Academic literature on the topic 'Strut-an-tie model'

The failure behavior of a reinforced concrete corbel is complicated due to the shear span-to-effective depth ratio, reinforcement patterns, load conditions, and material properties. In this study, an optimum first-order indeterminate strut-and-tie model that reflects all characteristics of the failure behavior is proposed for the rational design of reinforced concrete corbels with a shear span-to-effective depth ratio of less than 1.0. A load distribution ratio that transforms the indeterminate strut-and-tie model into a determinate model is also developed to help structural designers design reinforced concrete corbels using the strut-and-tie model methods of current design codes. For the development of the load distribution ratio, a material nonlinear finite element analysis of the proposed first-order indeterminate strut-and-tie model was conducted repeatedly by changing the combination of primary design variables of the corbels. To examine the validity of our results, the ultimate strengths of 294 reinforced concrete corbels tested to failure by other investigators were predicted using the proposed strut-and-tie model with the load distribution ratio, the existing determinate strut-and-tie models representing arch and truss load transfer mechanisms, and the American Concrete Institute 318 conventional design method based on a shear friction theory. The ultimate strengths predicted by the proposed strut-and-tie model agreed fairly well with the experimental results. The ratio of the experimental strength to the predicted strength (and coefficient of variation) was 1.09 (28.0%), implying that the proposed strut-and-tie model can represent the load transfer mechanisms of corbels most appropriately.

The strut-and-tie method is a rational approach to structural concrete design that results in a uniform and consistent design philosophy. A strut-and-tie model has been developed to model the punching-shear behaviour of thick concrete plates. This model provides a quick and simple approach to check the punching-shear behaviour. Thick concrete slabs (250–500 mm) without shear reinforcement can exhibit brittle shear failure under a central force and an unbalanced moment. Shear reinforcement has proven to be very effective in preventing such failures. The developed strut-and-tie model has also been used to evaluate the minimum shear reinforcement required to prevent brittle shear failure of two-way slabs in the vicinity of concentrated loads. The strut-and-tie model for symmetric punching consists of a “bottle-shaped” compressive zone in the upper section of the slab depth, leading to a “rectangular-stress” compressive zone in the lower section of the slab depth. Inclined shear cracking develops in the bottle-shaped zone prior to failure in the lower zone. Cracking in the bottle-shaped zone is related to the splitting tensile strength of concrete.

The aim of this study was to investigate the dynamic shear failure behavior of RC beams under rapid loading through an experimental study and also to set up a strut-and-tie model with loading rate effect to predict the dynamic shear resistance of RC beams. Thus, rapid loading test with 24 RC beams with a shear span-to-deep ratio of 1.9 was performed, in which shear reinforcement ratio and loading rate were variable. All of the RC beams exhibited shear compression failure. Although the shear resistance increases with increasing loading rate, the influence of loading rate on the shear resistance clearly depends on shear reinforcement ratio. The strut-and-tie model with loading rate effect was finally developed, in which the thickness of the compression strut was formulated to be increased with an increase in loading rate. The developed strut-and-tie model was good agreement with the experimental results.

Prestressed tendon constraint partial compression concrete is a new approach to solve the phenomenon of insufficient bearing capacity in partial compression concrete members .The keystone of Strut-and-tie theory is presented.The development of strut-and-tie model is in-depth analyzed based on the description of the stress distribution in the members , the author considers that this theory can yet be regard as an ideal calculation method in partial compression members which is constrained by prestressed tendon or steel mesh.

B-Regions are parts of the structure in which Bernoulli's principle of straight-line strain is used. D-Regions are parts of the structure with a complicated variation in strain. In essence, D-Regions contain the parts of structure which are near to the concentrated forces or steep changes in geometry which are so-called geometrical discontinuities or static discontinuities. Strut-and-Tie Model (STM) is one of the best models to analyse the D-regions. Nevertheless, according to the existing literature, there are still some challenges about STM which are addressed in this paper. STM and its details are investigated to show its common challenges presents some recommendations to overcome these challenges. According to this review, the major challenges in STM are related to the strut effectiveness factor, static uncertainties of STM, strain compatibility, and anchorage requirements in STM. The scope of this research is confined to the two dimensional STM.

By briefly introducing the main steps of using strut-and-tie (STM) , this paper showing the preliminary calculation process. In this paper, defining D-region is the very first step in design.Then paper gives the method to calculate the reinforcement needed to meet required tie capacities. In addition, checking the room for struts is also an important step in the calculation. Since it can examine the correctness of the STM designed by engineer.

A direct strut-and-tie model to calculate the ultimate shear strength of structural walls based on an interactive mechanical model (C.Y.Tang et al.) is presented. Two common failure modes, namely, diagonal splitting and concrete crushing, are examined in this paper. Ultimate shear strengths of structural walls are governed by both the transverse tensile stresses perpendicular to the diagonal strut, and the compressive stresses in the diagonal strut. Such proposed model is verified aganist three experimental case studies of structural walls. Generally, predictions by the proposed model are not only accurate and consistent in each case study, but also conservative.

Abstract : Deep reinforced concrete beams are commonly used as transfer girders or bridge bents, at which its safety is often crucial for the stability of the whole structure. Such elements are exposed to the aggressive environment in northern climates causing steel-corrosion problems due to the excessive use of de-icing salts. Fiber-reinforced polymers (FRP) emerged as non-corroded reinforcing materials to overcome such problems in RC elements. The present study aims to address the applicability of concrete deep beams totally reinforced with FRP bars. Ten full-scale deep beams with dimensions of 1200 × 300 × 5000 mm were constructed and tested to failure under two-point loading. Test variables were shear-span depth ratio (equal to 1.47, 1.13, and 0.83) and different configurations of web reinforcement (including vertical and/or horizontal web reinforcement). Failure of all specimens was preceded by crushing in the concrete diagonal strut, which is the typical failure of deep beams. The test results indicated that, all web reinforcement configurations employed in the tested specimens yielded insignificant effects on the ultimate strength. However, strength of specimens containing horizontal-only web reinforcement were unexpectedly lower than that of specimens without web reinforcement. The web reinforcement’s main contribution was significant crack-width control. The tested specimens exhibited reasonable deflection levels compared to the available steel-reinforced deep beams in the literature. The development of arch action was confirmed through the nearly uniform strain distribution along the length of the longitudinal reinforcement in all specimens. Additionally, the basic assumption of the strut-and-tie model (STM) was adequately used to predict the strain distribution along the longitudinal reinforcement, confirming the applicability of the STM for FRP-reinforced deep beams. Hence, a STM based model was proposed to predict the strength of FRP-reinforced deep beams using the experimental data, in addition to the available experimentally tested FRP-reinforced deep beams in the literature. Assessment of the available STMs in code provisions was conducted identifying the important parameters affecting the strut efficiency factor. The tendency of each parameter (concrete compressive strength, shear span-depth ratio, and strain in longitudinal reinforcement) was individually evaluated against the efficiency factor. Strain energy based calculations were performed to identify the appropriate truss model for detailing FRP-reinforced deep beams, hence, only four specimens with vertical web reinforcement exhibited the formation of two-panel truss model. The proposed model was capable to predict the ultimate capacity of the tested deep beams. The model was also verified against a compilation of a data-base of 172 steel-reinforced deep beams resulting in acceptable level of adequacy. The ultimate capacity and performance of the tested deep beams were also adequately predicted employing a 2D finite element program (VecTor2), which provide a powerful tool to predict the behavior of FRP-reinforced deep beams. The nonlinear finite element analysis was used to confirm some hypotheses associated with the experimental investigations.
Résumé : Les poutres profondes en béton armé (BA) sont couramment utilisées comme poutre de transfert ou coude de pont, comme quoi sa sécurité est souvent cruciale pour la sécurité de l’ensemble de la structure. Ces éléments sont exposés à un environnement agressif dans les climats nordiques causant des problèmes de corrosion de l’acier en raison de l’utilisation excessive de sels de déglaçage. Les polymères renforcés de fibres (PRF) sont apparus comme des matériaux de renforcement non corrodant pour surmonter ces problèmes dans les BA. La présente étude vise à examiner la question de l'applicabilité des poutres profondes en béton complètement renforcées de barres en PRF. Dix poutres profondes à grande échelle avec des dimensions de 1200 × 300 × 5000 mm ont été construites et testées jusqu’à la rupture sous chargement en deux points. Les variables testées comprenaient différents ratios de cisaillement porté/profondeur (égal à 1.47, 1.13 et 0.83) ainsi que différentes configurations d’armature dans l’âme (incluant un renforcement vertical avec ou sans renforcement horizontal). La rupture de tous les spécimens a été précédée par l’écrasement du béton dans le mât diagonal, ce qui est la rupture typique pour les poutres profondes en BA. Les résultats ont révélé que toutes les configurations de renforcement de l’âme employées dans les spécimens d'essais avaient un effet négligeable sur la résistance ultime. Toutefois, la résistance des spécimens contenant uniquement un renforcement horizontal était étonnamment inférieure à celle des spécimens sans renforcement. La contribution principale du renforcement de l’âme était dans le contrôle de la largeur de fissuration. Les spécimens examinés présentaient une déflexion raisonnable par rapport à ce qui est disponible pour les poutres profondes renforcées en acier dans la littérature. Le développement de l'effet d'arche a été confirmé par la distribution quasi uniforme des déformations le long du renforcement longitudinal dans tous les spécimens. En outre, l'hypothèse de base du modèle des bielles et tirants (MBT) a été utilisée adéquatement pour prédire la distribution de déformation le long du renforcement longitudinal, confirmant l'applicabilité du MBT pour les poutres profondes armées de PRF. Par conséquent, un modèle basé sur un MBT a été proposé afin de prédire la résistance des poutres profondes renforcées de PRF en utilisant les données expérimentales en plus de la mise à l'épreuve expérimentalement des poutres profondes renforcées de PRF trouvées dans la littérature. Une évaluation des MTB disponibles dans les dispositions des codes a été menée afin de déterminer les paramètres importants affectant le facteur d'efficacité de la bielle. La tendance de chaque paramètre (la résistance à la compression du béton, le ratio de cisaillement porté/profondeur, et la déformation dans le renforcement longitudinal) a été évaluée individuellement contre le facteur d'efficacité. Des calculs basés sur l’énergie des déformations ont été effectués pour identifier le modèle de treillis approprié afin de détailler les poutres profondes renforcées de PRF. Par conséquent, seulement quatre spécimens avec un renforcement vertical dans l’âme présentaient la formation de modèles avec deux panneaux de treillis. Le modèle proposé a été capable de prédire la capacité ultime des poutres profondes testées. Le modèle a également été vérifié contre une base de données de 172 poutres profondes renforcées en acier aboutissant en un niveau acceptable de pertinence. La capacité ultime et la performance des poutres profondes testées ont été également adéquatement prédites employant un programme d'éléments finis en 2D (VecTor2), ce qui fournira un puissant outil pour prédire le comportement des poutres profondes renforcées de PRF. L'analyse non linéaire par éléments finis a été utilisée afin de confirmer certaines hypothèses associées à l'étude expérimentale.

Steel and concrete construction can still be regarded as two distinct industrial sectors leading to separated design procedures. Even steel-concrete composite buildings remain designed as steel structures, with a limited benefit of the presence of concrete slabs. For some years however, a more integrated design between both materials is investigated. It tries to combine them in order to take advantage from their respective qualities : the high resistance of the steel on one hand and the low cost and good fire resistance of the concrete on the other hand, for example. One of the advantages of the concrete is also the easiness in the fabrication of joints, thanks to the monolithic nature of the concrete cast in place, whereas the metallic joints by bolting or welding ask for more technical work, and represent a non-negligible part of the cost of a structure. It is therefore rather natural, in a hybrid concrete-steel conception, to try to use this advantage of the concrete. In this context, this article presents a work that was made in the RFCS SMARTCOCO project. It focuses on the design of the support of a steel secondary beam crossing a primary beam in concrete, by simple direct contact. On the basis of an experimental campaign comprising five full-scale tests, the angle of diffusion of the forces and the distribution of the stresses in the stirrups are studied and a specific strut-and-tie model is developed. Specimens of this campaign consist of a simply supported concrete beam crossed in its middle by a steel profile, with or without stiffeners, loaded by two jacks, one at each end of the steel profile. First the experimental campaign is described. Then, internal stresses are compared with the predictions of a strut and tie model deduced from elastic stress trajectories. Finally, simplified design guidance is deduced.

Nuclear containments serve the critical function of providing a leak proof boundary for containment of radiation in nuclear power plants. The containments are, generally, steel, reinforced concrete or prestressed concrete depending upon the diameter and internal design pressure. Prestressed concrete containments are used in large nuclear containments with significant design internal pressure. In these situations, the externally applied prestressing serves to counter internal design pressure due to LOCA (loss of coolant accident) and other accident loads thus reducing the required thickness and reinforcement demand. The prestressing tendons are placed in sheathing within the concrete. After the concrete achieves its required strength, the tendons are stretched and locked off against the ends of the concrete called anchorage zones. These anchorage zones are thus subjected to substantial compressive and splitting stresses and need to be properly designed and detailed. Since anchorage zones are the primary location of the prestressing force transfer to concrete, they experience very large and localized bearing and splitting stresses which can have significant safety and structural consequences for the containment integrity. Simple analysis based on strut-and-tie model is generally used for design of prestressed concrete anchorage zones. But because of the stress concentrations and potential impact to structural integrity, it is prudent to utilize detailed finite element method to verify and/or substantiate the results from simple analysis. The finite element (FE) analysis of tendon anchorage zone requires a refined mesh in order to capture the geometry of details surrounding tendons. This paper presents a detailed and practical finite element model used to perform a comprehensive stress analysis of an anchorage zone of a large post-tensioned containment. Both local and general anchorage zones are evaluated. A fictitious case of tendon anchorage zone is established as an example case based on typical parameters of nuclear plants. A 3D finite element model is then developed using ANSYS Version 13.0, in which the effect of tendon sleeve / sheathing into concrete is modeled explicitly. This paper also discusses anchorage zone analysis approaches in various state-of-the-practice codes and standards using hand calculations. The result of finite element analysis are compared with analyses using various hand calculation approaches. In particular, importance of adequate reinforcement design and detailing in anchorage regions is discussed based on the stress profiles from FE analysis and compared with hand calculation methods. It is concluded that a detailed finite element evaluation of anchorage regions is necessary to develop a level of confidence required for ensuring safety and integrity of nuclear containments. The FE modeling also serves as verification for results from simple hand calculation methods.