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.

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.

Recent transonic airliner designs have generally converged upon a common cantilever low-wing configuration. It is unlikely that further large strides in performance are possible without a significant departure from the present design paradigm. One such alternative configuration is the strut-braced wing, which uses a strut for wing bending load alleviation, allowing increased aspect ratio and reduced wing thickness to increase the lift to drag ratio. The thinner wing has less transonic wave drag, permitting the wing to unsweep for increased areas of natural laminar flow and further structural weight savings. High aerodynamic efficiency translates into reduced fuel consumption and smaller, quieter, less expensive engines with lower noise pollution. A Multidisciplinary Design Optimization (MDO) approach is essential to understand the full potential of this synergistic configuration due to the strong interdependency of structures, aerodynamics and propulsion. NASA defined a need for a 325-passenger transport capable of flying 7500 nautical miles at Mach 0.85 for a 2010 date of entry into service. Lockheed Martin Aeronautical systems (LMAS), our industry partner, placed great emphasis on realistic constraints, projected technology levels, manufacturing and certification issues. Numerous design challenges specific to the strut-braced wing became apparent through the interactions with LMAS, and modifications had to be made to the Virginia Tech code to reflect these concerns, thus contributing realism to the MDO results. The SBW configuration is 9.2-17.4% lighter, burns 16.2-19.3% less fuel, requires 21.5-31.6% smaller engines and costs 3.8-7.2% less than equivalent cantilever wing aircraft. / Master of Science

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

In transonic flow, the aerodynamic interference that occurs on a strut-braced wing airplane, pylons, and other applications is significant. The purpose of this work is to provide relationships to estimate the interference drag of wing-strut, wing-pylon, and wing-body arrangements. Those equations are obtained by fitting a curve to the results obtained from numerous Computational Fluid Dynamics (CFD) calculations using state-of-the-art codes that employ the Spalart-Allmaras turbulence model. In order to estimate the effect of the strut thickness, the Reynolds number of the flow, and the angle made by the strut with an adjacent surface, inviscid and viscous calculations are performed on a symmetrical strut at an angle between parallel walls. The computations are conducted at a Mach number of 0.85 and Reynolds numbers of 5.3 and 10.6 million based on the strut chord. The interference drag is calculated as the drag increment of the arrangement compared to an equivalent two-dimensional strut of the same cross-section. The results show a rapid increase of the interference drag as the angle of the strut deviates from a position perpendicular to the wall. Separation regions appear for low intersection angles, but the viscosity generally provides a positive effect in alleviating the strength of the shock near the junction and thus the drag penalty. When the thickness-to-chord ratio of the strut is reduced, the flowfield is disturbed only locally at the intersection of the strut with the wall. This study provides an equation to estimate the interference drag of simple intersections in transonic flow. In the course of performing the calculations associated with this work, an unstructured flow solver was utilized. Accurate drag prediction requires a very fine grid and this leads to problems associated with the grid generator. Several challenges facing the unstructured grid methodology are discussed: slivers, grid refinement near the leading edge and at the trailing edge, grid convergence studies, volume grid generation, and other practical matters concerning such calculations. / Ph. D.

For controller design, design of experiments, and other dynamic simulation purposes there is a need to be able to predict the dynamic response and joint reaction forces of a quarter-car suspension. This need is addressed by this study through development and system identification of both a linear and a non-linear multibody dynamics McPherson strut quarter-car suspension model. Both models are developed using a method customary to multibody dynamics so that the same numerical integrator can be used to compare their respective performances. This method involves using the Lagrange multiplier form of the constrained equations of motion to assemble a set of differential algebraic equations that characterize each model's dynamic response. The response of these models to a band-limited random tire displacement time array is then simulated using a Hilber-Hughes-Taylor integrator. The models are constructed to match the dynamic response of a state-of-the-art quarter-car test rig that was designed, constructed, and installed at the Institute for Advanced Learning and Research (IALR) for the Performance Engineering Research Lab (PERL). Attached to the experimental quarter-car rig was the front left McPherson strut suspension from a 2004 Porsche 996 Grand American Cup GS Class race car. This quarter-car rig facilitated acquisition of the experimental reference data to which the simulated data is compared. After developing these models their optimal parameters are obtained by performing system identification. The performance of both models using their respective optimal parameters is presented and discussed in the context of the basic linearity of the experimental suspension. Additionally, a method for estimating the loads applied to the experimental quarter-car rig bearings is developed. Finally, conclusions and recommendations for future research and applications are presented. / Master of Science

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 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.

The main topic of this thesis concerns the behavior of concrete pile cap supported by four piles with two varying positions of longitudinal reinforcements. The positions include top of piles and bottom of the pile cap. For this purpose, non-linear finite element models of a pile cap are created using software ATENA 3D. The goal was to observe which position of reinforcement yields the higher bearing capacity and to observe the failure modes in the models. To achieve the above goals, a short review of theoretical background concerning shear phenomena is performed. This, in order to enhance the knowledge regarding shear stresses, shear transfer mechanism, factors affecting shear capacity, modes of shear failure and relate them to the behavior of pile cap. Furthermore, the calculation of shear resistance capacity based on Eurocode 2 using strut and tie method and sectional approach is presented. The numerical analysis started by creating four pile cap models in ATENA 3D. The difference between the models being the position and ratio of longitudinal reinforcement. The purpose behind two reinforcement ratios were to observe the behavior of pile cap model in two cases: a) when failure occurs prior to yielding of reinforcement; b) when failure occurs while reinforcement is yielding. The models are then analyzed using software ATENA Studio. The results revealed that placing the reinforcement on top of piles in case (a) increased the capacity of the model by 23.5 % and in case (b) increased the capacity by 18.5 %. This because the tensile stresses were found to be concentrated on top of piles rather than the bottom of the pile cap. The final failure mode in the model with top reinforcement position was crushing of the inclined compressive strut at the node beneath the column and in the model with bottom reinforcement position, the splitting of the compressive strut due to tensile stresses developed perpendicular to the inclined strut. The potential advantage of placing the reinforcement at the bottom were a better crack control in serviceability limit state and a slightly less fragile failure mode compared to the top position of reinforcement. A parametric study was performed in the model as well to observe the effects of various parameters on the results obtained. It was found that fracture energy had the most significant effect on the results obtained. Finally, a comparison between the results of numerical analysis and analytical design approaches based on strut and tie method and sectional approach was performed. The comparison reveals that the design values obtained based on strut and tie method for the model were very conservative. In particular, the equation for the strength of inclined compressive strut based on Eurocode 2 was very general. / Det huvudsakliga ämnet för den här avhandlingen handlar om beteendet hos pålfundament som stöds av fyra pålar med två olika positioner av längsgående armering. Positionerna inkluderar toppen av pålarna och botten av slagdynan. För detta ändamål skapas icke-linjära finita elementmodeller av en slagdyna med mjukvaran ATENA 3D. Målet var att observera vilket armeringsläge som ger den högre bärkapaciteten och att identifiera brottmekanismen i modellerna. För att uppnå ovanstående mål utförs en kort genomgång av teoretisk bakgrund rörande skjuvningsfenomen. Detta för att förbättra kunskapen om skjuvspänningar, skjuvöverföringsmekanism, faktorer som påverkar skjuvkapacitet, skjuvbrott och relaterar dem till beteendet hos slagdynan. Beräkningen av skjuvmotståndet baserad på Eurocode2 med hjälp av Srut and tie-metod och sektionsmetod. Den numeriska analysen började med att skapa fyra pålfundament i ATENA 3D. Skillnaden mellan modellerna är positionen och förhållandet mellan längsgående armering. Syftet bakom två armeringsförhållanden var att observera beteendet hos slagdynan i två fall: a) när brott inträffar innan armering plasticeras; b) när brott inträffar medan armeringen plasticeras. Modellerna analyseras sedan med hjälp av programvaran ATENA Studio. Resultaten visade att placering av armeringen ovanpå pålarna i fall a) ökade modellens kapacitet med 23,5% och i fall (b) ökade kapaciteten med 18,5%. Detta på grund av att dragspänningarna visade sig vara koncentrerade på toppen av pålarna snarare än på botten av slagdynan. Det slutliga brottet i modellen med topparmeringsposition var krossning av det lutande tryckstaget vid noden under pelaren. I modellen med bottenarmeringsposition delades kompressionsstaget på grund av dragspänningar vinkelrätt mot det lutande staget. The potential advantage of placing the reinforcement at the bottom were a better crack control and slightly less fragile failure mode compared to the top position of reinforcement. En parametrisk studie genomfördes också i modellen för att observera effekterna av olika parametrar på de erhållna resultaten. Det visade sig att brottenergi hade den mest signifikanta effekten på de erhållna resultaten. Slutligen genomfördes en jämförelse mellan resultaten från numerisk analys och analytiska designmetoder baserade på strut and tie-metoden och sektionsmetoden. Jämförelsen avslöjar att de designvärden som erhölls baserat på strut and tie-metoden för modellen var mycket konservativa. I synnerhet var ekvationen för kapaciteten hos det lutande tryckstag baserad på Eurocode 2 mycket generell.