Bi-directional Ground Motions Research Articles

Seismic response of non-structural components attached to reinforced concrete structures with different eccentricity ratios

This paper presents average numerical results of 2128 nonlinear dynamic finite element (FE) analyses of lightweight acceleration-sensitive non-structural components (NSCs) attached to the floors of one-bay three-storey reinforced concrete (RC) primary structures (P-structures) with different eccentricity ratios. The investigated parameters include the NSC to P-structure vibration period ratio, peak ground acceleration, P-structure eccentricity ratio, and NSC damping ratio. Appropriate constitutive relationships were used to model the behaviour of the RC P-structures. The NSCs were modelled as vertical cantilevers fixed at their bases with masses on the free ends and varying lengths so as to match the vibration periods of the P-structures. Full dynamic interaction was considered between the NSCs and P-structures. A set of seven natural bi-directional ground motions were used to evaluate the seismic response of the NSCs. The numerical results show that the acceleration response of the NSCs depends on the investigated parameters. The accelerations of the NSCs attached to the flexible sides of the P-structures increased with the increase in peak ground acceleration and P-structure eccentricity ratio but decreased with the increase in NSC damping ratio. Comparison between the FE results and Eurocode 8 (EC8) predictions suggests that, under tuned conditions, EC8 provisions underestimate the seismic response of the NSCs mounted on the flexible sides of the plan-irregular RC P-structures.

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.

Real-valued modal response history analysis for asymmetric-plan buildings with nonlinear viscous dampers

Modal analysis, which is clear in concept and simple in computation, is widely applied to evaluate the seismic responses of elastic structures with proportional damping. Nevertheless, nonlinear viscous dampers commonly installed in real buildings result in non-proportionally damped structures, which impede the modal analysis in real number field for such structures. This study develops the approach of performing real-valued modal response history analysis for elastic two-way asymmetric-plan buildings with nonlinear viscous dampers. To this end, this study first constructs the nonlinear three-degree-of-freedom (3DOF) modal equations of motion for such structures. The nonlinear 3DOF modal equations of motion retain the non-proportional damping characteristics in the modal space. Hence, by solving the nonlinear 3DOF modal equations of motion, the total response history is effectively attained by arithmetically summing up the modal response histories. This study uses nine two-way asymmetric-plan buildings, each equipped with nonlinear viscous dampers subjected to three bi-directional ground motions to verify the proposed approach. The investigation results show that the proposed simplified analysis approach provides satisfactory estimation of the seismic responses of common asymmetric-plan buildings with nonlinear viscous dampers.

Response analysis of a nuclear containment structure with nonlinear soil–structure interaction under bi-directional ground motion

Design of critical facilities such as nuclear power plant requires an accurate and precise evaluation of seismic demands, as any failure of these facilities poses immense threat to the community. Design complexity of these structures reinforces the necessity of a robust 3D modeling and analysis of the structure and the soil–foundation interface. Moreover, it is important to consider the multiple components of ground motion during time history analysis for a realistic simulation. Present study is focused on investigating the seismic response of a nuclear containment structure considering nonlinear Winkler-based approach to model the soil–foundation interface using a distributed array of inelastic springs, dashpots and gap elements. It is observed from this study that the natural period of the structure increases about 10 %, whereas the force demands decreases up to 24 % by considering the soil–structure interaction. Further, it is observed that foundation deformations, such as rotation and sliding are affected by the embedment ratio, indicating an increase of up to 56 % in these responses for a reduction of embedment from 0.5 to 0.05× the width of the footing.

Elimination of torsion and pounding of isolated asymmetric structures under near-fault ground motions

This paper aims at forcing the isolated asymmetric structures to behave as symmetric structures with, theoretically, no absolute torsional responses. In addition, it attempts to provide efficient protection to such structures against severe near-fault ground motions considering limited seismic gaps with no seismic pounding. To achieve these goals, the recently proposed multi-feature roll-in-cage (RNC) isolator is used. An improved full-feature sap2000 model (Computers and Structures, Inc., Walnut Creek, CA, USA) is first developed for the RNC isolator then validated using analytical and experimental results. Next, an RNC isolation method that could eliminate the eccentricities between both structural centers of mass and rigidity is employed to theoretically remove structural torsion. It is based on using different isolator sets with unequal elastic stiffness to allow for shifting the center of rigidity at the isolation level, having dominant lateral behavior in case of isolated structures, to coincide with the structural center of mass above that level. After that, the ability of the RNC isolator to provide efficient seismic isolation considering relatively limited seismic gaps is investigated under unidirectional and bidirectional near-fault earthquakes. This could be attained through the independent source of high hysteretic damping and pre-yield elastic stiffness of the RNC isolator, in addition to its integrated self-stopping or buffer mechanism. The obtained results demonstrate the capability of the RNC isolator to, theoretically, eliminate torsional responses of isolated asymmetric structures besides providing relatively efficient seismic isolation, with no seismic pounding, considering insufficient or limited seismic gaps under severe near-fault unidirectional and simultaneous bidirectional ground motions. Copyright © 2015 John Wiley & Sons, Ltd.

Seismic analysis of highway skew bridges with nonlinear soil–pile interaction

Performance of highway bridges during an intense seismic event is an issue of utmost importance. Of particular interest is the response of skewed highway bridges, where the skew angle and other related factors make the problem more complex. Although a number of studies had been carried out to address these issues in the past, most of them have neglected or over-simplified the soil–structure interaction effects, primarily relying upon the assumption that soil–structure interaction generally leads to a conservative estimation of seismic demands. The present study focuses on investigating the effect of skew angle on seismic response of a bridge-foundation system including nonlinear soil–pile interaction subjected to bi-directional ground motions. It has been observed that the rotational demand of the bridge deck is greatly affected by the skewness, indicating an increased vulnerability of skewed bridges due to rotational movement of the deck leading to deck unseating. It is also observed that the shear and moment demands of the piers increase significantly with increasing skew angle, as much as 54% and 37%, respectively. The maximum bending moment of the pile shaft is also found to increase upto 55%, indicating higher design requirements for the foundation components of the skew bridges compared to a similar normal bridge.

Parameters affecting the seismic response of buildings under bi-directional excitation

The present paper investigates the influence of the orientation of the ground-motion reference axes, the seismic incident angle and the seismic intensity level on the inelastic response of asymmetric reinforced concrete buildings. A single storey asymmetric building is analyzed by nonlinear dynamic analyses under twenty bi-directional ground motions. The analyses are performed for many angles of incidence and four seismic intensity levels. Moreover three different pairs of the horizontal accelerograms corresponding to the input seismic motion are considered: a) the recorded accelerograms, b) the corresponding uncorrelated accelerograms, and c) the completely correlated accelerograms. The nonlinear response is evaluated by the overall structural damage index. The results of this study demonstrate that the inelastic seismic response depends on the orientation of the ground-motion reference axes, since the three individual pairs of accelerograms corresponding to the same ground motion (recorded, uncorrelated and completely correlated) can cause different structural damage level for the same incident angle. Furthermore, the use of the recorded accelerograms as seismic input does not always lead to the critical case of study. It is also shown that there is not a particular seismic incident angle or range of angles that leads to the maximum values of damage index regardless of the seismic intensity level or the ground-motion reference axes.

A pushover procedure for seismic assessment of buildings with bi-axial eccentricity under bi-directional seismic excitation

A new modal pushover procedure is proposed for seismic assessment of asymmetric-plan buildings under bi-directional ground motions. Although the proposed procedure is a multi-mode procedure and the effects of the higher and torsional modes are considered, the simplicity of the pushover procedure is kept and the method requires only a single-run pushover analysis for each direction of excitation. The effects of the frequency content of a specific ground motion and the interaction between modes at each direction are all considered in the single-run pushover analysis. For each direction, the load pattern is derived from the combined modal story shear and torque profiles. The pushover analysis is conducted independently for each direction of motion (x and y), and then the responses due to excitation in each direction are combined using SRSS (Square Roots of Sum of Squares) combination rule. Accuracy of the proposed procedure is evaluated through two low- and medium-rise buildings with 10% two-way eccentricity under different pairs of ground motions. The results show promising accuracy for the proposed method in predicting the peak seismic responses of the sample buildings.

Spectral Matching of Real Ground Motions: Applications to Horizontally Irregular Systems in Elastic Range

In the context of performance-based seismic design (PBSD), ground motions are often scaled to certain convenient target spectra derived from probabilistic seismic hazard analysis (PSHA). While Uniform Hazard Spectrum (UHS) is more widely used, Conditional Mean Spectrum (CMS) is recently proposed to be more desirable for scaling of real accelerograms. In this backdrop, a set of near-field and far-field ground motions are spectrally scaled, using wavelets, to both UHS and CMS. Seismic demand of horizontally irregular structures under bi-directional ground motion is assessed under both scaled and seed records in the elastic range. Spectral matching, within limits, of both the horizontal components of real records to a single hazard spectrum is observed to adequately predict the amplification in response due to asymmetry (at least for the records and target spectra relevant to soil class D). Further, such scaling effectively reduces the variability in predicted magnification from one ground motion to other. Dynamic amplification factors recommended in international codes to apply in equivalent static design of asymmetric systems are shown to be deficient.

Inelastic seismic behavior of soil–pile raft–structure system under bi-directional ground motion

Performance based design of structure requires a reasonably accurate prediction of displacement or ductility demand. Generally, displacement demand of structure is estimated assuming fixity at base and considering base motion in one direction. In reality, ground motions occur in two orthogonal directions simultaneously resulting in bidirectional interaction in inelastic range, and soil–structure interaction (SSI) may change structural response too. Present study is an attempt to develop insight on the influence of bi-directional interaction and soil–pile raft–structure interaction for predicting the inelastic response of soil–pile raft–structure system in a more reasonably accurate manner. A recently developed hysteresis model capable to simulate biaxial interaction between deformations in two principal directions of any structural member under two orthogonal components of ground motion has been used. This study primarily shows that a considerable change may occur in inelastic demand of structures due to the combined effect of such phenomena.

Extended consecutive modal pushover procedure for estimating seismic responses of one-way asymmetric plan tall buildings considering soil-structure interaction

Performance based design becomes an effective method for estimating seismic demands of buildings. In asymmetric plan tall building the effects of higher modes and torsion are crucial. The consecutive modal pushover (CMP) procedure is one of the procedures that consider these effects. Also in previous studies the influence of soil-structure interaction (SSI) in pushover analysis is ignored. In this paper the CMP procedure is modified for one-way asymmetric plan mid and high-rise buildings considering SSI. The extended CMP (ECMP) procedure is proposed in order to overcome some limitations of the CMP procedure. In this regard, 10, 15 and 20 story buildings with asymmetric plan are studied considering SSI assuming three different soil conditions. Using nonlinear response history analysis under a set of bidirectional ground motion; the exact responses of these buildings are calculated. Then the ECMP procedure is evaluated by comparing the results of this procedure with nonlinear time history results as an exact solution as well as the modal pushover analysis procedure and FEMA 356 load patterns. The results demonstrate the accuracy of the ECMP procedure.

Torsional response of nonductile structures with soft‐first‐storey

SUMMARYIn this paper, torsional response of nonductile structures with soft‐first‐storey subjected to bidirectional ground motions is studied using a simplified two‐storey model with two‐way eccentricities. The stiffness ratio of second storey to first storey is varied to create different levels of soft‐first‐storey effect, while the stiffness eccentricity is varied to create torsional effects. Different overstrength ratios are used in the simplified models to study the response of structure with different structural capacity. Hysteretic model with strength deterioration and stiffness degradation properties is used to capture the deterioration of element stiffness and strength. Ductility capacity of 2.0 is used as the models are for nonductile structures. In general, displacement amplification of irregular model with respect to regular model increases as stiffness ratio increases, while no consistent trend of changes in displacement amplification is found with increase in stiffness eccentricity. It is found that the displacement amplification due to only soft‐first‐storey effect can be conservatively taken as 1.5. Coupling of torsional and soft‐first‐storey effects is more significant in affecting the displacement amplification of elements at flexible side. The trend of changes in displacement amplification of elastic system is similar to that of inelastic system. The displacement amplification of elements at the flexible side is larger than that at the stiff side. The elements at the flexible side in the direction of shorter uncoupled lateral period have larger displacement response than those in the orthogonal direction. Ductility demand–capacity curves subsequently constructed can be used to approximately assess the seismic performance of existing structures and as guidelines for designing structures in Singapore to withstand the maximum credible earthquake considering the coupling of torsional and soft‐first‐storey effects. Copyright © 2014 John Wiley & Sons, Ltd.

Seismic vulnerability of skew bridges under bi-directional ground motions

Past earthquakes have demonstrated that skew bridges are more vulnerable to earthquake induced failure than a normal bridge due to their complex load transfer mechanism. This study deals with the effect of skew angle on seismic vulnerability of these bridges under horizontal two-component (bi-directional) ground motions. For this purpose, representative models of two-span simply supported, typical highway overpasses with varying skew angles have been considered. Finite element models of these bridges, which have been designed using modern seismic provisions, are developed using a widely used software. A suite of bi-directional ground motions with varying strong motion properties and representing different hazard levels is used for nonlinear dynamic analysis and subsequent seismic vulnerability estimation using fragility curves. Deck unseating and damage of columns are considered as the damage measures for the vulnerability analysis. The effect of ground motion directionality on the vulnerability of bridges has also been investigated in this study. Results of this study indicate that as the skew angle increases, there is an increase in the probability of failure for a given ground motion intensity. It is also found that the dispersion of fragility curves for bi-directional ground motions can be minimized by using the square root of sum of squares (SRSS) of peak ground acceleration (PGA) of all components than the PGA of any component.

Bidirectional Pushover Analysis of Irregular Structures

AbstractPushover analysis is one of the most-used nonlinear static procedures for the seismic assessment of structures; therefore, nowadays it is extensively used by practicing engineers for the seismic analysis of virtually every type of building. This paper proposes a bidirectional pushover analysis (BPA) method to overcome the limitations of current pushover methods to assess the seismic response of irregular (both in plan and in elevation) buildings subjected to bidirectional ground motions. The extended N2 method and the proposed BPA method were applied to estimate the nonlinear response of six highly irregular reinforced concrete frame structures designed according to the requirements of Eurocode 8. Results in terms of interstory drifts and floor rotations are compared with those given by nonlinear response history analysis (NRHA). For the latter, a suite of twenty Italian bidirectional seismic ground motions was selected. It was found that results given by the proposed BPA method match those given ...

Robust optimal H-infinity control for irregular buildings with AMD via LMI approach

In view of the numerous uncertainties of seismic disturbances and structural parameters, the irregular building structure is uncertain. In this paper, a new robust optimal H∞ controller for irregular buildings is designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties. Such a control method can provide a convenient design procedure for active controllers to facilitate practical implementations of control systems through the use of a quadratic performance index and an efficient solution procedure based on linear matrix inequality (LMI). To verify the effectiveness of the control method, a MDOF (multipledegree-of-freedom) eccentric building structure with two active mass damper (AMD) systems on the orthogonal direction of the top storey subjected to bi-directional ground motions is analyzed. In the simulation, the active control forces of the AMD systems are designed by the robust optimal H∞ control algorithm, and the structural system uncertainties are assumed in the system and input matrices. The simulation results obtained from the proposed control method are compared with those obtained from traditional H∞ control method, which shows preliminarily that the performance of robust optimal H∞ controllers is remarkable and robust. Therefore, the robust optimal H∞ control method is quite promising for practical implementations of active control systems on seismically excited irregular buildings.

Nonlinear finite element modeling of reinforced masonry shear walls for bidirectional loading response

The objective of this paper is to analytically establish the effects of bidirectional loading on the response of reinforced masonry shear walls. To accomplish this, an efficient nonlinear 3D finite element modeling approach was used and proved capable of simulating the capacity (within 10%), failure modes and hysteretic response of both partially-grouted (PG) and fully-grouted (FG) masonry shear walls. This modeling approach was also validated for the prediction of out-of-plane response, and then used to examine the influence of bi-directional loading through a series of parametric studies with out-of-plane drift, wall aspect ratio and vertical stress as variables. Results from this study indicate that out-of-plane drifts corresponding to the collapse prevention limit state reduce the in-plane capacity of PG walls by more than 20%. Further, this study indicates that the sensitivity to out-of-plane drift is increased as the aspect ratio increases and as the vertical stress decreases. Although the capacity of PG walls is influenced by out-of-plane drifts, their hysteretic responses, and in particular, energy dissipation capacities as well as their ductility remain nearly unchanged. As a result, the seismic response of PG masonry walls is likely nominally affected by bi-directional ground motions.

Prediction of the largest peak nonlinear seismic response of asymmetric buildings under bi-directional excitation using pushover analyses

A simplified procedure is proposed to predict the largest peak seismic response of an asymmetric building to horizontal bi-directional ground motion, acting at an arbitrary angle of incidence. The main characteristics of the proposed procedure is as follows. (1) The properties of two independent equivalent single-degree-of-freedom models are determined according to the principal direction of the first modal response in each nonlinear stage, rather than according to the fixed axis based on the mode shape in the elastic stage; the principal direction of the first modal response in each nonlinear stage is determined based on pushover analysis results. (2) The bi-directional horizontal seismic input is simulated as identical spectra of the two horizontal components, and the contribution of each modal response is directly estimated based on the unidirectional response in the principal direction of each. (3) The drift demand at each frame is determined based on four pushover analyses considering the combination of bi-directional excitations. In the numerical example, nonlinear time-history analyses of six four-story torsionally stiff (TS) asymmetric buildings are carried out considering various directions of seismic inputs, and these results are compared with the predicted results. The results show that the proposed procedure satisfactorily predicts the largest peak response displacement at the flexible-side frame of a TS asymmetric building.

Lead core heating in lead rubber bearings subjected to bidirectional ground motion excitations in various soil types

SUMMARYThis paper investigates the response of lead rubber bearings (LRBs) under bidirectional earthquake excitations when lead core heating effect is of concern. For this purpose, a series of nonlinear response history analyses were conducted with a bilinear force‐deformation relation for LRBs. In the considered bilinear representation, the strength of LRBs deteriorates because of lead core heating under cyclic motions. Response of LRBs was studied in terms of maximum isolator displacements (MIDs) and maximum lead core temperature as a function of isolator characteristics (characteristic strength to weight ratio, Q/W, and post‐yield isolation period, T). Nonlinear response history analyses were performed using two sets of ground motions clustered according to their soil classifications. To quantify the interacted effects of coupled analysis and lead core heating on MID, unidirectional analyses were also performed. Furthermore, the efficacy of equivalent lateral force procedure in estimating the MID of LRBs was also tested for the cases in which temperature‐dependent behavior of LRBs was considered. The results demonstrate that the temperature rises in the lead core of LRBs in bidirectional analyses are approximately 50% higher than that of unidirectional ones. It decreases with increasing Q/W ratio and T. It is also revealed that equivalent lateral force procedure gives close estimations for MID with some overestimation even for temperature‐dependent behavior of LRBs. Copyright © 2013 John Wiley & Sons, Ltd.

Earthquake-Induced Lateral-Torsional Pounding between Two Equal Height Multi-Storey Buildings under Multiple Bi-Directional Ground Motions

Pounding between adjacent buildings, often characterized by different material properties, can be cause of significant or even severe structural damage. The aim of this paper is to present a detailed analytical study on earthquake induced lateral-torsional pounding between two equal height multi-storey buildings with equal storey heights. Both a non-linear viscoelastic model to simulate impact and a non-linear behaviour of the storey shear forces and torques are considered in the model. Pounding-involved response is evaluated in the hypothesis of frictionless contact. Torsional effects are taken into account by implementing the most probable impact scenarios, depending on the sign of the rotations of two adjacent floor-diaphragms. Asymmetric buildings with initial eccentricities just in the transverse direction are considered, while input ground motion is incorporated in the analysis in both directions. Multiple ground motions are implemented in the analysis, in order to investigate the sensitivity of the earthquake-induced pounding to the characteristics of the seismic excitation. The dynamic equation of motion is solved by proposing a suitable MATLAB numerical algorithm.

Seismic Response of Steel Buildings with Different Structural Typology

This study investigates the influence of the in-plan structural layout on the seismic response of symmetric and asymmetric steel structures. A five-storey steel frame building was used as reference structure and two different structural systems were employed to represent torsional stiff and torsional flexible structures. Accurate numerical models of the different typologies of structures were developed and both nonlinear static and dynamic analyses under bi-directional ground motion were carried out. The influence of axial force-bending moment interaction in columns in the two main directions and second order effects were taken into account in the numerical analyses. The results of the numerical investigations on symmetric structures showed that the reduction of the number of moment resisting connections may lead to an increase of the structural damage. Asymmetric variants of the investigated structures were created by assuming different mass eccentricities in each of the two main directions and extensive parametric studies were performed. For the torsionally flexible building, the influence of ground motion intensity was very strong. A transition from torsionally flexible to torsionally stiff behaviour in the weaker direction of the initially torsionally flexible structure was observed for severe seismic actions. The change of the stiffness of the structure in one direction due to high levels of plastic deformations affected the structural response in the orthogonal direction. Torsional effects decreased in case of severe seismic excitations and high levels of plastic deformations. The reduction of torsional effects observed for low seismic actions on the stiff side of torsionally stiff buildings disappeared under strong seismic excitations.