Simplified wide-column model for the blind prediction shake table test of a U-shaped wall building

Reinforced concrete (RC) structures with tri-dimensional asymmetries tend to exhibit torsional effects that are of great concern in the field of earthquake engineering, in particular at large ductility levels where they become more relevant [MAN09]. In nuclear facilities, this issue assumes particular relevance considering that these structures are designed to respond essentially in the elastic range with a controlled level of deformations and accelerations when subjected to strong ground motions. Within the previous framework, the research project SMART 2013 (‘Seismic design and best-estimate Methods Assessment for Reinforced concrete buildings subjected to Torsion and non-linear effects’) was conducted in order to improve the knowledge on the seismic response of irregular RC structures (experimental test) and to provide reference data for modelling developments and validation (benchmark). Past blind prediction contests showed that, by making use of appropriate modelling options, the seismic response of structures can be predicted with satisfactory accuracy [SOU14]. Nonetheless, they have also evidenced a significant dispersion of predictions between the different participating teams, as demonstrated by the results obtained in the past blind prediction contest [NEE10]. After a short description of the SMART 2013 mock-up and corresponding loading, the present paper describes the properties of the numerical model used by one the participating teams and the comparison of its results with those obtained from the experiments

From plastic hinge to shell models: Recommendations for RC wall models

The severe damage and collapse of many reinforced concrete (RC) wall buildings in the recent earthquakes of Chile (2010) and New Zealand (2011) have shown that RC walls did not perform as well as expected based on the design calculations required by the modern codes of both countries. In this context, it seems appropriate to intensify research efforts in more accurate simulations of damage indicators, in particular local engineering demand parameters such as material strains, which are central to the application of performance-based earthquake engineering. Potential modelling improvements will necessarily build on a thorough assessment of the limitations of current state-of-the-practice simulation approaches. This work aims to compare the response variability given by a spectrum of numerical tools commonly used by researchers and specialized practitioners, namely: plastic hinge analyses, distributed plasticity models, and detailed finite element simulations. It is shown that a multi-level assessment—wherein both the global and local levels are jointly investigated from the response analysis outcomes—is fundamental to define the dependability of the results. The latter is controlled by the attainment of material strain limits and the occurrence of numerical problems. Finally, the influence of shear deformations is analysed according to the same methodological framework

Axially equilibrated displacement-based beam element for simulating the cyclic inelastic behaviour of RC members

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits since they directly relate to damage and are therefore less dependent on member geometry and boundary conditions. However, predicting accurately strain demands still represents a major simulation challenge. Tension shift effects, which induce a linear curvature profile in the plastic hinge region of RC columns and walls, are one of the main causes for the mismatch between experimental and numerical estimates of local level quantities obtained through force-based formulations. Classical displacement-based approaches are instead suitable to simulate such linear curvature profile. Unfortunately, they verify equilibrium only on an average sense due to the wrong assumption on the axial displacement field, leading to poor deformation and force predictions. This paper presents a displacement-based element in which axial equilibrium is strictly verified along the element length. The assumed transversal displacement field ensures a linear curvature profile, connecting accurately global displacement and local strain demands. The proposed finite element is validated against two sets of quasi-static cyclic tests on RC bridge piers and walls. The results show that curvature and strain profiles for increasing ductility demands are significantly improved when axially equilibrated rather than classical displacement-based or force-based elements are used to model the structural members

Adequabilidade de deformações locais como parâmetro na avaliação sísmica de paredes de betão armado

O dano severo e o colapso de diversos edifícios com paredes estruturais em betão armado (BA) durante os recentes sismos do Chile (2010) e Nova Zelândia (2011) revelaram que muitas paredes de BA não tiveram o desempenho que seria expectável da aplicação das modernas técnicas de dimensionamento requeridas pelos regulamentos de ambos os países. Esta observação pode indiciar uma incapacidade dos actuais modelos em simular adequadamente indicadores de dano. Nesse âmbito, o presente artigo compara a variabilidade da resposta estimada por diversas técnicas de modelação correntemente utilizadas por investigadores e especialistas, em particular: análises de rótula plástica, elementos de viga com plasticidade distribuída, e modelos com elementos de membrana. Tendo em conta que estimativas de deformações locais, tais como extensões e curvaturas, têm sido progressivamente adoptadas como parâmetros de resposta estrutural, este estudo mostra e interpreta a variabilidade dos resultados das técnicas anteriores no contexto de uma avaliação multi-nível, em que a resposta ao nível local é analisada simultaneamente com a mais tradicional resposta ao nível global

Modelling of the Cyclic Response of an Unreinforced Masonry Wall through a Force Based Beam Element

The seismic assessment of existing masonry buildings is based on the prediction of their nonlinear response under lateral loading. This requires a reliable estimation of the force and displacement demand. For this purpose, modelling strategies using structural component elements are widely applied both in research and in engineering practice, since they can provide a satisfactory description of the cyclic behaviour of a masonry building with a limited computational cost. One of such modelling strategies are equivalent frame models, in which beam elements describe the response of piers and spandrels. This paper proposes the use of two-node, force-based beam elements with distributed inelasticity to model the in-plane response of modern unreinforced brick masonry panels. The nonlinearity of the response is described through the use of numerically integrated fibre sections and a suitable material model, implemented for this scope in the open-source platform “OpenSees”, describing a coupling at the local level between axial and shear response. Experimental results from a shear and compression test are used to validate the approach and justify some details of the proposed modelling strategy. Since the experimental data included also local displacement measures, the comparison of the numerical and experimental results is extended to curvatures and shear strains. The good agreement between numerical and experimental response confirms the applicability of the proposed approach for modelling the cyclic response of unreinforced brick masonry walls

Effect of damping models on the simulation of seismic axial forces in a reinforced concrete bridge pier

Post-reconnaissance findings after recent earthquakes have shown that the effect of the vertical acceleration component of the ground motion can be more damaging than typically considered thus far, particularly in near-field regions where the ratio of vertical-to-horizontal ground accelerations may exceed considerably the 2/3 scaling factor used in design. Besides, the usual period range for the constant-acceleration region of vertical acceleration spectra often overlaps with the range of vertical vibration periods in reinforced concrete (RC) structures. These reasons explain the appearance of large dynamic axial forces, which can reduce the column shear strength due to tensile demands or alternatively promote direct compressive failures. Estimating the change in the member axial forces during nonlinear seismic response due to the vertical ground motion component is therefore of paramount significance and can only be simulated through dynamic analyses, for which a specific damping model needs to be assigned. Using a cantilever bridge pier with a top mass as an illustrative example, the present paper assesses the effects of the most commonly used damping models and damping values on the simulation of axial forces. Distributed plasticity beam elements with distinct formulations are employed, and a range of top masses is considered. The results show that, even for very low damping values, distinct damping models can have a very significant influence on the simulation of the seismically-induced axial forces, which increases considerably for larger values of the top mass

Influence of Lap Splices on the Deformation Capacity of RC Walls. II: Shell Element Simulation and Equivalent Uniaxial Model

Spliced longitudinal reinforcement may result in a reduction of both strength and displacement capacity of reinforced concrete (RC) members. This applies in particular when lap splices are located in regions where inelastic deformations concentrate, such as the plastic zone at the base of RC walls. This paper introduces a simple numerical model suitable for engineering practice to simulate the force-displacement response of RC walls with lap splices. Based on experimental data from 16 test units, an equivalent uniaxial steel stress-strain law is proposed that represents the monotonic envelope of the cyclic response of spliced rebars in RC walls up to the onset of strength degradation. It allows for modeling lap splice response with finite element (FE) models while avoiding the use of complex interface bond-slip elements. A new semi-empirical expression for the strain at the onset of strength degradation is derived, which expresses the strain capacity of the lap splice as a function of the confining reinforcement ratio and the ratio of lap splice length to shear span of the wall. The proposed equivalent constitutive law was included in shell element models to predict the force-displacement response of the test unit set of RC walls. Results demonstrated the ability of this approach to adequately capture the peak strength and displacement capacity of the spliced units

Elemento de Viga Baseado em Formulação de Rigidez Enriquecido com Funções de Forma Adaptativas para Garantir Equilíbrio Axial

In the framework of Performance Based Earthquake Engineering (PBEE), assessing the inelastic behaviour of structures both at the global (force-displacement) and local (stress-strain) level is of priority importance. This goal is typically achieved by advanced nonlinear analysis that rely on the use of increasing computational power. Due to a good compromise between accuracy and processing time, distributed plasticity beam elements represent the most employed finite element in nonlinear structural analysis. In particular, displacement-based elements are the simplest in terms of implementation and the most efficient from the state determination viewpoint. However, a fundamental drawback of classical displacement-based formulations is related to the assigned axial displacement field. This limitation implies that equilibrium is only verified on an average sense and, in case of material nonlinearity, it yields different values of the axial force in distinct integration sections. This results in a misevaluation of the moment capacity of the structural member and therefore in a poor local and global performance of the finite element. In this paper a new displacement-based element strictly verifying the axial equilibrium condition is introduced. The latter was implemented by the authors in an ad hoc finite element software and its performance is presented by means of two application examples. Comparisons between classical displacement-based and force-based formulations are made, both at the global and local level