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.

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

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

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

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.