• Earthquakes and Structures
• /
• v.5 no.3
• /
• pp.359-378
• /
• 2013

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.3 no.2
• /
• pp.77-86
• /
• 1999

In the previous $paper^{(1),(2)}$, a geometrically non-linear finite element formulation of spatial cables subjected to self-weights and support motions was presented using multiple noded cable elements and how to determine the initial equililbrium state of cables was addressed. In this paper, in order to perform dynamic non-linear analysis of ocean cables subjected to support motions and earthquakes, a numerical method to calculate Morison forces and incorporate effects of earthquake motions is presented based on the Newmark method. Challenging example problems are presented in order to investigate dynamic non-linear behaviors of ocean cables subjected to support motions and earthquake loadings.

• Earthquakes and Structures
• /
• v.8 no.6
• /
• pp.1481-1497
• /
• 2015

Vertical earthquake ground motion may magnify vertical dynamic responses of structures, and thus cause serious damage to bridges. As main support structures, piers and bearings play an important role in vertical seismic response analysis of girder bridges. In this study, the pier and bearing are simplified as a vertical series spring system without mass. Then, based on the assumption of small displacement, the equation of motion governing the simply-supported straight girder bridge under vertical ground motion is established including effects of vertical deformation of support structures. Considering boundary conditions, the differential quadrature method (DQM) is applied to discretize the above equation of motion into a MDOF (multi-degree-of-freedom) system. Then seismic responses of this MDOF system are calculated by a step-by-step integration method. Effects of support structures on vertical dynamic responses of girder bridges are studied under different vertical strong earthquake motions. Results indicate that support structures may remarkably increase or decrease vertical seismic responses of girder bridges. So it is of great importance to consider effects of support structures in structural seismic design of girder bridges in near-fault region. Finally, optimization of support structures to resist vertical strong earthquake motions is discussed.

• Steel and Composite Structures
• /
• v.26 no.2
• /
• pp.197-211
• /
• 2018

The study presents the earthquake performance of the Bosphorus Bridge under multi-point earthquake excitation considering the spatially varying site-specific earthquake motions. The elaborate FE model of the bridge is firstly established depending on the new considerations of the used FEM software specifications, such as cable-sag effect, rigid link and gap elements. The modal analysis showed that singular modes of the deck and the tower were relatively effective in the dynamic behavior of the bridge due to higher total mass participation mass ratio of 80%. The parameters and requirements to be considered in simulation process are determined to generate the spatially varying site-specific ground motions. Total number of twelve simulated ground motions are defined for the multi-support earthquake analysis (Mp-sup). In order to easily implement multi-point earthquake excitation to the bridge, the practice-oriented procedure is summarized. The results demonstrated that the Mp-sup led to high increase in sectional forces of the critical components of the bridge, especially tower base section and tensile force of the main and back stay cables. A close relationship between the dynamic response and the behavior of the bridge under the Mp-sup was also obtained. Consequently, the outcomes from this study underscored the importance of the utilization of the multi-point earthquake analysis and the necessity of considering specifically generated earthquake motions for suspension bridges.

• Nuclear Engineering and Technology
• /
• v.52 no.5
• /
• pp.1066-1078
• /
• 2020

The present paper describes an analytic solution procedure for flexural vibration of a rotationally restrained hinged-hinged Timoshenko beam at the supports during an earthquake. Focusing on maximal magnitudes of internal loads such as bending moment and shearing force under wide variations of two parameters, kL/EI and kGAL²/EI, various beams under synchronous and asynchronous support motions are simulated. The simulations under asynchronous support motions show the following facts. The variations of the maximal magnitudes of internal loads of stocky beams due to the variation of kL/EI from zero to infinity show much wider variations than those of slender beams as kGAL²/EI decreases. The maximal magnitudes of internal loads of a beam tend to be governed by their static components as kL/EI increases and kGAL²/EI decreases. When the internal loads are governed by their static components, maximal magnitudes of internal loads of the stocky tend to increase monotonically as the value of kL/EI increases. However, the simulations under synchronous support motions show the static components of the internal loads vanish and the internal loads are governed by dynamic components irrespective of the two parameters.

• International Journal of High-Rise Buildings
• /
• v.5 no.3
• /
• pp.177-186
• /
• 2016

Along the subduction-zone of the western Japanese islands, large earthquakes are expected occur around the middle of this century, and long-period ground motions will reach major urban areas, shaking high-rise buildings violently. Since some old high-rise buildings were designed without considering long-period ground motions, reinforcing such buildings is an important issue. An effective method to reinforce existing high-rise buildings is installing additional dampers. However, a problem with ordinary dampers is that they require reinforcement of surrounding columns and girders to support large reaction forces generated during earthquake ground motion. To solve this problem, a deformation-dependent oil damper was developed. The most attractive feature of this damper is to reduce the damping force at the moment when the frame deformation comes close to its maximum value. Due to this feature, the reinforcement of columns, girders, and foundations are no longer required. The authors applied seismic retrofitting with a deformation-dependent oil damper to an existing 54-story office building (Shinjuku Center Building) located in Shinjuku ward, Tokyo, in 2009 to suppress vibration under the long period earthquake ground motions. The seismic responses were observed in the 2011 Tohoku Earthquake, and it is clarified that the damping ratio was higher and the response lower by 20% as compared to the building without dampers.

• Structural Engineering and Mechanics
• /
• v.62 no.2
• /
• pp.247-258
• /
• 2017

Beam-like structures such as bridge, high building and tower, pipes, flexible connecting rods and some robotic manipulators are often excited by support motions. These structures are important in machines and structures. So, this study proposes an analytic method to accurately predict the dynamic behaviors of the structures during support motions or an earthquake. Using Timoshenko beam theory which is valid even for non-slender beams and for high-frequency responses, the analytic responses of fixed-fixed beams subjected to a real seismic motions at supports are illustrated to show the principled approach to the proposed method. The responses of a slender beam obtained by using Timoshenko beam theory are compared with the solutions based on Euler-Bernoulli beam theory to validate the correctness of the proposed method. The dynamic analysis for the fixed-fixed beam subjected to support motions gives useful information to develop an understanding of the structural behavior of the beam. The bending moment and the shear force of a slender beam are governed by dynamic components while those of a stocky beam are governed by static components. Especially, the maximal magnitudes of the bending moment and the shear force of the thick beam are proportional to the difference of support displacements and they are influenced by the seismic wave velocity.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.7 no.6
• /
• pp.35-47
• /
• 2003

Seismic ground motion can vary significantly over distances comparable to the length of a majority of highway bridges on multiple supports. This paper presents results of fragility analysis of two actual highway bridges under ground motion with spatial variation. Ground motion time histories are artificially generated with different amplitudes, phases, as well as frequency contents at different support locations. Monte Carlo simulation is performed to study dynamic responses of the bridges under these ground motions. The effect of spatial variation on the seismic response is systematically examined and the resulting fragility curves are compared with those under identical support ground motion. This study shows that ductility demands for the bridge columns can be underestimated if the bridge is analyzed using identical support ground motions rather than differential support ground motions. Fragility curves are developed as functions of different measures of ground motion intensity including peak ground acceleration(PGA), peak ground velocity(PGV), spectral acceleration(SA), spectral velocity(SV) and spectral intensity(SI). This study represents a first attempt to develop fragility curves under spatially varying ground motion and provides information useful for improvement of the current seismic design codes so as to account for the effects of spatial variation in the seismic design of long-span bridges.

• Computers and Concrete
• /
• v.9 no.3
• /
• pp.195-213
• /
• 2012

This paper presents the investigation of the stochastic responses of seismically isolated bridges subjected to spatially varying earthquake ground motions including incoherence, wave-passage and site-response effects. The incoherence effect is examined by considering Harichandran and Vanmarcke coherency model. The effect of the wave-passage is dealt with various wave velocities in the response analysis. Homogeneous firm, medium and soft soil conditions are selected for considering the site-response effect where the bridge supports are constructed. The ground motion is described by filtered white noise and applied to each support points. For seismic isolation of the bridge, single and double concave friction pendulum bearings are used. Due to presence of friction on the concave surfaces of the isolation systems, the equation of motion of is non-linear. The non-linear equation of motion is solved by using equivalent linearization technique of non-linear stochastic analyses. Solutions obtained from the stochastic analyses of non-isolated and isolated bridges to spatially varying earthquake ground motions compared with each other for the special cases of the ground motion model. It is concluded that friction pendulum systems having single and double concave surfaces have important effects on the stochastic responses of bridges to spatially varying earthquake ground motions.

• Structural Engineering and Mechanics
• /
• v.65 no.5
• /
• pp.633-644
• /
• 2018

This paper presents the results of an assessment of the seismic fragility of a long, curved multi-frame bridge under multi-support earthquake excitations. To achieve this aim, the numerical model of columns retrofitted with elliptical steel jackets was developed and validated using existing experimental results. A detailed nonlinear numerical model of the bridge that can capture the inelastic response of various components was then created. Using nonlinear time-history analyses for a set of stochastically generated spatially variable ground motions, component demands were derived and then convolved with new capacity-based limit state models to obtain seismic fragility curves. The comparison of failure probabilities obtained from uniform and multi-support excitation analyses revealed that the consideration of spatial variability significantly reduced the median value of fragility curves for most components except for the abutments. This observation indicates that the assumption of uniform motions may considerably underestimate seismic demands. Moreover, the spatial correlation of ground motions resulted in reduced dispersion of demand models that consequently decreased the dispersion of fragility curves for all components. Therefore, the spatial variability of ground motions needs to be considered for reliable assessment of the seismic performance of long multi-frame bridge structures.