Abstract

A parametric model for capacity curves and capacity spectra is proposed. The capacity curve is considered to be composed of a linear part and a nonlinear part. The normalized nonlinear part is modelled by means of a cumulative lognormal function. Instead, the cumulative Beta function can be used. Moreover, this new conceptualization of the capacity curves allows defining stiffness and energy functions relative to the total energy loss and stiffness degradation at the ultimate capacity point. Based on these functions, a new damage index is proposed and it is shown that this index, obtained from nonlinear static analysis, is compatible with the Park and Ang index obtained from dynamic analysis. This capacity based damage index allows setting up a fragility model. Specific reinforced concrete buildings are used to illustrate the adequacy of the capacity, damage and fragility models. The usefulness of the models here proposed is highlighted showing how the parametric model is representative for a family of capacity curves having the same normalized nonlinear part and how important variables can be tabulated as empirical functions of the two main parameters defining the capacity model. The availability of this new mathematical model may be a powerful tool for current earthquake engineering research or practice, especially in probabilistic approaches where massive computations are needed.

Abstract

Recently proposed capacity-based damage indices and parametric models for capacity curves are applied to frame steel buildings located in soft soils of the Mexico City. To do that, the seismic performance of 2D models of low-, mid- and high-rise buildings is
assessed. Deterministic and probabilistic nonlinear static and incremental dynamic analyses are implemented. Monte Carlo simulations and the Latin Hypercube sampling technique are used. Seismic actions are selected among accelerograms recorded in the study area. Spectral matching techniques are applied, so that the acceleration time histories have a predefined mean response spectrum and controlled error. The design spectrum of the Mexican seismic code for the zone is used as target spectrum. The well-known Park and Ang damage index allows calibrating the capacity-based damage index. Both damage indices take into account the contribution to damage of the stiffness degradation and of the energy dissipation. Damage states and fragility curves are also obtained and discussed in detail. The results reveal the versatility, robustness and reliability of the parametric model for capacity curves, which allow modelling the nonlinear part of the capacity curves by the cumulative integral of a cumulative lognormal function. However, these new capacitybased damage index and capacity models have been tested for and applied to 2D frame buildings only; they have not been applied to 3D building models yet. The Park and Ang and the capacity-based damage indices show that for the analysed buildings, the contribution to damage of the stiffness degradation is in the range 66–77% and that of energy loss is in the range 29–34%. The lowest contribution of energy dissipation (29%) is found for the low-rise, more rigid, building. The energy contribution would raise with the ductility of the building and with the duration of the strong ground motion. High-rise frame buildings in soft soils of Mexico City show the worst performance so that the use of adequate braced frames to control the displacements could be recommended.

Abstract

To assess the expected seismic damage of a structure, non-linear dynamic analysis and the damage index of Park-Ang have been often used. Depending on the size of the structure and on the duration of the record, the computational effort in dynamic analyses is usually high. In this research a new damage index is proposed based on nonlinear static analysis. The damage index is a linear combination of two energy functions: 1) the strain energy associated to the stiffness variation and the ductility of the structure and 2) the energy dissipated associated to hysteretic cycles. These two energy functions are obtained from the capacity curve of the structure and from the energy balance with the spectral acceleration. To show the ability of the index to represent damage, low-rise steel buildings subjected to seismic actions expected in Mexico City are studied. The results obtained with the new method show a good agreement with those calculated by means of dynamic analyses using the Park-Ang damage index. In average, the Park-Ang damage index is well fitted by the combination of 62% of the strain energy and 38% of the energy dissipated by hysteresis. Moreover, this new damage index allows linking damage to certain characteristics of the seismic actions as, for instance, intensity and duration of the applied seismic action. Therefore, the new approach results in a practice and powerful tool for estimating the seismic damage in buildings, especially when considering probabilistic approaches, where massive computations are needed.

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

In this work, the structural damage to the head of a vehicular bridge with cut ends was identified by monitoring its change of dynamic properties (frequency and damping). The head is made of reinforced concrete and has double cantilever. The importance of the study relies on the fact that most of the reviews of the structural health of bridges that are currently carried out are through visual inspections, which are subjective in many cases. Thus, the need arises to develop quantitative methods and procedures, such as the one analyzed in this work, which will allow objective and reliable detection of the different levels of damage to building structures.

The behavior of a double-cantilever type reinforced concrete head, whose ends are cut to receive the girders that form the bridge superstructure, was analyzed. The damage assessment of the head was related to the changes that occurred in its dynamic properties (frequency and damping).