Floor response spectra in RC frame structures designed according to Eurocode 8

Nonstructural components (NSCs) should be subjected to a careful and rational seismic design, in order to reduce the economic loss and to avoid threats to the life safety, as well as what concerns structural elements. The design of NSCs is based on the evaluation of the maximum inertia force, which is related to the floor spectral accelerations. The question arises as to whether Eurocode 8 is able to predict actual floor response spectral accelerations occurring in structures designed according to Eurocode 8. A parametric study is conducted on five RC frame structures in order to evaluate the floor response spectra. The structures, designed according to Eurocode 8, are subjected to a set of earthquakes, compatible with the design response spectrum. Time-history analyses are performed both on elastic and inelastic models of the considered structures. Eurocode formulation for the evaluation of the seismic demand on NSCs does not well fit the numerical results. Some comments on the target spectrum provided by AC 156 for the seismic qualification of NSC are also included.     

Wavelet-based response spectrum compatible synthesis of accelerograms—Eurocode application (EC8)

An integrated approach for addressing the problem of synthesizing artificial seismic accelerograms compatible with a given displacement design/target spectrum is presented in conjunction with aseismic design applications. Initially, a stochastic dynamics solution is used to obtain a family of simulated non-stationary earthquake records whose response spectrum is on the average in good agreement with the target spectrum. The degree of the agreement depends significantly on the adoption of an appropriate parametric evolutionary power spectral form, which is related to the target spectrum in an approximate manner. The performance of two commonly used spectral forms along with a newly proposed one is assessed with respect to the elastic displacement design spectrum defined by the European code regulations (EC8). Subsequently, the computational versatility of the family of harmonic wavelets is employed to modify iteratively the simulated records to satisfy the compatibility criteria for artificial accelerograms prescribed by EC8. In the process, baseline correction steps, ordinarily taken to ensure that the obtained accelerograms are characterized by physically meaningful velocity and displacement traces, are elucidated. Obviously, the presented approach can be used not only in the case of the EC8, for which extensive numerical results/examples are included, but also for any code provisions mandated by regulatory agencies. In any case, the presented numerical results can be quite useful in any aseismic design process dominated by the EC8 specifications.     

Wavelet-based generation of spatially correlated accelerograms

For the seismic analysis of complex or nonlinear extended structures, it is useful to generate a set of properly correlated earthquake accelerograms that are consistent with a specified seismic hazard. A new simulation approach is presented in this paper for the generation of ensembles of spatially correlated accelerograms such that the simulated motions are consistent with (i) a parent accelerogram in the sense of temporal variations in frequency content, (ii) a design spectrum in the mean sense, and (iii) with a given instantaneous coherency structure. The formulation is based on the extension of stochastic decomposition technique to wavelet domain via the method of spectral factorization. A complex variant of the modified Littlewood-Paley wavelet function is proposed for the wavelet-based representation of earthquake accelerograms, such that this explicitly brings out the phase information of the signal, besides being able to decompose it into component time-histories having energy in non-overlapping frequency bands. The proposed approach is illustrated by generating ensembles of accelerograms at four stations.     

Seismic design of space steel frames using advanced methods of analysis

A rational and efficient seismic design methodology for regular space steel frames using an advanced time domain finite element method of analysis that takes into account geometrical and material nonlinearities is presented. Seismic loads are applied in the form of Eurocode 8 spectrum compatible real accelerograms along the two horizontal directions of the frame. The iterative design procedure starts with assumed member sections, continues with the response checks for the damage, ultimate and service limit states and ends with the adjustment of member sizes so as all the response checks to be satisfied for all limit states. Thus, the proposed design method deals with nonlinearities and member interactions at the global level and consequently separate member capacity checks through the interaction equations of Eurocode 3 or the usage of the conservative and crude q-factor of Eurocode 8 are not required. Two numerical examples dealing with the design of (a) a space three storey steel frame with one bay in both horizontal directions and (b) a space seven storey steel frame with two and three bays along its two horizontal directions are presented to illustrate the method and demonstrate its advantages.     

Influence of steel mechanical properties on EBF seismic behaviour

Among the resisting systems suitable for the design of ductile steel structures, Eurocode 8 proposes MRFs and EBFs. The formers are considered more efficient in terms of ductility, but they suffer a strong weakness in the lateral stiffness, with following cumbersome design procedures to avoid excessive lateral displacements maintaining a quite high ductile behaviour under seismic actions. Often, the design process leads to not optimized structural members, oversized with respect to the minimum seismic requirements due to lateral deformation limitations. EBFs combine high lateral stiffness, due to bracing elements, and high dissipative capacities, provided by the plastic hinges developed in links. Eurocode 8 proposes a design procedure for EBF structures in which iterative checks are required to design links with a defined level resistance dependent on all the other links’ strength. The present paper investigates the seismic behaviour of EBFs using Incremental Dynamic Analyses (IDA) to explore their mechanical response under increasing seismic action. IDAs are executed considering the influence of variability of steel mechanical properties on the behaviour of EBFs, using seven artificial accelerograms according to Eurocode 8. The aims of IDAs are the probabilistic assessment of the response of the system with respect to the variability of the material properties, the analysis of structural safety and the ability of the structures to internally redistribute plastic phenomena during the earthquake. Structural safety conditions will be defined according to a multi-level performance approach. The paper presents also some final suggestions for possible improvements and design simplifications.     

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

Generating multiple spectrum compatible accelerograms using stochastic neural networks

A new neural‐network‐based methodology for generating artificial earthquake spectrum compatible accelerograms from response spectra was proposed in 1997, in which, the learning capabilities of neural networks were used to develop the knowledge of the inverse mapping from the response spectra to earthquake accelerograms. Recently, this methodology has been further extended and enhanced. This paper presents a new stochastic neural network that is capable of generating multiple earthquake accelerograms from a single‐response spectrum. A new stochastic feature to the neural network has been combined with a new scheme for data compression using the replicator neural networks developed in the original method. A benefit of this extended methodology is gaining efficiency in compressing the earthquake accelerograms and extracting their characteristics. The proposed method produces a stochastic ensemble of earthquake accelerograms from any response spectra or design spectra. An example is presented that used 100 recorded accelerograms to train the neural network and several design spectra and response spectra to test this improved methodology. Copyright © 2001 John Wiley & Sons, Ltd.     

Probabilistic estimate of seismic response design values of RC frames

Probabilistically controlled design values of the nonlinear seismic response of reinforced concrete frames are obtained using a method previously proposed by the authors. The method allows to calculate conservative design values characterized by a predefined non‐exceedance probability, using a limited number of spectrum‐fitting generated accelerograms. Herein the method is applied to elastic‐strain hardening single degree of freedom systems representative of RC framed structures and is then assessed with reference to four reinforced concrete model frames designed according to EC8. The frames are characterized by different natural periods and aspect ratios. The results, compared with those obtained applying current EC8 recommendations, show the effectiveness of the proposed method. EC8 provides for design values of the seismic response of a structure with a nonlinear behavior computed as the mean value of the responses to seven accelerograms or as the maximum value of the responses to three accelerograms. These two criteria lead to design values characterized by very different and uncontrolled non‐exceedance probability levels, while the proposed method allows the analyst to directly control the non‐exceedance probability level of the calculated design values. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic ground amplification induced by box-shaped tunnels

The growing use of underground structures, specifically to facilitate urban transportation, highlights the need to scrutinize the effects of such spaces on the seismic ground response as well as the surrounding buildings. In this regard, the seismic ground amplification variations in the vicinity of single and twin box-shaped tunnels subjected to SV waves have been investigated by the finite difference method. To evaluate the effects, generalizable dimensionless diagrams based on the results of parametric numerical analysis considering factors such as variations in the tunnels’ depth, the distances between the tunnels, tunnel lining flexibility, and input wave frequency, have been presented. In addition, to assess the effects of underground box-shaped tunnels on the response spectrum of the ground surface, seven selected accelerograms have been matched based on a specific design spectrum for the stiff soil condition of Eurocode 8 (CEN, 2006). The results underline the significant amplification effect of the box-shaped tunnels on the ground motions, specifically in the case of horizontal twin tunnels, which should be given more attention in current seismic design practices for surface structures.

     

Effective linear damping and stiffness coefficients of nonlinear systems for design spectrum based analysis

A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum.     

Equivalent viscous damping for displacement-based seismic design of hysteretic damped braces for retrofitting framed buildings

A displacement-based design (DBD) procedure aiming to proportion hysteretic damped braces (HYDBs) in order to attain, for a specific level of seismic intensity, a designated performance level of a structure is proposed for the retrofitting of framed buildings. A key step for the reliability of the DBD procedure is the selection of the equivalent viscous damping in order to account for the energy dissipated by the damped braced frame. In this paper, expressions of the equivalent damping are obtained considering the energy dissipated by the HYDBs and the framed structure. To this end, dynamic analyses of an equivalent single degree of freedom system, whose response is idealized by a trilinear model, are carried out considering real accelerograms matching, on the average, Eurocode 8 (EC8) response spectrum for a medium subsoil class. Then, a three-storey reinforced concrete (r.c.) framed structure of a school building, designed in a medium-risk seismic region according to the Italian code in force in 1975, is supposed as retrofitted as if in a high-risk seismic region of the current seismic code (NTC08) by the insertion of HYDBs. Nonlinear static analyses are carried out to evaluate the vulnerability of the primary structure, characterized by the lack of interior girders along the floor slab direction, and to select optimal properties of the HYDBs. The effectiveness of the retrofitting solutions is checked referring to nonlinear dynamic analyses, considering artificially generated accelerograms whose response spectra match those adopted by NTC08 for the earthquake design levels corresponding to the serviceability and ultimate limit states.     

Current empirical ground-motion prediction equations for Europe and their application to Eurocode 8

The first ground-motion prediction equation derived from European and Middle Eastern strong-motion data was published more than 30 years ago; since then strong-motion networks and the resulting databank of accelerograms in the region have expanded significantly. Many equations for the prediction of peak ground-motion parameters and response spectral ordinates have been published in recent years both for the entire Euro-Mediterranean and Middle Eastern region as well as for individual countries within this region. Comparisons among empirical ground-motion models for these parameters, developed using large regional datasets, do not support the hypothesis of there being significant differences in earthquake ground-motions from one area of crustal seismicity to another. However, there are certain regions within Europe—affected by different tectonic regimes—for which the existing pan-European equations may not be applicable. The most recent European equations make it possible to now implement overdue modifications to the presentation of seismic design actions in Eurocode 8 that allow an improved approximation to the target uniform hazard spectrum (UHS). Using these recent equations, this study outlines a new approach via which an approximation to the UHS may be constructed using hazard maps calculated for peak ground velocity and the corner period T _D in addition to the maps for peak ground acceleration that underpin the current stipulations of Eurocode 8.     

Point and fault rupture stochastic methods for generating simulated accelerograms considering soil effects for structural analysis

Many seismic codes such as the Eurocode 8 allow the use of simulated accelerograms for structural analysis, provided that the samples used are adequately qualified with regard to the seismogenetic features of the sources and to the soil conditions appropriate to the site. In the present work we studied the possibility of using stochastic methods for that purpose. In that context, two computer programs for stochastic ground motion simulation considering soil effects were developed: ACELGER based on a point source model, and SIMULSIS based on a finite fault model. Both programs were used to simulate the 1992 Landers earthquake for their validation. Simulation results obtained with these programs were compared between each other to better understand the influence of source fault plane geometry in structural response. Results seem to indicate that finite fault models are better options for structural analysis, because only with them it is possible to reproduce directivity effects and non stationary structural response observed with recorded accelerograms. SIMULSIS was also used to carry out the simulation of the 1980 Azores earthquake (January 1, 1980, Portugal) in two islands, with different local site conditions, which were compared with observed damages, to better understand the influence of soil geology in structural response, and showed that site effects have a major importance in structural behaviour.     

On the design and seismic response of RC frame buildings designed with Eurocode 8

Performance-Based Seismic Design is now widely recognized as the pre-eminent seismic design and assessment methodology for building structures. In recognition of this, seismic codes may require that buildings achieve multiple performance objectives such as withstanding moderate, yet frequently occurring earthquakes with minimal structural and non-structural damage, while withstanding severe, but rare earthquakes without collapse and loss of life. These objectives are presumed to be satisfied by some codes if the force-based design procedures are followed. This paper investigates the efficacy of the Eurocode 8 force-based design provisions with respect to RC frame building design and expected seismic performance. Four, eight, and 16-storey moment frame buildings were designed and analyzed using the code modal response spectrum analysis provisions. Non-linear time-history analyses were subsequently performed to determine the simulated seismic response of the structures and to validate the Eurocode 8 force-based designs. The results indicate the design of flexural members in medium-to-long period structures is not significantly influenced by the choice of effective member stiffness; however, calculated interstorey drift demands are significantly affected. This finding was primarily attributed to the code’s enforcement of a minimum spectral ordinate on the design spectrum. Furthermore, design storey forces and interstorey drift demand estimates (and therefore damage), obtained by application of the code force-based design procedure varied substantially from those found through non-linear time-history analysis. Overall, the results suggest that though the Eurocode 8 may yield life-safe designs, the seismic performance of frame buildings of the same type and ductility class can be highly non-uniform.     

Numbers of scaled and matched accelerograms required for inelastic dynamic analyses

Selecting, scaling and matching accelerograms are critically important to engineering design and assessment, enabling structural response to be determined with greater confidence and through fewer analyses than if unscaled accelerograms are employed. This paper considers the response of an 8‐storey multiple‐degree‐of‐freedom reinforced concrete structure to accelerograms selected, linearly scaled or spectrally matched using five different techniques. The first method consists of selecting real records on the basis of seismological characteristics, while the remaining methods make an initial selection on the basis of magnitude and spectral shape before (1) scaling to the target spectral acceleration at the initial period; (2) scaling to the target spectrum over a range of periods; (3) using wavelet adjustments to match the target spectrum and (4) using wavelet adjustments to match multiple target spectra for multiple damping ratios. The analyses indicate that the number of records required to obtain a stable estimate of the response decreases drastically as one moves through these methods. The exact number varies among damage measures and is related to the predictability of the damage measure. For measures such as peak roof and inter‐storey drift, member end rotation and the Park and Ang damage index, as few as one or two records are required to estimate the response to within ±5% (for a 64% confidence level) if matching to multiple damping ratios is conducted. Bias checks are made using predictive equations of the expected response derived from the results of 1656 nonlinear time‐domain analyses of the structure under the action of unscaled accelerograms. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic demand on light acceleration‐sensitive nonstructural components in European reinforced concrete buildings

In this paper, a parametric study is conducted in order to evaluate the seismic demand on light acceleration‐sensitive nonstructural components caused by frequent earthquakes. The study is motivated by the inconsistent approach of current building codes to the design of nonstructural components; the extensive nonstructural damage recorded after recent low‐intensity earthquakes also encouraged such a study. A set of reinforced concrete frame structures with different number of stories, that is, 1 to 10 stories, are selected and designed according to Eurocode 8. The structures are subjected to a set of frequent earthquakes, that is, 63% probability of exceedance in 50 years. Dynamic nonlinear analyses are performed on the reference structures in order to assess the accuracy of the equations to predict seismic forces acting on nonstructural components and systems in Eurocode. It is concluded that the Eurocode equations underestimate the acceleration demand on nonstructural components for a wide range of periods, especially in the vicinity of the higher mode periods of vibration of the reference structures; for periods sufficiently larger than the fundamental period of the structure, instead, the Eurocode formulation gives a good approximation of the floor spectra. Finally, a novel formulation is proposed for an easy implementation in future building codes based on the actual Eurocode provisions. The proposed formulation gives a good estimation of the floor spectral accelerations and is able to envelope the floor spectral peaks owing to the higher modes. Copyright © 2014 John Wiley & Sons, Ltd.     

基于小波变换的拟合规范反应谱多维地震动模拟

本文提出一种基于小波变换的拟合规范反应谱的多维地震动模拟算法。首先将规范反应谱推广到三维相关设计反应谱,然后将已有的三维地震动加速度时间历程曲线分解为一系列不同频段上的地震动分量,调整每一个地震动分量的幅值使其在相应的频率范围内拟合设计反应谱,最后经过调整后的地震动分量进行重构得到更新的地震动时间历程曲线。将该时间历程曲线的反应谱与目标反应谱进行比较,重复该过程直到误差位于特定的范围内。该方法可以保留原始地震动的局部时-频特性,为多维地震动的模拟提供了一种新的方法。     

Simulation of three-dimensional strong ground motions along principal axes,San Fernando earthquake

Power spectral density which describes frequency content is considered one of the most significant properties to be taken into account when generating ground motions through the use of stochastic processes. Using a smoothed and normalized Fourier amplitude spectrum, frequency content for components of motion along a set of principal axes is estimated. Fourier amplitude spectra obtained by this moving-window technique are presented which show the time dependency of frequency content for motions produced by the San Fernando earthquake of 9 February 1971. A mathematical model to simulate ground motion processes is proposed for which both the intensity and frequency content are non-stationary. Using this mathematical model with parameter characteristics along principal axes similar to those of the motions recorded during the San Fernando earthquake, three-dimensional ground motions are synthetically generated. The properties of the simulated motions show general characteristics similar to the characteristics observed in real accelerograms. The suggested model is considered adequate for engineering purposes.     

Experimental investigation on the seismic performance of masonry buildings using shaking table testing

Masonry buildings worldwide exhibited severe damage and collapse in recent strong earthquake events. It is known that their brittle behavior, which is mainly due to the combination of low tensile strength, large mass and insufficient connection between structural elements, is the main limitation for their structural implementation in residential buildings. A new construction system for masonry buildings using concrete blocks units and trussed reinforcement is presented here and its seismic behavior is validated through shaking table tests. Dynamic tests of two geometrically identical two-story reduced scale (1:2) models have been carried out, considering artificial accelerograms compatible with the elastic response spectrum defined by the Eurocode 8. The first model was reinforced with the new proposed system while the second model was built with unreinforced masonry. The experimental analysis encompasses local and global parameters such as cracking patterns, failure mechanisms, and in-plane and out-of-plane behavior in terms of displacements and lateral drifts from where the global dynamic behavior of the two buildings is analyzed comparatively. Finally, behavior factors for the design recommendations in case of unreinforced masonry are also evaluated.