Discussion of "Simplified Model of Low Cycle Fatigue for RC Frames"

To model strength degradation due to low cycle fatigue, at least three different approaches can be considered. One possibility is based on the formulation of a new free energy function and damage energy release rate, as was proposed by Ju(1989). The second approach uses the notion of bounding surface introduced in cyclic plasticity by Dafalias and Popov (1975). From this concept, some models have been proposed to quantify damage in concrete or RC (Suaris et al. 1990). The model proposed by the author to include fatigue effects is based essentially in Marigo (1985) and can be included in this approach.

Low-cost retrofitting solutions for RC frames using masonry infill panels

A large number of reinforced concrete (RC) frame structures built in earthquake-prone areas such as Haiti are vulnerable to strong ground motions. Structures in developing countries need low-cost seismic retrofit solutions to reduce their vulnerability. This paper investigates the feasibility of using masonry infill walls to reduce deformations and damage caused by strong ground motions in brittle and weak RC frames designed only for gravity loads. A numerical experiment was conducted in which several idealized prototypes representing RC frame structures of school buildings damaged during the Port-au-Prince earthquake (Haiti, 2010) were strengthened by adding elements representing masonry infill walls arranged in different configurations. Each configuration was characterized by the ratio Rm of the area of walls in the direction of the ground motion (in plan) installed in each story to the total floor area. The numerical representations of these idealized RC frame structures with different values of Rm were (hypothetically) subjected to three major earthquakes with peak ground accelerations of approximately 0.5g. The results of the non-linear dynamic response analyses were summarized in tentative relationships between Rm and four parameters commonly used to characterize the seismic response of structures: interstory drift, Park and Ang indexes of damage, and total amount of energy dissipated by the main frame. It was found that Rm=4% is a reasonable minimum design value for seismic retrofitting purposes in cases in which available resources are not sufficient to afford conventional retrofit measures.

Shaking table tests of a RC frame structure equipped with hysteretic dampers

This paper provides partial results of an on-going research aimed at investigating the seismic response of reinforced concrete (RC) frames equipped with hysteretic-type energy dissipating devices (EDD). From a prototype RC frame structure designed only for gravity loads, a test model scaled in geometry to 2/5 was defined and built in the Laboratory of Structures of the University of Granada. Four EDDs were installed in the test model to provide the same seismic resistance than a conventional RC bare frame designed for sustain gravity and seismic loads following current codes. The test model with EDDs was subjected to several seismic simulations with the shaking table of Laboratory of structures of the University of Granada. The test results provide empirical evidences on the efficiency of the EDDs to prevent damage on the main frame and concentrating the inelastic deformations on the EDDs.

Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures

This paper deals with the application of the lumped dissipation model in the analysis of reinforced concrete structures, emphasizing the nonlinear behaviour of the materials The presented model is based on the original models developed by Cipollina and Florez-Lopez (1995) [12]. Florez-Lopez (1995) [13] and Picon and Florez-Lopez (2000) [14] However, some modifications were introduced in the functions that control the damage evolution in order to improve the results obtained. The efficiency of the new approach is evaluated by means of a comparison with experimental results on reinforced concrete structures such as simply supported beams, plane frames and beam-to-column connections Finally, the adequacy of the numerical model representing the global behaviour of framed structures is investigated and the limits of the analysis are discussed (C) 2009 Elsevier Ltd All rights reserved

Valutazione dell'efficacia delle procedure di Pushover convenzionali, modali ed adattive applicate a telai piani in c.a. regolari ed irregolari in elevazione.

The research performed during the PhD and presented in this thesis, allowed to make judgments on pushover analysis method about its application in evaluating the correct structural seismic response. In this sense, the extensive critical review of existing pushover procedures (illustrated in chapter 1) outlined their major issues related to assumptions and to hypothesis made in the application of the method. Therefore, with the purpose of evaluate the effectiveness of pushover procedures, a wide numerical investigation have been performed. In particular the attention has been focused on the structural irregularity on elevation, on the choice of the load vector and on its updating criteria. In the study eight pushover procedures have been considered, of which four are conventional type, one is multi-modal, and three are adaptive. The evaluation of their effectiveness in the identification of the correct dynamic structural response, has been done by performing several dynamic and static non-linear analysis on eight RC frames, characterized by different proprieties in terms of regularity in elevation. The comparisons of static and dynamic results have then permitted to evaluate the examined pushover procedures and to identify the expected margin of error by using each of them. Both on base shear-top displacement curves and on considered storey parameters, the best agreement with the dynamic response has been noticed on Multi-Modal Pushover procedure. Therefore the attention has been focused on Displacement-based Adative Pushover, coming to define for it an improvement strategy, and on modal combination rules, advancing an innovative method based on a quadratic combination of the modal shapes (QMC). This latter has been implemented in a conventional pushover procedure, whose results have been compared with those obtained by other multi-modal procedures. The development of research on pushover analysis is very important because the objective is to come to the definition of a simple, effective and reliable analysis method, indispensable tool in the seismic evaluation of new or existing structures.

Approccio agli spostamenti per la valutazione della vulnerabilità sismica di telai in conglomerato cementizio armato.

Il presente lavoro ha lo scopo di presentare gli studi e i risultati ottenuti durante l’attività di ricerca svolta sul Displacement-based Assessment (DBA) dei telai in cemento armato. Dopo alcune considerazioni iniziali sul tema della vulnerabilità sismica e sui metodi di analisi e verifica, si procede alla descrizione teorica del metodo. Sono stati analizzati tre casi studio di telai piani, progettati per soli carichi verticali e secondo normative non più in vigore che non prevedevano l’applicazione della gerarchia delle resistenze. I telai considerati, destinati ad abitazione civile, hanno diversa altezza e numero di piani, e diverso numero di campate. Si è proceduto all’applicazione del metodo, alla valutazione della vulnerabilità sismica in base alla domanda in termini di spostamento costituita da uno spettro elastico previsto dall’EC8 e alla validazione dei risultati ottenuti mediante analisi non lineari statiche e dinamiche e mediante l’applicazione dei teoremi dell’Analisi limite dei telai, proposta come procedura alternativa per la determinazione del meccanismo anelastico e della capacità in termini di taglio alla base. In ultimo si è applicata la procedura DBA per la valutazione della vulnerabilità sismica di un edificio scolastico, realizzato tra il 1969 e il 1975 in un sito caratterizzato da una accelerazione di picco orizzontale pari a 0,24g e una probabilità di superamento del 10% in 75 anni.

Seismic performance and damage evaluation of a reinforced concrete frame with hysteretic dampers through shake-table tests

Passive energy dissipation devices are increasingly implemented in frame structures to improve their performance under seismic loading. Most guidelines for designing this type of system retain the requirements applicable to frames without dampers, and this hinders taking full advantage of the benefits of implementing dampers. Further, assessing the extent of damage suffered by the frame and by the dampers for different levels of seismic hazard is of paramount importance in the framework of performance-based design. This paper presents an experimental investigation whose objectives are to provide empirical data on the response of reinforced concrete (RC) frames equipped with hysteretic dampers (dynamic response and damage) and to evaluate the need for the frame to form a strong column-weak beam mechanism and dissipate large amounts of plastic strain energy. To this end, shake-table tests were conducted on a 2/5-scale RC frame with hysteretic dampers. The frame was designed only for gravitational loads. The dampers provided lateral strength and stiffness, respectively, three and 12 times greater than those of the frame. The test structure was subjected to a sequence of seismic simulations that represented different levels of seismic hazard. The RC frame showed a performance level of "immediate occupancy", with maximum rotation demands below 20% of the ultimate capacity. The dampers dissipated most of the energy input by the earthquake. It is shown that combining hysteretic dampers with flexible reinforced concrete frames leads to structures with improved seismic performance and that requirements of conventional RC frames (without dampers) can be relieved.

In-plane and out-of plane experimental characterization of rc masonry infilled frames

Seismic investigations of typical south European masonry infilled frames were performed by testing two reduced scale specimens: one in the in-plane direction and another in the out-ofplane direction. Information about geometry and reinforcement scheme of those structures constructed in 1980s were obtained by [1]. The specimen to be tested in the in-plane direction was constructed as double leaf masonry while the specimen for testing in the out-of-plane direction is constructed with only its exterior leaf since the recent earthquakes have highlighted the vulnerability of the external leaf of the infills in out-of-plane direction [2]. The tests were performed by applying the pre-defined values of displacements in the in-plane and out-of-plane directions in the control points. For in-plane testing it was done by hydraulic actuator and for out-of-plane testing through the application of an airbag. Input and output air in the airbag was controlled by using a software to apply a specific displacement in the control point of the infill wall. Mid-point of the infill was assumed as a control point for outof- plane testing. Deformation and crack patterns of the infill confirm the formation of two-way arching mechanism of the masonry infill until collapse of the upper horizontal interface between infill and frame which is known as weakest interface due to difficulties in filling the mortar between bricks of last row and upper beam. This results in the crack opening through a welldefined path and the consequent collapse of the infill.

A fatigue damage model for seismic response of RC structures

Numerous damage models have been developed in order to analyze seismic behavior. Among the different possibilities existing in the literature, it is very clear that models developed along the lines of continuum damage mechanics are more consistent with the definition of damage as a phenomenon with mechanical consequences because they include explicitly the coupling between damage and mechanical behavior. On the other hand, for seismic processes, phenomena such as low cycle fatigue may have a pronounced effect on the overall behavior of the frames and, therefore, its consideration turns out to be very important. However, most of existing models evaluate the damage only as a function of the maximum amplitude of cyclic deformation without considering the number of cycles. In this paper, a generalization of the simplified model proposed by Cipollina et al. [Cipollina A, López-Hinojosa A, Flórez-López J. Comput Struct 1995;54:1113–26] is made in order to include the low cycle fatigue. Such a model employs in its formulation irreversible thermodynamics and internal state variable theory.

Modelization of low cycle fatigue damage in frames

Damage models based on the Continuum Damage Mechanics (CDM) include explicitly the coupling between damage and mechanical behavior and, therefore, are consistent with the definition of damage as a phenomenon with mechanical consequences. However, this kind of models is characterized by their complexity. Using the concept of lumped models, possible simplifications of the coupled models have been proposed in the literature to adapt them to the study of beams and frames. On the other hand, in most of these coupled models damage is associated only with the damage energy release rate which is shown to be the elastic strain energy. According to this, damage is a function of the maximum amplitude of cyclic deformation but does not depend on the number of cycles. Therefore, low cycle effects are not taking into account. From the simplified model proposed by Flórez-López, it is the purpose of this paper to present a formulation that allows to take into account the degradation produced not only by the peak values but also by the cumulative effects such as the low cycle fatigue. For it, the classical damage dissipative potential based on the concept of damage energy release rate is modified using a fatigue function in order to include cumulative effects. The fatigue function is determined through parameters such as the cumulative rotation and the total rotation and the number of cycles to failure. Those parameters can be measured or identified physically through the haracteristics of the RC. So the main advantage of the proposed model is the possibility of simulating the low cycle fatigue behavior without introducing parameters with no suitable physical meaning. The good performance of the proposed model is shown through a comparison between numerical and test results under cycling loading.

Vulnerability analysis of RC buildings with wide beams located in moderate seismicity regions

A significant number of short-to-mid height RC buildings with wide beams have been constructed in areas of moderate seismicity of Spain, mainly for housing and administrative use. The buildings have a framed structure with one-way slabs; the wide beams constitute the distinctive characteristic, their depth being equal to that of the rest of the slab, thus providing a flat lower surface, convenient for construction and the layout of facilities. Seismic behavior in the direction of the wide beams appears to be deficient because of: (i) low lateral strength, mainly because of the small effective depth of the beams, (ii) inherent low ductility of the wide beams, generated by high amount of reinforcement, (iii) the big strut compressive forces developed inside the column-beam connections due to the low height of the beams, and (iv) the fact that the wide beams are wider than the columns, meaning that the contribution of the outer zones to the resistance of the beam-column joints is unreliable because there is no torsion reinforcement. In the orthogonal direction, the behavior is worse since the only members of the slabs that contribute to the lateral resistance are the joists and the façade beams. Moreover, these buildings were designed with codes that did not include ductility requirements and required only a low lateral resistance; indeed, in many cases, seismic action was not considered at all. Consequently, the seismic capacity of these structures is not reliable. The objective of this research is to assess numerically this capability, whereas further research will aim to propose retrofit strategies. The research approach consists of: (i) selecting a number of 3-story and 6-story buildings that represent the vast majority of the existing ones and (ii) evaluating their vulnerability through three types of analyses, namely: code-type, push-over and nonlinear dynamic analysis. Given the low lateral resistance of the main frames, the cooperation of the masonry infill walls is accounted for; for each representative building, three wall densities are considered. The results of the analyses show that the buildings in question exhibit inadequate seismic behavior in most of the examined situations. In general, the relative performance is less deficient for Target Drift CP (Collapse Prevention) than for IO (Immediate Occupancy). Since these buildings are selected to be representative of the vast majority of buildings with wide beams that were constructed in Spain without accounting for any seismic consideration, our conclusions can be extrapolated to a broader scenario.

Estudo de filtros RC para baixas e altas freqüências por meio de um circuito para superposição de sinais

Apresentamos nesse trabalho, um experimento realizado nos Laboratórios didáticos do Instituto de Física da USP, relacionado ao estudo do funcionamento de filtros RC para baixas e altas freqüências. Para tal, foi especialmente projetado um circuito que efetua a superposição de um sinal gerado internamente, a uma onda senoidal externa. Várias situações experimentais podem ser geradas, por meio da variação da freqüência, tanto do sinal interno quanto da onda senoidal externa. Um estudo das componentes de freqüência de Fourier é também realizado para se estabelecer os parâmetros de funcionamento dos filtros. O funcionamento dos circuitos como integradores e diferenciadores também é explorado. Os estudantes são, portanto, levados a compreender a eficácia desses filtros mais simples, dependendo das freqüências dos sinais de entrada e correspondentes componentes de Fourier, e das freqüências de corte estabelecidas.

A solid-like FEM for geometrically non-linear 3D frames

This study presents a solid-like finite element formulation to solve geometric non-linear three-dimensional inhomogeneous frames. To achieve the desired representation, unconstrained vectors are used instead of the classic rigid director triad; as a consequence, the resulting formulation does not use finite rotation schemes. High order curved elements with any cross section are developed using a full three-dimensional constitutive elastic relation. Warping and variable thickness strain modes are introduced to avoid locking. The warping mode is solved numerically in FEM pre-processing computational code, which is coupled to the main program. The extra calculations are relatively small when the number of finite elements. with the same cross section, increases. The warping mode is based on a 2D free torsion (Saint-Venant) problem that considers inhomogeneous material. A scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element. General examples are solved to check the objectivity, path independence, locking free behavior, generality and accuracy of the proposed formulation. (C) 2009 Elsevier B.V. All rights reserved.

Preloaded RC columns strengthened with high-strength concrete jackets under uniaxial compression

Although use of high-strength reinforced concrete (RC) jackets has become common practice worldwide, there are still two unresolved issues regarding the contribution of the original concrete and the effects of existing loads. Twelve RC-jacketed columns were tested with and without preloading under uniaxial compression. Tests showed the entire core to contribute to the capacity of the jacketed column, as long as adequate confinement is provided. Also, preloading does not adversely affect the capacity of the jacketed column, while it may increase its deformability, especially in square sections. Transverse reinforcement in the jacket directly improves ductility of the strengthened column, especially in circular sections.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.