Strength Eccentricity Research Articles

一軸偏心した1層木質耐力壁構造における弾塑性捩れ振動の簡易評価法

Displacement mode including torsion when subjected to major earthquake is clearly related to strength balance of each frame while elastic torsional vibration is characterized by stiffness balance. In the previous research, we presented a displacement mode prediction method especially focusing on single-story timber structure having large strength eccentricity. The method is improved by taking the effect of plasticity of transverse walls and bi-axial input motion into account. Finally, necessary additional strength for seismic design of torsionally coupled structure is calculated and is related to eccentricity index. The accuracy of the evaluation method is demonstrated via numerous time history analyses.

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’.

Optimal Performance-Based Configurations of Stiffness and Strength Centers in Multi-Story Wall-Frame Asymmetric Buildings Including Soil–Structure Interaction Effects

ABSTRACT In this paper, the probabilistic performance-based approach is adopted to evaluate the seismic performance of multi-story reinforced concrete wall-frame asymmetric buildings considering soil–structure interaction (SSI) and identify appropriate stiffness and strength centers configurations. A group of fixed- and flexible-base models with different stiffness and strength eccentricities were considered for parametric studies, and their seismic performance was compared in three different limit states. The optimum configuration of centers was found to be a function of base condition and performance objective. The proposed configurations can be adopted in the performance-based design of asymmetric buildings. Furthermore, the results indicate a detrimental effect of SSI in the Life Safety and Collapse Prevention limit states.

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 irregularity indices for the seismic demand assessment of RC moment resisting frame buildings

Design standards across the world use different parameters to quantify degree of torsional irregularity of buildings. Popular among such descriptors are the normalized static eccentricity ratio, torsional radius to mass radius of gyration ratio, maximum to minimum (or average) elastic floor displacement ratio, etc. However prior research, particularly on idealized single storey systems have indicated that these parameters do not correlate well with the seismic demands at all stages of structural behaviour (i.e. elastic and inelastic). The present study aims to identify a robust torsional irregularity index that captures the susceptibility of a structure to torsional effects at all ground motion intensity levels. To this end, the correlation between the maximum interstorey drift demands and popular torsional irregularity descriptors is first examined under different intensities of ground shaking using an approach that integrates multiple stripe analysis and statistical regression analysis. The numerical study is based on the nonlinear seismic assessment of thirteen three-storey gravity designed RC moment frame buildings subjected to bidirectional seismic excitation. The results indicate that none of the scalar indices considered correlate well with the drift demands at all intensities of ground shaking. A vector comprising of the normalized static eccentricity ratio and the torsional radius to mass radius of gyration ratio is found to perform well at low shaking intensity levels, where the structure responds in an elastic manner. However, at high intensity levels where the structure undergoes significant excursions into the inelastic range of behaviour, the strength eccentricity is observed to be a better descriptor of torsional irregularity. A three-element vector comprising of the above indices is found to capture the maximum interstorey drifts accurately at all ground motion intensity levels. A seismic demand model for maximum interstorey drift, sensitive to the above torsional irregularity descriptors, is also defined.

Seismic fragility analysis of strength eccentric structures subjected to pulse‐like ground motions

AbstractThe seismic fragility of reinforced concrete (RC) frame systems considering the disadvantages of both structural eccentricities and pulse‐like earthquake effects is investigated. A total of 24,000 nonlinear time history analyses are performed using CANNY program. The influence of pulse‐like ground motion and strength eccentricity on the seismic fragility is studied quantitatively, in terms of interstorey drift, ductility, and floor rotation. The results show that the probability of reaching and exceeding a predefined damage state (Pf) is apparently higher for pulse‐like case than for non‐pulse‐like case. At a moderate eccentricity level of 0.2 and a moderate damage state (selected moderate case) with a peak ground acceleration (PGA) of 0.4 g, the Pf values of interstorey drift and ductility for pulse‐like case are 14 and 10% larger, respectively, than those for non‐pulse‐like case. The strength eccentricity also has a great effect on the structural seismic fragility. The PGA at a given probability level decreases with increasing eccentricity. For the selected moderate case, the PGAs at an exceeding probability of 50% are 0.40, 0.56, and 1.15 g for the Pf values of interstorey drift, ductility, and floor rotation, respectively. The obtained fragility curves could help to quantitatively evaluate the seismic behavior of eccentric RC frame structures subjected to pulse‐like ground motions.

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.

Improving the seismic torsional behavior of plan-asymmetric, single-storey, concrete moment resisting buildings with fluid viscous dampers

The optimal distribution of fluid viscous dampers (FVD) in controlling the seismic response of eccentric, single-storey, moment resisting concrete structures is investigated using the previously defined center of damping constant (CDC). For this purpose, a number of structural models with different one-way stiffness and strength eccentricities are considered. Extensive nonlinear time history analyses are carried out for various arrangements of FVDs. It is shown that the arrangement of FVDs for controlling the torsional behavior due to asymmetry in the concrete structures is very dependent on the intensity of the peak ground acceleration (PGA) and the extent of the structural stiffness and strength eccentricities. The results indicate that, in the linear range of structural behavior the stiffness eccentricity es which is the main parameter in determining the location of optimal CDC, is found to be less or smaller than the optimal damping constant eccentricity e*d, i.e., |e*d| > |es|. But, in the nonlinear range of structural behavior where the strength eccentricity er is the dominant factor in determining the location of optimal CDC, |e*d| > |er|. It is also concluded that for the majority of the plan-asymmetric, concrete structures considered in this study with er ≠ 0, the optimal CDC approaches the center of mass as er decreases.

リンク式流体慣性ダンパによる建物の制振に関する研究

Recently, Inertia Mass Dampers have been developed and realized. The damper can exert negative stiffness with neither energy supply from outside nor complicated electronic control devices. It is possible for the damper to exert inertia mass much greater than physical mass. In practical applications to controlling relatively large structures, great mass would be required inertia mass. But in the case of controlling small structures, smaller inertia force yielded by flowing fluid would be enough. In this paper, we propose a Linked Fluid Inertia Mass Damper (LFIMD) which is effective to reduce seismic response of low-rise structure. The damper is composed of two cylinders, two piston rods and two link tubes that connect two oil chambers of each cylinder. There is no orifice in the piston and the fluid runs in the tube at high velocity when piston rod moves back and forth. The ratio of two piston displacements can be adjusted based on the ratio of cross section area of two oil chambers linked with a tube. The damper works in three ways. They are viscous damping effect by flowing fluid, negative stiffness by inertia mass effect with moving fluid at high velocity in the tube and the displacement control by hydraulic link mechanism. The damper is quite effective in reducing acceleration response, because load-displacement relationship of the damper has negative stiffness by inertia force, decreasing the maximum shear force of a total structure. The LFIMD yields negative stiffness by means of simple passive mechanism. It can prevent damage concentration to a specific part of a multi-story building, as well as the torsional vibration of a building with stiffness or strength eccentricity. In the first part of the paper, we propose seismic response control method with LFIMD and show its dynamic mechanical properties by performance test on a LFIMD. Important findings are; there exists constant internal friction force between the cylinder and the piston, the damping force depends on the squared piston velocity, inertia force depends on frequency and linking force depends on the compression stiffness of the fluid and rigidity of the tube. It was confirmed that the test results conclude with simulated results fairly well. We perform seismic response analysis of a wooden house with LFIMDs. It is shown that LFIMD is capable of exerting seismic response control in multiple ways. In the case of no damper, the deformation and absorbed energy are concentrated to either of the story. On the other hand, in the case of using LFIMDs, it is possible to make structural deflection distribution uniform and to reduce the maximum deformation with link mechanism. Maximum acceleration is reduced due to negative stiffness by inertia force. Finally, we confirmed the use of LFIMD is quite effective in reducing seismic response of low to mid rise building structure.

Modification of Ductility Reduction Factor for Strength Eccentric Structures Subjected to Pulse-Like Ground Motions

This article investigates the ductility reduction factors for RC eccentric frame structures subjected to pulse-like ground motions. The structural models are with the strength eccentricities which are much disadvantageous than the stiffness eccentricities during the inelastic response range. A method to determine the ductility reduction factors of the strength eccentric structures is suggested by modifying those of reference symmetric structures through an eccentricity modification factor. The four factors of strength eccentricity ratio, ductility ratio, story number and velocity pulse of ground motions, are investigated to gain insight into this modification factor. It shows that the ductility reduction factors of the eccentric structures are clearly smaller than those of the symmetric structures. The eccentricity modification factor is mainly affected by the strength eccentricity and the ductility ratio, decreasing with the increment of the eccentricity or the decrement of the ductility ratio in a medium eccentricity range. The earthquake pulse-like effect and the eccentricity have coupling influence on the modification factor, while the effect of story number is not apparent. Based on the results of a comprehensive statistical study a simplified expression is suggested, which can estimate the eccentricity modification factors for both pulse-like and nonpulse-like ground motion cases.

Predicting displacement demand of multi-storey asymmetric buildings by nonlinear static analysis and corrective eccentricities

Nonlinear static methods are not always effective in the assessment of multi-storey asymmetric structures because of the errors committed in the evaluation of the deck rotation. To overcome this problem, some of the authors have recently proposed the use of two nonlinear static analyses, characterised by lateral forces applied to different points of the deck. For each of these two analyses, the distance between the point of application of the lateral force and the centre of mass of the deck (corrective eccentricity) is given by relations resulting from a parametric study on a large set of single-storey systems subjected to bidirectional ground motions. The corrective eccentricity depends on four parameters: the rigidity eccentricity, the strength eccentricity, the ratio of the uncoupled torsional to lateral frequencies and the ratio of the elastic strength demand to the actual strength of the system. In this paper, the effectiveness of the proposed method is evaluated for different values of the abovementioned parameters, considering two seismic excitation levels and multi-storey buildings with r.c. framed structure or steel structure equipped with buckling restrained braces. The seismic response of the structures is evaluated by nonlinear time-history analysis and compared with that resulting from the application of the proposed nonlinear static method. To highlight the accuracy of the proposed method, a comparison is also made with the response obtained from the standard application of the nonlinear static method, i.e. without corrective eccentricities, and with the response predicted by the extended N2 method.

Inelastic rotational response of single story lateral load resisting structures

The rotational response of inelastic asymmetric systems is the objective in this paper. As building structures of low or medium height are usually designed by a pseudo-static approach using a base shear much lower than that predicted from an elastic spectrum, the question which arises is what element strength assignment provides the minimum rotational response in the case of a strong ground motion. Several single story structural models are examined subject to six different ground motions and it is demonstrated that any strength distribution which produces low values of strength eccentricity and strength unbalance results in a low or moderate torsional behavior. A convenient method to achieve such reduced parameters is to apply a static analysis assuming that the design shear is passing through the center of mass, neglecting the existence of the orthogonal elements into the torsional stiffness of the system.

Seismic reliability analysis of buildings with torsional eccentricities

SummaryA study is presented of the influence of stiffness and strength eccentricities on the inelastic torsional response of buildings under the action of two simultaneous orthogonal horizontal ground motion components. Asymmetric buildings were obtained from their respective symmetric systems and were characterized by their stiffness and strength torsional eccentricities in both orthogonal directions. Based on the results of inelastic response of both building types (symmetric and asymmetric), the seismic reliability functions are determined for each system, and their forms of variation with different global system parameters are evaluated. Illustrative examples are presented about the use of this information for the formulation of seismic design criteria for in‐plan asymmetric multistory systems, in order to attain the same reliability levels implicit for symmetric systems designed in accordance with current seismic design codes. Copyright © 2014 John Wiley & Sons, Ltd.

Bearing Capacity Factors for Eccentrically Loaded Strip Footings Using Variational Analysis

Bearing capacity factors for eccentrically loaded strip smooth footings on homogenous cohesive frictional material are deduced by the variational limit equilibrium method and by assuming general shear failure along continuous curved slip surface. From the calculated results, the effective width rule suggested by Meyerhof for bearing capacity factors due to cohesion of soil is justified, and the superposition principle of bearing capacity for eccentrically loaded strip smooth footings is derived together with the bearing capacity factors for cohesion and unit weight of soil. The two factors are represented by soil strength parameters and eccentricity of load. The bearing capacity factor related to unit weight for cohesionless soil is less than that for cohesive frictional soil. The reason for this discrepancy lies in the existence of the soil cohesion, for the shape of the critical rupture surface of footing soil depends on both soil strength parameters rather than on friction angle alone in the previous limit equilibrium solutions. The contact between footing and soil is decided by both the load and the mechanical properties of soil. Under conditions of higher eccentricity and less strength properties of soil, part of the footing will separate from the underlying soil.

Effect of Strength Eccentricity on Torsional Behaviour of RC Frame Buildings

This study attempts to understand the inelastic seismic behaviour of asymmetric multistory RC buildings using non-linear dynamic time history analysis. Both inherently asymmetric and artificially generated eccentric building models were considered. Two categories of artificially generated models were considered. In the first category, groups of mass symmetric systems (MSS) having strength, stiffness and both strength and stiffness eccentricities were considered. In the second category of models, mass eccentricity was introduced in otherwise symmetric models. Building systems were modelled as 3D space frame with lumped plasticity. The response is evaluated using the peak rotational ductility demand of beams of the different frames as measures of their inelastic response. Investigations of first category of artificially generated MSS showed that the response can be better co-related with the strength eccentricity. The results from the second category of systems not designed for torsion indicated that there is significant variation in the beam ductility demands of different frames, whereas systems designed for torsion indicated a shift in the center of strength towards the center of mass and exhibited almost uniform ductility demand in beams of various frames for smaller eccentricities.

Dynamic collapse test on eccentric reinforced concrete structures with and without seismic retrofit

Reconnaissance reports on structures damaged or collapsed by severe earthquakes have revealed several common characteristics in their structural members and systems, such as insufficient reinforcement details in beam-column joints and transverse confinements, low aspect ratios, soft and or weak stories, and eccentric plans. Dynamic tests were carried out to investigate the collapse process of reinforced concrete structures that had seismically deficient reinforcement details (light transverse reinforcement) and seismic systems (soft/weak stories and eccentric plans). A comparison of collapse behaviors with and without seismic retrofits also verified the effectiveness of the SRF (super reinforced with flexibility) strengthening method, which was developed to prevent the loss of axial load carrying capacity even at excessive lateral deformation. The columns of one specimen were strengthened with polyester fiber belts and its shear walls with polyester fiber sheets, while the members of the other were not. Each specimen was designed following old (1970s) reinforcement detail practice in Japan, and is a one-third-scale reinforced concrete structure with considerable stiffness and strength eccentricity in the first story. The specimens were composed of independent column frame and shear wall frame. Torsional response resulting from the eccentricity in the 1st story induced a displacement concentration on the weak frame, and eventually the independent columns of the RC specimen failed in shear and lost their axial load carrying capacity. On the other hand, the SRF specimen survived not only an identical earthquake load to the one that caused the RC specimen to fail, but also three additional earthquake loads, although significant strength deterioration and considerable lateral and vertical deformation were generated at the end of the test. The following conclusions were drawn from the comparison of the two specimens’ responses: axial column collapse cannot be predicted from vertical responses since the vertical behavior of bare RC columns was not discernibly different from that of SRF columns until axial collapse was initiated, and the SRF strengthening method is effective in confining the column and preventing the cracking progress, thus modifying the failure mode of the RC columns from brittle shear failure after flexural yield to flexural dominant behavior.

Effect of Soil-Structure Interaction on Torsional Response of Asymmetric Wall Type Systems

Generally in the analysis of structures, the base of structures is assumed to be fixed. Whereas, the soil under the structures foundation modify earthquake loading and also change the structural properties. Therefore, considering the fixed base in the structure analysis is not realistic. On the other hand, recent studies have pointed out that for an important class of widely used structural elements such as reinforced concrete flexural walls; stiffness is a strength dependent parameter. This implies that the lateral stiffness distribution in an asymmetric wall-type system cannot be evaluated prior to the assignment of elements’ strength. Consequently, both stiffness and strength eccentricity are important parameters affecting the seismic response of asymmetric wall-type systems. In this study, for different position of stiffness and strength eccentricity, torsional response of asymmetric wall-type system is evaluated. In this evolution the effect of foundation flexibility, is assumed.

Theoretical study on concrete-filled steel tubes under static and variable repeated loadings

This paper presents an analytical study for modelling the behaviour of concrete-filled steel tubular (CFST) columns subjected to Static Loading (SL) and Variable Repeated Loading (VRL). The variables considered in this study are concrete strength and load eccentricity. Simple mathematical models are developed and used in the analysis. The analytical results show that the incremental collapse (IC) occurs in high load ranges in CFST columns under VRL and instability failure occurs under SL. The CFST columns with large end load eccentricity were found to fail at a low upper limit load level than that with small eccentricity of loading. The IC failure was found to be unaffected by the strength of concrete infill. The hollow steel tubular (HST) columns showed similar behaviour under SL and VRL protocols. The study showed that the theoretical analyses satisfactorily model the actual behaviour of the columns under SL and VRL protocols.

Reliability analysis of net cross-section resistance with accidental eccentricity of holes

The aim of the research was to determine reliability function of net cross-section resistance in relation to accidental eccentricity of nominally centric holes. The response surface method was used by taking into account the relevant Eurocode design provisions and reliability requirements. Within the response surface method, the central composite design method and the least square method were used with the employment of Monte Carlo simulations. The probable distributed variables such as strength fy, breadth b, thickness t, diameter d0 and eccentricity e were determined by the central composite design method. 280 different numerical simulations were set up with varying variables. A log-normal distribution for strength (fy) and a normal distribution for geometrical variables (b, t, d0,e) were employed by taking into account the coefficients of variations: Vfy=0.07, Vb,=0.005, Vl=0.05 and Vd0=0.005. In order to determine the influence of eccentricity on partial safety factor, several normal distributions with different variation factors were applied in the analysis. The influence of the edge distance of the hole e2 over d0 ratio on the partial safety factor was determined by varying mean values of variable b. For comparison, two types of steel were used: structural steel S235 and high strength steel S690. Numerical simulations of the net cross-section resistance Fu were performed with ABAQUS 6.7. The response surface for the net cross-section resistance was determined by introducing a quadratic approximation function and by applying the least square method. The partial safely factor was then (statistically) obtained by means of robust Monte Carlo simulations on the calculated response surface.

Nonlinear seismic analysis of asymmetric in plan buildings

In many buildings the centres of resistance do not coincide with the centres of mass. As a consequence, lateral base motion during an earthquake gives rise to torsional vibration of the structure. The inelastic seismic behaviour of asymmetric-plan buildings is considered using the histories of base shear and torque. The procedure to construct the base shear and torque (BST) surface of the system with an arbitrary number of resisting elements in the direction of asymmetry and of ground motion is proposed. The factors that determine the shape of the BST surface are the strength eccentricity, lateral and torsional capacity of the system and planwise distribution of strength. The BST surface contains most of information necessary to describe the inelastic properties of a system. However, the inelastic deformation cannot be computed unless a nonlinear static or dynamic analysis is performed.