Shear force and torsion in reinforced concrete beam elements: theoretical analysis based on Brazilian Standard Code ABNT NBR 6118:2007

Reinforced concrete beam elements are submitted to applicable loads along their life cycle that cause shear and torsion. These elements may be subject to only shear, pure torsion or both, torsion and shear combined. The Brazilian Standard Code ABNT NBR 6118:2007 [1] fixes conditions to calculate the transverse reinforcement area in beam reinforced concrete elements, using two design models, based on the strut and tie analogy model, first studied by Mörsch [2]. The strut angle θ (theta) can be considered constant and equal to 45º (Model I), or varying between 30º and 45º (Model II). In the case of transversal ties (stirrups), the variation of angle α (alpha) is between 45º and 90º. When the equilibrium torsion is required, a resistant model based on space truss with hollow section is considered. The space truss admits an inclination angle θ between 30º and 45º, in accordance with beam elements subjected to shear. This paper presents a theoretical study of models I and II for combined shear and torsion, in which ranges the geometry and intensity of action in reinforced concrete beams, aimed to verify the consumption of transverse reinforcement in accordance with the calculation model adopted As the strut angle on model II ranges from 30º to 45º, transverse reinforcement area (Asw) decreases, and total reinforcement area, which includes longitudinal torsion reinforcement (Asℓ), increases. It appears that, when considering model II with strut angle above 40º, under shear only, transverse reinforcement area increases 22% compared to values obtained using model I.

Flexural strengthening of reinforced concrete beams with carbon fibers reinforced polymer (CFRP) sheet bonded to a transition layer of high performance cement-based composite

Resistance to corrosion, high tensile strength, low weight, easiness and rapidity of application, are characteristics that have contributed to the spread of the strengthening technique characterized by bonding of carbon fibers reinforced polymer (CFRP). This research aimed to develop an innovate strengthening method for RC beams, based on a high performance cement-based composite of steel fibers (macro + microfibers) to be applied as a transition layer. The purpose of this transition layer is better control the cracking of concrete and detain or even avoid premature debonding of strengthening. A preliminary study in short beams molded with steel fibers and strengthened with CFRP sheet, was carried out where was verified that the conception of the transition layer is valid. Tests were developed to get a cement-based composite with adequate characteristics to constitute the layer transition. Results showed the possibility to develop a high performance material with a pseudo strain-hardening behavior, high strength and fracture toughness. The application of the strengthening on the transition layer surface had significantly to improve the performance levels of the strengthened beam. It summary, it was proven the efficiency of the new strengthening technique, and much information can be used as criteria of projects for repaired and strengthened structures.

Shear strength of reinforced concrete circular cross-section beams

A proposed adequation of NBR 6118, Item 7.4, related to shear strength of reinforced concrete beams is presented with aims to application on circular cross-section. The actual expressions are most suitable to rectangular cross-section and some misleading occurs when applied to circular sections at determination of VRd2, Vc and Vsw, as consequence of bw (beam width) and d (effective depth) definitions as well as the real effectiveness of circular stirrups. The proposed adequation is based on extensive bibliographic review and practical experience with a great number of infrastructure elements, such as anchored retaining pile walls, where the use of circular reinforced concrete members is frequent.

Design of compression reinforcement in reinforced concrete membrane

This paper presents a method to design membrane elements of concrete with orthogonal mesh of reinforcement which are subject to compressive stress. Design methods, in general, define how to quantify the reinforcement necessary to support the tension stress and verify if the compression in concrete is within the strength limit. In case the compression in membrane is excessive, it is possible to use reinforcements subject to compression. However, there is not much information in the literature about how to design reinforcement for these cases. For that, this paper presents a procedure which uses the model based on Baumann's [1] criteria. The strength limits used herein are those recommended by CEB [3], however, a model is proposed in which this limit varies according to the tensile strain which occur perpendicular to compression. This resistance model is based on concepts proposed by Vecchio e Collins [2].

Experimental Data on Fire-Resistance Behavior of Reinforced Concrete Structures with Example Calculations

This thesis selects concrete, steel and their relation as research subjects, mainly commentary and discusses the property changes of steel and concrete materials under and after high temperature.The differences and comparisons of reasearch methods and ways between different researchers and different papers,particularly for chinese researches and chinese papers,and partly for comparison between chinese papers methods and Euro-Amercian papers methods about Fire Resistance Behavior of Reinforced Concrete will be summarized and analyzed.The researches on fire-resistance behavior of reinforced concrete become more and more important all over the world. And I would find differences between Chinese researches results, between Chinese researches results and other countries researches results.

Shear behavior of reinforced concrete slabs under concentrated load: an investigation through Sequentially Linear Analysis

ABSTRACT (italiano) Con crescente attenzione riguardo al problema della sicurezza di ponti e viadotti esistenti nei Paesi Bassi, lo scopo della presente tesi è quello di studiare, mediante la modellazione con Elementi Finiti ed il continuo confronto con risultati sperimentali, la risposta in esercizio di elementi che compongono infrastrutture del genere, ovvero lastre in calcestruzzo armato sollecitate da carichi concentrati. Tali elementi sono caratterizzati da un comportamento ed una crisi per taglio, la cui modellazione è, da un punto di vista computazionale, una sfida piuttosto ardua, a causa del loro comportamento fragile combinato a vari effetti tridimensionali. La tesi è incentrata sull'utilizzo della Sequentially Linear Analysis (SLA), un metodo di soluzione agli Elementi Finiti alternativo rispetto ai classici approcci incrementali e iterativi. Il vantaggio della SLA è quello di evitare i ben noti problemi di convergenza tipici delle analisi non lineari, specificando direttamente l'incremento di danno sull'elemento finito, attraverso la riduzione di rigidezze e resistenze nel particolare elemento finito, invece dell'incremento di carico o di spostamento. Il confronto tra i risultati di due prove di laboratorio su lastre in calcestruzzo armato e quelli della SLA ha dimostrato in entrambi i casi la robustezza del metodo, in termini di accuratezza dei diagrammi carico-spostamento, di distribuzione di tensioni e deformazioni e di rappresentazione del quadro fessurativo e dei meccanismi di crisi per taglio. Diverse variazioni dei più importanti parametri del modello sono state eseguite, evidenziando la forte incidenza sulle soluzioni dell'energia di frattura e del modello scelto per la riduzione del modulo elastico trasversale. Infine è stato effettuato un paragone tra la SLA ed il metodo non lineare di Newton-Raphson, il quale mostra la maggiore affidabilità della SLA nella valutazione di carichi e spostamenti ultimi insieme ad una significativa riduzione dei tempi computazionali. ABSTRACT (english) With increasing attention to the assessment of safety in existing dutch bridges and viaducts, the aim of the present thesis is to study, through the Finite Element modeling method and the continuous comparison with experimental results, the real response of elements that compose these infrastructures, i.e. reinforced concrete slabs subjected to concentrated loads. These elements are characterized by shear behavior and crisis, whose modeling is, from a computational point of view, a hard challenge, due to their brittle behavior combined with various 3D effects. The thesis is focused on the use of Sequentially Linear Analysis (SLA), an alternative solution technique to classical non linear Finite Element analyses that are based on incremental and iterative approaches. The advantage of SLA is to avoid the well-known convergence problems of non linear analyses by directly specifying a damage increment, in terms of a reduction of stiffness and strength in the particular finite element, instead of a load or displacement increment. The comparison between the results of two laboratory tests on reinforced concrete slabs and those obtained by SLA has shown in both the cases the robustness of the method, in terms of accuracy of load-displacements diagrams, of the distribution of stress and strain and of the representation of the cracking pattern and of the shear failure mechanisms. Different variations of the most important parameters have been performed, pointing out the strong incidence on the solutions of the fracture energy and of the chosen shear retention model. At last a confrontation between SLA and the non linear Newton-Raphson method has been executed, showing the better reliability of the SLA in the evaluation of the ultimate loads and displacements, together with a significant reduction of computational times.

Time-dependent behaviour of reinforced concrete slabs

In this thesis is studied the long-term behaviour of steel reinforced slabs paying particular attention to the effects due to shrinkage and creep. Despite the universal popularity of using this kind of slabs for simply construction floors, the major world codes focus their attention in a design based on the ultimate limit state, restraining the exercise limit state to a simply verification after the design. For Australia, on the contrary, this is not true. In fact, since this country is not subjected to seismic effects, the main concern is related to the long-term behaviour of the structure. Even if there are a lot of studies about long-term effects of shrinkage and creep, up to date, there are not so many studies concerning the behaviour of slabs with a cracked cross section and how shrinkage and creep influence it. For this reason, a series of ten full scale reinforced slabs was prepared and monitored under laboratory conditions to investigate this behaviour. A wide range of situations is studied in order to cover as many cases as possible, as for example the use of a fog room able to reproduce an environment of 100% humidity. The results show how there is a huge difference in terms of deflections between the case of slabs which are subjected to both shrinkage and creep effects soon after the partial cracking of the cross section, and the case of slabs which have already experienced shrinkage effects for several weeks, when the section has not still cracked, and creep effects only after the cracking.

Steel and macro-synthetic self-compacting fibre reinforced concrete, experimental study on the long-term deformations

Experimental study on the long-term deformations of the fibre reinforced concrete. Steel and macro-synthetic fibers were used to evaluate the shrinkage, creep, mid-span deflection, cracking and rupture analysis of three different types of samples. At the end the main topics of ACI guidelines were analyzed in order to perform an overview of design.

Pushover analysis of an existing reinforced concrete bridge:Jamboree Road Overcrossing in Irvine, California

The work for the present thesis started in California, during my semester as an exchange student overseas. California is known worldwide for its seismicity and its effort in the earthquake engineering research field. For this reason, I immediately found interesting the Structural Dynamics Professor, Maria Q. Feng's proposal, to work on a pushover analysis of the existing Jamboree Road Overcrossing bridge. Concrete is a popular building material in California, and for the most part, it serves its functions well. However, concrete is inherently brittle and performs poorly during earthquakes if not reinforced properly. The San Fernando Earthquake of 1971 dramatically demonstrated this characteristic. Shortly thereafter, code writers revised the design provisions for new concrete buildings so to provide adequate ductility to resist strong ground shaking. There remain, nonetheless, millions of square feet of non-ductile concrete buildings in California. The purpose of this work is to perform a Pushover Analysis and compare the results with those of a Nonlinear Time-History Analysis of an existing bridge, located in Southern California. The analyses have been executed through the software OpenSees, the Open System for Earthquake Engineering Simulation. The bridge Jamboree Road Overcrossing is classified as a Standard Ordinary Bridge. In fact, the JRO is a typical three-span continuous cast-in-place prestressed post-tension box-girder. The total length of the bridge is 366 ft., and the height of the two bents are respectively 26,41 ft. and 28,41 ft.. Both the Pushover Analysis and the Nonlinear Time-History Analysis require the use of a model that takes into account for the nonlinearities of the system. In fact, in order to execute nonlinear analyses of highway bridges it is essential to incorporate an accurate model of the material behavior. It has been observed that, after the occurrence of destructive earthquakes, one of the most damaged elements on highway bridges is a column. To evaluate the performance of bridge columns during seismic events an adequate model of the column must be incorporated. Part of the work of the present thesis is, in fact, dedicated to the modeling of bents. Different types of nonlinear element have been studied and modeled, with emphasis on the plasticity zone length determination and location. Furthermore, different models for concrete and steel materials have been considered, and the selection of the parameters that define the constitutive laws of the different materials have been accurate. The work is structured into four chapters, to follow a brief overview of the content. The first chapter introduces the concepts related to capacity design, as the actual philosophy of seismic design. Furthermore, nonlinear analyses both static, pushover, and dynamic, time-history, are presented. The final paragraph concludes with a short description on how to determine the seismic demand at a specific site, according to the latest design criteria in California. The second chapter deals with the formulation of force-based finite elements and the issues regarding the objectivity of the response in nonlinear field. Both concentrated and distributed plasticity elements are discussed into detail. The third chapter presents the existing structure, the software used OpenSees, and the modeling assumptions and issues. The creation of the nonlinear model represents a central part in this work. Nonlinear material constitutive laws, for concrete and reinforcing steel, are discussed into detail; as well as the different scenarios employed in the columns modeling. Finally, the results of the pushover analysis are presented in chapter four. Capacity curves are examined for the different model scenarios used, and failure modes of concrete and steel are discussed. Capacity curve is converted into capacity spectrum and intersected with the design spectrum. In the last paragraph, the results of nonlinear time-history analyses are compared to those of pushover analysis.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.