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

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 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.

There exists several different methods that can be used to implement a level of safety when performing non-linear finite element analysis of a structure. These methods are called safety formats and they estimate safety by different means and formulas which are partly discussed further in this thesis. The aim of this master thesis is to evaluate a model uncertainty factor for one safety format method called the estimation of coefficient of variation method (ECOV) since it is suggested to be included in the next version of Eurocode. The ECOV method will also be compared with the most common and widely used safety format which is the partial factor method (PF). The first part of this thesis presents the different safety formats more thoroughly followed by a theoretical part. The theory part aims to provide a deeper knowledge for the finite element method and non-linear finite element analysis together with some beam theory that explains shear mechanism in different beam types. The study was conducted on six beams in total, three deep beams and three slender beams. The deep beams were previously tested in the 1970s and the slender beams were previously tested in the 1990s, both test series were performed in a laboratory. All beams failed due to shear in the experimental tests. A detailed description of the beams are presented in the thesis. The simulations of the beams were all performed in the FEM- programme ATENA 2D to obtain high resemblance to the experimental test. In the results from the simulations it could be observed that the ECOV method generally got a higher capacity than the PF method. For the slender beams both methods received rather high design capacities with a mean of about 82% of the experimental capacity. For the deep beams both method reached low design capacities with a mean of around 46% of the experimental capacity. The results regarding the model uncertainty factor showed that the mean value for slender beams should be around 1.06 and for deep beams it should be around 1.25.

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. / Higher Education Institute in the Libyan Government

No description available.

Condition assessment of existing concrete bridge pier caps using the general shear provisions of the AASHTO LRFD Bridge Design Specification has caused the Georgia Department of Transportation (GDOT) to post a large number of bridges in the State of Georgia. Posting of bridges disrupts the free flow of goods within the region served by the bridge and has a negative economic impact. To prevent structural deterioration, diagonal cracking or failure of concrete pier caps in shear, the GDOT employs an in-situ strengthening technique that utilizes an external vertical post-tensioning system. However, the fundamental mechanics of this system and its effectiveness under service load have not been examined previously. This research examines the behavior of reinforced concrete pier caps that utilize the above strengthening system in a combined analytical and experimental program. In the experimental part of the study, two groups of full-scale reinforced concrete deep beam specimens were tested. The first group consisted of six deep beams with shear span/depth ratios of approximately 1.0, which is typical of bridge pier caps; of these six, two included the external post-tensioning system. In the second group, nine deep beam specimens that included a segment of the column representing the pier were tested; four of those tests included the external post-tensioning system. The tests revealed that the shear capacity computed using the AASHTO LRFD Bridge Design Specifications provided a conservative estimate of the specimen capacity in all but one case when compared to the experimental results. However, the AASHTO strut and tie provisions were found to provide a much closer assessment of the load carrying mechanism in the pier cap than the general shear provisions, in that they were able to predict the load at which yielding of the tension reinforcement occurred as well as the angle of the compression strut. The presence of the column segment in the second group had a significant impact on the failure mechanism developed in the specimen near ultimate load. The stress concentration at the reentrant corner between the pier cap and column interface served as an attractor for the formation of diagonal shear cracks, a mechanism not observed in previous deep beam tests in shear. The research has led to recommendations for improving the design of pier caps and the external post-tensioning system, where required, based on mechanics which are consistent with the results of the experimental program.

Experiments were conducted to investigate the shear behaviour of large deep beams subjected to uniform load. Six tests were performed on specimens with identical cross sections and reinforcing, but under different loading configurations. Variables included: span, degree of cracking prior to loading, proximity to a disturbed region near a reaction, and type of flexural stress on the loaded face. The findings indicate a specific set of variables resulting in unconservative predictions made using a strut-and-tie model for simply-supported beams subjected to uniform load, confirming and validating recent results by other researchers. A fanning strut model is proposed and is shown to provide more conservative results. The emerging trend of high capacity in continuous uniformly-loaded specimens is supported by the experimental results, as is the high capacity of specimens uniformly-loaded on their flexural tension face. Further, the high strength of specimens with suboptimal crack orientations supports recent experimental work.

Experiments were conducted to investigate the shear behaviour of large deep beams subjected to uniform load. Six tests were performed on specimens with identical cross sections and reinforcing, but under different loading configurations. Variables included: span, degree of cracking prior to loading, proximity to a disturbed region near a reaction, and type of flexural stress on the loaded face. The findings indicate a specific set of variables resulting in unconservative predictions made using a strut-and-tie model for simply-supported beams subjected to uniform load, confirming and validating recent results by other researchers. A fanning strut model is proposed and is shown to provide more conservative results. The emerging trend of high capacity in continuous uniformly-loaded specimens is supported by the experimental results, as is the high capacity of specimens uniformly-loaded on their flexural tension face. Further, the high strength of specimens with suboptimal crack orientations supports recent experimental work.

Detta examensarbete vid Luleå tekniska universitet har utförts i samarbete med avdelningen för byggkonstruktionvid det nordiska konsultföretaget Norconsult AB. Arbetet bygger på en önskan från Norconsultatt ta fram en beräkningsmodell för höga balkar i överensstämmelse med Eurokod 2 motsvarande densom finns i BBK 04. Eurokod 2 har endast en knapphändig beskrivning av hur höga balkar bör dimensioneras.Detta skapar frustration och osäkerhet hos konstruktörer. Den tidigare svenska betongnormen,BBK 04, innehöll en tydlig och enkel mer empirisk beräkningsmetod för höga balkar, vilket gav en störresäkerhet vid projekteringen. Arbetet begränsas till att studera enkelt upplagda och kontinuerliga balkar i två spann belastade med enpunktlast mitt i vartdera spannet. Geometrin är densamma för samtliga balkar och armeringsmängdenvarieras tillsammans med brottlasten. Initialt utfördes en litteraturstudie för att erhålla en fördjupad kunskap om området samt att bygga uppen förståelse för teorin för höga balkar och den fackverksmodell som används i Eurokod 2. Vidare presenterasen försöksrapport, Rogowsky et al. (1983), som redovisar en experimentell laboratoriestudie därhöga balkar belastas till brott. Resultaten som presenteras är brottlast, töjning i betong och armering,sprickmönster samt nedböjning. Fyra enkelt upplagda och fyra kontinuerliga balkar väljs ut för vidarejämförelse och analys. Härvid används det ickelinjära beräkningsprogrammet ATENA 2D, där studeradebalkar modelleras. Handberäkningar enligt EK2 och BBK 04 utförs för respektive balk och tillhörandearmeringsmängd beräknas. En maximal brottlast itereras fram för respektive balk och beräkningsmetod (EK2 eller BBK 04). Armeringsmängdensom ges av denna beräkning modelleras i ATENA 2D och motsvarande balk analyseras.Resultaten jämförs sedan. Erhållna resultat sammanställs och jämförs med varandra: Rogowsky et al. (1983), ATENA 2D och handberäkningarnaenligt både Eurokod 2 och BBK 04. Jämförelsen visar att det finns få likheter mellan EK2och BKK 04, med avseende på erhållen armeringsmängd. BBK kräver generellt större armeringsmängdän Eurokod 2. Studien visar att beräkningarna med ATENA 2D stämmer väl överens med laboratorieförsöken.Resultaten visar även att antaganden enligt Eurokod 2 stämmer väl överens med hur de studeradebalkarna beter sig i verkligheten. En enkel beräkningsmodell som motsvarar BBKs konservativa modell är inte möjlig att ta fram inom deramar och begränsningar som finns för detta examensarbete. Istället sammanställs en modell i form av enpunktlista som förtydligar, sammanfattar och exemplifierar den mer verklighetstrogna beräkningsgångenför höga balkar enligt Eurokod 2.