Distribution Of Hysteretic Energy Research Articles

A direct energy-based design method for damping control reinforced concrete structure: methodology and application

Energy-based seismic design, which integrates both the accumulated hysteretic energy and plastic deformation of the structure, provides a more comprehensive evaluation of structural seismic performance compared to other performance-based seismic design methods. In damping control structures, the distribution of hysteretic energy is clearly defined, with the expected positions for energy dissipation and damage concentrated in the dampers. This facilitates the application of an energy-based design method in such structures. This research presented a novel direct energy-based design (DEBD) method for damping control reinforced concrete (RC) structures, following the principle that the energy dissipation capacity of the structural members and dampers exceeds the hysteretic energy dissipation demand. With this principle, an energy-based damage index, which is directly correlated with structural damage state, was introduced. Subsequently, a detailed energy-based design process was provided. To achieve the desired seismic performance, the required energy dissipation capacity of dampers was determined using a pre-select damage index, and thereby, identifying the design parameters of the dampers. Finally, to validate the feasibility of the proposed design method, an 8-story RC frame with friction dampers was chosen as an example. The energy dissipation capacity and damage state of the designed structure were evaluated through nonlinear time-history analyses, and the results demonstrate the successfully achievement of the predefined seismic performance.

Hysteretic energy distribution model of CFDST composite frame with metallic dampers using coupled shear-flexural beam model

Novel steel–concrete composite structures have drawn increasingly attention in recent years especially in high-rise buildings owing to its superior structural performance over conventional concrete and steel structures. Moreover, energy dissipation devices such as metallic dampers and buckling-restrained braces (BRB) were necessarily added in this type of structure to resist seismic loads. However, the existing research regarding to the dual system consisting of composite frame and energy dissipation was limited. In this paper, the dual system consisting of concrete-filled double skin steel tubular (CFDST) composite frame and metallic damper was set as the research subject, especially focusing on the analysis of hysteretic energy distribution along the height. The 10- and 20-story dual systems were designed with different parameters revealing the influence of semi-rigid connection and metallic damper. Nonlinear models of structures established by Opensees software were validated by the test results. Afterwards, the energy distributions of all stories were discussed. It demonstrated that the metallic damper could absorb considerable energy under seismic loads while a semi-rigid connection with relatively high moment strength had a detrimental effect on the column. Moreover, the semi-rigid connection in the span without metallic damper in high story exhibited significantly larger rotation than that in the span with metallic damper. Finally, the method to estimate the energy distribution estimation of the dual system was developed, in which the lateral displacement pattern was observed by the coupled shear-flexural beam model to fully consider the flexural deformation of the dual system. An equivalent distribution of the shear and bending stiffness was also proposed considering the effect of the semi-rigid in the span without metallic damper. The predicted results from the model were validated by the analysis results derived from the nonlinear model. The theoretical and analytical results of the paper could activate the application of the dual system and provide a reasonable method to estimate the hysteretic energy distribution of the dual system.

Estimation of hysteretic energy distribution for energy-based design of structures equipped with dampers

Distribution of hysteretic energy along the stories of the building structures is a challenging topic in the energy-based design methods as the key design parameter. This paper aims to determine the vertical distribution of seismic hysteretic energy in the buildings equipped with hysteretic dampers required for the development of reliable energy-based design methods for such complex systems. In this regard, about 250 steel frame structures, 2 to 14 stories in height and equipped with triangular-plate added damping and stiffness (TADAS) dampers are studied. To exploit the maximum energy dissipation capacity of dampers, the frames are designed to achieve a uniform distribution of ductility demands in all stories. The effects of key design parameters such as target ductility capacity, frame-to-damper stiffness ratio, and brace-to-damper stiffness ratio on the vertical distribution of energy are investigated. The results indicate that in the frame structures equipped with hysteretic dampers, if the ductility demands are uniformly distributed along the stories, the energy distribution in the stories can be considered similar to the distribution of story shear forces with very good consistency. It is also shown that the code-proposed linear and power equations adequately estimate the distribution of story shear forces, and hence, can be used to predict the vertical distribution of hysteretic energy in such structures required for energy-based seismic design methods.

Distribution of strong earthquake input energy in tall buildings equipped with damped outriggers

SummaryThe seismic design of optimal damped outrigger structures relies on the assumption that most of the input energy will be absorbed by the dampers, whilst the rest of the structure remains elastic. When subjected to strong earthquakes, nevertheless, the building structure may exhibit plastic hinges before the dampers begin to work. In order to determine to which extent the use of viscously damped outriggers would avoid damage, both the host structure's hysteretic behaviour and the dampers' performance need to be evaluated in parallel. This article provides a parametric study on the factors that influence the distribution of seismic energy in tall buildings equipped with damped outriggers: First, the influence of outrigger's location, damping coefficients, and rigidity ratios core‐to‐outrigger and core‐to‐column in the seismic performance of a 60‐story building with conventional and with damped outriggers is studied. In parallel, nonlinear behaviour of the outrigger with and without viscous dampers is examined under small, moderate, strong, and severe long‐period earthquakes to assess the hysteretic energy distribution through the core and outriggers. The results show that, as the ground motion becomes stronger, viscous dampers effectively reduce the potential of damage in the structure if compared to conventional outriggers. However, the use of dampers cannot entirely prevent damage under critical excitations.

Comparing Hysteretic Energy and inter-story drift in steel frames with V-shaped brace under near and far fault earthquakes

Different researches have shown that during destructive earthquakes, most structures enter non-reactionary range. Hysteretic Energy, which is wasted after the yield within its hysteresis rings, is very influential on generating structural damage of the system, being the most important component in the equation of the energy, inflicted on the structures. Therefore, controlling this amount of energy leads to controlling the structure behavior. The amount of Hysteretic Energy in a structure could be an index of its damage level or its malleability. The current paper carries out a nonlinear dynamic analysis on steel buildings with a V-shaped (Chevron) brace, hence surveying Hysteretic Energy distribution as well as maximum inter-story drift in the stories of these buildings, under the influence of equalized near and far fault records. Results show that the inter-story drift need for equalized near fault records is more than the far fault ones. Also the results show Hysteretic Energy caused by near fault records that are more than the far fault ones. What is more, as the building height rises, the share of building’s higher stories from the Hysteretic Energy increases.

Estimation of earthquake induced story hysteretic energy of multi-Story buildings

The goal of energy-based seismic design is to obtain a structural design with a higher energy dissipation capacity than the energy dissipation demands incurred under earthquake motions. Accurate estimation of the story hysteretic energy demand of a multi-story structure is the key to meeting this goal. Based on the assumption of a mode-equivalent single-degree-of-freedom system, the energy equilibrium relationship of a multi-story structure under seismic action is transformed into that of a multi-mode analysis of several single degree-of-freedom systems. A simplified equation for the estimation of the story seismic hysteretic energy demand was then derived according to the story shear force and deformation of multi-story buildings, and the deformation and energy relationships between the mode-equivalent single-degree-of-freedom system and the original structure. Sites were categorized into three types based on soil hardness, namely, hard soil, intermediate hard (soft) soil, and soft soil. For each site type, a 5-story and 10-story reinforced concrete frame structure were designed and employed as calculation examples. Fifty-six earthquake acceleration records were used as horizontal excitations to validate the accuracy of the proposed method. The results verify the following. (1) The distribution of seismic hysteretic energy along the stories demonstrate a degree of regularity. (2) For the low rise buildings, use of only the first mode shape provides reasonably accurate results, whereas, for the medium or high rise buildings, several mode shapes should be included and superposed to achieve high precision. (3) The estimated hysteretic energy distribution of bottom stories tends to be underestimated, which should be modified in actual applications.

Comparative Study of Damage and Hysteretic Energy Characteristics of an RC Continuous Girder Bridge under Strong Near-Fault and Far-Field Earthquakes

AbstractA finite element model of a bridge that considers the nonlinear mechanical behavior of piers was built using a reinforced concrete continuous girder bridge in an expressway as the subject. Comparative analysis via nonlinear time history integration was conducted to determine the influences of frequency characteristics, peak ground acceleration (PGA), and effective duration on the magnitude and distribution of hysteretic energy and structural damage under selected typical near-fault and far-field earthquake records. The following conclusions were drawn from the result: (1) the frequency characteristics of ground motion significantly influenced the seismic response of the bridge structure, and an increase in PGA would obviously increase hysteretic energy and damage; (2) the hysteretic energy and damage of the bridge piers under near-fault earthquakes were greater than those under far-field earthquakes at the same PGA and duration, and the position of damage was considerably higher; (3) the proportio...

Demands and distribution of hysteretic energy in moment resistant self-centering steel frames

Post-tensioned (PT) steel moment resisting frames (MRFs) with semi-rigid connections (SRC) can be used to control the hysteretic energy demands and to reduce the maximum inter-story drift (γ). In this study the seismic behavior of steel MRFs with PT connections is estimated by incremental nonlinear dynamic analysis in terms of dissipated hysteretic energy (EH) demands. For this aim, five PT steel MRFs are subjected to 30 long duration earthquake ground motions recorded on soft soil sites. To assess the energy dissipated in the frames with PT connections, a new expression is proposed for the hysteretic behavior of semi-rigid connections validated by experimental tests. The performance was estimated not only for the global EH demands in the steel frames; but also for, the distribution and demands of hysteretic energy in beams, columns and connections considering several levels of deformation. The results show that EH varies with γ, and that most of EH is dissipated by the connections. It is observed in all the cases a log-normal distribution of EH through the building height. The largest demand of EH occurs between 0.25 and 0.5 of the height. Finally, an equation is proposed to calculate the distribution of EH in terms of the normalized height of the stories (h/H) and the inter-story drift.

A method for evaluating earthquake-induced structural damage based on displacement and hysteretic energy

Rather than viewing earthquake-induced structural damage as a single index of maximal deformation, it can be viewed as a combination of two indices, that is, the deformation demand and dissipation of energy. A method for evaluating the earthquake-induced damage of multi-storey buildings is presented that considers the maximal storey drift and the storey hysteretic energy. In this method, the maximal storey drift is estimated by means of the strength reduction factor spectrum, pushover analysis and distribution formula of deformation along structural storeys, which is based on the modal decomposition hypothesis in the nonlinear response stage of structures. For estimating the storey hysteretic energy demand, the normalized hysteretic energy spectrum of constant ductility factors is established, where the normalized hysteretic energy is defined as the ratio of the hysteretic energy to the square of the peak ground acceleration, and the formula for the distribution of hysteretic energy along structural storeys is derived based on the relation of the simplified internal forces of structures. For demonstrating the process of the proposed method and verifying its accuracy, an example is implemented, and the analysis results of the example indicate the following: (1) the method proposed in this article is a simple and easily implemented method for evaluating the structural damage induced by earthquakes and (2) the distribution formulas of the maximal drift and hysteretic energy along structural storeys derived in this article are relatively accurate.

Analysis on Seismic Energy Response of Reinforced Concrete Frame-Core Wall

Elastio-plastic dynamic analyses of 5 reinforced concrete frame-core wall structures with different structural characteristics were carried out under several sets of ground motions. The earthquake total input energy of the structure under ground motion, and the regularity of the total input energy between hysteretic energy and damping energy were discussed; the distribution of hysteretic energy among shear wall, coupling beams and frames were studied, as well as the distribution of hysteretic energy along different stories. The results show that the hysteretic energy is increased with the peak ground acceleration. The earthquake records with different spectrum characteristics have a great influence on hysteretic energy. Although the total hysteretic energy among different structural members are steady, the distribution of hysteretic energy among shear wall, coupling beams and frames may vary significantly. It is found that the bottom portion of shear walls and coupling beams in middle floors are the predominant energy dissipated area.

The Influence of the Strong Aftershocks on Seismic Performance on Long-Span Arch Bridges Based on the Energy Method

Equivalent seismic wave can be formed by a main wave and two strong aftershock waves on the basis of energy equivalent principle. With a long-span arch bridge as a research object, the hysteretic energy distribution of the pier and arch were got by the action of the main wave and equivalent seismic wave based on energy method. And then the situation of bridge damage was assessed by Seismic Ditao Niu damage index, the regular pattern of structure damage affected by strong aftershock was revealed as well.

Seismic damage assessment of reinforced concrete frames with shear wall according to load pattern

Studies have shown that most structures subjected to strong ground motions fall into an inelastic state. Therefore, it is necessary to study the inelastic behaviour of structures undergoing such earthquakes. In this study, three reinforced concrete (RC) frames with shear wall are considered. The preliminary designs of these frames are based on equivalent static forces in accordance with six patterns of loading distribution (namely Uniform Building Code (UBC), National Earthquake Hazards Reduction Program (NEHRP), Iranian seismic code, modified rectangular, first mode and the first three modes). The aim of this study is to investigate the distribution of damage in accordance with these six load patterns. IDARC 2D software has been used to calculate maximum drift, hysteretic energy and structural damage index when subjected to severe earthquakes. The results show that the current seismic design based on strength principles, even considering uniform strength distribution, does not lead to a uniform distribution of hysteretic energy, drift and damage index in storey height. However, modified rectangular and the first three mode patterns show more uniform distribution of damage than the others.

A Study on Dissipation of Cumulative Hysteretic Energy in Reinforced Concrete Frame Structures

Earthquake input energy and structural energy dissipation are key indicators to assess the seismic performance of structures. To study the rules of distribution of hysteretic energy within structures, a 6-storey regular reinforced concrete frame structure model is analyzed through elasto-plastic time-history dynamic analysis using the El Centro and Northridge accelerograms. Based on the comparison between numerical results for the earthquake input energy and structural hysteretic energy under the minor, moderate and major earthquakes of Grade 8 and 9, the distribution of the ratio of the storey hysteretic energy to the total hysteretic energy through the height was further studied. It shows that the computed results corresponding to the two earthquake records are in good agreement under different ground motion severity. And the percentage of structural hysteretic energy to input energy is basically stable. The distribution pattern of storey hysteretic energy through the height is that the value of the upper stories is smaller than the value of the lower stories. And the ground motion severity has a minor influence on the distribution pattern when the plasticity of structure develops more sufficiently.

Cyclic tests of four two‐story narrow steel plate shear walls. Part 2: experimental results and design implications

AbstractThis paper is the second part of a two‐part paper presenting the cyclic tests of four two‐story narrow steel plate shear walls (SPSWs). The first paper introduces the analytical studies and the specimen designs. This paper describes the test results. Some design implications including the capacity design for the first story column and the width‐to‐thickness ratio check for the beam web are discussed based on key observations from the tests. Test results confirm that the simplified strip model can accurately predict the inelastic responses of the specimens. Test results also confirm that the proposed capacity design method is effective in ensuring the plastic hinge formation at the bottom end of the first story column for SPSW with or without restrainers. Test results also show that the horizontal restrainers are effective in reducing the member forces in the boundary beam and column elements. Comparing the test results of the typical SPSW with those of the restrained SPSW (R‐SPSW) specimens, it is found that the R‐SPSW possesses an improved cyclic performance and reduced material weight. Analytical results predict the compressed column moments at the onset of the column plastic hinge formation well. The analytical hysteretic energy distribution in the first story column agrees very well with the observed inelastic actions developed in the four specimens. The detailed frame response analyses and the test results confirm that the assumptions made in developing the proposed column capacity design method are reasonable. Copyright © 2009 John Wiley & Sons, Ltd.

좌굴이 방지된 가새가 설치된 철골조 건물의 에너지 요구량

본 연구에서는 지진하중에 의하여 철골 모멘트저항골조(MRF)와 좌굴이 방지된 가새골조(BRBF) 그리고 힌지로 접합된 좌굴이 방지된 가새골조(HBRBF)에서 발생하는 층별 이력에너지의 분포에 대하여 고찰하였다. 예제 구조물의 에너지 요구량을 산정하기 위하여 다른 지반조건에서 계측된 60개의 지진기록을 사용하였다. 해석결과에 따르면 MRF와 BRBF에서의 이력에너지는 밑면에서 최대가 되고 상부층으로 갈수록 점진적으로 감소하여, 상부층에서는 부재의 이력거동이 거의 발생하지 않았다. 그러나 HBRBF에서의 층별 이력에너지는 구조물의 높이에 따라 상대적으로 균등하게 분포하였으며, 이러한 경우 손상이 한 층에 집중적으로 발생하지 않아 다른 시스템에 비하여 보다 바람직하다고 할 수 있다. 연암 지반, 연약한 토사, 단층 근처의 지반 조건에 따른 에너지의 분포형태는 거의 동일하게 나타났다. In this study, a story-wise distribution of hysteretic energy in steel moment resisting framse(MRF), buckling restrained braced frames(BRBF), and hinge-connected framed structures with buckling restrained braces(HBRBF) subjected to various earthquake ground excitations was investigated. Sixty earthquake ground motions recorded in different soil conditions were used to compute the energy demand in model structure. According to analysis results, the hysteretic energy in MRF and BRBF turned out to be the maximum at the base and monotonically diminishes with increasing height. However the story-wise distribution of hysteretic energy in HBRBF was relatively uniform over the height of the structure. In this case damage is not concentrated in a single story, and therefore it is considered to be more desirable than other systems. The story-wise energy distribution pattern under three different soil types turned out to be approximately the same.

Seismic Torsional Provisions: Influence on Element Energy Dissipation

Code torsional provisions primarily aim to limit the additional response of lateral load-resisting elements arising from plan eccentricity. Intensive research has addressed this issue exclusively by evaluating additional ductility and deformation demands in plan-eccentric or torsionally unbalanced (TU) structural systems, and comparing the results with well-established seismic design criteria. This paper adopts an alternative approach toward providing complementary data for code evaluation by first analyzing the distribution of hysteretic energy dissipated by the inelastic response of the various lateral restraining elements, and assessing the influence of various seismic code torsional provisions on this energy absorption distribution. Second, in order to evaluate the adequacy of code torsional provisions in restricting inelastic damage effects in TU systems, an energy dissipation index based on the equivalent hysteretic ductility is proposed. This index provides a first step in the development of a wide...