Estimating the seismic displacement of friction pendulum isolators based on non‐linear response history analysis

A procedure for developing equations that estimate the isolator displacement due to strong ground motion is applied to buildings isolated with the friction pendulum system. The resulting design equations, based on rigorous non‐linear analysis, offer an alternative to the iterative equivalent‐linear methods used by current U.S. building codes. The governing equations of the system are reduced to a form such that the median normalized displacement of the system due to an ensemble of ground motions is found to depend on only the isolation period—a function of the curvature of the isolator—and the friction force at incipient slip normalized by peak ground velocity. The normalization is effective in minimizing the dispersion of the normalized displacement for an ensemble of ground motions, implying that the median normalized displacement is a reliable estimate of response. The design equations reflect the significant (20 to 38%) increase in displacement when the excitation includes two lateral components of ground motion instead of just one component. Equivalent‐linear methods are shown to underestimate by up to 30% the exact median displacement determined by non‐linear response history analysis for one component of ground motion, and building codes include at most a 4.4% increase for a second component. Copyright © 2003 John Wiley & Sons, Ltd.     

Strain field measurements of rubber by image analysis and design criteria for laminated rubber bearings (LRB)

Although seismic isolation rubber bearings in bridges and buildings have proven to be a very effective passive method for reducing earthquake‐induced forces, a detailed mechanical modeling of the rubber that is used in bearings under large strains has not been established. Therefore, a 3D model of failure behavior and the design criteria for the safety evaluation of seismic isolation bearings have not yet been developed. This paper presents: (1) correlation‐based template‐matching algorithms to measure large strain fields of continua; (2) a failure criterion for rubber; and (3) the design criteria for the safety evaluation of laminated algorithms, data‐validation algorithms were developed and implemented to eliminate possible unrealistic displacement vectors present in the measured displacement field. The algorithms were successfully employed in the strain field measurement of LRB and rubber materials that are subjected to failure. The measured local strains for rubber material at failure were used to develop a failure criterion for rubber. The validity of the proposed criterion was evaluated by applying it to the LRB; the criterion was introduced into a 3D finite element model of LRB, compared with the experimental results of bearings failure, and verified. Finally, design criteria are proposed for LRB for the safety evaluation. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic response of a cable‐stayed bridge deck under multi‐component non‐stationary random ground motion

A Markov method of analysis is presented for obtaining the seismic response of cable‐stayed bridges to non‐stationary random ground motion. A uniformly modulated non‐stationary model of the random ground motion is assumed which is specified by the evolutionary r.m.s. ground acceleration. Both vertical and horizontal components of the motion are considered to act simultaneously at the bridge supports. The analysis duly takes into account the angle of incidence of the earthquake, the spatial correlation of ground motion and the quasi‐static excitation. A cable‐stayed bridge is analysed under a set of parametric variations in order to study the non‐stationary response of the bridge. The results of the numerical study indicate that (i) frequency domain spectral analysis with peak r.m.s. acceleration as input could provide more r.m.s. response than the peak r.m.s. response obtained by the non‐stationary analysis; (ii) the longitudinal component of the ground motion significantly influences the vertical vibration of the bridge; and (iii) the angle of incidence of the earthquake has considerable influence on the deck response. Copyright © 2003 John Wiley & Sons, Ltd.     

Frequency domain modal analysis of earthquake input energy to highly damped passive control structures

A new complex modal analysis‐based method is developed in the frequency domain for efficient computation of the earthquake input energy to a highly damped linear elastic passive control structure. The input energy to the structure during an earthquake is an important measure of seismic demand. Because of generality and applicability to non‐linear structures, the earthquake input energy has usually been computed in the time domain. It is shown here that the formulation of the earthquake input energy in the frequency domain is essential for deriving a bound on the earthquake input energy for a class of ground motions and for understanding the robustness of passively controlled structures to disturbances with various frequency contents. From the viewpoint of computational efficiency, a modal analysis‐based method is developed. The importance of overdamped modes in the energy computation of specific non‐proportionally damped models is demonstrated by comparing the energy transfer functions and the displacement transfer functions. Through numerical examinations for four recorded ground motions, it is shown that the modal analysis‐based method in the frequency domain is very efficient in the computation of the earthquake input energy. Copyright © 2004 John Wiley & Sons, Ltd.     

Fundamental study on the response characteristics of drivers during an earthquake based on driving simulator experiments

After the 1995 Kobe earthquake, the expressway structures in Japan were retrofitted and they will not now be seriously damaged under a certain level of strong earthquake motion. However, the stability of a moving vehicle has not been investigated yet. It has been reported that drivers feel seismically induced vibrations, especially in the transverse direction of vehicles. Owing to this phenomenon, drivers have some difficulty in controlling the vehicles during strong shaking. For further safety promotion of the expressway networks, it is important to understand the drivers' reactions to seismic motion. The present authors have performed a series of seismic response analyses of a moving vehicle to investigate its response characteristics based on numerical simulation. However, the responses of the driver were not considered in the simulation process. In order to investigate the drivers' reactions during an earthquake, a series of virtual tests were conducted using a driving simulator. This driving simulator has six servomotor‐powered electric actuators that control its motions. Several types of tests were carried out for different examinees to investigate drivers' responses while controlling the simulator under seismic motion. The results of this study showed that a larger response time lag to strong shaking and over turning of the steering wheel may shift the vehicle into the next lane. According to this finding, trafficaccidents could possibly occur under strong ground shaking in the case of heavy traffic. Copyright © 2004 John Wiley & Sons, Ltd.     

A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.     

The seismic shear of ductile cantilever wall systems in multistorey structures

The distribution of seismic base shear demand among ductile flexural cantilever walls, comprising the lateral load resisting system of a multistorey building, is studied. It is shown that the base shear force demand depends on the sequence of hinge formation at the wall bases, and this in turn depends on the relative wall lengths. Hence, the routine elastic approach in which the shear forces are allocated per relative flexural rigidity or (when some consideration is given to plastic hinge formation) to moment capacity at the wall base, may appreciably underestimate the shear force demand on the walls, particularly the shorter (usually the more flexible) ones. A simple procedure yielding the results of ‘cyclic’ pushover analysis is proposed to predict the peak seismic wall forces for a given total base shear when plastification is confined to the wall base. The effects of plastic hinges developing at higher floors on (1) shear distribution among the walls and (2) the in‐plane floor forces are also considered. Two numerical examples are presented to demonstrate the main points made. Copyright © 2004 John Wiley & Sons, Ltd.     

Approximate modal decomposition of inelastic dynamic responses of wall buildings

Two approximate methods for decomposing complicated inelastic dynamic responses of wall buildings into simple modal responses are presented. Both methods are based on the equivalent linear concept, where a non‐linear structure is represented by a set of equivalent linear models. One linear model is used for representing only one vibration mode of the non‐linear structure, and its equivalent linear parameters are identified from the inelastic response time histories by using a numerical optimizer. Several theoretical relations essential for the modal decomposition are derived under the framework of complex modal analysis. Various numerical examinations have been carried out to check the validity of the proposed modal decomposition methods, and the results are quite satisfactory in all cases. Fluctuating bending moment and shear at any location along the wall height contributed by each individual vibration mode can be obtained. Modal contributions to shear and flexural strength demands, as well as the corresponding modal properties, under various seismic loading conditions can also be identified and examined in detail. Furthermore, the effects of higher vibration modes on seismic demands of wall buildings are investigated by using the modal decomposition methods. Several new insights into the complicated inelastic dynamics of multi‐story wall buildings are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Seismic performance evaluation of steel arch bridges against major earthquakes. Part 1: dynamic analysis approach

In this study the inelastic behavior of steel arch bridges subjected to strong ground motions from major earthquakes is investigated by dynamic analyses of a typical steel arch bridge using a three‐dimensional (3D) analytical model, since checking seismic performance against severe earthquakes is not usually performed when designing such kinds of bridge. The bridge considered is an upper‐deck steel arch bridge having a reinforced concrete (RC) deck, steel I‐section girders and steel arch ribs. The input ground motions are accelerograms which are modified ground motions based on the records from the 1995 Hyogoken‐Nanbu earthquake. Both the longitudinal and transverse dynamic characteristics of the bridge are studied by investigation of time‐history responses of the main parameters. It is found that seismic responses are small when subjected to the longitudinal excitation, but significantly large under the transverse ground motion due to plasticization formed in some segments such as arch rib ends and side pier bases where axial force levels are very high. Finally, a seismic performance evaluation method based on the response strain index is proposed for such steel bridge structures. Copyright © 2004 John Wiley & Sons, Ltd.     

Seismic tests on reinforced concrete and steel frames retrofitted with dissipative braces

Seismic tests have been conducted on two 3‐storey structures protected with pressurized fluid‐viscous spring damper devices. One of the structures was a reinforced concrete frame with clay elements in the slabs, while the other one was a steel frame with steel/concrete composite slabs. The spring dampers were installed through K bracing in between the floors. The tests were performed by means of the pseudodynamic method, which allowed the use of large and full‐size specimens, and by implementing a specific compensation strategy for the strain‐rate effect at the devices. The test results allowed the verification of the adequacy of the attachment system as well as the comparison of the behaviour of the unprotected buildings with several protected configurations, showing the benefits of the application of the devices and the characteristics of their performance. The response of the protected structures was always safer than that of the unprotected ones mainly due to a significant increase of equivalent damping. The increase in the damping ratio depends on the level of deformation. Copyright © 2004 John Wiley & Sons, Ltd.