Significant diagonal cracking in reinforced concrete inverted-T straddle bent caps has been reported throughout the State of Texas. Many of the distressed structures were recently constructed and all have been in service for less than two decades. The unique nature of the problem prompted a more detailed look into the design and behavior of such structural components. Strut-and-tie modeling is currently recommended for design of deep (rectangular) beams, but its application to more complex structures has not been fully explored. Due to concerns with current design provisions the application of strut-and-tie modeling to inverted-T beams was investigated along with serviceability-related considerations in this dissertation. An experimental study was conducted in which thirty-three reinforced concrete inverted-T beam tests were conducted. The effects of the following variables were evaluated: ledge depth and length, quantity of web reinforcement, number of point loads, member depth, and shear span-to-depth ratio. A strut-and-tie design method proposed by Birrcher et. al (2009), initially calibrated for compression-chord loaded deep beams, was investigated. It was concluded that the strut-and-tie method was a simple and accurate design method, and it was recommended for use in inverted-T beam design. A vi recommendation was also made for the amount of minimum web reinforcement needed for strength and serviceability considerations. A simple service-load check was proposed for the purpose of limiting diagonal cracking under service loads. Finally, a chart was created to aid in the evaluation of distressed, diagonally-cracked inverted-T bent caps in the field. / text

Bridge bents (deep beams) in the State of Texas have experienced diagonal cracking problems with increasing frequency. These field related issues, taken in combination with discrepancies that exist between design provisions for strut and tie modeling (STM), were the impetus for the funding of the current project. The overall objective of the project was to develop safe and consistent design guidelines in regard to both the strength and serviceability of deep beams. In order to accomplish this research objective and related tasks, a database of 868 deep beam tests was assembled from previous research. Inadvertently, many of the beams in this database were considerably smaller, did not contain sufficient information, or contained very little shear reinforcement. As a result, filtering criteria were used to remove 724 tests from the database. The criteria were chosen to consider only beams that represent bent caps designed in the field. In addition to the 144 tests that remained in the database, 34 tests were conducted as part of the current experimental program resulting in 178 total tests available for evaluation purposes. Two additional tests were conducted on beams without shear reinforcement, thus they did not meet the filtering criteria. However, the results from these tests provided valuable information regarding deep beam behavior. Beams that were fabricated and tested as part of the current experimental program ranged in size from, 36"x48", 21"x75", 21"x42", and 21"x23". These tests represent some of the largest deep beam shear tests ever conducted. STM details that were investigated included: (i) the influence that triaxial confinement of the load or support plate has on strength and serviceability performance; and (ii) the influence that multiple stirrup legs distributed across the web has on strength and serviceability performance. Based on the findings of the experimental and analytical program, a new strut-and-tie modeling procedure was proposed for the design of deep beam regions. The procedure is based on an explicitly defined single-panel truss model with non-hydrostatic nodes. An important aspect of the new STM design methodology is that it was comprehensively derived based on all the stress checks that constitute an STM design. Thus, the new method considers every facet of a STM design. The newly proposed STM procedure is simple, more accurate, and more conservative in comparison with the ACI 318-08 and AASHTO LRFD (2008) STM design provisions. As such, the implementation of the new design provisions into ACI 318 and AASHTO LRFD is recommended. / text

Significant diagonal cracking in reinforced concrete inverted-T (IT) straddle bent caps has been reported throughout the State of Texas. Many of the distressed structures were recently constructed and have generally been in service for less than two decades. The unique nature of the problem prompted a closer look into the design and behavior of such structural components. A preliminary investigation highlighted outdated design requirements and a scarcity of experimental investigations pertaining to inverted-T bent caps. This research project (TxDOT Project 0-6416, Shear Cracking in Inverted-T Straddle Bents) aims to improve current understanding of the behavior of inverted-T caps, while providing updated design provisions. In order to develop strength and serviceability guidelines for inverted-T beams, an extensive experimental program was developed. This series of large scale tests was used to evaluate the strength and serviceability of IT deep beams in relation to the following parameters – shear span-to-depth (a/d) ratio, web reinforcement ratio, ledge height, ledge length, number of point loads, and member depth. This report focuses mainly on results from a first series of tests conducted within this experimental program. / text

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.

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 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

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.

yes / There are very few, if any, available experimental investigations on aggregate interlock capacity along diagonal cracks in lightweight concrete deep beams. As a result, the shear design provisions including the modification factor of ACI 318-08 and EC 2 for lightweight concrete continuous deep beams are generally developed and validated using normal weight simple deep beam specimens. This paper presents the testing of 12 continuous beams made of all-lightweight, sand-lightweight and normal weight concrete having maximum aggregate sizes of 4, 8, 13 and 19 mm. The load capacities of beams tested are compared with the predictions of strut-and-tie models recommended in ACI 318-08 and EC 2 provisions including the modification factor for lightweight concrete. The beam load capacity increased with the increase of maximum aggregate size, though the aggregate interlock contribution to the load capacity of lightweight concrete deep beams was less than that of normal weight concrete deep beams. It was also shown that the lightweight concrete modification factor in EC 2 is generally unconservative, while that in ACI 318-08 is conservative for all-lightweight concrete but turns to be unconservative for sand-lightweight concrete with a maximum aggregate size above 13 mm. The conservatism of the strut-and-tie models specified in ACI 318-08 and EC 2 decreased with the decrease of maximum aggregate size, and was less in lightweight concrete deep beams than in normal weight concrete deep beams.

Yes / The test results on eight two-span deep beams made of self-compacting concrete (SCC) are presented and discussed in this paper. The main parameters investigated were the shear span-to-depth ratio, and the amount and configuration of steel reinforcement. All beams failed due to a major diagonal crack formed between the applied mid-span load and the intermediate support separating the beam into two blocks: the first one rotated around the end support leaving the other block resting on the other two supports. Both concrete compressive strength and web reinforcement had a major effect in controlling the shear capacity of the beams tested. For the shear span-to-depth ratio considered, the vertical web reinforcement had more influence on the shear capacity of the specimens than the horizontal web reinforcement. The shear provisions of the ACI 318M-11 are unconservative for most of the beams tested. Comparisons of test results with the strut-and-tie model (STM) suggested by ACI 318M-11, EC2 and CSA23.4-04 showed that the predictions are reasonable for continuous deep beams made with low and medium compressive strength. Although the equation suggested by ACI 318M-11 is very simple, its prediction is more accurate than the STM suggested by different design codes. / This research investigation was funded by the Higher Education Ministry in The Libyan Government.