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.

Several reinforced concrete bent caps (deep beams) in Texas have developed significant diagonal cracks in service. The cracking in two bent caps was so extensive that costly retrofits were implemented to strengthen the structures. Strut-and-tie modeling is currently recommended in most U.S. design specifications for the design of reinforced concrete bent caps and deep beams. Designers have expressed concerns with the lack of clarity and serviceability-related considerations in strut-and-tie model design provisions. Due to concerns with strut-and-tie modeling design provisions and field problems of in-service bent caps, TxDOT Project 5253 was funded. Several tasks conducted within Project 5253 are addressed in this dissertation. The effects of minimum web reinforcement and member depth on the strength and serviceability behavior of deep beams are presented. The transition between deep beam shear capacity and sectional shear capacity near a shear-span-to-depth (a/d) ratio of 2 is addressed. A service-load shear check to limit diagonal cracking in service is outlined. Lastly, a simple chart that correlates the maximum width of diagonal cracks in a deep beam to its residual capacity is developed. To accomplish the objectives of Project 5253, thirty-seven tests were conducted on reinforced concrete beams with the following cross-sectional dimensions: 21”x23”, 21”x42”, 21”x44”, 21”x75”, and 36”x48.” The specimens were loaded with a/d ratios of 1.2, 1.85, and 2.5. The test specimens are among the largest reinforced concrete deep beams in the literature. To supplement the findings of the experimental program, a database of deep beam test results was compiled. Entries in the database that lacked sufficient information and that did not meet established cross-sectional size or web reinforcement criteria were filtered from the database. The use of the database in conjunction with the experimental program enabled each objective to be addressed from both broad and specific viewpoints. Several recommendations for improving the strength and serviceability design of deep beams are presented including a minimum web reinforcement requirement, provisions to ease the transition between calculated deep beam and sectional shear capacity, and a design check to limit diagonal cracking in service. / text

Esta pesquisa realiza a análise do comportamento estrutural de blocos rígidos de concreto armado sobre duas estacas submetidos à ação de força vertical centrada, com pilares de seções quadradas e retangulares e diferentes taxas de armaduras de pilares. Nestes elementos utilizam-se o método das Bielas e Tirantes para o projeto estrutural, mas normalmente não se considera a influência da seção geométrica dos pilares e suas taxas de armadura no projeto do bloco. Apresenta-se um estudo experimental de doze modelos de blocos sobre duas estacas, na escala 1:2. Foi desenvolvida uma análise numérica tridimensional e não linear, pelo método dos elementos finitos, com o auxílio de um programa de computador. Com a análise experimental e numérica foi investigada a distribuição do fluxo das tensões principais de compressão e tração nos modelos e constataram-se diferenças na transmissão de forças para os blocos quando se altera a taxa de armadura e a seção transversal dos pilares. Esta constatação modifica o modelo de Biela e Tirante inicialmente adotado. As deformações em armaduras construtivas complementares também foram estudadas possibilitando o entendimento do modelo estrutural. Um modelo de Bielas e Tirantes para blocos sobre estaca com pilares alongados foi proposto. / This research presents an analysis of the rigid two-pile caps structural behavior. The models were subjected to force action centered and supported columns with different rate of armor and square and rectangular cross sections. These elements can be rigid or flexible, rigid pile-caps can be sized using the Method of Strut and Tie. In most cases the Method of Strut and Tie and the influence of column reinforcement are not considered in the pile-cap´s structural projects. This research presents an experimental investigation of two-pile caps with the objective of improve criteria structural projects. Twelve rigid two-pile caps were builded using 1:2 scaled models. Three-dimensional numerical analyses using software based on element finite method (FEM) were developed considering the reinforced concrete nonlinear behavior. Using results of experimental analysis and numerical analysis an investigation of the flow distribution of the principal stresses of compression and tension in the models was performed, differences in the transmission of forces to the pile-caps, when changing the reinforcement ratio and the cross section of the columns, were detected. The initial model of strut and tie may be modified due to results. The understanding of the structural model was also possible by analysis of the stirrups and upper constructive reinforcement stress-strain behavior. A strut and tie model for pile-caps with an elongated rectangular column was proposed.

A pesquisa teve como objetivo analisar e discutir o comportamento de blocos de concreto armado sobre duas estacas submetidos à ação de força centrada e excêntrica. Desenvolveu-se uma análise numérica tridimensional não-linear de blocos de concreto armado sobre duas estacas. A análise numérica levou em consideração a fissuração do concreto e a influência das armaduras no comportamento estrutural dos blocos. Por meio da análise numérica, foi possível perceber o comportamento e a forma geométrica das bielas de compressão, com isso, obteve-se melhor entendimento do modelo de bielas (escoras) e tirantes aplicado a blocos de concreto armado sobre duas estacas. A geometria observada nos modelos numéricos analisados preliminarmente difere da usualmente sugerida por vários autores. Realizou-se investigação experimental de blocos, com o fim principal de observar, de modo mais abrangente, a geometria das bielas de compressão. A instrumentação foi posicionada nas faces dos blocos com extensômetros espaçados de modo a ocuparem boa parte da largura e, conseqüentemente, indicarem as suas geometrias. A análise experimental de blocos sobre duas estacas submetidos à ação de força excêntrica permitiu observar o comportamento das bielas e tirantes que diferem dos observados quando a força é centrada. Também foi analisada a eficiência dos ganchos das barras de aço que compõem os tirantes, verificando-se que os ganchos podem ser omitidos sem prejuízo da segurança estrutural dos blocos. Em função dos resultados obtidos por meio das análises experimental e numérica desenvolveram-se modelos de bielas e tirantes aplicados a blocos sobre duas estacas / The research had as objective to analyze and to argue about the behavior of two pile caps submitted to the action of a centered and eccentric load. A nonlinear three-dimensional numerical analysis of two pile caps was developed. The numerical analysis included the cracking and the influence of the reinforcement in the structural behavior of the pile caps. By the numerical analysis, it was possible to perceive the behavior and the geometric form of the strut, with this understand the model strut-and-tie applied to the two pile caps. The geometry observed in the numerical models analyzed at first differs from the usually suggested by some authors. This project realized experimental tests of piles caps to observe the geometry of the struts. The instrumentation was located in the faces of the pile caps with spaced strain-gages in order to occupy good part of the width and, consequently, indicate its geometry. The experimental analysis of two pile caps submitted to the eccentric load allowed the behavior observation of the strut and tie that differ from the one observed when the load was centered. Also the efficiency of the hooks of the reinforced bar was analyzed, therefore, in the experimental analysis of pile caps already developed, it was verified that the hooks can be omitted without damage of the structural security of the pile caps. For treating the procedure defined in the project, and taking advantage of the experimental analysis realized, it was understood that this requirement can be analyzed and that the results will bring benefits to the project. In function of the results obtained through the experimental and numeric analysis strut-and-tie models were developed to be applied in two pile caps

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.

The interstate highway system is vitally dependent upon current and future bridges. These bridges must be designed economically to continue the serviceability with limited maintenance. For precast bridge construction a portion of the design must consider the bridge connections. Some current connections have proved insufficient in serviceability as there is uncontrolled cracking. In other connections there are uncertainties in the calculations (or lack of calculations) which require design guidelines. This thesis presents design recommendations for precast decking u-bar reinforcement in tension which results from negative moment over a pier. Testing results from the University of Tennessee were analyzed to determine the design recommendations. The calculated capacity of the specimens was determined first by strut and tie modeling by AASHTO and ACI, but was shown to be insufficient. Proposed changes to the current calculation of the strut width as specified in AASHTO and ACI STM methods were discussed in order to match the test results. However, strut and tie modeling demonstrated that the design for the lacer bar was inadequate. Since the strut and tie modeling method resulted in an inaccurate lacer bar size, another method was developed. A triangular shape develops from the flow of forces in the connection joint zone; as a result, a free body diagram (FBD) was developed from the concrete triangular shape. This diagram showed how the forces flow in the in-situ joint as well as how they are resisted. A formula was developed from the FBD to determine the capacity of the joint which accurately reflected the capacities from tests. A FBD was also made of the lacer bar utilizing the forces and geometry calculated from the capacity calculations. A computer analysis program was used to determine the forces in the lacer bar. The lacer bar could then be designed since the required forces to resist (moment and shear) were known. A comparison of the strut and tie model to the triangular method led to the conclusion that both can determine the longitudinal reinforcement spacing, joint overlap length, and concrete strength, but only the triangular method can determine a more sufficient lacer bar size.

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

The present research is conducted to investigate the structural behaviour of continuously supported deep beams made with SCC. A series of tests on eight reinforced two-span continuous deep beams made with SCC was performed. The main parameters investigated were the shear span-to-depth ratio, the amount and configuration of web reinforcement and the main longitudinal reinforcement ratio. 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 rest of the beam fixed on the other two supports. The amount and configuration of web reinforcement had a major effect in controlling the shear capacity of SCC continuous deep beams. The shear provisions of the ACI 318M-11 reasonably predicted the load capacity of SCC continuous deep beams. The strut-and-tie model recommended by different design codes showed conservative results for all SCC continuous deep beams. The ACI Building Code (ACI 318M-11) predictions were more accurate than those of the EC2 and Canadian Code (CSA23.3-04). The proposed effectiveness factor equations for the strut-and-tie model showed accurate predictions compared to the experimental results. The different equations of the effectiveness factor used in upper-bound analysis can reasonably be applied to the prediction of the load capacity of continuously supported SCC deep beams although they were proposed for normal concrete (NC). The proposed three dimensional FE model accurately predicted the failure modes, the load capacity and the load-deflection response of the beams tested.

A pesquisa teve como objetivo analisar e discutir o comportamento de blocos de concreto armado sobre duas estacas submetidos à ação de força centrada e excêntrica. Desenvolveu-se uma análise numérica tridimensional não-linear de blocos de concreto armado sobre duas estacas. A análise numérica levou em consideração a fissuração do concreto e a influência das armaduras no comportamento estrutural dos blocos. Por meio da análise numérica, foi possível perceber o comportamento e a forma geométrica das bielas de compressão, com isso, obteve-se melhor entendimento do modelo de bielas (escoras) e tirantes aplicado a blocos de concreto armado sobre duas estacas. A geometria observada nos modelos numéricos analisados preliminarmente difere da usualmente sugerida por vários autores. Realizou-se investigação experimental de blocos, com o fim principal de observar, de modo mais abrangente, a geometria das bielas de compressão. A instrumentação foi posicionada nas faces dos blocos com extensômetros espaçados de modo a ocuparem boa parte da largura e, conseqüentemente, indicarem as suas geometrias. A análise experimental de blocos sobre duas estacas submetidos à ação de força excêntrica permitiu observar o comportamento das bielas e tirantes que diferem dos observados quando a força é centrada. Também foi analisada a eficiência dos ganchos das barras de aço que compõem os tirantes, verificando-se que os ganchos podem ser omitidos sem prejuízo da segurança estrutural dos blocos. Em função dos resultados obtidos por meio das análises experimental e numérica desenvolveram-se modelos de bielas e tirantes aplicados a blocos sobre duas estacas / The research had as objective to analyze and to argue about the behavior of two pile caps submitted to the action of a centered and eccentric load. A nonlinear three-dimensional numerical analysis of two pile caps was developed. The numerical analysis included the cracking and the influence of the reinforcement in the structural behavior of the pile caps. By the numerical analysis, it was possible to perceive the behavior and the geometric form of the strut, with this understand the model strut-and-tie applied to the two pile caps. The geometry observed in the numerical models analyzed at first differs from the usually suggested by some authors. This project realized experimental tests of piles caps to observe the geometry of the struts. The instrumentation was located in the faces of the pile caps with spaced strain-gages in order to occupy good part of the width and, consequently, indicate its geometry. The experimental analysis of two pile caps submitted to the eccentric load allowed the behavior observation of the strut and tie that differ from the one observed when the load was centered. Also the efficiency of the hooks of the reinforced bar was analyzed, therefore, in the experimental analysis of pile caps already developed, it was verified that the hooks can be omitted without damage of the structural security of the pile caps. For treating the procedure defined in the project, and taking advantage of the experimental analysis realized, it was understood that this requirement can be analyzed and that the results will bring benefits to the project. In function of the results obtained through the experimental and numeric analysis strut-and-tie models were developed to be applied in two pile caps

Esta pesquisa realiza a análise do comportamento estrutural de blocos rígidos de concreto armado sobre duas estacas submetidos à ação de força vertical centrada, com pilares de seções quadradas e retangulares e diferentes taxas de armaduras de pilares. Nestes elementos utilizam-se o método das Bielas e Tirantes para o projeto estrutural, mas normalmente não se considera a influência da seção geométrica dos pilares e suas taxas de armadura no projeto do bloco. Apresenta-se um estudo experimental de doze modelos de blocos sobre duas estacas, na escala 1:2. Foi desenvolvida uma análise numérica tridimensional e não linear, pelo método dos elementos finitos, com o auxílio de um programa de computador. Com a análise experimental e numérica foi investigada a distribuição do fluxo das tensões principais de compressão e tração nos modelos e constataram-se diferenças na transmissão de forças para os blocos quando se altera a taxa de armadura e a seção transversal dos pilares. Esta constatação modifica o modelo de Biela e Tirante inicialmente adotado. As deformações em armaduras construtivas complementares também foram estudadas possibilitando o entendimento do modelo estrutural. Um modelo de Bielas e Tirantes para blocos sobre estaca com pilares alongados foi proposto. / This research presents an analysis of the rigid two-pile caps structural behavior. The models were subjected to force action centered and supported columns with different rate of armor and square and rectangular cross sections. These elements can be rigid or flexible, rigid pile-caps can be sized using the Method of Strut and Tie. In most cases the Method of Strut and Tie and the influence of column reinforcement are not considered in the pile-cap´s structural projects. This research presents an experimental investigation of two-pile caps with the objective of improve criteria structural projects. Twelve rigid two-pile caps were builded using 1:2 scaled models. Three-dimensional numerical analyses using software based on element finite method (FEM) were developed considering the reinforced concrete nonlinear behavior. Using results of experimental analysis and numerical analysis an investigation of the flow distribution of the principal stresses of compression and tension in the models was performed, differences in the transmission of forces to the pile-caps, when changing the reinforcement ratio and the cross section of the columns, were detected. The initial model of strut and tie may be modified due to results. The understanding of the structural model was also possible by analysis of the stirrups and upper constructive reinforcement stress-strain behavior. A strut and tie model for pile-caps with an elongated rectangular column was proposed.