Stiffness Eccentricity Research Articles

Coupled wind-induced response of inter-story isolated eccentric tall buildings with friction-pendulum bearings

The isolation technology is widely used to protect structures against strong earthquake. For the inter-story isolated tall building located in strong wind-prone area, the soft isolation layer prolongs the structural period, which can make the wind effects significant. This study presents an analytical framework for assessing three-dimensional coupled wind-induced response of inter-story isolated eccentric tall buildings employing friction-pendulum bearings. The framework utilizes a biaxial Bouc-Wen hysteresis model and a velocity-dependent friction coefficient to describe the coupled frictional forces at each bearing. To enhance the computational efficiency, a simplified model with reduced degrees of freedom is proposed to represent the building. This study investigates eighty combinations of stiffness and mass eccentricities of lower and upper structures relative to isolation layer to analyze their impact on building acceleration. A spherical and two aspheric sliding surfaces of the bearing are examined to understand their effects on building response. The findings suggest that the stiffness eccentricity of either lower or upper building solely affects its own response without influencing other part of the structure. Conversely, the mass eccentricity of upper building induces significant mode coupling, resulting in noticeable impact on the accelerations of both upper and lower buildings. Moreover, the acceleration of the story conner farther from the mass eccentric position experiences significantly amplification. The proposed aspherical bearing demonstrates the capability to substantially reduce the bearing displacement, although with a limited increase in other building responses not exceeding 20 %.

Global performance of multi-story stiffness-eccentric RC structures subjected to progressive seismic excitations: Shaking table investigations

Asymmetric structures have demonstrated poor seismic performance while experiencing major earthquakes in the past. Such structures exhibit complex vibration characteristics under seismic shaking as there is coupling between the lateral and torsional components of vibration. These coupled vibrations tend to cause weak locations under torsional distress, which eventually leads to the global failure of the structure. This paper presents the experimental evaluation of a plan-asymmetric structure with stiffness eccentricity. The experimental investigation was conducted by means of shake table testing on a 1/4-scaled reinforced concrete (RC) frame shear wall structure exposed to progressive seismic excitations. The structural response is monitored from a global failure perspective both in the elastic and inelastic states under increased torsional vibrations. The experimental findings indicate that: (1) irregularities in a structure can lead to significant amplification of the dynamic response due to induced torsional vibrations (2) the damage in the structure influences the dynamic properties of the structure, which eventually tend to influence the global structural response (3) structural acceleration response is more sensitive to seismic excitations and appears to have more influence on local oscillations compared with structural displacement response and (4) floor rotations excessively increase with the increasing damage state of the structure. Based on the physical inspection and extracted measurements, the shear wall sustained severe damage, whereas beams and columns at the flexible edge of the structure formed plastic hinges in critical zones.

Interstory drift based scaling of bi‐directional ground motions

AbstractThe interstory drift‐based scaling procedure (IDS) developed recently by the authors for plane frames under single component horizontal ground motions, has been extended to three‐dimensional structures possessing torsional coupling under bi‐axial ground motions which are represented by their geometric mean spectrum. The ground motion‐scaling factor is defined as the ratio of average interstory drift along building height under target spectrum versus that under the associated ground motion spectrum. Hence, scaling is conditioned on structural response, which is in turn a function of seismic intensity. IDS for 3D systems is applied to 20‐story and 3‐story concrete space frames with mass and stiffness eccentricity, respectively. Accuracy and efficiency of the IDS procedure is assessed under a set of near‐fault strong motion pairs from large magnitude events. The results revealed that the proposed procedure is accurate and noticeably more efficient as compared to conventional procedures suggested in seismic codes and in literature. Further, the intensity measure employed in the IDS procedure is proved as a good predictor of fundamental demand measures (maximum interstory drift ratio and maximum plastic rotations) obtained from nonlinear dynamic analyses under individual ground motion pairs. Hence, employing the intensity measure of IDS for ground motion scaling in intensity‐based evaluation of structures is proposed for reliable estimation of structural performance under code‐prescribed seismic hazard.

Inelastic seismic behavior of asymmetric structures with mass and stiffness eccentricity under bidirectional ground motions

SummaryStructures with an asymmetric plan have proved to be severely vulnerable during the past earthquakes. The vulnerability may arise due to the uneven distribution of stiffness or mass. Most of the research focused on studying the eccentricity arising due to the irregular stiffness distribution. On the other hand, the systems with mass eccentricity arising due to the uneven distribution of mass at floor level are given relatively little attention. Hence, the present paper comprehensively studied the stiffness and mass eccentric systems together. In each case, the structure is subjected to bidirectional components of ground motion, which reflects the real situation more closely. So, for the lateral load‐resisting elements (columns), effect of biaxial interaction due to simultaneous bidirectional movement is included in the hysteresis behavior as explained in the paper to make a reasonably accurate prediction. Primarily idealized single‐story systems were used to study how asymmetric structures are vulnerable if they have stiffness or mass eccentricity. Further, the three‐story asymmetric systems were also included in the scope of the study to observe the effect of higher modes. To simulate a more practical situation, the present paper considers higher eccentricity in the first story of the three‐story system due to functional reasons, while the upper stories have lesser eccentricities compared to the first story. The present study shows that mass eccentric systems are equally vulnerable to earthquakes as stiffness eccentric systems. Further, three‐story systems show a manifold increase in response compared to its single‐story counterparts. Such a study may help to develop more insight into the generic behavior of plan asymmetric systems, leading to the improvement of design guidelines.

A seismic fragility model accounting for torsional irregularity in low‐rise non‐ductile RC moment‐resisting frames

AbstractBuildings characterized by torsional irregularity are notorious for their vulnerability to earthquakes. However, most fragility/vulnerability models used for regional seismic risk assessment fail to distinguish between buildings with torsionally balanced and unbalanced configurations. The present study aims to develop a seismic fragility model sensitive to torsional irregularity for low‐rise non‐ductile RC moment frame buildings. To this end, a numerical investigation centred on 13 three‐storied plan‐asymmetric models, each characterized by a distinct combination of normalized stiffness eccentricity, torsional radius to mass radius of gyration ratio and normalized strength eccentricity, is presented. Using high‐dimensional model representation (HDMR), a metamodel for the maximum inter‐storey drift under bi‐directional seismic action is calibrated, considering average spectral acceleration and the above trio of torsional irregularity descriptors (TIDs) as the predictor variables. Carrying out numerical simulations on limit state functions formulated using the above demand model and appropriate capacity thresholds, the seismic fragility is estimated. The parameters of a lognormal fragility function compatible with the above estimates are determined using the method of maximum likelihood. A strong correlation is observed between the TIDs and the fragility function parameters. This reinforces the importance of accounting for all three TIDs while rating the seismic fragility of a building. Using least‐square error minimization technique, a functional relationship is established between the fragility model parameters and the TIDs. The framework described herein provides a simple, yet rational means to develop the next generation of seismic fragility models accounting for one of the most critical factors governing seismic behaviour––‘torsional irregularity’.

Nonlinear Dynamic Analysis of Rotor-Bearing System with Cubic Nonlinearity

Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.

Effect of torsional component of earthquakes on response of symmetric/asymmetric buildings

Although buildings are excited by translational and rotational earthquake components, only translational components are considered in seismic loads. The effects of earthquake torsional components on building responses were studied in this work. For this purpose, the torsional component of 14 earthquakes was extracted from their translational components. Symmetric and asymmetric idealised single-storey models were analysed by considering the torsional and translational components. The models considered five different values of the uncoupled torsional frequency to uncoupled translational frequency ratio (Ω = ωθ/ωx = 1·5, 1·25, 1, 0·75, 0·5), with their lateral period varying from 0·05 to 2 s. The displacements of the left-hand side, right-hand side and centre of the diaphragm, the diaphragm rotation about the centre of mass and the base shear were studied. The results indicated that the effect of the torsional component on the non-linear responses of the building was considerable, and ignoring this effect led to an underestimation of the responses. The increase in the building's responses due to the torsional component was found to depend significantly on the value of Ω and the stiffness eccentricity. The maximum growth of the displacement of torsionally stiff and torsionally flexible buildings was 51% and 155%, respectively. The diaphragm rotation can be increased to 154% in the asymmetric systems.

Effect of steel braces buckling on inelastic torsion and design prevention of steel braced concrete frame structure

The influence of steel brace buckling on inelastic torsion of steel braced concrete frame structure is studied. On the background of a project, the shaking table test results of two structural models with ordinary steel brace (BRC) and buckling-restrained brace (BRB) are compared, and the inelastic torsion and sudden increase caused by steel brace buckling is confirmed. Finite element analysis models with BRC, BRB and floor load eccentricity are established, in which the restoring force model of steel brace considered the asymmetry of tensile and compressive bearing capacity, and the concrete beam and column members considered M3 and PMM hinge respectively to study the process and characteristics of the influence of BRC buckling on the nonlinear torsion of the structure. The mechanism of inelastic torsion of steel braced concrete frame structure (F-BRC) induced by BRC buckling is studied, and the principle that the dynamic BRC buckling makes the structure acquire inertial force as well as inertial torsion moment is found out. It is more reasonable to explain the inelastic torsional process and the mechanical characteristics of the structure by this principle than by the theory of strength eccentricity and stiffness eccentricity. Finally, based on the principle, six numerical examples with different brace schemes under the excitation of eight earthquake waves are calculated, and the changing rules of the torsional moment are studied. Some design limitation suggestions are put forward.

Torsional ductility spectrum for predicting ductility distribution in simple asymmetric‐plan structures

SummaryAn analytical procedure is developed for predicting the ductility demands in simple asymmetric‐plan structures under earthquake ground motions. The procedure governs regular structures dominated by the lower vibration modes where inelastic response occurs only at the bases of first story columns and at the beam ends, in conformance with the capacity design principles. Torsional ductility spectra are generated for expressing the maximum ductility response of torsionally coupled, generic, single‐story, 2‐degree‐of‐freedom inelastic parametric systems. Five parameters characterize the parametric systems: first mode period, uncoupled frequency ratio, stiffness eccentricity, stiff‐to‐flexible edge strength ratio, and ductility reduction factor. A surrogate modeling approach is developed for converting the properties of the actual systems to those of the parametric system. Mean maximum ductilities of torsionally stiff, equally stiff, and torsionally flexible systems are calculated under a set of design spectrum compatible strong motions for the possible combinations of characteristic parameters. The results obtained from case studies revealed reasonable accuracy of the estimations. The results have indicated that the flexible side frames of torsionally stiff and equally stiff code conforming designs are mainly responsible for providing the intended ductility and energy dissipation capacity whereas the stiff side frames play a secondary role, particularly when the stiff edge is significantly stronger than the flexible edge. However, ductility demands in torsionally flexible systems are significantly larger at both sides compared with torsionally stiff systems.

Effect of in-plan eccentricity on vertically stiffness irregular buildings under earthquake loading

A regular building happens to be an idealized concept since real buildings have numerous discrepancies or irregularities along the height or along the planar directions. These buildings under the effect of wind, earthquake, or other dynamic loads, exhibit torsional behavior attributed to the significance of the higher modes of vibration. The present study evaluates the seismic responses of buildings with an integration of vertical stiffness irregularities as well as in-plan eccentricity in stiffness distribution. Transient analysis was carried out on three dimensional building frames with stiffness irregularities in plan as well as along the height by subjecting them to seismic loading and the torsional response of the irregular configurations were assessed in terms of the variations in natural period, base shear, roof deflection, roof rotation and storey drifts. Soft storey at the base of the building is the most critical case which when combined with the in-plan stiffness eccentricity has the most adverse effect on the seismic behavior of the buildings. A new coefficient to quantify the irregularity in a vertically stiffness irregular building based on its geometrical dimensions, in-plan stiffness eccentricity and location of stiffness irregularity along the height has also been proposed.

Analytical investigation of torsional mode in symmetric and asymmetric systems with mass or stiffness eccentricity

At the first glance, it seems that asymmetry in geometry, mass, and stiffness cause torsion, while there are systems in which, despite the symmetry in all these parameters, the transferred energy to the torsional mode is more than the translational mode. The main purpose of this research was to study the torsional mode of a symmetric system in terms of geometry, mass, and stiffness, then investigate the effect of mass eccentricity and stiffness eccentricity. This is a fundamental problem and its main applications are in the buildings, automobile industry, and offshore structures. Parametric calculations on the free vibration equation of a completely symmetric system show that in a system with the specific values of the aspect ratio and the stiffness ratio of two directions, torsion occurs in the second mode. The results of these calculations were presented as a two-dimensional curve. Similar calculations were made on systems with eccentricity and the results were presented as three-dimensional curves. Accordingly, the greater mass eccentricity or stiffness eccentricity is, the greater area in which torsion occurs in the second mode will be. In the case of systems with mass eccentricity, there is a small area in which torsion occurs in the first mode.

Torsion control in structures isolated with the triple friction pendulum system

A parametric study was carried out to investigate the torsional response of structures isolated with the Triple Friction Pendulum (TFP) system with building properties such as uncoupled torsional to lateral frequency ratio, Ωs, building slenderness, and mass and stiffness eccentricities. A simplified model of a parametric multistory structure and a small deformation model of the TFP, but with the ability to capture uplift, were used to perform parametric 3D non-linear dynamic analyses. The input ground motions were 20 Chilean records selected using a conditional mean spectrum. Response history results showed that uplift in the devices occurs in structures with large mass eccentricity, and in some extreme cases, normal force values in the TFPs may be as large as 6 times the nominal average gravitational load in each isolator. Torsional envelope response results also show that mass eccentric systems may undergo larger normalized edge amplification factors relative to stiffness eccentric systems, with values 2.5 and 1.8, respectively, and that torsional balance cannot be achieved naturally. Although rotations are small in magnitude due to seismic isolation, displacement values in resisting planes of the superstructure equidistant from the geometric center of the plan will be different. Moreover, structures with large Ωs present correlation values between response histories of torsion and translation measured at the geometric center of the plan near one, as well as values above zero for different Ωs and plan eccentricity, which implies no torsional control in the weak sense. It is concluded that parameter Ωs strongly influences the torsional amplification values computed herein.

Experimental and numerical investigation on the complex behaviour of the localised seismic response in a multi-storey plan-asymmetric structure

Asymmetric structures experience higher seismic damage compared with their symmetric counterparts. This damage is mainly attributed to the coupled torsional vibrations, which tend to induce twisting in the structural floors and increase the shear demands in the corner column of the flexible side (CCFE) of asymmetric structures with in-plan stiffness eccentricity. Such floor twisting consequently leads towards the damage concentration in the critical region of CCFE and produce relatively higher local deformations and stiffness degradation of the structural component. Therefore, the investigation of such damage concentration is important as it can potentially lead towards local and global seismic failure. In this regard, this research aims at evaluating the damage behaviour of CCFE of a plan-asymmetric reinforced concrete (RC) structure. For this purpose, a quarter scaled asymmetric structure with in-plan stiffness eccentricity was experimentally tested under progressive seismic excitations. Internal seismic damage in the critical region of CCFE was monitored using Fibre Bragg grating (FBG) sensors during the structure’s transformation from elastic state to a highly plastic state. To validate the experimental findings, a calibrated finite element model was established in ABAQUS and a comparison of the damage behaviour of CCFE is presented to highlight the influence of stiffness eccentricity on damage concentration in the critical structural element. Finally, based on the experimental and numerical investigations, the mechanism of the local response behaviour both at the flexible and stiff edge of the plan-asymmetric structure is discussed and compared. This research concludes that CCFE in plan-asymmetric structures requires substantial design redundancy and special seismic detailing to resist extreme seismic events.

Performance of torsionally eccentric RC wall frame buildings designed to DDBD under bi-directional seismic excitation

The seismic performance of a class of reinforced concrete eccentric wall frame buildings under bi-directional ground motion excitation is investigated. For this purpose, four and eight-storey RC buildings comprising structural walls, flat-plates and gravity columns, having different strength and stiffness eccentricity and torsional restrain, are designed in accordance with the Direct Displacement Based Design (DDBD) method for damage control. The structures are analysed under static and dynamic inelastic response, considering ten ground motion record pairs, three intensity levels and different angles of incidence. Several global and local engineering demand parameters, namely, inter-storey drift, slab rotation, member plastic rotations and wall internal forces are evaluated and compared with the DDBD limits. It is shown that ground motion directionality effects are small, and the average drift and wall moment profiles are within DDBD predictions and, often, considerably lower than DDBD demanded. However, wall shear force and local inelastic demands are underpredicted by both DDBD and static inelastic analyses and, more significantly so, for the torsionally flexible structures.

Reliability-Based Seismic Assessment of Multi-Story Box System Buildings under the Accidental Torsion

ABSTRACT Performance analysis of reinforced concrete (RC) buildings during past earthquakes has shown that irregular distribution of mass, stiffness, and strength may cause severe damage in structural elements. Accidental torsion, one of the most common reasons of damage and failure under the strong ground motions, is a complex phenomenon in which several variables are involved. The box-type structural system is considerably sensitive to torsion due to shear wall arrangement and that the torsional mode which governs structural response. Thus, understanding and evaluating accidental torsion is a fundamental step in seismic reliability evaluation of this structural system in comparison with other common structures. Therefore, in this study, seismic sensitivity of the box-type structural system is evaluated for various configurations of mass, stiffness, and strength centers. Several analyses, such as eigen-value, push-over, nonlinear time history, and seismic reliability analysis are performed using artificial records to predict structural characteristics and probabilities of failure. The results show that the mass eccentricity has a greater effect on the seismic response in comparison with the strength and stiffness eccentricities. The most critical condition occurs when the mass and stiffness centers are shifted in the same direction, so the story drift under the design and maximum credible earthquakes are 2.45 and 2.26 times the symmetrical model drift, respectively. Furthermore, it is shown that this box-type structural system demonstrates acceptable seismic reliability under the accidental torsion since the main elements of lateral bearing system remain in an immediate occupancy performance level under the design earthquake.

Impact of strong repeated ground excitation to the on-plan rotation of asymmetric building with various strength and stiffness eccentricities

Buildings subjected to torsional effect may result to the floors of the building not only translate laterally but also rotate vertically. Torsional effects may significantly modify the seismic response of buildings, and even cause severe damage or collapse of structures. The current practices in earthquake design is to apply single earthquake on structure during modelling and analysis. However, in real earthquake occurrence, the earthquakes normally occurred repeatedly after the first event. This phenomenon can affect the stiffness and strength of the structural system especially for repeated strong motions. With greater damage expected and lack of time, any rehabilitation action is impractical. Slab rotation, a major response parameter to represent the severity of the torsional response of eccentric systems, is considered. The centre of strength (CR) and centre of stiffness (CS), as two interdependent and important factors to the torsional response of buildings, are investigated via eighty positions of strength eccentricities (er) and stiffness eccentricities (es). Hence, this paper presents the torsional behaviour of a single storey, three-dimensional asymmetric building under the excitation of single and repeated strong ground motions. These motions are applied in the z-direction and analysed for elastic and inelastic conditions. The results are interpreted based on two position models. Position Model A concludes that the effectiveness of CS reduces gradually until CS ratio (es/bz) ≤0.2; thereafter effectiveness of CR increases to cause elastic slab rotation. With repeated ground motion, the magnitude of inelastic rotation is increased; however es/bz ≤0.2 is maintained showing effectiveness of stiffness eccentricity irrespective of nature of ground motion. Position Model B shows that slab rotation is affected by repeated ground motion. Elastic/inelastic analysis under repeated ground motion must be conducted in oppose to current practice, so that the designed structure can undertake the elastic/inelastic demand; especially for the lower CR ratio values.

Fundamental period of vibrations influencing characteristics of torsional irregularity in reinforced concrete buildings

This paper presents an analysis of irregular reinforced concrete buildings with respect to fundamental period of vibrations. During earthquake, reinforced concrete building with asymmetric building system experience extensive damage due to this torsional irregularity. Torsional irregularity of reinforced concrete buildings has been analysed with taking the strength and stiffness eccentricities as the main parameters of the rectangular in-plan building system. Displacement demand in reinforced concrete building has been determined in terms of fundamental period of vibrations and the behaviour of the building system was presented using the normalised displacement of buildings. The hypothetical model has been analysed has been set up using varies values of fundamental period of vibrations using Ruaumoko program and the lateral displacement of the building were extracted using Fortran program. The results indicated through the damage index showed that the fundamental period of vibration plays an important role in earthquake studies on reinforced concrete building since earthquake induced excessive displacement to the building system under the increment of the fundamental period of vibrations.

Effect of torsional ground motion on the seismic response of highway bridges

Seismological aspects of rotational ground motions can be found in published research, however, studies on implications for the seismic response of structural systems are rare. This preliminary study investigates the effects of torsional component of the ground motions (TGM) on the overall seismic response of bridges and interactions among their components. For this purpose, a series of computational models of bridges were developed. The models assume linear-elastic substructure with continuous rigid deck, sliding supports and rigid abutments, and vary key parameters including skew angle (β), normalized stiffness eccentricity between the center of mass and rigidity (ex/r), gap size between deck and abutments, dominant frequency ratios. However, inelastic impact between the superstructure and abutments is modeled explicitly to ensure that consequential in-plane deck rotations are accounted for. It was shown that larger deck rotations due to TGM lead to larger impact forces, which further amplifies deck rotations. The adverse effects may be more pronounced in symmetric bridges and in bridges with significant skew. All response quantities; deformations and substructure forces, are amplified significantly due to TGMs which suggests that current design codes may underestimate seismic deformation and force demand.

STUDI PARAMETRIK DEFORMASI TORSI LANTAI BANGUNAN ASIMETRIS SEBIDANG DIPENGARUHI OLEH GEMPA PULSE DAN TANPA PULSE

Earthquake resistant building must be designed with a proper plan configuration. Although the regular and symmetrical building plans have been known to have a good behaviour under earthquake loads, but the facts have demonstrated that many asymmetrical plan buildings are built for the architectural reasons. Irregular plan buildings cause mass distribution, stiffness, and strength asymmetries which in turn produce the eccentricity to the centre of mass. In this research, the asymmetrical buildings are simulated under earthquake ground motion containing pulse. The study aims to evaluate the drift and floor rotations that occur in the asymmetrical buildings. The results indicate that the difference in drift of symmetrical and asymmetrical buildings reach 8% to 20%. The rotation occurred on the rigid side (high stiffness side) is smaller than the flexible side (low stiffness side). The difference in eccentricity affects clearly the inelastic floor rotation.Keywords: Eccentricity Stiffness, Pulse Ground Motion, Floor Rotation

Frequency-Domain Physical-Parameter System Identification of Building Structures with Stiffness Eccentricity

A frequency-domain method of physical-parameter system identification is developed for three-dimensional building structures with stiffness eccentricity. Equations of motion in the time domain are transformed into the frequency domain. The dynamic equilibrium of the free body above the j-th story is used to identify the j-th story stiffness and damping. It is required to measure the horizontal and rotational accelerations at all stories to identify the story stiffness and damping coefficients of all stories. Compared to the previous approach using the special identification function, the limit manipulation at zero frequency is unnecessary and is robust for noise. Furthermore, it should be remarked that the quantities of eccentricities in all stories can be identified using the slopes of the functions for torsional stiffness identification in the frequency domain.