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.     

Seismic isolation of cable‐stayed bridges for near‐field ground motions

This study examines the efficacy of using seismic isolation to favorably influence the seismic response of cable‐stayed bridges subjected to near‐field earthquake ground motions. In near‐field earthquake ground motions, large amplitude spectral accelerations can occur at long periods where many cable‐stayed bridges have significant structural response modes. This combination of factors can result in large tower accelerations and base shears. In this study, lead–rubber bearing seismic isolators were modeled for three cable‐stayed bridges, and three cases of isolation were examined for each bridge. The nine isolated bridge configurations, plus three non‐isolated configurations as references, were subjected to near‐field earthquake ground motions using three‐dimensional time‐history analyses. Introduction of a small amount of isolation is shown to be very beneficial in reducing seismic accelerations and forces while at the same time producing only a modest increase in the structural displacements. There is a low marginal benefit to continue to increase the amount of isolation by further lengthening the period of the structure because structural forces and accelerations reduce at a diminishing rate whereas structural displacements increase substantially. In virtually all cases the base shears in the isolated bridges were reduced by at least 50several instances by up to 80individual near‐field records showed large variability from one record to the next, with coefficients of variation about the mean as large as 50assessing the characteristics of near‐field ground motion for use in isolation design of cable‐stayed bridges. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic performance of twin curved cable‐stayed bridges

The dynamic behaviour of two curved cable‐stayed bridges, recently constructed in northern Italy, has been investigated by full‐scale testing and theoretical models. Two different excitation techniques were employed in the dynamic tests: traffic‐induced ambient vibrations and free vibrations. Since the modal behaviour identified from the two types of test are very well correlated and a greater number of normal modes was detected during ambient vibration tests, the validity of the ambient vibration survey is assessed in view of future monitoring. For both bridges, 11 vibration modes were identified in the frequency range of 0ndash;10Hz, being a one‐to‐one correspondence between the observed modes of the two bridges. Successively, the information obtained from the field tests was used to validate and improve 3D finite elements so that the dynamic performance of the two systems were assessed and compared based on both the experimental results and the updated theoretical models. Copyright © 2003 John Wiley & Sons, Ltd.     

System identification applied to long‐span cable‐supported bridges using seismic records

This paper presents the application of system identification (SI) to long‐span cable‐supported bridges using seismic records. The SI method is based on the System Realization using Information Matrix (SRIM) that utilizes correlations between base motions and bridge accelerations to identify coefficient matrices of a state‐space model. Numerical simulations using a benchmark cable‐stayed bridge demonstrate the advantages of this method in dealing with multiple‐input multiple‐output (MIMO) data from relatively short seismic records. Important issues related to the effects of sensor arrangement, measurement noise, input inclusion, and the types of input with respect to identification results are also investigated. The method is applied to identify modal parameters of the Yokohama Bay Bridge, Rainbow Bridge, and Tsurumi Fairway Bridge using the records from the 2004 Chuetsu‐Niigata earthquake. Comparison of modal parameters with the results of ambient vibration tests, forced vibration tests, and analytical models are presented together with discussions regarding the effects of earthquake excitation amplitude on global and local structural modes. Copyright © 2007 John Wiley & Sons, Ltd.     

Novel coupling Rosenbrock‐based algorithms for real‐time dynamic substructure testing

Real‐time testing with dynamic substructuring is a novel experimental technique capable of assessing the behaviour of structures subjected to dynamic loadings including earthquakes. The technique involves recreating the dynamics of the entire structure by combining an experimental test piece consisting of part of the structure with a numerical model simulating the remainder of the structure. These substructures interact in real time to emulate the behaviour of the entire structure. Time integration is the most versatile method for analysing the general case of linear and non‐linear semi‐discretized equations of motion. In this paper we propose for substructure testing, L‐stable real‐time (LSRT) compatible integrators with two and three stages derived from the Rosenbrock methods. These algorithms are unconditionally stable for uncoupled problems and entail a moderate computational cost for real‐time performance. They can also effectively deal with stiff problems, i.e. complex emulated structures for which solutions can change on a time scale that is very short compared with the interval of time integration, but where the solution of interest changes on a much longer time scale. Stability conditions of the coupled substructures are analysed by means of the zero‐stability approach, and the accuracy of the novel algorithms in the coupled case is assessed in both the unforced and forced conditions. LSRT algorithms are shown to be more competitive than popular Runge–Kutta methods in terms of stability, accuracy and ease of implementation. Numerical simulations and real‐time substructure tests are used to demonstrate the favourable properties of the proposed algorithms. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic performance of a 3D full‐scale high‐ductile steel–concrete composite moment‐resisting frame—Part II: Test results and analytical validation

This paper presents the results of a multi‐level pseudo‐dynamic seismic test program that was performed to assess the performance of a full‐scale three‐bay, two‐storey steel–concrete composite moment‐resisting frame built with partially encased composite columns and partial‐strength beam‐to‐column joints. The system was designed to develop a ductile response in the joint components of beam‐to‐column joints including flexural yielding of beam end plates and shear yielding of the column web panel zone. The ground motion producing the damageability limit state interstorey drift caused minor damage while the ultimate limit state ground motion level entailed column web panel yielding, connection yielding and plastic hinging at the column base connections. The earthquake level chosen to approach the collapse limit state induced more damage and was accompanied by further column web panel yielding, connection yielding and inelastic phenomena at column base connections without local buckling. During the final quasi‐static cyclic test with stepwise increasing displacement–amplitudes up to an interstorey drift angle of 4.6%, the behaviour was ductile although cracking of beam‐to‐end‐plate welds was observed. Correlations with numerical simulations taking into account the inelastic cyclic response of beam‐to‐column and column base joints are also presented in the paper together. Inelastic static pushover and time history analysis procedures are used to estimate the structural behaviour and overstrength factors of the structural system under study. Copyright © 2008 John Wiley & Sons, Ltd.     

Traffic‐induced variability in dynamic properties of cable‐stayed bridge

The traffic‐induced variability in the dynamic properties of a cable‐stayed bridge is investigated using ambient vibration measurements. Under a relatively steady wind and temperature environment, the ambient vibration test was conducted on the bridge with normal traffic conditions and totally 24 h acceleration response time histories were recorded. These data are divided into 12 sections with each data section containing 2 h measurements. Thereby the modal variability due to changing traffic loading is investigated through post‐processing of the data in each section in both amplitude and frequency domains. The result indicates that the natural frequencies of the global modes can exhibit as much as 1% variation within a day. The modal amplitudes of each mode as well as the modal deflection at each measurement position vary insignificantly. The damping ratios however are sensitive to the vibration intensity, especially when the deck vibration exceeds a certain level. Copyright © 2002 John Wiley & Sons, Ltd.     

Hybrid seismic protection of cable‐stayed bridges

This paper proposes a hybrid control strategy combining passive and semi‐active control systems for seismic protection of cable‐stayed bridges. The efficacy of this control strategy is verified by examining the ASCE first‐generation benchmark problem for a seismically excited cable‐stayed bridge, which employs a three‐dimensional linearized evaluation bridge model as a testbed structure. Herein, conventional lead–rubber bearings are introduced as base isolation devices, and semi‐active dampers (e.g., variable orifice damper, controllable fluid damper, etc.) are considered as supplemental damping devices. For the semi‐active dampers, a clipped‐optimal control algorithm, shown to perform well in previous studies involving controllable dampers, is considered. Because the semi‐active damper is a controllable energy‐dissipation device that cannot add mechanical energy to the structural system, the proposed hybrid control strategy is fail‐safe in that the bounded‐input, bounded‐output stability of the controlled structure is guaranteed. Numerical simulation results show that the performance of the proposed hybrid control strategy is quite effective in protecting seismically excited cable‐stayed bridges. Copyright © 2004 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure

A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

Non‐stationary seismic response of tanks with soil interaction by wavelets

A wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic drift demands in multi‐storey cross‐laminated timber buildings

This paper investigates the seismic response of multi‐storey cross‐laminated timber (CLT) buildings and its relationship with salient ground‐motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground‐motion periods ratio is different for low‐ and high‐rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi‐storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.     

Design of hysteretic dampers with optimal ductility for the transverse seismic control of cable‐stayed bridges

Cable‐stayed bridges require a careful consideration of the lateral force exerted by the deck on the towers under strong earthquakes. This work explores the seismic response of cable‐stayed bridges with yielding metallic dampers composed of triangular plates that connect the deck with the supports in the transverse direction. A design method based on an equivalent single‐degree of freedom approximation is proposed. This is proved valid for conventional cable‐stayed bridges with 200‐ and 400‐m main spans, but not 600 m. The height of the plates is chosen to (1) achieve a yielding capacity that limits the maximum force transmitted from the deck to the towers, and to (2) control the hysteretic energy that the dampers dissipate by defining their design ductility. In order to select the optimal ductility and the damper configuration, a multi‐objective response factor that accounts for the energy dissipation, peak damper displacement and low‐cycle fatigue is introduced. The design method is applied to cable‐stayed bridges with different spans and deck–support connections. The results show that the dissipation by plastic deformation in the dampers prevents significant damage in the towers of the short‐to‐medium‐span bridges under the extreme seismic actions. However, the transverse response of the towers in the bridge with a 600‐m main span is less sensitive to the dampers. Copyright © 2017 John Wiley & Sons, Ltd.     

Experimental–numerical investigation on the seismic behaviour of moment‐resisting timber frames with densified veneer wood‐reinforced timber joints and expanded tube fasteners

This paper investigates the seismic behaviour of moment‐resisting timber frames with beam‐column joints fastened with expanded tubes and reinforced with densified veneer wood. Laboratory experiments are carried out on single joints to investigate the cyclic behaviour and, more specifically, the impairment of strength, the ductility ratio and the equivalent viscous damping ratio. A phenomenological numerical model is proposed, where the beams and columns are schematized using linear‐elastic beam elements, and the joints with non‐linear hysteretic spring calibrated on the results of the experimental tests. The model is used to analyse some representative moment‐transmitting structures characterised by different number of bays and storeys. After an estimation of the lateral load‐carrying capacity using a pushover analysis, the numerical model is used to estimate the behaviour factor. An incremental dynamic analysis is performed using a set of accelerograms spectrum consistent with a chosen design spectrum. The analyses lead to an estimation of the behaviour factor of 3 and 6 for a portal frame and a five‐storey, three‐bay frame, respectively, which confirms the highly dissipative behaviour of this kind of moment connection. Copyright © 2017 John Wiley & Sons, Ltd.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of a kinematic self‐centring seismic isolator

This investigation deals with the analytical formulation and experimental validation of a prestressed reinforced concrete seismic isolator with kinematic constraints at both ends. The kinematic isolator was proposed initially as a low‐cost solution for seismic protection of low‐income people housing usually placed at the periphery of big cities where regular to bad soil conditions are common. So, the isolator is also a pile foundation with a central prestressed cable and two rolling steel surfaces at the top and bottom ends. By varying the shapes of the end rolling surfaces, different force–deformation constitutive relationships for the isolator may be obtained. Energy dissipation is introduced by yielding of passive reinforcement at the rolling interphase. Apart from stating the large‐deformation formulation of the element, several relevant aspects of the behaviour of these devices are studied herein, such as the increase in the tension of the central prestressed cable, responsible for the self‐centring action of the isolator, the floor uplift that results from the geometry of the isolator, and the vertical stability of the system. Experimental and theoretical results obtained for a group of 9 testing specimens show an excellent agreement in the force–deformation constitutive relationship. Although not the intent of this article, the device proposed may be extended directly as a coupling beam element for shear wall systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Systematic lumped‐parameter models for foundations based on polynomial‐fraction approximation

Based on the approximation by polynomial‐fraction, a series of systematic lumped‐parameter models are developed in this paper for efficiently representing the dynamic behaviour of unbounded soil. Concise formulation is first employed to represent the dynamic flexibility function of foundation with a ratio of two polynomials. By defining an appropriate quadratic error function, the optimal coefficients of the polynomials can be directly solved from a system of linear equations. Through performing partial‐fraction expansion on this polynomial‐fraction and designing two basic discrete‐element models corresponding to the partial fractions, systematic lumped‐parameter models can be conveniently established by connecting these basic units in series. Since the systematic lumped‐parameter models are configured without introducing any mass, the foundation input motion can be directly applied to these models for their applications to the analysis of seismic excitation. The effectiveness of these new models is strictly validated by successfully simulating a semi‐infinite bar on an elastic foundation. Subsequently, these models are applied for representing the dynamic stiffness functions for different types of foundation. Comparison of the new models with the other existing lumped‐parameter models is also made to illustrate their advantages in requiring fewer parameters and featuring a more systematic expansion. Copyright © 2002 John Wiley & Sons, Ltd.