Academic literature on the topic 'Strut-and-tie model design'

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.

Abstract There are many methods for designing pile caps, but there is still no consensus on which one provides the best approach for the practical engineers. In Brazil, many structural designers use the classical Blévot method; however, the applicability of the method has been questioned after the revision of the NBR 6118 standard for design of concrete structures in 2014. To support structural designers, a strut-and-tie model has recently been developed that relates the classical method to the most current concepts of strut-and-tie models. The theoretical bearing capacity of four-pile cap obtained through several strut-and-tie models are compared with experimental tests. The results show that this recently developed model is suitable for the design of deep pile cap.

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.

Introduction: The sandwich joints casted core area with weaker strength concrete of beam, has more advantages than the traditional joints casted core area with higher strength concrete of column, such as the simple construction and quality assurance, while China design codes are too simple about the sandwich joints and have no clear calculation methods. Methods: Due to the scarcity of rational models for predicting the strength of RC beam-column sandwich joints, a modified simplified softened strut-and-tie model suggests a more rational calculation method for the effective compressive strength and the height of the joint concrete based on the simplified softened strut-and-tie. The shear strength of existing tested 15 sandwich interior joints is calculated by using the modified simplified softened strut-and-tie model. Furthermore, the theory results are compared with those of the code method and those of the simplified softened strut-and-tie model. Results and Conclusion: The results indicate that the code method is more conservative, and the modified simplified softened strut-and-tie can more precisely predict the joint shear strength than that of the softened strut-and-tie model and more secure than that of the code method. Thus, the modified simplified softened strut-and-tie model can reasonable reveal the failure mechanism of RC beam-column sandwich interior joints.

The strut-and-tie models are appropriate to design and to detail certain types of structural elements in reinforced concrete and in regions of stress concentrations, called "D" regions. This is a good model representation of the structural behavior and mechanism. The numerical techniques presented herein are used to identify stress regions which represent the strut-and-tie elements and to quantify their respective efforts. Elastic linear plane problems are analyzed using strut-and-tie models by coupling the classical evolutionary structural optimization, ESO, and a new variant called SESO - Smoothing ESO, for finite element formulation. The SESO method is based on the procedure of gradual reduction of stiffness contribution of the inefficient elements at lower stress until it no longer has any influence. Optimal topologies of strut-and-tie models are presented in several instances with good settings comparing with other pioneer works allowing the design of reinforcement for structural elements.

ABSTRACTIn general, the design of the pile cap structure still uses conventional method assuming all regions experience linear strain. However, in reality the strain distribution in the cross section of the structure is not always linear so that a rational analysis method is needed with the assumption that is close to the actual condition using the strut and tie model method. This study aims to determine the behavior of crack pattern in the pile cap designed using the strut and tie model method (SNI 2847:2013 Appendix A) compared to conventional methods (SNI 2847:2013 Article 15). The specimen is the pile cap with three-piles and concentrated load, each of which has three methods. Loading is a static load that is channeled through a column located centric towards the structure of the pile cap. The results show that: the entire test object based on the two methods have flexural crack pattern. The average load capacity of the first crack (Pcr) on the specimen was designed using the strut and tie model and the conventional method were 239.0 kN and 193.7 kN. The average of crack width on the specimen using the strut and tie model and the conventional method were 0.68 mm and 3.88 mm.Keywords: crack pattern, pile cap, three-piles, strut and tie model ABSTRAK Pada umumnya perancangan struktur pile cap masih menggunakan metode konvensional dengan asumsi semua daerah mengalami regangan linier. Akan tetapi pada kenyataannya distribusi regangan pada penampang struktur tidak selalu linier sehingga diperlukan suatu metode analisis yang rasional dengan asumsi yang mendekati kondisi sebenarnya yaitu menggunakan metode strut and tie model. Penelitian ini bertujuan untuk mengetahui perilaku pola retak pada pile cap yang dirancang dengan metode strut and tie model (SNI 2847:2013 Lampiran A) dibandingkan dengan metode konvensional (SNI 2847:2013 Pasal 15). Pada setiap metode terdiri dari tiga buah benda uji berupa pile cap tiga tiang dengan beban sentris. Pembebanan berupa beban statis yang disalurkan melalui kolom yang terletak sentris terhadap struktur pile cap. Hasil pengujian menunjukkan bahwa keseluruhan benda uji berdasarkan kedua metode mempunyai pola retak lentur (flexural crack). Untuk rata-rata kapasitas beban saat retak pertama (Pcr) pada benda uji yang dirancang menggunakan metode strut and tie model dan metode konvensional adalah sebesar 239,0 kN dan 193,7 kN. Kemudian rata-rata lebar retak pada benda uji menggunakan metode strut and tie model dan metode konvensional adalah sebesar 0,68 mm dan 3,88 mm. Kata kunci: pola retak, pile cap, tiga tiang, strut and tie model

Reinforced concrete (RC) corbel is one of a disturbed region of elements of the structure. SNI 2847: 2013 as a guideline from Ministry of Public Works provides the design of RC corbels by the conventional method and with Strut and Tie Model (STM). The aim of this study is to determine and compare the behaviors of corbels experimentally that designed with both methods. The testing was conducted on two series of specimens and each series consisted of two specimens. Group 1 was designed using conventional method while group 2 designed using Strut and Tie Model. The axial column was tested under 50 kN fixed axial loads and corbels was tested under monotonic loads gradually increased up to failure. The results showed that with the provided steel and compressive strength of concrete, the shear capacity using the conventional method by analysis and experimental respectively were 363.164 kN and 345.7 kN, while the shear capacity using Strut and Tie Model by analysis and experimental respectively were 306.953 kN and 299.35 kN. The shear capacity of specimens using conventional method was 13.40 % greater than by using Strut and Tie Model and the shear capacity for each conventional and STM method were 1.9232 and 1.6653 greater than designated load.

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

En stor del av projekteringsskedet är framtagandet av bygghandlingar, främst ritningar i 2D. En modernare metod är istället att samla all information om ett byggnadsprojekt i en samordnad 3D-modell, så kallad BIM-modell. Building Information Modeling (BIM) är en välkänd projekteringsmetod som bygger på att digitala 3D-modeller innehåller tillräcklig information för att beställas och produceras i fysisk form. Modellen består av parametrar som representerar olika egenskaper och när en parameter ändras uppdateras modellen automatiskt. Parametrarna kan nås och modifieras av insticksprogram, så kallade plug-ins som utökar den ursprungliga programvarans funktionalitet med hjälp av programkod. Grafisk programmering är en modern programmeringsmetod med ett visuellt gränssnitt som underlättar för oerfarna användare. Med hjälp av grafisk programmering kan parameterstyrning av 3D-modeller effektiviseras och värdefull tid sparas. Av denna anledning har Dynamo, ett plug-in utvecklat av företaget Autodesk för Revit, studerats för att ta fram ett så kallat skript som automatiserar 3D-modelleringsprocesser i Revit kopplat till placering av armering i pålfundament. Dessutom har möjligheter till standardisering undersökts, samt för- och nackdelar med metoden. I detta examensarbete redogörs för potentialen med Dynamo och de skript som skapats genom en empirisk studie. En enklare fallstudie utfördes för att kunna åskådliggöra graden av tidsbesparing gentemot motsvarande arbete manuellt i Revit. För att komplettera armeringsskripten togs beräkningsmallar fram som, enligt fackverksmetoden och Eurokod 2, försåg skripten med korrekt indata. Resultatet av projektet visar på att Dynamo och grafisk programmering kan effektivisera armeringsplacering i pålfundament. Graden av effektivisering beror på varje enskilt fall, men fallstudien visade på ca 85–90% sparad tid. En generell slutsats pekar mot att ju mer komplicerad utformning av armering desto mer tid finns att spara. Då grafisk programmering bygger på automatisering av arbetsprocesser av upprepande karaktär finns stor potential för att standardisera projektering med hjälp av dynamoskript. Företag kan då skapa rutiner som ökar kontinuitet och kvalitet i sina projekt. Automatiseringen leder även till färre mänskliga fel och utförandet blir effektivare. Uppdragsgivaren uppmanas att vidareutveckla metoden genom att implementera tydliga rutiner vad gäller 3D-modellering med grafisk programmering, samt undersöka möjligheten med automatiserad armering i andra bärande konstruktioner.
Most of the time spent on project planning is dedicated to the development of construction documents, mainly 2D-drawings. A more modern method is to gather all information about a building project in a coordinated 3D-model, so called BIM-model. Building information modelling (BIM) is a well-known design method based on a digital 3D model having enough information to enable procurement work and actual production. The model consists of parameters that represent different properties and when a parameter is changed, the model is updated automatically. These parameters can be accessed and modified through external programs, so called plug-ins that extend the original software’s functionality using program code. Visual programming is a modern programming method which utilizes a visual interface that favours users with little or no experience. Using visual programming, parameter control can be made more efficient and save valuable time. For this reason, Dynamo (a plugin developed by the company Autodesk for Revit), has been studied to create a so-called script that automates 3D modelling processes in Revit linked to placement of reinforcement in pile caps. In addition, possibilities for standardization have been investigated, as well as the advantages and disadvantages of the method. With this project, the potential of Dynamo and the scripts created through an empirical study is described, where a relatively simple case study is carried out in order to illustrate the amount of time saved through visual programming compared to corresponding work manually done in Revit. Furthermore, calculation templates were created, according to the strut and tie model and Eurocode 2, to provide the script in Dynamo with the correct inputs. The result shows that Dynamo and visual programming can make placement of reinforcement in pile caps more efficient. While the degree of efficiency is case dependent, the case study showed an overall 85-90% time saving. A general conclusion suggests that the more complicated rebar designs, the more time there is to be saved. Since visual programming is based on the automation of repetitive processes, there is great potential to standardize structural design with the help of Dynamo scripts. Companies can thus create routines that increase continuity and quality in their projects. The automation also leads to fewer human errors and a more efficient execution. The client is advised to further develop this method by implementing explicit routines regarding 3D modelling with visual programming and investigate the possibilities of automation of reinforcement design in other load-bearing structures.

The finite element method is a powerful analysis tool which has facilitated a better understanding of the behaviour of reinforced concrete structures. Its use in the research field is widespread and complements experimental tests and the development of new analytical models. Its application in practice engineering has permitted to deal with complex elements. However, the general structural engineer is still reluctant to consider finite element modelling for his work as he finds most of these models excessively sophisticated for his needs and knowledge. In particular, complexity of many finite element tools usually derives from the adoption of advanced concrete constitutive models. Implementation of more simple models based on engineering practice could facilitate its use by less experienced finite element users. In structural engineering practice finite element analysis can be of great usefulness to deal with those more problematic elements and/or where the application of traditional analysis methods presents limitations. This includes the so-called D-regions with a 3D behaviour. The strut-and-tie method and the stress field method are consistent and rational tools for the analysis and design of D-regions, but while their application to 2D elements is well covered in literature, its extension to 3D is problematic. This generally explains why excessively conservative assumptions are still common in the design of these elements. Refinement of current analytical and design approaches or the use of finite element analysis could lead to more rational solutions which in turn will reduce material requirements and costs. A 3D nonlinear finite element-based tool was developed in this thesis oriented towards the analysis and design of 3D D-regions by less experienced finite element users. Regarding material modelling, an orthotropic concrete model was adopted to permit the use of uniaxial stress-strain relationships. Only one single parameter, the uniaxial compressive strength of concrete, needs to be defined. Additionally, several aid functions were implemented, among which the following can be highlighted: a comprehensive, embedded reinforcement model to facilitate the introduction of complex rebar geometries; special support and load elements permitting an integrated and simple treatment of the boundary conditions imposed by them; and a simple design algorithm for the automatic determination of the required rebar areas. Three examples of applications to representative 3D D-regions are presented to show the capabilities of the tool. In particular, the analyses of fourteen four-pile caps, three socket base column-to-foundations connections and one anchorage block are described in the third part of the thesis. Results prove that realistic response predictions can be obtained considering relatively simple constitutive models. The capacity of the tool to configure consistent stress field models depending on the reinforcement arrangement is also demonstrated. The generation of rational reinforcement configurations by applying the implemented design algorithm is also shown. A strut-and-tie-based method for the analysis and design of four-pile caps with rectangular geometries is proposed in the fourth part. The method is based on a refined 3D strut-and-tie model and the consideration of three potential modes of failure: exceeding the reinforcement strength, crushing of the diagonal strut at the base of the column with narrowing of the strut and splitting of the diagonal strut due to transverse cracking. The main innovation is that the strut inclination is not fixed as in current strut-and-tie-based design procedures, but determined by maximizing the pile cap strength. The method accounts for strength softening of cracked concrete, compatibility constraints and reinforcement details. Its application to 162 specimens of literature led to very good predictions of the ultimate strength and, to a lesser extent, of the mode of failure.
El método de los elementos finitos es una potente herramienta de análisis que ha facilitado un mejor conocimiento del comportamiento de las estructuras de hormigón armado. Su uso en el ámbito de la investigación está ampliamente extendido. Su aplicación en la práctica ingenieril ha permitido la resolución de elementos complejos. Sin embargo, el ingeniero estructural común todavía es reticente a usar la modelización por elementos finitos ya que considera que la mayoría de estos modelos son excesivamente sofisticados para sus necesidades. La complejidad de muchas herramientas de elementos finitos suele derivarse de la adopción de modelos constitutivos de hormigón avanzados. La implementación de modelos más sencillos podría facilitar su uso por usuarios menos experimentados. En la práctica ingenieril el análisis con elementos finitos puede ser de gran utilidad para tratar aquellos elementos más problemáticos y/o donde la aplicación de los métodos de análisis tradicionales presenta limitaciones. Esto incluye las llamadas regiones D con comportamiento 3D. El método de bielas y tirantes y el método de campos de tensiones son herramientas racionales para el análisis y dimensionamiento de regiones D, pero su extensión a 3D es problemática. Este hecho explica por qué se adoptan todavía hipótesis excesivamente conservadoras en el dimensionamiento de estos elementos. La propuesta de métodos analíticos y de diseño más adecuados o la modelización con elementos finitos podría conducir a soluciones más racionales, lo que a su vez reduciría las necesidades de material y los costes. Como parte de esta tesis se ha desarrollado una herramienta de cálculo no lineal basada en el método de los elementos finitos orientada al análisis y dimensionamiento de regiones D tridimensionales por usuarios con menos experiencia en la modelización con elementos finitos. Se ha adoptado un modelo ortotrópico para el hormigón para permitir el uso de relaciones uniaxiales de tensión-deformación. Sólo es necesario definir un único parámetro, la resistencia a compresión uniaxial del hormigón. Adicionalmente, se han implementado varias funciones de ayuda, entre las que destacan: un modelo de armadura embebida para facilitar la introducción de geometrías de armado complejas; elementos especiales de apoyo y de carga que permiten un tratamiento integral de las condiciones de contorno; y un algoritmo de diseño para la determinación automática del área de armado necesaria. Se presentan tres ejemplos de aplicación a regiones D 3D representativas para mostrar las capacidades de la herramienta. En concreto, en la tercera parte del documento se describen los análisis de catorce encepados, tres cálices de cimentación y un bloque de anclaje. Los resultados muestran que se pueden obtener predicciones bastante realistas considerando modelos constitutivos relativamente sencillos. También se demuestra la capacidad de la herramienta para configurar modelos de campo de tensiones consistentes dependiendo de la configuración de armado. Además se muestra la capacidad del algoritmo de diseño para configurar disposiciones de armado racionales. En la cuarta parte se propone un método para el análisis y dimensionamiento de encepados sobre cuatro pilotes con geometría rectangular. El método se basa en un modelo 3D de bielas y tirantes refinado y la consideración de tres modos de fallo posibles: rotura del acero, aplastamiento de la biela diagonal en la base de la columna con estrechamiento de la misma y splitting de la biela diagonal debido a la fisuración transversal. La principal novedad es que el ángulo de la biela no se fija como en otros modelos, sino que se determina mediante la maximización de la resistencia del encepado. El método considera el debilitamiento de la resistencia del hormigón fisurado, condiciones de compatibilidad de deformaciones y detalles de armado. Su aplicación a 162 especímenes dio luga
El mètode dels elements finits és una potent eina d'anàlisi que ha facilitat un millor coneixement del comportament de les estructures de formigó armat. El seu ús en l'àmbit de la investigació està àmpliament estès. La seua aplicació en la pràctica enginyeril ha permès la resolució d'elements més complexos. No obstant això, l'enginyer estructural comú encara és reticent a fer servir la modelització per elements finits ja que considera que la majoria d'aquests models són excessivament sofisticats per a les seues necessitats i el seu conèixement. En concret, la complexitat de moltes eines d'elements finits sol derivar-se de l'adopció de models constitutius avançats de formigó. La implementació de models més senzills basats en la pràctica enginyeril podria facilitar el seu ús per a usuaris menys experimentats en la modelització amb elements finits. A la pràctica enginyeril l'anàlisi amb elements finits pot ser de gran utilitat per a tractar aquells elements més problemàtics i/o on l'aplicació dels mètodes d'anàlisi tradicionals presenta limitacions. Això inclou les anomenades regions D amb comportament 3D. El mètode de bieles i tirants i el mètode de camps de tensions són eines racionals per a l'anàlisi i dimensionament de regions D, però la seua extensió a 3D és problemàtica. Aquest fet explica per què s'adopten encara hipòtesis excessivament conservadores en el dimensionament d'aquests elements. La proposta de mètodes analítics i de disseny més adequats o la modelització amb elements finits podria conduir a solucions més racionals, amb el que també es reduirien les necessitats de material i els costos. Com a part d'aquesta tesi s'ha desenvolupat una eina de càlcul no lineal basada en el mètode dels elements finits orientada a l'anàlisi i dimensionament de regions D tridimensionals per a usuaris amb menys experiència en la modelització amb elements finits. S'ha adoptat un model ortotròpic per al formigó per permetre l'ús de relacions uniaxials de tensió-deformació. Només cal definir un únic paràmetre, la resistència a compressió uniaxial del formigó. Addicionalment, s'han implementat diverses funcions d'ajuda, entre les quals destaquen: un model d'armadura embeguda per facilitar la introducció de geometries d'armat complexes; elements especials de suport i de càrrega que permeten un tractament integral i senzill de les condicions de contorn; i un algoritme de disseny per a la determinació automàtica de l'àrea d'armat necessari. Es presenten tres exemples d'aplicació a regions D 3D representatives per mostrar les capacitats de l'eina. En particular, en la tercera part del document es descriuen les anàlisis de catorze enceps sobre quatre pilons, 3 calzes de fonamentació i un bloc d'ancoratge. Els resultats mostren que es poden obtenir prediccions prou realistes considerant models constitutius relativament senzills. També es demostra la capacitat de l'eina per configurar models de camp de tensions consistents depenent de la configuració d'armat. A més es mostra la capacitat de l'algoritme de disseny per configurar disposicions d'armat racionals. En la quarta part es proposa un mètode per a l'anàlisi i dimensionament d'enceps sobre quatre pilons amb geometria rectangular. El mètode es basa en un model 3D de bieles i tirants refinat i la consideració de tres modes de fallada possibles: trencament de l'acer, aixafament de la biela diagonal a la base de la columna amb estrenyiment de la mateixa i splitting de la biela diagonal per causa de la fissuració transversal. La principal novetat és que l'angle de la biela no es fixa com en els models actuals de bieles i tirants, sinó que es determina mitjan\c{c}ant la maximització de la resistència de l'encep. El mètode proposat considera el debilitament de la resistència del formigó fissurat, condicions de compatibilitat de deformacions i detalls d'armat. La seua aplicació a 162 espècimens de la liter
Meléndez Gimeno, C. (2017). A finite element-based approach for the analysis and design of 3D reinforced concrete elements and its applications to D-regions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86193
TESIS

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.

As the main topic this thesis describes the design and evaluation of selected reinforced concrete members of the prefabricated reinforced concrete industrial building with administration at ultimate limit state in accordance with applicable standards. Movable overhead crane with carrying capacity of 50 tons is the main distinction of the industrial hall. Lateral frame whit main structural parts which are roof prestressed girder, load-bearing column supporting the overhead crane and drilled pile transferring loads from the upper construction to the load bearing subsoil, is designed in particular. Furthermore, design of the Gerber beam which forms the slab construction in the administrational part of the building is elaborated. Structural design and evaluation of other structures of the building is not part of this thesis.

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.
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碩士
國立臺灣大學
土木工程學研究所
104
The ACI 318-14 design procedure for a coupling beam or a grade beam with clear span-depth ratio less than or equal to 4 , which are considered as deep reinforced concrete members, still has some problems need to be investigated. For example, the ACI approach for a deep coupling beam is argued because it determines the amount of diagonal reinforcement to meet shear demands by ignoring the contribution of concrete, which might cause over-supply of diagonal bars and adverse effects to the coupled wall system. The ACI 318-14 is also criticized for lack of specific provision for an intermediate span-depth ratio coupling beam , as it gives engineers freedom to choose either a diagonal or a conventional reinforcement layout, without knowing the consequences. Besides, the ACI strut-and-tie model approach for a grade beam is quite complicated and may not practical for engineering use. Based on the findings from a six-year experimental and analytical program of previous projects about coupling beams in National Taiwan University from 2010 through 2015, this study continues developing proposed design procedures for coupling beams, which suggest proportioning the amount of flexural reinforcement to meet flexural demand at the Design Based Earthquake (DBE) level. Then, by adopting a capacity concept, the design procedures intend to provide sufficient shear strength at Maximum Considered Earthquake (MCE) level to resist plastic shear demand. In addition, design procedures based on softened strut-and-tie model are developed for grade beams. Five numerical examples of coupling beams and grade beams are also included for illustration

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.
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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.

Abstract Finite element models used in the dynamic analysis of structures benefit from correlation with experimental data at each step in the analytical development. The steps Aircraft Landing Systems has followed in obtaining both modal and operational data for the validation of aircraft wheel, brake, and strut FEA models are discussed in this paper. These steps include the creation of a valid experimental modal model for major components in the structure, correlation of the modal results to tie FE model results, testing of sub-assemblies, and collecting data from dynamometer tests of the system and their correlation to the assembled FE model of the system. Various procedures are described which have been developed and adapted by Aircraft Landing Systems and which enable practical correlation to frequencies as high as 2000 Hz. The application of the procedures are demonstrated with examples from recent testing.

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.

<p>A significant portion of the nation’s aging bridge inventory consists of bridges with deep cap beams which were not designed to carry modern traffic loads. A strength assessment of these bridges is required for accurately predicting their load and deformation capacities. This paper proposes a two-stage strength assessment methodology for deep cap beams based on a nonlinear finite element analysis. To validate the finite element modeling approach, five pier caps experimentally investigated in the literature were analyzed. Crack patterns, load-displacement response, failure modes, and governing critical members were investigated under near collapse conditions. The complete proposed methodology was employed on a case study involving five existing bridges located in Ohio and the predicted capacities were compared with the traditional sectional and strut-and-tie methods. The proposed methodology has the potential to reduce the number of bridges found overloaded using traditional methods, resulting in significant cost savings.</p>