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This volume gathers the latest advances, innovations, and applications in the field of seismic engineering, as presented by leading researchers and engineers at the 1st International Workshop on Energy-Based Seismic Engineering (IWEBSE), held in Madrid, Spain, on May 24-26, 2021. The contributions cover a diverse range of topics, including energy-based EDPs, damage potential of ground motion, structural modeling in energy-based damage assessment of structures, energy dissipation demand on structural components, innovative structures with energy dissipation systems or seismic isolation, as well as seismic design and analysis. Selected by means of a rigorous peer-review process, they will spur novel research directions and foster future multidisciplinary collaborations.



Assessment of Plastic Energy Demand Spectra on Frame Systems

Determination of structural resistance to seismic loads is a complex problem. To overcome the complexity, simple but efficient methods have been developed for engineers. In that process for the sake of simplicity and practicality, certain assumptions are made in defining seismic demand. One of the them is energy dissipation by structural members during seismic actions. However, energy dissipation is directly related to damage occurrence and propagation in the member. Calculation of plastic energy to be dissipated by structural member requires definition of energy demand on the structural system. This study aims to assess plastic energy spectrum approach on frame type reinforced concrete structures. Plastic energy demand values on three frame systems representing low- to mid-rise buildings are obtained from plastic energy spectrum and also nonlinear time history analysis (NLTH). Plastic energy spectrum is taken from the previous study of the authors. Comprehensive NLTH analyses on selected frame systems are conducted on the pre-designed systems which consists of concentrated plastic hinges. Moment and rotation response time histories of the structural members are used in calculation of energy dissipation. Comparisons between spectra- and NLTH-based results are made on three systems. For low-rise system, both plastic energy dissipation values are found approximate whereas for mid-rise systems, plastic energy spectrum is found conservative. The numerical examples reveal that plastic energy spectrum is a robust concept for energy-based design methodologies.
Ahmet Anıl Dindar, Gökhan Polat, Cem Yalçın, Ercan Yüksel, Hasan Özkaynak, Oral Büyüköztürk

Effects of Pre-existing Damage on Fragility of URM and RC Frame Buildings

After the recent earthquake sequences that have hit Italy, New Zealand, and other parts of the world, the evidence that damage in buildings that experienced multiple shocks is, in general, more severe at the end of the sequence than after the mainshock is even more apparent and better documented. However, analytical studies still struggle in providing realistic estimates of how the damage progresses during a sequence of shocks. Predicting damage accumulation is of paramount importance for achieving accurate risk estimates for building stocks in all regions of the world where earthquake sequences are common. This study attempts to provide a framework for generating damage-state-dependent seismic fragility functions for two types of structures: unreinforced masonry buildings (URMs) and reinforced concrete frame buildings (RCFs). We adopted a component-based approach for estimating damage, built on energy-based parameters. In the case of URMs, we consider the energy released through shear damage of masonry components. For RCFs, we utilized the modified Park and Ang damage index. The findings suggest that estimates of maximum global or local deformation experienced during a shock are not fit to model damage progression throughout earthquake sequences. Furthermore, a component-based methodology with local parameters is superior to using global response parameters, such as maximum inter-story drift ratio. However, this study’s results suggest that the ground to cover before achieving defensible cumulative damage estimates is still considerable. The need to develop and calibrate demand parameters to capture the progression of damage through all damage states with better precision is needed but not yet within our reach.
P. García de Quevedo Iñarritu, N. Šipčić, M. Kohrangi, P. Bazzurro

Energy Dissipation Capacity of RC Columns Subjected to Dynamic Biaxial Seismic Loadings on a Shake Table

Knowing the (ultimate) energy dissipation capacity of structural members is a key aspect of seismic design based on the energy-balance, since it is the main parameter for verification. The gap in knowledge about the energy dissipation capacity of structural members is considerable, particularly for reinforced concrete (RC) structural elements. In this study, the energy dissipation capacity of three RC columns subjected to dynamic seismic loadings on a shake table is investigated. The columns are tested within a structure that represents a scaled portion of a three-story prototype building. Two of the columns reached failure and the third one was severely damaged. It is found that the total ultimate energy dissipation capacity of the two columns that failed is very similar, although they followed different loading paths and dissipated very different amounts of energy in the X and Y directions. Finally, it is shown that the chord rotation (at least alone) is not a good indicator of damage.
Amadeo Benavent-Climent, David Escolano-Margarit, Leandro Morillas

Spatial Distribution of Hysteretic Energy in Reinforced Concrete Moment Resisting Frames

Nowadays, structural engineers perceive that conventional force-based seismic design method is not still the unique way of designing structures subjected to ground motions. The reason is that it does not consider inelastic displacement, plastic structural behavior and duration of seismic motion. At the present time, there are new and popular alternatives like displacement-based method, in which the aforementioned issues are mostly handled. Energy-based approach is another convenient tool to examine the seismic response of structures under seismic action and probably the best way to include duration of ground motion within the analysis. In this approach, the energy input to the structure should be dissipated through inelastic action (hysteretic energy) and damping. Hence it is an important challenge to obtain the distribution of hysteretic energy within the building in order to develop energy-based design and analysis tools. Such studies have been conducted for steel frames previously, but not extensively for RC frame structures. Accordingly, this study is focused on the story-wise and component-wise distribution of hysteretic energy in RC moment resisting frames. For this purpose, RC frames with different number of stories and bays are designed according to the 2018 Turkish Seismic Code. Then the designed frames are modeled by using lumped plasticity approach. The developed models are subjected to a set of strong ground motion records and the distributions of hysteretic energy for each frame and analysis are obtained. The results indicate that it is possible to set up some rules for the hysteretic energy distribution in RC frames that can be used in energy-based design and analysis procedures.
M. Altug Erberik, Mahyar Azizi

Reinforced Concrete Columns: Insight on Energy-Based Assessment from Biaxial Tests with Different Load Paths

Results from a recently concluded experimental campaign on non-conforming reinforced concrete cantilever columns failing in both flexure and flexure-shear modes under five different load paths are used to discuss whether an energy-based failure criterion would be advantageous with respect to a deformation-based one. Based on the limited evidence of these 18 tests it appears that the relation between energy and damage, compared to that of drift ratio and damage, is influenced to a lesser extent by load path, but this only holds in some cases and cannot be generalized. In particular, the occurrence of any phenomenon that interrupts the stable energy dissipation mechanism through inelastic flexure leads to failure prior to the attainment of the energy threshold. This can occur in many practical situations indicating that it may not be feasible to use energy as a useful measure in the seismic assessment of existing frames.
Paolo Franchin, Andrea Lucchini, José Miranda Melo

Evaluation of Different Approaches to Estimate Seismic Input Energy and Top Displacement Demand of Moment Resisting Frames

Energy-based seismic design (EBSD) has many advantages over the conventional design approaches (force- and displacement-based) provided by the current seismic design codes since it accounts for duration, frequency content and pulse-type of the ground motion. Cumulative damage potential of the earthquake excitation is also taken into consideration by this approach. In order to obtain a satisfactory design, energy capacity of a structure should exceed the energy demand from an earthquake in EBSD. The structural damage indicators like inelastic top displacement demand (δtop) of MDOF system, which can be used as a crucial input data for general nonlinear static analysis procedures, are claimed to be accurately predicted using the input energy. Primarily, seismic input energy per unit mass (EI/m) imparted into a MDOF frame system during an earthquake is determined by only using modal properties of the system and input energy time series of earthquake ground motion on its equivalent SDOF systems. Using the determined seismic input energy per unit mass, δtop is predicted by literature equations. Effects of spectral matching on the success of seismic input energy and inelastic displacement demand estimations were also investigated. Evaluation of the predictions of δtop was achieved by comparing with the results of nonlinear time history analyses (NLTHA) on two distinct three-story moment resisting frames. It was observed that the relative differences between analyses results and the predicted values were calculated as 18% (input energy prediction) and 30% (top displacement prediction) for the original records whereas they were 12 and 20% for the spectrally matched ground motions.
Furkan Çalım, Ahmet Güllü, Ercan Yüksel

NDSHA—A Reliable Modern Approach for Alternative Seismic Input Modelling

The energy-based design concept considers earthquake effect as an energy input and how this energy is distributed within the structure. The structural damage indicates that some of this energy was not duly dissipated by the structure. Realistic alternative time histories representation of seismic action is crucial for reliable assessment of the earthquake energy input, transmitted to the structures, as well as for relevant damage capacity of the site-specific seismic actions. The Neo-Deterministic Seismic Hazard Assessment approach, NDSHA formulated at the turn of Millennium provides a reliable base for further cause–failure–impact analyses and can be applied for SHA at local, national, and regional scales. NDSHA, in its standard form, defines the hazard as the largest ground shaking at the site, computed considering a large set of scenario earthquakes, including the maximum credible earthquake (MCE), whose magnitude and focal mechanism is defined from regional seismic history and seismotectonics. This approach allows for a realistic description of the seismic ground motion due to an earthquake of given epicentral distance and magnitude at any point of interest within a given construction site. It relies on the existing acquired expert information—usually available via the technical documentation of the infrastructure projects—e.g., the comprehensive geological reports that provides detailed geological and geophysical data on the site. This contribution provides a brief description of the worldwide-validated NDSHA tools and illustrates their relevance for the energy-based design concept.
Mihaela Kouteva-Guentcheva, Giuliano F. Panza

A Review on Performance-Based Plastic Design Method: Concept and Recent Developments

The Performance-based Plastic Design (PBPD) Method is a practical seismic design and evaluation approach based on an energy concept. The required frame strength is derived corresponding to a target deformation level and a selected yield mechanism using the energy balance concept. The method directly accounts for inelastic behavior and considers the internal force distribution at the ultimate limit state by ensuring the formation of a pre-selected yield mechanism. Plastic design is specifically used to design the structure to achieve the selected mechanism and ensure uniform damage. Since its inception, the method has been successfully applied to a variety of steel and RC framing systems. The underlying energy equation has also been used for seismic evaluation and retrofitting design of existing structures. This paper provides an overview of the concept, the framework, and the development of the PBPD method. Key aspects of the PBPD method including the energy demand calculation, the force and member strength distribution to achieve uniform damage, and hysteretic consideration are reviewed and discussed. An example that illustrates the PBPD concept is provided. Finally, recent developments of the PBPD method in the literature are also summarized and discussed.
Sutat Leelataviwat, Piseth Doung, Nattakarn Naiyana

Effect of Kinematic Hardening and Ductility Ratio on Inelastic Input Energy Spectra of Near-Fault Ground Motions

In energy-based seismic design of structures, ground motion effect is considered as an energy input to the systems. Consistent development of input energy spectra is of great importance for the energy-based seismic design since the total energy input to structural systems can be practically obtained by means of these graphs. The main purpose of the present study is to investigate the influence of post-yield stiffness ratio and ductility demand on inelastic input energy spectra of near-fault ground motions. A wide range of nonlinear single-degreed-of-freedom (SDOF) systems characterized by their natural periods ranging from 0.02 to 3.0 s and normalized lateral strength are considered. Bilinear elastoplastic (BEP) hysteresis models with six different post-yield stiffness ratios are used to generate the results for constant ductility ratios ranging from 2 to 5. Mean ± one standard deviation input energy equivalent velocity spectra of a set of 21 near-fault accelerograms exhibiting pulse-like characteristics are computed based on nonlinear time history analyses of SDOF systems with 5% damping. The analytical results have shown that the influence of post-yield stiffness ratio on inelastic input energy spectra of near-fault ground motions can be neglected practically, whereas the influence of ductility ratio is more obvious. Moreover, a transition period of approximately 0.7 s between the increasing and decreasing input energy equivalent velocity spectra based on ductility ratio is identified.
Taner Ucar, Onur Merter

Least-Square Effective Stiffness to be Used for Equivalent Linear Model

This work introduces a method for the identification of linear stiffness and viscous damping parameters from a one-degree-of-freedom force-displacement cycle. Using an original approach, the stiffness parameter is derived by a least-square formula from the discrete input force-displacement point coordinates of the loop. The damping ratio is obtained in a classic manner from the quotient of absorbed and elastic energy. The obtained stiffness and damping parameters are proposed to be used, with the known mass, as an equivalent linear mass-spring-damper that should predict the response to a known load for the original nonlinear system associated to the input force-displacement cycle. As an example study, the effectiveness of such prediction is qualitatively shown in the case of the steady-state response to a harmonic load for a particular hysteretic numerical model, by using a range of values for some dimensionless parameters. This kind of study is susceptible to be extended to other kinds of loading and/or numerical and experimental hysteretic models, as well as to other identification procedures available in the literature.
Francisco J. Molina, Pierre Pegon

Key Points and Pending Issues in the Energy-Based Seismic Design Approach

Since the pioneering works conducted by Housner in the 1960s, energy-based seismic design (EBD) has evolved thanks to many researchers. Notwithstanding, it is overshadowed by the force-based design (FBD) approach, and its implementation in seismic codes is currently limited to structures with energy dissipation systems in Japan. The “Vision 2000” report on future design codes identified EBD as a most promising approach towards the paradigm of performance-based design, however. This paper revises key aspects of EBD, particularly how it differs from FBD and displacement-based design (DBD). Important issues to be addressed in the future so as to implement EBD in the seismic design of conventional structures are underlined. New relations between cumulative energy dissipation and maximum displacement for two different restoring force rules—and for two types of ground motions (with and without pulses)—are presented. Furthermore, a simple means of determining the design-value of the ultimate energy dissipation capacity of non-degrading steel components is put forth.
Amadeo Benavent-Climent, Jesús Donaire-Ávila, Fabrizio Mollaioli

A Damage Index for the Seismic Evaluation of Buckling-Restrained Braces

This paper focuses on evaluating whether a buckling-restrained brace (BRB) element should be replaced after an earthquake event. For this purpose, a damage index is proposed based on the experimental data obtained from a series of tests conducted on different BRB specimens. In total 19 full-scale BRB specimens were manufactured with local industry and workforce, and tested. 14 BRB specimens were tested using a low-cycle loading protocol, and five BRB specimens were tested using a high-cycle fatigue loading protocol. For the low-cycle protocol, the axial strain in the BRB core was continuously increased until failure, while for the fatigue protocol, the axial strain in the core was increased from zero to 1.5%, and continued at 1.5% strain until core failure occurred. The proposed damage index has been calibrated based on the experimental results, and is capable of considering the effect of the maximum core strain attained as well as the cumulative deformation effect. A qualification scale has been assigned to the proposed damage index as a tool for evaluating whether the BRB element should be replaced or left on site. Furthermore, a series of nonlinear dynamic analyses were carried out on a sample building in order to validate the proposed damage index when subjected to ground motions. Finally, the results suggest that the proposed damaged index can be useful in structural design practice.
J. A. Oviedo-Amezquita, N. Jaramillo-Santana, C. A. Blandon-Uribe, A. M. Bernal-Zuluaga

An Energy-Based Prediction of Deformation Demand on Low- to Mid-Rise R/C Buildings with Hysteretic Dampers

This study focuses on frame buildings equipped with hysteretic dampers, and presents an energy-based methodology to estimate the earthquake deformation demand after damper installation. The proposed methodology considers not only structural and dynamic characteristics of the main frame and dampers, but also input ground motion characteristics. For this purpose, five R/C building structures with 2, 4, 6, 8 and 10 stories were designed according to the Colombian seismic code, and further converted into equivalent single-degree-of-freedom (SDOF) system models. Hysteretic dampers with varying mechanical properties were then installed into the SDOF models, and the models were then subjected to a series of 30 input ground motions. The input motions were modified to represent the seismic intensity given in the Colombian code and to grant certain control over the input energy. Furthermore, a discussion over the results of a three-dimension sample R/C frame building is presented. The predicted deformation demand obtained from the proposed methodology was compared with that obtained from the analysis. The methodology was shown to be useful for the preliminary assessment of the earthquake response of frame buildings with dampers.
J. A. Oviedo-Amezquita, S. Henao-Munoz, A. M. Bernal-Zuluaga

Energy-Based Topology Optimization Under Stochastic Seismic Ground Motion: Preliminary Framework

The growing availability of suitable computational resources to support the design of complex and large buildings makes the topology optimization more and more attractive to achieve high structural performances while reducing the use of building materials and thus cutting the total costs. In case of buildings under dynamic loads, displacement- and acceleration-based criteria are most commonly employed in topology optimization for preventing damage in structural components and protecting high-frequency sensitive non-structural components, respectively. The present work introduces the energy-based topology optimization of large structures as a more effective design approach to mitigate damage due to earthquake. The inherent randomness of the seismic excitation is taken into account by means of the random vibration theory, in such a way to avoid the direct integration of the motion equations for a large number of records. Topology optimization is performed via Solid Isotropic Material with Penalization (SIMP) method and resorting to an analytical evaluation of the gradient. A stationary-type stochastic seismic ground motion is considered in the preliminary framework presented in this study, whereas the final case study here discussed is concerned the search of the optimal layout for a lateral resisting system in a multi-story building subjected to earthquake.
Giulia Angelucci, Giuseppe Quaranta, Fabrizio Mollaioli

Energy-Based Seismic Design Method for Coupled CLT Shear Walls

Ductile cross-laminated timber (CLT) shear walls can be achieved by vertically joining a series of CLT panels with ductile connectors. When such multi-panel systems have a well-defined center of rotation, the resulting kinematic behavior is termed as coupled-panel (CP). In this paper, an iterative energy-based design (EBD) method is proposed for CLT shear walls based on energy balance established on their CP kinematic. Holz-Stahl-Komposit (HSK) connectors were utilized for both hold-downs and vertical joints. The seismic energy demands were estimated from constant ductility hysteretic energy spectra established for elastic-perfectly-plastic single-degree-of-freedom oscillators. The lateral force-deformation characteristics were derived considering the CP behavior in elastic and plastic ranges. Subsequently, the ductility demand was evaluated from these force-deformation relations. The story-wise hysteric seismic energy demands were balanced by the cyclic energy supply. While the lateral yield resistances were attributed to the hold-downs and vertical joints, the lateral plastic deformations were attributed to the vertical joints. The proposed EBD method accounts for the preferred failure mode together with performance criteria derived from either target deformation limit-states or local deformation capacities of the energy dissipative components.
Selamawit Dires, Thomas Tannert, Solomon Tesfamariam

Energy-Based Design Process for Passive Control Structures Considering Torsional Effect

The seismic performance of structures associated with dampers, called as passive vibration-controlled structures, depends considerably on the damper’s mechanical characteristics, which is expected to dissipate most of seismic energy by their nonlinear hysteretic behavior. Force-based design procedure presented in ASCE7, mostly referred for the design of structures with dampers, has limitations in quantifying the plastic deformation capacity required for dampers. Moreover, there is a lack of knowledge in formulation for torsional effect, which is potential by irregularities according to variations in damper characteristics and irregular arrangement of the dampers. Therefore, it inevitably requires repetitive analysis to verify the seismic performance in the design. In this research, a design method is proposed based on energy-based design approach to consider the torsional effect on passive control structures. The proposed method is the prediction of seismic response of structures, which is obtained throughout a large number of nonlinear analysis. The yield strength distribution of dampers through the height of structure was found be vital parameter for energy dissipation. Therefore, the optimum yield strength distribution of dampers is suggested to evenly distribute the accumulated plastic deformation ratio in torsional systems. Also, the yield deformation ratio between dampers and structural members is suggested in order to induce the most of damage concentrated to dampers at each floor. The analysis shows that by selecting the appropriate range of damper’s characteristics such as strength and stiffness, the response of structures can be controlled in accordance with design objectives.
Sanghoon Oh, Seunghoon Shin, Bahador Bagheri

Efficiency of Viscous Damping in Seismic Energy Dissipation and Response Reduction

Input energy accumulates at a specific rate, and viscous damping dissipates the accumulated input energy at a slower pace. The difference between the two energy time histories at a time t is the vibration energy Ev(t), which is the sum of kinetic and potential energies at time t. Maximum displacement occurs shortly after Ev attains its maximum value during the following cycle when potential energy is maximum and kinetic energy is zero. An efficient damping produces lower Ev, accordingly lower maximum displacement. We choose to define the damping efficiency as the ratio of dissipated energy ED to input energy EI at the time tmax when Ev(t) attains its maximum value for a SDOF system with period T. The influence of earthquake magnitude, fault distance, soil type and fault type on damping efficiency are assessed here under a large set of earthquake ground motions that represent the distribution of such characteristics effectively. A large set of free-field strong motion records are selected from the NGA database. Damping ratio, soil class, distance to epicenter (Repi), moment magnitude (Mw), and fault mechanism are selected as the basic parameters in order to characterize source and site properties of ground motions. Based on the employed GM database, it has been found that damping efficiency is affected most by the earthquake magnitude, soil type, and expectedly by the damping ratio.
Fırat Soner Alıcı, Halûk Sucuoğlu

Vector-Valued Intensity Measures to Predict Peak and Hysteretic Energy Demands of 3D R/C Buildings

In this study, several peak and energy vector-valued ground motion intensity measures (IMs) are proposed to predict maximum inter-story drift and hysteretic energy demands of 3D reinforced concrete (R/C) buildings subjected to narrow-band motions. The selected vector-valued IMs are based on the spectral acceleration, pseudo-velocity, velocity and input energy at first mode of the structure as first component. As the second component, ground motion parameters based on peak, integral and spectral shape proxies such as the well-known Np are used. The objective of the present study is to provide vector-valued IMs whit the ability to predict the maximum inter-story drift and hysteretic energy demands on 3D framed structures. It is observed that vector-valued IMs based on Np provide a high relation whit maximum inter-story drift and hysteretic energy demands of reinforced concrete framed buildings.
José I. Torres, Edén Bojórquez, Alfredo Reyes, Juan Bojórquez

Evaluation of Earthquake Resistance of Steel Moment Resisting Frames

Proper evaluation of the energy dissipation capacity of a structure, along with proper assessment of inputs, is an important basis of energy-based seismic design. Earthquake response analysis is a useful tool for establishing and calibrating a design method. The reliability of the design method depends largely on the reliability of the analysis. The reliability of the analysis result improves according with the accuracy of the hysteresis model applied to the analysis. In this study, first, based on the experimental results of cyclic loading tests conducted with various loading condition and loading protocol, and analytical results of numerical study, realistic hysteresis model of steel structural members subjected to cyclic bending under axial force is modeled. Next, to evaluate the ultimate earthquake resistance of steel moment resisting frames (MRFs), some series of response analyses of steel MRFs adopted to the proposed hysteresis model are conducted. From the analysis results, the effects of various parameters related to the MRFs, such as the deformation capacity of the column determined by local buckling, the elastic stiffness and strength of the column base, on the ultimate earthquake resistance of the steel MRFs are evaluated. Furthermore, seismic performance of MRFs under multiple strong excitations are examined.
Satoshi Yamada

Energy-Based Design Theory for Self-Centering Structures

Although conventional structures can be designed to avoid collapse under seismic actions, unrecoverable nonlinear deformations would still occur to dissipate earthquake energy. It enlarges structural damages and residual deformations, which leads to repair costs increased and downtime prolonged. Self-centering structures are introduced for the resilience demand in seismic engineering. Inelastic behaviors can be limited within specific areas, which would prevent key components from unrecoverable damages. This paper presents an energy-based design theory (EBDT) for self-centering structures. A damage model considering both residual deformation and hysteretic energy EH is proposed. Based on the design energy spectrum and the damage model, EH is introduced as a design parameter and accounted in the design procedure. EBDT enables designers to select multiple performance objectives for different seismic hazards. The design procedure is elaborated with an example. The results show that EBDT can provide a reliable design procedure for self-centering structures.
Ge Song, Ying Zhou, T. Y. Yang
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