Abstract

The probabilistic analysis of the seismic performance of a structure requires quantifying the uncertainties of the involved variables and parameters, including the seismic action and mechanical properties of its elements. In this article, the seismic performance of high-rise, mid-rise and low-rise of steel buildings, subjected to long duration seismic actions like those of Mexico City, is analyzed. The analysis is conducted by using a probabilistic approach. The seismic actions are selected to be compatible with the design spectra of the Mexican seismic code for soft soils and long duration earthquakes, characteristic for this region. The dynamic analyses are performed by using Monte Carlo simulations. The strength and ductility of the beams and columns are considered random variables; the seismic actions are also modelled in a probabilistic way. The damage index of Park and Ang is used. The results show that the uncertainties expected in the response are significant, being the randomness of the seismic action the main cause. From the comparison between the mean values of the probabilistic approach and those corresponding to the deterministic case, a good consistency of the result obtained for low-rise and mid-rise buildings is observed. Nevertheless, the consistency is lower in the case of high-rise buildings. The analyzed low-rise and mid-rise buildings show a good seismic performance to seismic actions, but the high-rise buildings show slight or moderate damage. It is concluded that the probabilistic approach provides a more complete information on the structural response.

Abstract

The purpose of this paper is to investigate a reinforced concrete multi-storey building with dissipative structural walls. These walls can improve the behaviour of a tall multi-storey building. The damage of a building with dissipative walls is compared with that of a building with solid walls. The comparative nonlinear dynamic analysis  is performed by means of the SAP2000 software, using a layer model. In order to increase the seismic performance of a building with structural walls is to create slit zones with short connections into the walls. The short connections are introduced as a link element with multi-linear pivot hysteretic plasticity behaviour. The hysteretic rules and parameters of these short connections were proposed by the authors and used in this study. Using the proposed computational model for the slit wall, a seismic analysis of a multi-storey building with slit walls was done. From the results obtained, the advantages of the
proposed model are observed. Unlike other studies on slit walls with short connections, which are focused mostly on the nonlinear dynamic behaviour of the short connections, in this paper the authors take into consideration the whole structural system, wall, connections and frames.

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 static and seismic analysis of Janneh arch-gravity dam (157 m) is carried out by considering a combination of self-weight, hydrostatic, uplift and seismic loads. Linear and nonlinear analyses are performed for both static and seismic cases. Nonlinear behavior is studied by means of joint elements in the contact between the rock foundation and the dam following a bilinear cohesive law. The hydrodynamic effects derived to seismic loads are also considered. Hydrodynamic Westergaard’s approach is applied in the pseudo-static analysis, and the Westergaard’s generalized added mass is used for time-history case.

Abstract

A computational algorithm for predicting the nonlinear dynamic response of a structure is presented. The nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a Rayleigh-Ritz analysis. The basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing. Only a few basis updatings are required during the whole time integration.

The truncation error introduced at every change of basis is pointed out as the cause for a divergence-type behaviour, and some means for eliminating it are discussed.

Results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations.

Abstract

As it is widely known nonlinear dynamic analyses are mostly carried out in the time domain. In this paper an alternate procedure to carry out nonlinear computations in the frequency domain is proposed. This method is a powerful extension of the widely known equivalent nonlinear method that takes into account approximately the dynamic nonlinearities of the soil behavior using the complex response approach. There is no doubt that true nonlinear dynamic analyses can only be carried out in the time domain, where the dynamic material properties (mainly the dynamic material stiffness) are modified every time step. Accordingly, the stiffness matrix must be modified and hence the dynamic equation’s system has to be solved again for each new time step. Obviously, nonlinear analysis of large structures subject to strong seismic events will require great amounts of computer time, which hinder detailed studies to pinpoint the variables that control the behavior of complex structural problems. Accordingly, a new simple yet accurate procedure to perform nonlinear and linear structural analyses was developed and is presented in this paper. It consists in dividing the excitation time history in a specific number of stretches (windows in the time domain) and applying the Short-Time Fourier Transform to each window to map them into the frequency domain. The analysis is performed marching forward along the resulting frequency stretches, considering that the excitation is integrated by the power spectral density of the signal-stretch we are positioned in the frequency domain and the corresponding cross power spectral densities with the previous and posterior neighboring stretches, as shown in the paper. From the analysis results the dynamic material properties are modified according to the equivalent linear approach. It should be mentioned that this procedure is a generalization of the equivalent nonlinear method where the whole input motion (one window) is considered. Needless to stress the fact that when the input motion is divided into several stretches (windows) the actual response approximation will be improved significantly. The accuracy of the procedure advanced here is then evaluated through comparisons with the widely recognized nonlinear computer code named NONSAP. The comparison of the results obtained with both methods show not only the accuracy of the advanced procedure but its much lower consuming time, making it quite appealing to be used in practice.

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

Abstract