Abstract

There is a general interest in civil engineering to quantify the damage produced in structures by catastrophic actions. It would be convenient, from a practical point of view, to describe the state of a structure by means of a single figure that clarifies whether the structure is capable of supporting the service charges or not; if it will survive to another extraordinary load in the future; how does the present damaged state influence in its future behavior; where the most damaged points are located; what capacity of resistance remains in each point; and, in general, all kind of information that help to make design or repair decisions. The authors have proposed a solution to this problem in the specific case of earthquakes acting upon reinforced concrete building structures. A methodology has been formulated for the definition of an index of damage that can be typified for all the structures belonging to the same class and that allows classifying them according to their seismic vulnerability. In the monograph, simple beam structures are first studied in order to better describe the concepts involved and the parameters that influence the solution to the problem. The developed methodology, which models the structures using the finite element method, is directly and easily extended to shells, plates or 3D solids. The fundamental idea of ​​this work is to apply constitutive equations formulated in 3D at a material point instead of using constitutive laws formulated in generalized forces-displacements such as, for example, bending moment-curvature, shear force-angular distortion, etc. This allows modeling the behavior of composite materials directly since for each component material its own constitutive law is considered. In this way, it is sufficient to have a single 3D constitutive model and a methodology to calculate the components of the stress and strain tensors at any point of the beam section.

Abstract

This study determines the structural behavior of a four level framed building with composite RC and steel structure designed according Venezuelan seismic codes. The structural system consists of RC frames in the first three levels and steel frames in the fourth. It was performed linear analysis to design all structural elements. Capacity curves and performance points were obtained with pushover analysis. Results showed greater ductility in the X frames’ direction and greater resistance reserve in the external frames. Performing points showed adequate resistance values but low stiffness in two Y frames’ directions. Seismic action is carried on through synthetic accelerograms defined by the seismic codes used in this study. Dynamic analysis is used to compute parameters of ductility, over strength and displacements. In one case the collapse Limit State was reached, implying a general collapse of the building. Incremental dynamic analysis was performed to obtain fragility curves and damage probability matrix; a very high probability of significant lateral displacement and damage was evidenced from this despite a normative design of structural elements.

Abstract

The objective of this study is to determine the seismic response and torsional effects of an existing Reinforced Concrete building with irregular plant and five levels projected according to an older version of Venezuelan seismic design code. Two structures were analysed: the original building and a redesigned version. Nonlinear static analysis and nonlinear 3D dynamic analysis were applied, based on registers of three synthetic accelerograms compatible with the elastic design spectrum for the used code. In 3D analysis, four structures were simulated, with and without rigid diaphragms so as to compare the seismic behaviour of the buildings. Through this nonlinear analysis parameters were determined that define the behaviour of the structure, torsional moments and rotations in columns reached for simulated buildings. Also, to obtain damage fragility curves for five states damage were generated. Results show that the original structure has an inadequate resistant behaviour and a high probability of exceeding the moderate damage state, while the redesigned structure presents good performance under seismic events according to the existing code. It was also observed that maximum torsional effects occur in the entrant corners of the  irregular plant, which are reduced in mid-rise buildings by using a rigid diaphragm.

Abstract

The incremental dynamic analysis is a powerful tool for evaluating the seismic vulnerability and risk of buildings. It allows calculating the global damage of structures for different PGAs and representing this result by means of damage curves. Such curves are used by many methods to obtain seismic risk scenarios at urban level. Even if the use of this method in a probabilistic environment requires a relevant computational effort, it should be the reference method for seismic risk evaluation. In this article we propose to assess the seismic expected damage by using nonlinear dynamic analysis. We will obtain damage curves by means of the incremental dynamic analysis combined with the damage index of Park & Ang. The uncertainties related to the mechanical properties of the materials and the seismic action will be considered. The probabilistic damage curves obtained can be used to calculate not only seismic risk scenarios at urban level, but also to estimate economic losses.

Abstract

Considering the effects of earthquakes occurred during the last 15 years, this article focusses on finding solutions to minimize the human and economic losses. Several methodologies were developed in order to assess the vulnerability of the built environment with special reference to one of the most suitable structural systems in seismic areas for dwellings, offices or other functionalities, which is the reinforced concrete framed structure. Thus, the present article studies the influence on the vulnerability of reinforced concrete framed structures of geometric structural characteristics like the slab thickness, the building height and the plan configuration. Referring to the slab, it adds supplementary stiffness to the structure that can significantly influence upon its overall failure mechanism. 3D static nonlinear analyses are conducted by means of the SAP2000 computer program. The results are capacity curves which are used to develop the vulnerability curves. Three thicknesses are considered for the slab: 0.1 cm, 0.12 cm and 0.15 m. Medium and high rise structures are considered, with 4, and 8 levels, respectively, in order to determine the influence of the building height on the vulnerability index. Three plan configurations of the buildings are compared: a square one, a rectangular one and an L shaped one. For all the analyzed cases, the corresponding vulnerability curves are compared. The obtained results reveal that more realistic results for the behavior of the structure can be obtained if special attention is given to the structural characteristics, especially during the conceptual design process.

Abstract

The main objective of this article is to propose a simplified methodology to assess the expected seismic damage in reinforced concrete buildings from a probabilistic point of view by using Monte Carlo simulation. In order to do so, the seismic behaviour of the building was studied by using random capacity obtained by considering the mechanical properties of the materials as random variables. From the capacity curves, the damage states and fragility curves can be obtained, and curves describing the expected seismic damage to the structure as a function of a seismic hazard characteristic can be developed. The latter can be calculated using the capacity spectrum and the demand spectrum according to the methodology proposed by the Risk-UE project. In order to define the seismic demand as a random variable, a set of real accelerograms were obtained from European and Spanish databases in such a way that the mean of their elastic response spectra was similar to an elastic response spectrum selected from Eurocode 8. In order to combine the uncertainties associated with the seismic action and the mechanical properties of materials, two procedures are considered to obtain functions relating the peak ground acceleration to the maximum spectral displacements. The first method is based on a series of non-linear dynamic analyses, while the second is based on the well-known ATC-40 procedure called equal displacement approximation. After applying both procedures, the probability density functions of the maximum displacement at the roof of the building are gathered and compared. The expected structural damage is finally obtained by replacing the spectral displacement calculated using ATC-40 and the incremental dynamic procedure. In the damage functions, the results obtained from incremental static and dynamic analyses are compared and discussed from a probabilistic point of view.

Abstract

 The codes used in seismic design of waffled-slab floors buildings (WSFB), such as the Spanish NCSE-02 earthquake-resistant design code, assign them restricted ductility, utilise linear structural analysis based on modal analysis, but also consider the structural ductility concept. Uncertainties arise whenever these codes are applied to the special case of buildings with waffled-slab floors, the ductility of which is doubtful. In many cases, during earthquakes, buildings with restricted ductility are unable to reach the ductility values assumed in the design process, although they may exhibit adequate values of overstrength. This paper therefore studies typical WSFB by applying static incremental non-linear analysis procedures (pushover analysis) in order to calculate their actual structural ductility and overstrength values. Fragility curves corresponding to different damage states and damage probability matrices are also calculated and compared with those of moment-resisting frame buildings (MRFB) in order to obtain useful conclusions for earthquake resistant design. One of the most relevant conclusions of this article is that the use of a better confinement and of ductile steel can only improve the seismic behaviour of MRFB but not that of WSFB.

Abstract

Most of buildings and structures are usually projected according to two main axes. However, the geographical position of these buildings varies randomly. Such random distributions of the azimuthal positions of structures, in most of the cities, generally, are not accounted for when assessing their seismic risk; certainly, the direction of the seismic loads is another highly random variable. Moreover, an additional important source of uncertainty is related to the structural response, mainly due to the random character of the mechanical properties. There is a consensus that uncertainties must be considered for adequately assessing the seismic risk of structures, but these directionality effects have not been deeply explored so far. In this article, the influence of the high uncertainty involved in these input variables on the expected seismic damage is analysed. Thus, an actual earthquake, which affected the southern part of Spain, is studied. Notably, damages on a group of affected buildings, located close to the epicentre, are analysed and discussed in detail. The results show that the influence of the random azimuthal position of structures is an important source of uncertainty and that it should be taken into account when estimating the expected seismic risk in urban areas.

Abstract

The most relevant seismic vulnerability and risk analysis methods are discussed and compared in this article using, as  a pilot urban area, the city of Barcelona, Spain, where risk studies have been carried out over the last 15 years in the framework of different research projects. Most of the buildings in Barcelona, which have unreinforced masonry structure or reinforced concrete structure with waffled slab floors, show a high degree of vulnerability to earthquakes. The physical seismic risk but also the socio-economic implications of risk are considered in the article. The robustness of the innovative holistic approach, based on indicators related to the physical exposure, the social fragilities and the lack of resilience of urban area, is also proved. Using a geographic information system (GIS), the seismic risk results are described by means of scenarios of expected losses, but also as scenarios of probabilities of occurrence of predefined damage states.

Abstract

As the recent research by Trybicki and Sobczyk has demonstrated [1-3] the principle of maximum entropy is a powerful tool for solving stochastic differential equations. In particular, its use in connection with the moment equations generated by the Ito formula provides accurate estimations of the probability density evolution of some oscillators for which conventional methods such as the diverse closure schemes are not applicable. A major computational requirement of the method, however, lies in the need of calculating a large number of multidimensional integrals at each time step -a numerical task for which both accurate and economic algorithms are required. In this paper it is shown that conventional economic integration techniques often lead to numerical collapse of the solution, especially when dealing with higly nonlinear oscillators. A strategy that overcomes this difficulty is proposed. In essence, the integrals are reformulated in terms of multidimensional Fourier transforms, which are solved by an ad hoe FFT algorithm aimed at obtaining only one single "frequency" point. It is demonstrated that the numerical stability and the accuracy of the proposed algorithm are superior to those afforded by other integration schemes.