Christos LACHANAS
Christos holds a Diploma (5-year program, integrated master) in Civil Engineering with major in Structural Engineering from the National Technical University of Athens (NTUA, 2013), an M.Sc. in Analysis and Design of Earthquake Resistant Structures (2016) and a Ph.D. in Civil Engineering (2022) from the same university. His Ph.D. dissertation is entitled “Seismic response standardization and risk assessment of simple rocking bodies: Cultural heritage protection, content losses, and decision support solutions”. Dr. Lachanas joined the School of Civil Engineering at NTUA in 2018 as a Ph.D. candidate and now works as a research associate (post-doctoral researcher) and member of The Lambda Lab research group. Christos’ research interests are focused on the investigation of the seismic response and risk assessment of rocking structures (e.g., monuments, building contents etc.) via nonlinear analysis methods and state-of-the-art probabilistic methodologies. Moreover, he is also interested into the structural dynamics, the quantification of the uncertainties that are associated with the seismic response of structures, and the performance-based earthquake engineering in general. He has worked as a Teaching Assistant in the School of Civil Engineering, NTUA (2019-2022), for undergraduate and post-graduate courses teaching the Design of Steel Structures, Seismic Assessment of Structures and other courses. He is participating in research projects, co-funded by EU and Greek agencies. Christos is a licensed Civil Engineer (2014) and works as a self-employed consultant engineer since 2014.
JOURNAL PAPERS
Now - 2021
Dasiou M-E., Lachanas C.G., Melissianos V.E., Vamvatsikos D. (2024). Seismic performance of the temple of Aphaia in Aegina island, Greece. Earthquake Engineering and Structural Dynamics, 53(2):573-592
Abstract | The seismic performance assessment of the ancient Temple of Aphaia in Aegina island, Greece, is presented. The Temple of Aphaia was erected around 500BC using porous limestone and is one of the most characteristic examples of Doric architecture. The assessment is performed within a performance-based framework using state-of-the-art tools of earthquake engineering. In the first part, the seismic hazard of the site was calculated using the European Seismic Hazard Model and hazard-consistent records were selected. Then, the Temple was scanned by drone and the point cloud was used to develop the numerical structural model. The Temple was analyzed using the discrete element method. Appropriate engineering demand parameters and limit state thresholds were defined. Fragility curves for the structural elements, namely, columns and architraves, of the Temple were computed via multi-stripe analysis. Finally, the seismic risk of the Temple was evaluated using long-term estimates in terms of return periods of exceeding limit states and total loss. The outcomes of the study offer valuable information to engineers, architects, and archaeologists regarding the current status of the monument in terms of identifying its most vulnerable elements and allowing the prioritization of short- and long-term restoration actions.
Lachanas C.G., Vamvatsikos D., Dimitrakopoulos E.G. (2023). Intensity measures as interfacing variables versus response proxies: The case of rigid rocking blocks. Earthquake Engineering and Structural Dynamics, 52(6):1722-1739.
Abstract |A comparative study of alternative Intensity Measures (IMs) for structures of rocking response is presented, focusing on the salient characteristics that define the selection of an optimal IM for the problem at hand. An IM may play the role of an interfacing variable, linking hazard with fragility/vulnerability for the risk assessment of structures, or it may only be employed as a proxy for predicting structural response under a given ground motion. In the first case, low conditional variability (high efficiency) and low conditional dependence on seismological parameters (high sufficiency) are needed. For response proxy usage, one may place more importance on the predictive capability of the IM within a simple regression model, favoring high correlation and low fitting errors over an extended range of response. The results showcased that (i) the peak ground acceleration and peak ground velocity, tend to be highly efficient and sufficient in specific regions of rocking response, that is, onset of rocking and overturning, respectively, but not necessarily everywhere; (ii) the average spectral acceleration shows a more consistent performance at the cost of requiring the definition of a proper period range; (iii) magnitude sufficiency is generally more difficult to achieve, compared to the distance from the rupture, and (iv) IMs that may be unsuitable for risk and vulnerability assessment, can still be highly effective as response predictors in statistical models.
Lachanas C.G., Vamvatsikos D., Dimitrakopoulos E.G. (2022). Statistical property parameterization of simple rocking block response. Earthquake Engineering and Structural Dynamics, 52(2):394-414.
Abstract | The parametric representation of rocking fragilities is statistically investigated. Initially, the potential normalization of the rocking parameters to reduce the problem’s dimensionality is tackled by undertaking comparisons both on a single-record and a sample-of-records basis. It is found that the slenderness angle can be normalized out when probabilistically considering the rocking response of simple rocking blocks with the same semi-diagonal length. Then, the robustness of the lognormal distribution for characterizing the rocking motion is investigated. Sets of pulse-like and ordinary ground motions are employed to test the lognormal fit for the full range of rocking response when the peak ground acceleration or the peak ground velocity are employed as intensity measures. In both cases, the lognormal distribution offers an adequate, but often imperfect, baseline model of the rocking fragility curves. Instead, a shifted lognormal that accounts for the absence of response below the rocking initiation intensity is an enhanced solution that can form the basis for offering simplified response model surrogates.
Kazantzi A.K., Lachanas C.G., Vamvatsikos D. (2022). Seismic response distribution expressions for rocking building contents under ordinary ground motions. Bulletin of Earthquake Engineering, 20: 6659–6682.
Abstract | Analytical expressions are proposed for predicting the rocking response of rigid free-standing building contents subjected to seismic-induced floor excitations. The study considers a wide range of rigid block geometries and seismic floor acceleration histories that were recorded during actual earthquakes in instrumented Californian buildings, so as to cover, in a fully probabilistic manner, the entire spectrum of potential pure rocking responses, i.e. from the initiation of rocking up to the block overturning. Contrary to past observations on anchored building contents (prior to any failure in their anchorage system that could alter their response and mode of failure), it is shown that the response of free-standing blocks is not influenced by the predominant period of the supporting structure. The proposed set of equations can be utilised for estimating the response statistics and consequently for undertaking an analytical seismic fragility assessment on rocking building contents.
[pre-print version]
Reggiani Manzo N., Lachanas C.G., Vassiliou M.F., Vamvatsikos D. (2022). Uniform risk spectra for rocking structures. Earthquake Engineering and Structural Dynamics, 51(11): 2610–2626.
Abstract | This paper presents uniform risk spectra for zero stiffness bilinear elastic (ZSBE) systems. The ZSBE oscillator is a bilinear elastic system with zero post-“yield” stiffness that satisfactorily predicts the response of different systems with negative lateral stiffness (e.g., free-standing or restrained rocking blocks). It can be described by a single parameter; thus, it is simpler to produce its spectrum. Using the ZSBE proxy, this paper provides the uniform risk spectra for sites in six locations in Europe. The spectra are constructed using two distinct intensity measures (IMs): peak ground velocity (PGV) and peak ground acceleration (PGA). The efficiency of both IMs at different ranges of displacement demands is discussed and analytical approximations of the spectra are proposed.
Lachanas C.G., Vamvatsikos D., Vassiliou M.F. (2022). The influence of the vertical component of ground motion on the probabilistic treatment of the rocking response of free-standing blocks. Earthquake Engineering and Structural Dynamics. 51(8): 1874-1894.
Abstract | The influence of the vertical component of ground motion is investigated for assessing the distribution of the seismic response of unanchored rigid blocks. Multiple stripes of site-hazard-consistent ground motions are employed for calculating the seismic response of rigid rocking blocks with and without the inclusion of the vertical component. The comparison of the resulting response is being made both for single records and full suites, employing a paired record versus an ensemble-statistics comparison, respectively. It is shown that on a single record basis, the vertical component may have a non-negligible but highly variable influence on the rocking response, sometimes detrimental, sometimes beneficial. Still, when considering any large ensemble of records, the effect becomes statistically insignificant, except for the very specific case of rocking uplift for stocky blocks. To this end, for cases where the appearance of uplift is associated with damage, closed-form expressions are proposed to modify the lognormal fragility function of rocking initiation given the block slenderness and the ratio of the peak vertical over the peak horizontal ground acceleration.
[pre-print version]
Lachanas C.G., Vamvatsikos D. (2022). Rocking incremental dynamic analysis. Earthquake Engineering and Structural Dynamics, 51(3):688-703.
Abstract | The seismic response assessment of rocking systems via Incremental Dynamic Analysis (IDA) is investigated, focusing on the issues that arise in the analysis and postprocessing stages. Rocking IDA curves generally differ from those of hysteretic structural systems due to (i) the frequent appearance of resurrections; (ii) their highly weaving non-monotonic behavior; and (iii) their overall high variability. Hence, including or ignoring analysis results above the first resurrection level, deriving statistics given a response level versus an intensity measure level, as well as selecting an adequate number of ground motion records and runs per record, become challenging issues with non-trivial impact on the probabilistic characterization of rocking response. This necessitates a fresh view on analysis choices and post-processing techniques, aiming to assure the accuracy and fidelity of rocking IDA results. As an example, the effect of different choices and techniques are showcased on two-dimensional rigid blocks that are assumed to represent simplified models of monolithic ancient columns of different slenderness.
Lachanas C.G., Vamvatsikos D. (2021). Model type effects on the estimated seismic response of a 20-story steel moment resisting frame. ASCE Journal of Structural Engineering, 147(6): 04021078.
Abstract | Finite-element models of varying sophistication may be employed to determine a building’s seismic response with increasing complexity, potentially offering a higher fidelity at the cost of the computational load. To account for this effect on the reliability of performance assessment, model-type uncertainty needs to be incorporated as distinct to the uncertainty related to a given model’s parameters. At present, only placeholder values are available in seismic guidelines. Instead, we attempt to quantify them accurately for a modern 20-story steel moment-resisting frame. Different types of three-dimensional (3D), two-dimensional (2D) multibay, and 2D single-bay multidegree-of-freedom models are investigated, together with their equivalent single-degree-of-freedom ones, to evaluate the model dependency of the response both within each broad model category, as well as among different categories. In conclusion, ensemble values are recommended for the uncertainty in each model category showing that for the perfectly-symmetric perimeter-frame P–ΔP-Δ sensitive building under investigation, the uncertainty stemming from 3D versus 2D or distributed versus lumped plasticity models is lower than the governing record-to-record variability.
Kazantzi A.K., Lachanas C.G., Vamvatsikos D. (2021). Seismic response distribution expressions for on-ground rigid rocking blocks under ordinary ground motions. Earthquake Engineering and Structural Dynamics, 50(12):3311-3331.
Abstract | Predictive relationships are offered for the response of on-ground 2D rigid blocks undergoing rocking. Among others, this is pertinent to (1) modern or classical antiquity structures that utilize rocking as a seismic protection mechanism and (2) freestanding contents (e.g., cabinets, bookcases, and museum artifacts) located on the ground or lower floors of stiff buildings. Blocks of varying dimensions were subjected to a full range assessment of seismic response under increasing intensity levels of ordinary (no-pulse and no-long-duration) ground motions, parameterized by peak ground acceleration or velocity. Both response and intensity were normalized, allowing the fitting of general-purpose parametric expressions to determine the mean and dispersion of response for an arbitrary block of interest. These can be utilized in the same way as conventional strength-ratio/ductility/period relationships of yielding oscillators, to enable the rapid assessment or design of simple rocking systems.
CONFERENCE PAPERS
Now - 2019
Lachanas C.G., Vamvatsikos D., Kazantzi A.K. (2023). Intensity measures for assessing the rocking response of server racks in steel buildings. Proceedings of the 10th Hellenic National Conference on Steel Structures, Athens, Greece. (in greek)
Abstract | Alternative seismic intensity measures (IMs) are examined for the case of non-structural rocking building contents and in particular for the case of server racks standing freely on the higher floors of steel buildings. Observations following recent earthquakes in developed countries have revealed that most of the damages after a seismic event consider non-structural building contents of high value. On the other hand, the selection of a robust
IM is a basic requirement in the context of the performance-based earthquake engineering framework for assessing the seismic risk and the consequential loss/damage of engineering structures or non-structural contents with high fidelity. Hence, a bunch of alternative IMs are tested in terms of efficiency and sufficiency as potential IMs for rocking vulnerability studies. The simple planar rocking block model is employed for running nonlinear dynamic analysis with a set of 34 floor motions that were recorded during past earthquakes on the roof of instrumented steel buildings. Rocking blocks of various shapes and sizes are analyzed that resemble two-dimensional analogues of server racks. After analysis, efficiency and sufficiency of the examined IMs are compared aiming to propose optimal IMs for the case of rocking contents in the different stages of rocking response from rocking uplift to overturning.
[paper]
Vamvatsikos D., Lachanas C.G. (2023). Stranger things in seismic response and statistical tools to resolve them. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | Demogorgons, monsters, and mythical creatures do not appear only in Soviet research labs, secretive government facilities or just plain Hawkins, Indiana. They frequently cross-over to earthquake engineering in the form of questions that conform to the paradigm of “Does X matter in seismic response?”. X can be a seismological characteristic, such as duration, vertical component, incident angle, or near-field directivity; it can also be a structural property, such as building period, rocking block size, or plan asymmetry. We, as investigative structural engineers, are vastly more familiar with the latter set of queries and we are clearly better equipped to handle them. We can sometimes even provide definitive answers that most, if not all of us, would agree upon. Instead, questions involving seismological characteristics seem to leave us baffled and stuck in an Upside Down world that resembles structural engineering but is not exactly the same. Wading through its murk, it is good to have some investigative tools and processes that will help us find our way home. In the end, though, we may end up equal parts enlightened and confused, as most questions of whether something of the seismologist world matters for the structural one are nearly-universally answered by uttering “It depends”.
[paper]
Lachanas C.G., Vamvatsikos D., Dimitrakopoulos E.G., (2023). Rocking intensity measures: From interface variables to response proxies. Proceedings of the SECED 2023 Conference, Cambridge, UK.
Abstract | In the context of the performance-based earthquake engineering (PBEE) framework an intensity measure (IM) is the interface (or interfacing) variable that links the seismic hazard with the structural fragility/vulnerability for the risk assessment of structures. On the other hand, from the standpoint of structural dynamics, an IM may be used as a proxy for predicting the structural response under a specific ground motion. Hence, depending on the usage per case, different criteria of optimality should be employed. An interface variable needs to be efficient (low conditional dispersion) and sufficient (low dependence on seismological parameters), whereas also its hazard needs to be assessable via available ground motion prediction equations. For the case of a proxy, hazard computability is not necessary, whereas the most important criterion is the capability of the IM to predict the engineering demand parameter (EDP) within a (simple) regression model. Thus, a response proxy needs mainly to offer high correlation and low fitting errors within IM-EDP regression models. Herein, after addressing these two different cases of IM usage, a comparison of alternative IMs for rocking structures is presented, mainly focusing on their use within a PBEE framework for risk assessment. Simple rocking bodies are employed for running incremental dynamic analysis with a set of 105 ordinary (no-pulse-like, no-long-duration) natural ground motions. It is shown that some well-established IMs are both efficient and sufficient for the case of rocking bodies. Still, due to the nature of rocking response, some (e.g., peak ground acceleration) tend to be optimal only in specific regions of response (e.g., rocking initiation). Moreover, dependence on the magnitude of the earthquake is found to be higher than for the distance from the rupture. Finally, IMs that are inefficient and insufficient for risk assessment can be at the same time very effective when used as response proxies.
[paper]
Lachanas C.G., Vamvatsikos D., Vassileiou M.F. (2022). The influence of the vertical component of the seismic excitation on the probabilistic treatment of the seismic response of rocking rigid bodies. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract |
Vamvatsikos D., Lachanas C.G. (2022). Probabilistic distribution of ground motion via observations of rocking rigid bodies. Proceedings of the 5th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek).
Abstract |
Lachanas C.G., Vamvatsikos D. (2022). Preliminary seismic risk assessment of ancient columns across Attica for application in decision support systems. Proceedings of the 3rd European Conference on Earthquake Engineering and Seismology (3ECEES), Bucharest, Romania.
Abstract | An approach for preliminary seismic risk assessment is presented for portfolios of cultural heritage assets of classical antiquity. As an example, three ancient columns are considered, located at different sites throughout Attica: The Temple of Aphaia in Aegina, the Temple of Olympian Zeus in the centre of Athens, and the Temple of Poseidon in Sounio. Event-based probabilistic seismic hazard analysis is used for the definition of the seismic hazard via multiple correlated intensity measure fields. The seismic response of the columns is assessed via simplified equations for the prediction of the central value and the dispersion of the lognormal fragility function for rocking blocks. Afterwards, the seismic risk per asset is assessed both in terms of long-term averages, calculating the mean annual frequency of exceeding pre-defined limit states, as well as on an event-by-event basis, calculating the probability of exceeding limit states of interest per asset in scenario events. Overall, a comprehensive tool is offered for supporting decision-making on prioritizing rehabilitation actions for a portfolio of monumental structures.
[paper]
Vamvatsikos D., Lachanas C.G. (2022). Tomb raiders of the lost accelerogram: A fresh look on a stale problem. In: Vacareanu, R., Ionescu, C. (eds) Progresses in European Earthquake Engineering and Seismology. ECEES 2022. Springer Proceedings in Earth and Environmental Sciences. Springer, Cham. DOI: 10.1007/978-3-031-15104-0_4
Abstract | Throughout recorded history, accelerograms have displayed an unfortunate tendency to become unrecorded and lost. Statistically speaking, even after the advent of low-cost accelerometers, the ground motion retains an almost 100% chance of staying unobserved at any given point. One may only place some limits on the peak amplitude of ground motion by observing its effects, or lack thereof. To do so, seismologists run to the mountains, looking for fragile geological features, such as precariously balanced rocks. Structural engineers take a slightly more cinematic and sinister approach. They put on their fedora hats (or tank top and shorts, for video game enthusiasts) and go tomb raiding, searching for rocking rigid bodies that may have survived or toppled in graveyards, tombs, mausoleums, churches, and temples. Yet how is one to best make sense of such low-entropy (and sometimes contradictory) uncertain information? Let’s have some fun by blowing an old problem to smithereens, perhaps needlessly bringing to bear all the tools of contemporary earthquake engineering, ranging from ground motion prediction models and correlation structures to rocking body fragilities and Bayesian analysis.
Kazantzi A.K., Lachanas C.G., Vamvatsikos D. (2022). Normalized response distribution expressions for ground-supported rigid rocking bodies. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | Estimating the seismic response of ground-supported rocking rigid blocks, is a topic that has attracted significant research interest in the past few decades, since it concerns, among others: (a) several modern structures or ancient monolithic columns that utilize rocking as a seismic protection mechanism and (b) numerous free-standing contents (e.g. museum artefacts) located on the ground floor or lower floors of stiff buildings. In the present research work, by means of a parametric study, utilizing two-dimensional rectangular blocks of varying sizes and ordinary earthquake records, the rocking response at increasing intensity levels was assessed through Incremental Dynamic Analyses. Following the demand evaluation and in order to allow for an easier utilization of the findings in practical applications, simplified approximate equations have been obtained via nonlinear regression analysis. The proposed equations provide an estimate of the peak rocking response distribution, expressed in terms of the normalized, to the dimensionless slenderness angle , peak rocking angle, at increasing ground motion intensity levels.
[paper]
Reggiani Manzo N.R., Vassiliou M., Lachanas C.G., Vamvatsikos D. (2022). Α Risk-Based Design Procedure for Negative Stiffness Bilinear Elastic Systems. Proceedings of the 3rd International Conference on Natural Hazards & Infrastructure ICONHIC 2022, Athens, Greece.
Abstract | This paper presents uniform risk spectra for systems with lateral negative stiffness, such as free-standing, restrained or curved-end rocking blocks. The spectra are constructed using a simplified system, the Zero Stiffness Bilinear Elastic system, which can satisfactorily predict the response of different systems with negative lateral stiffness. The paper offers the step-by-step methodology for the construction of the spectra. It presents the construction and discussion of the spectra for a site in Athens, Greece using two distinct intensity measures: Peak Ground Velocity and Peak Ground Acceleration.
[paper]
Lachanas, C. G., Melissianos, V. E., and Vamvatsikos, D. (2021). Spatial variability of ground motion hazard and preliminary regional damage assessment of ancient monuments. Proceedings of the 4th International Conference on Protection of Historical Constructions (PROHITECH 2020), Athens, Greece
Abstract | The seismic hazard is a spatial variable and its distribution depends on the site and soil conditions, the distance from the influencing faults, their geometric characteristics etc. To characterize a future seismic event, multiple correlated Intensity Measure (IM) fields are employed. In Greece and especially in the Attica region, there are numerous monuments of classical antiquity that are spread throughout the territory, e.g., the Temple of Poseidon in Sounio, the Ancient Walls of Piraeus etc., and not only in the center of the city of Athens, where the well-known Parthenon, the Temple of Olympian Zeus, etc. lie. To capture the ensemble risk of such widely distributed antiquities a regional risk assessment approach is adopted, based on the principles of the Performance-Based Earthquake Engineering. Event-Based Probabilistic Seismic Hazard Analysis (PSHA) is used as basis, where the distribution of the ΙΜ fields is evaluated for a stochastic event set, spanning thou-sands of realizations, allowing the estimation of damages over an entire region on an event-by-event basis. A basic application is offered by considering a typical single multi-drum column at each site of interest to assess its performance. Different fragility representation schemes are employed, and their consequences are compared for both the event-based and the classical approach of PSHA as a first decisive step towards the formulation of a comprehensive methodology for the assessment of seismic damages of ancient monuments within a region.
Melissianos, V. E., Lachanas, C. G., and Vamvatsikos, D. (2021). Preliminary seismic risk assessment of monolithic columns of the Aphaia Temple in Aegina. Proceedings of the 4th International Conference on Protection of Historical Constructions (PROHITECH 2020), Athens, Greece
Abstract | Studies on the seismic assessment of monumental structures of antiquity are mostly focused on the estimation of the structural behavior and do not involve the pertinent uncertainties. Towards filling this research gap, a preliminary seismic risk assessment of monolithic columns of the Aphaia Temple in Aegina island, Greece, is presented. A comprehensive application of the framework of Performance-Based Earthquake Engineering is carried out. Site-specific seismic hazard estimation is performed at first by employing Probabilistic Seismic Hazard Analysis. The rocking column is analyzed under seismic excitation by numerically solving the equation of motion in order to extract the fragility curves. Finally, the convolving of seismic hazard and structural response yields the seismic risk of the column that is used to estimate the mean annual rate of exceeding predefined limit states that are associated with damage and collapse of the column.
Reggiani Manzo N., Lachanas C.G., Vassiliou M.F., Vamvatsikos D. (2021). Uniform risk spectra for negative stiffness systems. Proceedings of the COMPDYN2021 Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Athens, Greece.
Abstract | This paper presents uniform risk spectra for negative stiffness systems that do not exhibit hysteretic damping, named Negative Stiffness Bilinear Elastic (NSBE) systems. The NSBE oscillator can be used to describe the dynamics of deformable rocking systems with or without restraining systems flexible enough to lead to an overall negative stiffness. It can also be used to describe rocking systems equipped with curved extensions at their base. It has been shown that the response of an NSBE system can be well predicted using the response of a Zero Stiffness Bilinear Elastic (ZSBE) system, which is a bilinear system of constant restoring force. The ZSBE system is a single parameter system; therefore it is simple to construct design spectra for it. For a wide range of ZSBE system strength values, this paper employs Incremental Dynamic Analysis using 105 ordinary (non-pulse-like, non-long-duration) ground motions to obtain the fragility functions for predefined limit-states of the ZSBE seismic response. Fragility functions per limit-state are convolved with the seismic hazard to compute the Mean Annual Frequency of exceedance (MAF). For this study, the seismic hazard curve for a site at Athens Greece is used as it is obtained via probabilistic seismic hazard analysis. Finally, uniform risk spectra per limit-state are obtained by computing the MAF for all the ZSBE oscillators. These spectra can be used for the design of NSBE systems, including rocking oscillators.
Manzo N.R., Lachanas C.G., Vassiliou M., Vamvatsikos D. (2021). Uniform risk spectra for negative stiffness systems. Proceedings of the 8th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN 2021, Athens, Greece.
https://doi.org/10.3929/ethz-b-000492004
[paper]
Abstract | This paper presents uniform risk spectra for negative stiffness systems that do not exhibit hysteretic damping, named Negative Stiffness Bilinear Elastic (NSBE) systems. The NSBE oscillator can be used to describe the dynamics of deformable rocking systems with or without restraining systems flexible enough to lead to an overall negative stiffness. It can also be used to describe rocking systems equipped with curved extensions at their base. It has been shown that the response of an NSBE system can be well predicted using the response of a Zero Stiffness Bilinear Elastic (ZSBE) system, which is a bilinear system of constant restoring force. The ZSBE system is a single parameter system; therefore it is simple to construct design spectra for it. For a wide range of ZSBE system strength values, this paper employs Incremental Dynamic Analysis using 105 ordinary (non-pulse-like, non-long-duration) ground motions to obtain the fragility functions for predefined limit-states of the ZSBE seismic response. Fragility functions per limit-state are convolved with the seismic hazard to compute the Mean Annual Frequency of exceedance (MAF). For this study, the seismic hazard curve for a site at Athens Greece is used as it is obtained via probabilistic seismic hazard analysis. Finally, uniform risk spectra per limit-state are obtained by computing the MAF for all the ZSBE oscillators. These spectra can be used for the design of NSBE systems, including rocking oscillators.
Lachanas C., Vamvatsikos D. (2019). Model influence on the estimated seismic response of a 20-story steel moment-resisting frame. Proceedings of the 4th Panhellenic Conference on Earthquake Engineering and Engineering Seismology, Athens, Greece (in greek)
Περίληψη | Τα σύγχρονα λογισμικά πεπερασμένων στοιχείων, παρέχουν τη δυνατότητα μελέτης της συμπεριφοράς των κατασκευών μέσω προσομοιωμάτων διαφορετικών βαθμών πολυπλοκότητας. Εστιάζοντας στην εκτίμηση της σεισμικής απόκρισης ενός κτιρίου μέσω μη γραμμικών δυναμικών αναλύσεων, η αύξηση της πολυπλοκότητας του προσομοιώματος συνεπάγεται αύξηση στο υπολογιστικό κόστος, προκρίνοντας τη χρήση απλούστερων ισοδύναμων προσομοιωμάτων με συνεπαγόμενη αύξηση της αβεβαιότητας. Για μια πρώτη ποσοτικοποίηση της αβεβαιότητας που αφορά τον τύπο του προσομοιώματος, μελετάται ένα σύγχρονα σχεδιασμένο 20-όροφο μεταλλικό κτίριο με πλαισιακό φορέα. Ξεκινώντας από το τρισδιάστατο προσομοίωμα του κτιρίου και ακολουθώντας σταδιακή απλοποίηση του προσομοιώματος σε δισδιάστατο προσομοίωμα πλαισίου πολλών ανοιγμάτων και δισδιάστατο προσομοίωμα πλαισίου ενός ανοίγματος, καταλήγουμε στο ισοδύναμο μονοβάθμιο προσομοίωμα. Στα προσομοιώματα εκτελείται Ικανοτική Δυναμική Ανάλυση.
Από τη σύγκριση προκύπτει ότι για το υπό μελέτη κτίριο η αβεβαιότητα λόγω τύπου προσομοιώματος είναι σχετικά περιορισμένη, ενώ η συνολική αβεβαιότητα κυριαρχείται από τη σημαντική διασπορά στην απόκριση μεταξύ των καταγραφών εντός του κάθε προσομοιώματος.