applying the Finite Element Method and Strut and Tie Method. It was analyzed the following aspects: the effect of orthotropy on the behavior of the panels; distribution of horizontal forces between panels for buildings; comparison between Equivalent Frame and Finite Elements models; panels design with the Strut and Tie Method. The results showed that one should not disregard the orthotropy, otherwise this can lead to models stiffer than the real. Regarding the distribution of horizontal forces, showed that the disregard of lintels and shear deformation leads to significant differences in the simplified model. The results showed also that the models in Finite Element and Equivalent Frame exhibit similar behavior in respect to stiffness of panels and stress distribution over the sessions requested. It was discussing criteria for designing Strut and Tie Method models in one floor panels. Then, the theoretical strength these panels was compared with the rupture strength of panels tested in the literature. The theoretical maximum strength were always less than the rupture strength of the panels obtained in tests, due to the fact that the proposed model cannot represent the behavior of the masonry after the start of the panel cracking due to plasticization of the reinforcement / O objetivo principal desta disserta??o foi o estudo de pain?is de contraventamento de alvenaria estrutural, atrav?s da aplica??o do M?todo dos Elementos Finitos e do M?todo de Bielas e Tirantes. Foram analisados os seguintes aspectos: o efeito da ortotropia no comportamento de pain?is; distribui??o de for?as horizontais entre pain?is de edif?cios; compara??o entre os modelos de P?rtico Equivalente e Elementos Finitos; c?lculo de pain?is com o M?todo de Bielas e Tirantes. Os resultados permitiram concluir que n?o se deve desconsiderar a ortotropia, sob pena de conduzir a modelos mais r?gidos que o real. Em rela??o ? distribui??o de for?as horizontais, evidenciou-se que a desconsidera??o dos lint?is e da deforma??o por cisalhamento acarretam diferen?as significativas relativamente ao modelo de barras isoladas. Os resultados permitiram concluir, ainda que os modelos em Elementos Finitos e de P?rtico Equivalente apresentam comportamento semelhante no que se refere ? rigidez de pain?is e distribui??o de tens?es nas sess?es mais solicitadas. Foram discutidos crit?rios para a concep??o de modelos de bielas e tirantes em pain?is isolados. Em seguida, a for?a horizontal te?rica destes pain?is foi comparada com a carga de ruptura de pain?is ensaiados dispon?veis na literatura. As for?as m?ximas te?ricas foram sempre inferiores ? for?a de ruptura dos pain?is, obtidas em ensaios, devido ao fato de que o modelo proposto n?o ? capaz de representar o comportamento da alvenaria ap?s o inicio da fissura??o do painel devido ? plastifica??o das armaduras

O dimensionamento de Regiões D (regiões em que não é aplicável a Hipótese de Bernoulli), embora amplamente estudado e discutido, é um tópico ainda em desenvolvimento e com normatização relativamente escassa. Os métodos mais comumente empregados são o Método dos Elementos Finitos (MEF) e o Método de Bielas e Tirantes (MBT). A dissertação expõe a base teórica e a metodologia dos dois métodos no dimensionamento de estruturas de concreto armado ao Estado Limite Último e aborda a utilização da otimização, em especial da otimização topológica, na definição dos modelos para o MBT. Metodologias para a aplicação dos dois métodos são propostas e aplicadas a exemplos práticos de Regiões D com recomendações normativas específicas para seu dimensionamento (consolo e viga parede biapoiada) e também a uma viga parede de geometria complexa, os resultados através de diferentes técnicas de dimensionamento são comparados e discutidos, assim como a utilização da otimização como meio de obtenção de modelos. / The design of D-Regions (Regions where the Bernoulli hypothesis is not valid), although widely studied and discussed, is a topic still under development and with relatively little standardization, especially in Brazil. The most commonly used methods are the Finite Element Method (FEM) and the Strut-And-Tie Method (STM). The theoretical basis and methodology of both methods in the design of reinforced concrete structures are presented as well as the use of optimization, especially topology optimization, in the definition of STM models. Procedures are proposed for both methods and applied to practical examples of D-Regions with specific recommendations for its design (Corbel and Deep Beam) as well as a deep beam with complex geometry, the results using the different design methods are compared and discussed as well as the use of optimization as a means of obtaining STM models.

Esta pesquisa discorre a respeito do comportamento estrutural de blocos de concreto armado sobre cinco estacas, dispostas nos vértices de um trapézio, e sobre seis estacas, com o arranjo retangular, considerado pilar com força centrada. Foram estudados diversos métodos analíticos para o dimensionamento dos blocos, no intuito de avaliar a compatibilidade entre o comportamento dos blocos e as hipóteses de cada método. Foi desenvolvida análise numérica tridimensional utilizando programa baseado no método dos elementos finitos. Nos blocos estudados variou-se a deformabilidade do solo de apoio das estacas, por meio de molas elásticas, a seção transversal do pilar, considerando pilar quadrado e pilar retangular, as alturas dos blocos sobre estacas e a resistência do concreto. A configuração do fluxo de tensões, vista em perspectiva, indicou a formação de bielas comprimidas discretas ligando o pilar ao topo das estacas. Observou-se que quanto mais deformável for o solo, mais uniformes são as distribuições das reações entre as estacas e das tensões de tração nas barras das armaduras principais. Verificou-se que as configurações das bielas mudaram conforme se alterou a seção transversal do pilar, indicando a importância de se considerar esse aspecto no dimensionamento analítico dos blocos. A altura influenciou de maneira significativa na rigidez e na resistência dos blocos. No entanto, os blocos com grandes alturas não apresentaram bom comportamento estrutural e os blocos com pequenas alturas não indicaram boa distribuição das reações nas estacas, com as tensões de tração se concentrando entre as barras das armaduras entre as estacas mais próximas do pilar. Observou-se que o aumento da resistência do concreto acarretou no aumento da resistência dos blocos, porém não influenciou na rigidez de modo significativo. Os métodos analíticos que se baseiam nas verificações das resistências a momento fletor e à força cortante não foram compatíveis com o fluxo de tensões obtido, que por sua vez indicou melhor compatibilidade com o método de bielas e tirantes. Por fim, foi possível verificar a aplicabilidade de um método analítico, já existente, que emprega conceitos do método de bielas e tirantes, é simples e de fácil utilização para o dimensionamento de blocos sobre cinco e seis estacas. Esse método considera a altura dos blocos por meio do ângulo de inclinação das bielas, a variação da seção transversal do pilar e diferentes arranjos para as estacas. / This research treats about the structural behavior of reinforced concrete pile caps with five piles arranged at the trapezium vertices and with six piles in rectangular arrangement, considering centered load at column. Several analytical methods were studied for pile caps design in order to assess the compatibility between the pile caps behavior and assumptions of each method. A three-dimensional numerical analysis was developed using program based on finite element method. In pile caps studied, the deformability of soil of support piles were varied, through elastic springs, the column cross section, considering square and rectangular column, the pile caps height and the concrete resistances. The flow stress configuration, visualized in perspective, indicated the formation of discrete compressed struts connecting the column base to the piles top. It was observed that the more deformable is the soil, better uniforms are the reactions distribution between the piles and tensile stresses in the main reinforcement bars. It was found that the struts settings changed with the variation of the cross section column, indicating the importance of this variable in the analytical pile caps design. The height of the pile caps significantly affects the stiffness and strength. However, the higher pile caps did not show good structural behavior and the smaller pile cap indicated poor reactions distribution in piles, with tensile stresses concentrated among the bars reinforcement between the piles closest to the column. It was observed that the increasing in the concrete strength resulted in a higher pile caps resistance, but did not influence the stiffness significantly. The analytical methods, which are based on the resistance verification of bending moment and shear force, are not compatible with the tension flow obtained, which indicated better compatibility with the strut and tie method. Finally, it was possible to verify the applicability of a well known analytical method which uses concepts of strut and tie method, which is simple and easy to apply for five and six pile caps. This method considers the height by means of the inclination angle of struts, the column cross section variation and different piles arrangements.

O dimensionamento de Regiões D (regiões em que não é aplicável a Hipótese de Bernoulli), embora amplamente estudado e discutido, é um tópico ainda em desenvolvimento e com normatização relativamente escassa. Os métodos mais comumente empregados são o Método dos Elementos Finitos (MEF) e o Método de Bielas e Tirantes (MBT). A dissertação expõe a base teórica e a metodologia dos dois métodos no dimensionamento de estruturas de concreto armado ao Estado Limite Último e aborda a utilização da otimização, em especial da otimização topológica, na definição dos modelos para o MBT. Metodologias para a aplicação dos dois métodos são propostas e aplicadas a exemplos práticos de Regiões D com recomendações normativas específicas para seu dimensionamento (consolo e viga parede biapoiada) e também a uma viga parede de geometria complexa, os resultados através de diferentes técnicas de dimensionamento são comparados e discutidos, assim como a utilização da otimização como meio de obtenção de modelos. / The design of D-Regions (Regions where the Bernoulli hypothesis is not valid), although widely studied and discussed, is a topic still under development and with relatively little standardization, especially in Brazil. The most commonly used methods are the Finite Element Method (FEM) and the Strut-And-Tie Method (STM). The theoretical basis and methodology of both methods in the design of reinforced concrete structures are presented as well as the use of optimization, especially topology optimization, in the definition of STM models. Procedures are proposed for both methods and applied to practical examples of D-Regions with specific recommendations for its design (Corbel and Deep Beam) as well as a deep beam with complex geometry, the results using the different design methods are compared and discussed as well as the use of optimization as a means of obtaining STM models.

Esta pesquisa discorre a respeito do comportamento estrutural de blocos de concreto armado sobre cinco estacas, dispostas nos vértices de um trapézio, e sobre seis estacas, com o arranjo retangular, considerado pilar com força centrada. Foram estudados diversos métodos analíticos para o dimensionamento dos blocos, no intuito de avaliar a compatibilidade entre o comportamento dos blocos e as hipóteses de cada método. Foi desenvolvida análise numérica tridimensional utilizando programa baseado no método dos elementos finitos. Nos blocos estudados variou-se a deformabilidade do solo de apoio das estacas, por meio de molas elásticas, a seção transversal do pilar, considerando pilar quadrado e pilar retangular, as alturas dos blocos sobre estacas e a resistência do concreto. A configuração do fluxo de tensões, vista em perspectiva, indicou a formação de bielas comprimidas discretas ligando o pilar ao topo das estacas. Observou-se que quanto mais deformável for o solo, mais uniformes são as distribuições das reações entre as estacas e das tensões de tração nas barras das armaduras principais. Verificou-se que as configurações das bielas mudaram conforme se alterou a seção transversal do pilar, indicando a importância de se considerar esse aspecto no dimensionamento analítico dos blocos. A altura influenciou de maneira significativa na rigidez e na resistência dos blocos. No entanto, os blocos com grandes alturas não apresentaram bom comportamento estrutural e os blocos com pequenas alturas não indicaram boa distribuição das reações nas estacas, com as tensões de tração se concentrando entre as barras das armaduras entre as estacas mais próximas do pilar. Observou-se que o aumento da resistência do concreto acarretou no aumento da resistência dos blocos, porém não influenciou na rigidez de modo significativo. Os métodos analíticos que se baseiam nas verificações das resistências a momento fletor e à força cortante não foram compatíveis com o fluxo de tensões obtido, que por sua vez indicou melhor compatibilidade com o método de bielas e tirantes. Por fim, foi possível verificar a aplicabilidade de um método analítico, já existente, que emprega conceitos do método de bielas e tirantes, é simples e de fácil utilização para o dimensionamento de blocos sobre cinco e seis estacas. Esse método considera a altura dos blocos por meio do ângulo de inclinação das bielas, a variação da seção transversal do pilar e diferentes arranjos para as estacas. / This research treats about the structural behavior of reinforced concrete pile caps with five piles arranged at the trapezium vertices and with six piles in rectangular arrangement, considering centered load at column. Several analytical methods were studied for pile caps design in order to assess the compatibility between the pile caps behavior and assumptions of each method. A three-dimensional numerical analysis was developed using program based on finite element method. In pile caps studied, the deformability of soil of support piles were varied, through elastic springs, the column cross section, considering square and rectangular column, the pile caps height and the concrete resistances. The flow stress configuration, visualized in perspective, indicated the formation of discrete compressed struts connecting the column base to the piles top. It was observed that the more deformable is the soil, better uniforms are the reactions distribution between the piles and tensile stresses in the main reinforcement bars. It was found that the struts settings changed with the variation of the cross section column, indicating the importance of this variable in the analytical pile caps design. The height of the pile caps significantly affects the stiffness and strength. However, the higher pile caps did not show good structural behavior and the smaller pile cap indicated poor reactions distribution in piles, with tensile stresses concentrated among the bars reinforcement between the piles closest to the column. It was observed that the increasing in the concrete strength resulted in a higher pile caps resistance, but did not influence the stiffness significantly. The analytical methods, which are based on the resistance verification of bending moment and shear force, are not compatible with the tension flow obtained, which indicated better compatibility with the strut and tie method. Finally, it was possible to verify the applicability of a well known analytical method which uses concepts of strut and tie method, which is simple and easy to apply for five and six pile caps. This method considers the height by means of the inclination angle of struts, the column cross section variation and different piles arrangements.

<p>U disertaciji su analizirani armiranobetonski ravanski nosači<br />primenom metode pritisnutih štapova i zatega. Optimizacija nosača<br />urađena je diskretnom topološkom otimizacijom kojom se pun nosač<br />zamenjuje ekvivalentnim rešetkastim. Dat je predlog algoritamskog<br />dobijanja Strut-and-Tie modela koji je implementiran u program sopstvene<br />izrade pod nazivom &bdquo;ST method&ldquo;. Provera pouzdanosti predloženog<br />algoritma utvrđena je primerima iz referentne literature, sopstvenim<br />eksperimentalnim ispitivanjem i numeričkom analizom u komercijalnim<br />programima. Rezulatati analiza su pokazali da se predloženi algoritam u<br />programu &bdquo;ST method&ldquo; može koristiti za dobijanje Strut-and-Tie modela i<br />njihovo dimenzionisanje i da se pri odabiru nekih modela mora koristiti<br />inženjersko iskustvo.</p> / <p>In dissertation thesis, reinforced concrete plane members have been analyzed by<br />the Strut-and-Tie method. Optimizing of the members is made by discrete<br />topological otimization which replaces full member with equivalent truss system.<br />Algorithmic manner of Strut-and-Tie model obtaining has been suggested, which<br />is implemented in the program of an own creation called &quot;ST method&quot;. The<br />reliability of the proposed algorithm is determined by the examples from reference<br />literature, an own experimental test and numerical analysis in commercial<br />programs. The results of the analysis showed that the proposed algorithm in the<br />&quot;ST method&quot; can be used to obtain Strut-and-tie models and their dimensioning<br />and that in certain models, the engineering experience must be used.</p>

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.