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<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>

Master of Science / Department of Architectural Engineering and Construction Science / Kimberly W. Kramer / Strut-and-Tie models are useful in designing reinforced concrete structures with discontinuity regions where linear stress distribution is not valid. Deep beams are typically short girders with a large point load or multiple point loads. These point loads, in conjunction with the depth and length of the members, contribute to a member with primarily discontinuity regions. ACI 318-08 Building Code Requirements for Structural Concrete provides a method for designing deep beams using either Strut-and-Tie models (STM) or Deep Beam Method (DBM). This report compares dimension requirements, concrete quantities, steel quantities, and constructability of the two methods through the design of three different deep beams. The three designs consider the same single span deep beam with varying height and loading patterns. The first design is a single span deep beam with a large point load at the center girder. The second design is the deep beam with the same large point load at a quarter point of the girder. The last design is the deep beam with half the load at the midpoint and the other half at the quarter point. These three designs allow consideration of different shear and STM model geometry and design considerations. Comparing the two different designs shows the shear or cracking control reinforcement reduces by an average 13% because the STM considers the extra shear capacity through arching action. The tension steel used for either flexure or the tension tie increases by an average of 16% from deep beam in STM design. This is due to STM taking shear force through tension in the tension reinforcement through arching action. The main advantage of the STM is the ability to decreased member depth without decreasing shear reinforcement spacing. If the member depth is not a concern in the design, the preferred method is DBM unless the designer is familiar with STMs due to the similarity of deep beam and regular beam design theory.

Dans le domaine des structures en Béton Armé (BA) et plus spécifiquement, lors de la conception d'éléments non-flexibles tels que les corbeaux, les poutres bayonets et les poutres profondes, la Méthode Bielle-Tirant (MBT) présente des avantages par rapport aux algorithmes classiques de calcul de ferraillage basé sur l'analyse FE (par exemple Wood-Armor ou Capra-Maury).La Methode Bielle-Tirant reste une alternative adaptée pour la conception de structures en béton présentant un comportement élastique ou plastique dont le cadre d'application est bien défini dans les codes de conception des structures en béton comme les EuroCodes et les spécifications de conception des ponts AASHTO-LRFD.Néanmoins, cette méthode présente l'inconvénient majeur de nécessiter un investissement important en ressources humaines ou en capacité de calcul pour, respectivement, son application manuelle ou une approche automatique par optimisation de topologie.Le document propose une alternative légère, en termes d'itérations requises, à l'automatisation de la MBT, qui part de l'affirmation que les entretoises résultantes et les attaches d'un modèle ST approprié peuvent être distribuées selon la direction des contraintes principales, $sigma_{III}$ et $sigma_{I}$, obtenus à partir d'un planaire modèle aux EF / Within the field of Reinforced Concrete (RC) structures and more specifically, at the design of non-flexural elements such as corbels, nibs, and deep beams, the rational procedure of conception and justification referred as Strut-and-Tie Method (STM) has shown some advantages over classical algorithms of reinforcement computation based on FE analysis (eg. Wood-Armer or Capra-Maury).The STM remains a suitable alternative for the design of concrete structures presenting either elastic or plastic behaviour whose application framework is well defined in concrete structures’ design codes like the EuroCodes and the AASHTO-LRFD Bridge Design Specifications.Nevertheless, this method has the main inconvenient of requiring a high amount of resources investment in terms of highly experienced personal or in terms of computational capacity for, respectively, its manual application or an automatic approach through topology optimisation.The document proposes a light alternative, in terms of required iterations, to the automation of the STM, which starts from the statement that the resultant struts and ties of a suitable ST model can be distributed according to the direction of the principal stresses, $sigma_{III}$ and $sigma_{I}$ , obtained from a planar or a three-dimensional FE model

Construction practices are constantly evolving in order to adapt to physical locations and economic conditions. These adaptations may result in more cost-effective designs, but may also come at a cost of strength. In masonry shear walls, it is becoming more common to reduce the amount of grouting from every cell to only those with reinforcement, a practice known as partial-grouting. Partially-grouted masonry responds differently and in a more complex matter to lateral loads as compared to fully-grouted masonry. The response is made even more complex by wall discontinuities in the form of openings. The main objective of this study is to validate the strut-and-tie procedure for the in-plane lateral strength prediction of partially-grouted, multistory, reinforced concrete masonry walls with openings. The research included testing six three story, half-scale masonry shear walls. Half of the walls had door openings while the other half had window openings. The configurations were selected to represent typical walls in multi-story buildings. The measured lateral strength was compared to estimations from the equations in the US masonry code and to those from an equivalent truss model and a strut-and-tie model. The results show that the U.S. masonry code equations over predicts while the equivalent truss model under predicts the lateral strength of the walls. The results further show that the strut-and-tie model is the most accurate method for lateral strength prediction and is able to account for wall openings and partial-grouting.

Several recently built inverted-T bent caps in Texas have shown significant inclined cracking triggering concern about current design procedures for such structures. The repair of such structures is very costly and often requires lane closures. For these reasons TxDOT funded Project 0-6416 aimed at obtaining a better understanding of the structural behavior of inverted-T bent caps and developing new design criteria to minimize such cracking in the future. Several tasks of the aforementioned project are addressed in this dissertation with particular focus on developing design criteria for strength and serviceability of inverted-T bent caps. Literature review revealed a scarcity of experimental investigation of inverted-T specimens. As part of this dissertation, an inverted-T database was assembled with experimental results from the literature and the current project. An extensive experimental program was completed to accomplish the objectives of the project with thirty one full-scale tests conducted on inverted-T beams. Experimental parameters varied in the study were: ledge length, ledge depth, web reinforcement, number of point loads, web depth, and shear span-to-depth ratio. The dissertation focuses on the effects of ledge length, ledge depth, number of point loads, and developing design criteria for strength and serviceability of inverted-T beams. Most inverted-T bent caps in Texas are designed using the traditional empirical design procedures outlined in the TxDOT bridge design manual LRFD (2011 current version) that follows closely the AASHTO LRFD bridge design specifications (2012 current version). Given the observed cracking in inverted-T bent caps, the accuracy and conservatism of the traditional design methods were evaluated based on experimental results. The accuracy and conservatism of STM design provisions recently developed in a TxDOT study (TxDOT Project 0-5253, Strength and Serviceability Design of Reinforced Concrete Deep Beams) were also evaluated. / text

The research conducted was sponsored by JVI of Pittsfield, Massachusetts. JVI has developed a steel embedded connection, referred to as a shooter. The shooter is provided in capacities, a 40 kip capacity shooter and a 50 kip capacity shooter. This steel connection is embedded near the end of a double-tee prestressed girder. Double-tee prestressed girders are a primary component used in the construction of parking garages. Typical double-tee lengths are 60 to 75 feet; however, for this research 20 ft long segments were cast and tested with the shooter installed. This project had three main goals. The first goal was to develop a preliminary design for the reinforcement around the shooter and test the shooters' capacity in the laboratory to determine if the stated capacity was correct. Four different designs were created, two designs for the 40 kip capacity shooter and 2 designs for the 50 kip capacity shooter. Each design was placed in one stem of the double-tee and tested at the laboratory. Results from these tests indicate that that each specimen achieved the stated capacity. However, failure was not a connection failure but a shear bond failure. The second goal was to take the information gathered from testing and develop a design model that could be used for other situations for this type of connection. The design model was created according to the guidelines in the ACI 318-08 code. Two different methods were used, a strut-and-tie model and a modified ACI code approach. From these designs it was determined that the strut-and-tie model should be used for the design of these connections; however, more research needs to be done before using the modified ACI code approach. The final goal was to determine if finite element analysis could be used to determine if the load at which large cracks that immediately proceed failure occur could be predicted. From this analysis it was determined that a load range could be predicted in which a crack could form as well as a range of what the transfer length of the strands could be. / Master of Science

Precast/Prestressed concrete girders are commonly used in bridge construction in the United States. The application and diffusion of the prestress force in a pretensioned girder causes a vertical tension force to develop near the end of the beam. Field surveys of the beam ends of pretensioned bridge girders indicate that many of the PCBT beams used in the Commonwealth of Virginia develop cracks within the anchorage zone region. The lengths and widths of these cracks range from acceptable to poor and in need of repair. Field observations also indicate deeper cross sections, very heavily prestressed sections, and girders with lightweight concrete tend to be most susceptible to crack formation. This research examined a new strut-and-tie based design approach to the anchorage zone design of the PCBT bridge girders used in Virginia. Case study girders surveyed during site visits are discussed and used to illustrate the nature of the problem and support the calibration of the strut-and-tie based model. A parametric study was conducted using this proposed design model and the results of this study were consolidated into anchorage zone design tables. The results of the parametric study were compared to the results obtained using existing anchorage zone design models, international bridge codes, and standard anchorage zone details used by other states. A set of new standard details was developed for the PCBT girders which incorporates elements of the new design approach and is compatible with the anchorage zone design aids. A 65 ft PCBT-53 girder was fabricated to verify the new strut-and-tie based design model. This girder contained anchorage zone details designed with the new model. The new anchorage zone details were successful at controlling the development of anchorage zone cracks. The new design approach is recommended for implementation by the Virginia Department of Transportation. / Master of Science

Yes / Test results of 24 reinforced concrete continuous deep beams are reported. The main variables studied were concrete strength, shear span-to-overall depth ratio (a/h) and the amount and configuration of shear reinforcement. The results of this study show that the load transfer capacity of shear reinforcement was much more prominent in continuous deep beams than in simply supported deep beams. For beams having an a/ h of 0.5, horizontal shear reinforcement was always more effective than vertical shear reinforcement. The ratio of the load capacity measured and that predicted by the strutand-tie model recommended by ACI 318-05 dropped against the increase of a/h. This decrease rate was more remarkable in continuous deep beams than that in simple deep beams. The strut-and-tie model recommended by ACI 318-05 overestimated the strength of continuous deep beams having a/ h more than 1.0.

Yes / This paper reviews the application of the plasticity theory to reinforced concrete deep beams. Both the truss analogy and mechanism approach were employed to predict the capacity of reinforced concrete deep beams. In addition, most current codes of practice, for example Eurocode 1992 and ACI 318-05, recommend the strut-and-tie model for designing reinforced concrete deep beams. Compared with methods based on empirical or semi-empirical equations, the strut-and-tie model and mechanism analyses are more rational, adequately accurate and sufficiently simple for estimating the load capacity of reinforced concrete deep beams. However, there is a problem of selecting the effectiveness factor of concrete as reflected in the wide range of values reported in the literature for deep beams.