Nonlinear modelling of reinforced concrete structures

Non-linear modelling of structures is a crucial tool in order to understand complex structural behaviour, improve new design and to face the problem of assuring specific performance levels under complex loading. In this paper three main research lines are described which focus on different aspects of nonlinear modelling of reinforced concrete structures and to improve knowledge of the material behaviour.Postprint (published version

B-spline sectional model for general 3D effects in reinforced concrete elements

In this paper, an efficient sectional model for the nonlinear analysis of reinforced concrete elements sensible to 3D stress-components effects is presented. The classic plane-sections kinematic hypothesis is enhanced with a warping-distortion displacement field, which enables the model to reproduce the interaction between normal and tangential forces. The complementary field is obtained explicitly considering the inter-fiber equilibrium. This is solved using b-splines interpolation on the cross-section domain. The proposed method significantly reduces the number of unknowns compared with a finite element solution. The model is able to reproduce the interaction of longitudinal and transverse reinforcement with the concrete matrix. The validation shows that the presented model reproduces accurately complex failure modes as pure shear and coupling between bending and torsion. Further, as the transverse reinforcement is considered explicitly, confinement can be simulated in an objective manner. The presented model is an efficient tool for nonlinear analysis of reinforced concrete sections under general loading.Peer ReviewedPostprint (author's final draft

A new concrete plastic-damage model with an evolutive dilatancy parameter

Typical plastic-damage models for concrete use a constant dilatancy parameter. On problems sensitive to confinement and shear softening, this parameter needs ad hoc calibration to fit experimental observations. This makes the model not objective for general applications. To overcome this issue, in this paper, a constitutive plastic-damage model with evolutive dilatancy is proposed for concrete. The evolution of dilatancy is made dependent on the plastic-damage and stress states. The proposed evolution law is validated by comparison of numerical simulations with available experimental results. The validation includes: concrete specimens under uniaxial compression measuring the free expansion, passively confined concrete specimens with different confining materials, and reinforced concrete panels under in-plane shear. It is concluded that the model accurately reproduces concrete lateral expansion through different nonlinear states. Proper modeling of concrete nonlinear expansion proves essential for capturing the response in a number of situations: softening under high shear stresses, confinement, and ductility assessment.Peer ReviewedPostprint (author's final draft

Generación automática de esquemas de bielas y tirantes considerando criterios constructivos

El método de bielas y tirantes (BT) es de gran utilidad en el dimensionamiento a rotura de elementos de hormigón, particularmente en casos de regiones D donde las hipótesis clásicas de vigas y placas no son aplicables. Aunque el método viene recogido en muchas normativas modernas, existen al menos tres aspectos que limitan un uso más extendido en la práctica: no da información en servicio, la selección de esquemas factibles no es trivial en casos complejos y la solución no es única. En este artículo se propone un método que genera esquemas factibles de BT mediante el uso de análisis lineales y criterios de optimización para modificar la distribución de propiedades del material en la región de estudio. No es necesario disponer un armado inicial y permite considerar criterios constructivos; en particular, se aborda el de armado ortogonal. Se incluyen casos de estudio y ofrecen conclusiones y perspectivas futuras. Strut-and-Tie (ST) method is very useful in the Ultimate Limit State design of reinforced concrete elements, particularly in the case of D regions where beam and plate theories cannot be applied. In spite of being included in most modern design codes, there are at least three issues that limit a more extended use of this method in practice: it doesn’t provide information in service, the selection of suitable schemes is not trivial for complex cases and the solution isn’t unique. In this paper a novel method to produce suitable ST schemes is proposed by combining linear elastic analyses and optimization criteria. It is based on suitable modifications of the distribution of elastic parameters in the structural model. Without requiring initial distribution of reinforcement, it is capable of considering constructability conditions, particularly the condition of orthogonal reinforcement layout is considered in this paper. A series of case-studies are presented and analyzed; finally, conclusions are drawn.Postprint (published version

Assessment of the expected seismic damage in the aggregated masonry buildings of the late XIX century of Barcelona, Spain

This paper aims at the evaluation of expected seismic damage of aggregated masonry buildings system, formed by a line of buildings along of the street; real buildings were studied of whom structural drawings were available. Each structure was individually built without any gaps between them, producing interaction among the buildings under lateral loads. Numerical model consists of 7 buildings: 5 in-row with rectangular shape and 2 corners (in the intersection of two streets) with a pentagonal shape. Damage probability matrices were obtained from pushover analysis using the capacity and fragility curves. Seismic hazard is considered for the acceleration of Barcelona. Four damage states were considered: slight, moderate, extensive and complete (collapse). The results showed that aggregated system analysed presents slight damage in a hard soil while very extensive damage occur in soft soil, furthermore, the expected seismic damage is high considering the low seismic action of Barcelona.Peer ReviewedPostprint (published version

Seismic assessment of the masonry buildings typical of Barcelona using the Risk-UE methodology

En este trabajo se realiza un estudio para evaluar la vulnerabilidad y el daño sísmico en edificios de obra de fábrica de ladrillo no reforzada. Se han elegido 3 modelos de edificios representativos del distrito Eixample de Barcelona. El análisis de la vulnerabilidad sísmica se lleva a cabo mediante la metodología Risk-UE. La demanda sísmica se define a partir del espectro de proyecto elástico con 5% de amortiguamiento, definido, en este caso, por el Eurocódigo 8. Las curvas de fragilidad se obtienen a partir de un análisis no lineal, teniendo en cuenta los espectros de capacidad. El daño sísmico esperado se consigue con las matrices de probabilidad de daño, las cuales indican la probabilidad de ocurrencia de un estado de daño para una demanda sísmica específica. La modelización de los edificios se realiza con el programa TreMuri mediante un modelo de macroelementos, el cual representa las paredes de los edificios. Los edificios aquí analizados son reales y se dispuso de planos e informes específicos. Los resultados obtenidos muestran una vulnerabilidad importante en este tipo de edificios, teniendo en cuenta el escenario sísmico considerado el daño sísmico esperado es alto.In this work, a study about the vulnerability and seismic damage of unreinforced masonry buildings is carried out. Three models of buildings representatives of the Eixample district of Barcelona have been chosen. The seismic vulnerability is evaluated by means of the Risk-UE methodology. The seismic demand is described by elastic project spectrum, in this case, defined by the Eurocode 8. Fragility curves are obtained from a nonlinear analysis, considering the capacity spectra. Expected seismic damage is gotten with the damage probability matrices, which indicate the occurrence probability of a damage state for a seismic demand given. The analysis of the buildings has been performed by TreMuri program by means of a macroelements model, which represents of a whole masonry panel. The buildings, here, analyzed are real and detailed structural drawings and reports have been used to model them. The results shown a considerable vulnerability in this type of buildings, therefore, in spite of the seismic hazard the expected seismic risk is significant.Peer Reviewe

3D FEM model development from 3D optical measurement technique applied to corroded steel bars

Understanding the mechanical effects of the corrosion pits on the steel surface requires an accurate definition of their geometry and distribution along the rebar. 3D optical measurement technique is used to obtain the outer geometry of artificially corroded bars tested under cyclic or monotonic loads. 3D FEM model development from the 3D scanning results were carried out in order to investigate the failure process and local effects on the pits, which are responsible of the variation of the mechanical properties in corroded steel reinforcement. In addition, a validation of a simplified model, which allows the mechanical steel properties determination given an estimated corrosion level, is presented. 3D models were convenient to observe and measure the local effects on the pits.Peer ReviewedPostprint (author's final draft

Analytical modeling of reinforced concrete columns subjected to bidirectional shear

Under general seismic loading, reinforced concrete columns may be subjected to lateral loads in more than one direction. Available experimental data on columns subjected to bidirectional forces indicate that higher levels of damage and a higher loss of ductility and strength have been observed compared to similar tests under unidirectional shear forces. In this study, an experimental program was conducted in which six lightly reinforced concrete columns were subjected to unidirectional and bidirectional cyclic shear forces. This observation was used to identify the mechanisms and parameters governing the behavior of columns subjected to cyclic bidirectional lateral loads. Hence, a new conceptual model was developed to obtain the capacity of member. The shear forces were analyzed and an analytical formulation was derived to account for the effects in the concrete stress-strain relationship, the moment-curvature diagram and the plastic hinge length. These equations were used along with a structural model with concentrated plastic hinges to obtain the capacity curve of the column. The results of the formulations developed were verified using the results of the experiments performed on columns subjected to unidirectional and bidirectional cyclic lateral forces.Peer ReviewedPostprint (author's final draft

Influence of time-dependent restrained strains in the shear response of RC frames

The final publication is available at Springer via http://dx.doi.org/10.1617/s11527-016-0875-8Time-dependent strains, when restrained, can lead to important tensile forces and damage, affecting, among other aspects, the shear response and ultimate load carrying capacity of shear-critical RC frames. This paper presents a detailed study of this problematic by means of an extension of a shear-sensitive fibre beam model to time dependent behaviour of concrete. The model is firstly validated with experimental tests on diagonally pre-cracked beams under sustained loads. From these analyses, the contributions of shear distortions and bending curvatures to the total long-term deflection of the beams are discerned. Afterwards, the model is applied to study the influence of restraining strains due to long-term creep and shrinkage in the service and ultimate shear response of frames. In contrast with flexural resistant mechanisms, delayed strains may influence the latter shear resistance of integral structures by reducing the concrete contribution to shear resistance and leading to a sooner activation of the transversal reinforcement. These aspects can be relevant in assessing existing structures and this model, due to its relative simplicity, can be advantageous for practical applications.Peer ReviewedPostprint (author's final draft

Safety factor calibration for a new model of shear strength of reinforced concrete building beams and slabs

When assessing existing structures, the availability of adequate safety factors, calibrated with the most accurate models, and for established target reliability indexes, is of critical importance in order to take the right decision regarding the maintenance/repair/strengthening interventions. In the case of shear resistance in reinforced concrete (RC) structures, when using the current design codes provisions for new constructions in assessment results that, in many cases, existing structures may be considered unsafe, implying large economic costs in strengthening or even dismantling. In this research, a proposal of safety factor relative to a recently developed model for shear strength, for elements with and without transversal reinforcement, based on a reliability-based calibration is presented. A formulation is proposed to determine the adequate strength factor for a selected target reliability index of the existing structure and desired remaining service life by means of a safety factor format, considering the load factors present in the Eurocodes. The calibration is carried out considering typical geometry and load ratios of building floors, as well as normal and high strength concrete. The derived safety factor is almost independent of the chosen remaining service life.Peer ReviewedPostprint (author's final draft