Completeness Verification of Complex Response Spectrum Method for Underdamped and Overdamped Multiple-Support Systems Regarding the Decoupled Damping as Mathematical Parameter without Physical Meaning

The completeness of the complex response spectrum method for both formally underdamped and overdamped modes is theoretically proved, and the physical meanings of the decoupled modes as well as involved parameters are recognized and clarified in this paper. For the system with relatively large non-classical damping, the eigenvalue pairs generated by the complex mode decomposition method are real and the so-called modal damping ratios are larger than unity. In this paper, we firstly clarified that the decoupled modes are virtual and the so-called modal frequency and damping ratio are mathematical parameters that have no physical meaning. Then, the completeness of the complex response spectrum method for both formally underdamped and overdamped modes is rigorously proved by allowing the “damping frequency” to be an imaginary number. For the virtually overdamped modes, Duhamel integral involved in the calculation for formally underdamped modes automatically convert to hyperbolic Duhamel integral. A numerical example taken from the published literature is given to verify this method. Structural responses for the system with coupled damping under multi-support seismic excitations are further analyzed and numerical results indicate the accuracy of complex response spectrum method.     

Seismic Analysis of Non Proportionally Damped Two-Way Asymmetric Elastic Buildings Under Bi-Directional Seismic Ground Motions

This study investigates the effectiveness of the modal analysis using three-degree-of freedom (3DOF) modal equations of motion to deal with the seismic analysis of two-way asymmetric elastic systems with supplemental damping. The 3DOF modal equations of motion possessing the non proportional damping property enable the two modal translations and one modal rotation to be non proportional in an elastic state. The simple approximation method is to use the single degree-of-freedom (SDOF) modal equations of motion, which are obtained by neglecting the off-diagonal elements of the transformed damping matrix. One, one-story and one, three-story non proportionally damped two-way asymmetric buildings under the excitation of bi-directional seismic ground motions are analyzed. The analytical results are obtained by using the proposed method, noted simple approximation method, and direct integration of the equation of motion. It is seen that the proposed method can significantly improve the accuracy of the analytical results compared with those obtained by using the simple approximation method. Moreover, the proposed method does not substantially increase the computational efforts.     

A Microscale Approach for the Seismic Response of MDOF Structures Including Soil-Foundation-Structure Interaction

In this article, a three-dimensional microscale computational framework utilizing the discrete element method is presented to analyze the seismic response of soil-foundation- MDOF structure systems. The proposed approach is used to explore the response of MDOF structures on a square embedded footing founded on a dry granular deposit. Computational simulations were conducted to investigate the response of the system to several base excitations. The impact of replacing a MDOF structure with its equivalent single degree of freedom (ESDOF) structure while accounting for soil-foundation-structure interaction (SFSI) is investigated. Detrimental or beneficial effect of SFSI on the response is also examined.     

A New Seismic Intensity Parameter to Estimate Damage in Buried Pipelines due to Seismic Wave Propagation

A new seismic intensity parameter to estimate damage in buried pipelines due to seismic wave propagation is proposed. This parameter depends on the peak ground velocity (PGV) and the peak ground acceleration (PGA). It is shown that PGV²/PGA is related to displacement, a parameter directly related to ground strain, which is the main cause of buried pipeline damage. For the case of Mexico City, this parameter exhibits higher correlation with damage than PGA or PGV alone. Finally, we presented intensity-damage relations for the Mexico City's primary water system using PGV²/PGA as the measure of seismic intensity.     

Seismic Evaluation of Tall Buildings Using a Simplified but Accurate Analysis Procedure

A simplified analysis procedure for evaluating the nonlinear seismic responses of tall reinforced concrete (RC) buildings is examined in this study. It is called the Uncoupled Modal Response History Analysis (UMRHA) procedure. It can be viewed as an extended version of the classical modal analysis procedure, where the nonlinear response of each vibration mode is first computed, and they are later on combined into the total response of the structure. The procedure requires the knowledge of the modal hysteretic behavior, which can be obtained from a cyclic modal pushover analysis. The responses of four tall buildings in Bangkok to distant large earthquakes are computed by this procedure and compared with those obtained from the Nonlinear Response History Analysis (NLRHA) procedure. These four buildings have different heights—varying from 20 to 44 stories, different configurations of floor plan, and different arrangement of RC walls. The comparison shows that the UMRHA procedure is able to accurately compute the story shears and story overturning moments, floor accelerations, and inter-story drifts of all these tall buildings. The required computational effort is also extremely low compared to that of the NLRHA procedure. Moreover, since the UMRHA procedure computes the response of each individual vibration mode, it provides more understanding and insight into the complex nonlinear seismic responses of these tall buildings.     

Dynamic Analysis and Seismic Response of Planar Circular Arches with Variable Cross-Section

The aim of this paper is to investigate the dynamic response of planar circular arches with variable cross-section subjected to seismic ground motions. Arches have a wide range of application (e.g. bridges, roofs) thanks to their capacity to span large areas by resolving vertical actions into compressive stresses and confining tensile stresses. The full understanding of their dynamic response is a challenging technical and computational problem, especially when seismic loading is considered. For example, the assumption of axial inextensibility simplifies the differential equations but overestimates the vibration frequencies, especially those of shallow arches since axial forces are of paramount importance (as opposed to beams). In lieu of the above, our formulation incorporates the effect of axial extension, and the arches are modeled using a new generic curved beam model that includes both axial (tangential) and transverse (normal) to the arch centerline deformations, and is able to account for variable mass and stiffness properties, as well as elastic support or restraint. The resulting dynamic governing equations of the circular arch are formulated in terms of the displacements, and solved using an efficient integral equation method. Three circular arches with variable rectangular cross-section are analyzed in order to investigate their dynamic properties and seismic performance. Using both time history and modal analysis useful conclusions are drawn with regard to the contribution of each mode on the calculation of different response quantities.     

HINTS ABOUT SITE AMPLIFICATION EFFECTS COMPARING MACROSEISMIC HAZARD ESTIMATE WITH MICROTREMOR MEASUREMENTS: THE AGRI VALLEY (ITALY) EXAMPLE

We approach from a new standpoint the problem of estimating seismic hazard for some towns and villages located in Val d'Agri area (Southern Italy) that in the past have been affected by several seismic events. The estimates are carried out using a method that is based on the analysis of site seismic history extracted from macroseismic catalogues. To study the influence of site effects two different procedures have been performed: in the first, seismic hazard estimates have been deduced from epicentral data only, in the second, intensity data actually observed at the site are also considered. The difference between the two estimates can be correlated with local variations of seismic response due to local geological features which are responsible for possible cases of amplification. In order to validate the presence of such correlation, seismic hazard estimates have been compared to site amplification measurements obtained by using the HVSR (Horizontal to Vertical Spectral Ratio) technique. Our findings reveal a good correlation between seismic hazard enhancements and the presence of site amplification effects. The application of this kind of analysis to the Val d'Agri area has pointed out that the joint estimates of site seismic hazard enhancement and HVSR measurements could be a helpful tool to identify problems related to seismic microzonation.     

A Single-Run Dynamic-Based Approach for Pushover Analysis of Structures Subjected to Near-Fault Pulse-Like Ground Motions

In this paper, a fairly effective procedure called dynamic load pattern (DLP), is proposed to account for the effects of near-fault ground motions in estimating the seismic demands of structures from pushover analyses. The seismic demands are obtained by enveloping the results of single-run conventional first-mode and single-run DLP pushover analyses. Improving the estimation of target displacement is another objective, implemented by performing response-spectrum analysis. Three special steel moment-resisting frames are considered and the seismic demands resulting from DLP are compared to those from the nonlinear time-history analysis as a benchmark solution, as well as to those predicted from modal pushover analysis.     

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.     

Seismic Assessment of the Lima Cathedral Bell Towers via Kinematic and Nonlinear Static Pushover Analyses

ABSTRACT

The protection of cultural heritage against earthquake induced actions is one of the main challenges the earthquake engineering science and practice are facing. This article presents a seismic assessment study on one of the most ancient colonial buildings present in Peru, the Cathedral of Lima, focusing on its towers. A historical review highlighted how these structures, together with the whole Cathedral, suffered intense damage and partial collapse during previous earthquakes. In order to identify the structure main deficiencies, both linear kinematic analyses and nonlinear static analyses have been performed. Different nonlinear finite element models have been created to evaluate the influence of the adjacent walls. Different load distributions have been compared to evaluate how simplified patterns could provide results close to load distributions taken from a modal analysis of the complex. A simple retrofit strategy, consisting on the introduction of steel ties, has also been studied as a reference. Results show good correlation between kinematic and pushover analyses. The construction, when compared to the requirements of the national code for new buildings, results significantly vulnerable, pointing out the need to accept some structural damage even after seismic retrofit.     

故宫太和殿动力特性与常遇地震响应

为更好地保护故宫太和殿,采用有限元分析方法,研究了太和殿的动力特性及常遇地震作用下的响应。采用弹簧单元模拟榫卯节点及斗拱构造,并考虑柱础为铰接,建立了太和殿有限元模型。通过模态分析,获得了太和殿基频及主振型;通过对模型进行时程分析,获得了典型节点的位移、加速度响应曲线,以及典型单元的内力响应曲线,评价了太和殿的抗震性能。结果表明:太和殿基频为0.9Hz,主振型以平动为主;常遇地震作用下,太和殿能保持稳定振动状态,结构的内力和变形均在容许范围内,且斗拱及榫卯节点均能发挥一定的减震作用。     

Seismic Response of Rolling Isolation Systems with Concave Friction Distribution

This article attempted to improve the isolation performance of a rolling isolation system by assuming that the rolling friction force gradually and linearly increased with the relative displacement between the isolator and the ground. After the rolling isolation system under different ground motions was calculated by a numerical analysis method, it obtained more regular results than that of other uneven friction distributions. Results shows that the considered concavely distributed friction force can not only dissipate the earthquake energy, but also change the structural natural period. These functions improve the seismic isolation efficiency of the structural relative displacement in comparison with the general uniform distribution of rolling friction coefficient.     

Predicting the Seismic Response of Capacity-Designed Structures by Equivalent Linearization

An equivalent linearization procedure is developed for predicting the inelastic deformations and internal forces of capacity-designed structures under earthquake excitations. The procedure employs response spectrum analysis, and mainly consists of the construction of an equivalent linear system by reducing the stiffness of structural members that are expected to respond in the inelastic range. These members are well defined in structures designed with capacity principles. Maximum modal displacement demands of the equivalent linear system are determined either from the equal displacement rule, or from independent nonlinear response history analysis of SDOF systems representing inelastic modes.

Predictions obtained from the proposed equivalent linearization procedure are evaluated comparatively by using the results of nonlinear response history analysis as benchmark, linear elastic response spectrum analysis and conventional pushover analysis. The deformations and capacity controlled actions of a 12-story symmetrical plan concrete frame and a 6-story unsymmetrical plan concrete frame are obtained by each method under 96 strong ground motions. It is observed that the proposed procedure results in better accuracy in estimating the inelastic seismic displacement response parameters and capacity controlled forces than the other two approximate methods.     

日本新能源产业的发展模式

从能源安全、经济发展和生态环境考虑,日本制定了详细而切实可行的新能源产业扶持政策,在官、产、学一体化积极推动下,新能源产业取得了巨大发展,为日本经济的可持续发展奠定了坚实的基础。     

PERFORMANCE-BASED SEISMIC RESPONSE OF FRAME STRUCTURES INCLUDING RESIDUAL DEFORMATIONS. PART II: MULTI-DEGREE OF FREEDOM SYSTEMS

The role of residual deformations when evaluating the performance of multi-storey frame structures subjected to ground motion is investigated in this paper. The limitations of damage indices available in the literature, either based on ductility, energy dissipation or a combination of both, in capturing such a significant aspect of the seismic response of frame structures are discussed. The concept of residual deformations as a critical complementary indicator to cumulative damage, introduced in a companion paper (Part I) for single-degree-of-freedom (SDOF) systems, is herein extended to multi-degree-of-freedom (MDOF) frame systems. The seismic performance of multi-storey frame structures, either representative of new designed or existing structures, is investigated, focusing on the response in terms of residual deformations. Residual deformations are shown to be sensitive to the hysteretic rule adopted, to the system inelastic mechanism as well as to the seismic intensity. The influence of higher modes and P-Δ effects on the final residual deformations is addressed. A combination of maximum drift and residual drift in the format of a performance matrix is used to define the system's global performance levels and is then extended to a framework for an alternative performance-based seismic design and assessment approach.     

Unusual Overshooting in Steady-state Response for Structure-dependent Integration Methods

It is numerically illustrated that an unusual overshooting phenomenon might occur in the solution of a forced vibration response if a structure-dependent integration method is applied to conduct the analysis, such as Chang explicit method [2002] and CR explicit method [2008]. This overshooting may occur in the steady-state response of a high frequency mode and it becomes significant as the natural frequency of the mode increases. This unusual overshooting behavior can be successfully detected by using a local truncation error derived from a forced vibration response rather than a free vibration response. A missing loading term in the difference equation for displacement increment is responsible for this unusual overshoot. It is analytically and numerically verified that the unusual overshooting behavior will automatically disappear after introducing the missing loading term into the difference equation for displacement increment.     

A SIMPLE METHOD FOR ANALYSIS OF SLIDING STRUCTURES CONSIDERING VARIATIONS OF FRICTION COEFFICIENT

In this paper, the responses of multidegree of freedom (MDOF) structures on sliding foundations, subjected to harmonic or random base motions, are investigated taking into consideration the variations of friction forces. The variation of friction force is a consequence of variation of friction coefficient, which depends on such parameters as relative velocity and the existing pressure. Modelling of the friction force under the foundation raft is accomplished by using a fictitious rigid link with a rigid-perfectly plastic material. This results in identical equations of motion for the sliding structure, both in the sliding and nonsliding (stick) phases and considerably decreases the required number of time steps for the nonlinear analysis. Since the force in the link is of constant value, to consider the varying friction force, a compensatory force, which is the difference between the exact friction force and the constant force in the rigid link, is applied to the foundation raft. A model of variable friction coefficient for Teflon-steel interfaces is used for the assessment of the method and the results are compared with existing literature, through which, the capability of the method is illustrated. It is shown that by using exact model of friction lower values for the superstructure responses are predicted compared with those obtained by using Coulomb friction model. Furthermore the effect of the stiffness of the structure on the differences between the results of the two models is also studied.     

NONLINEAR SHAKE TABLE IDENTIFICATION AND CONTROL FOR NEAR-FIELD EARTHQUAKE TESTING

The primary focus of a structural shake table system is the accurate reproduction of acceleration records for testing. However, many systems deliver variable and less than optimal performance, particularly when reproducing large near-field seismic events that require extreme table performance. Improved identification and control methods are developed for large hydraulic servo-actuated shake table systems that can exhibit unacceptable tracking response for large, near-field seismic testing. The research is presented in the context of a 5-tonne shake table facility at the University of Canterbury that is of typical design. The system is identified using a frequency response approach that accounts for the actual magnitudes and frequencies of motion encountered in seismic testing. The models and methods developed are experimentally verified and the impact of different feedback variables such as acceleration, velocity and displacement are examined.

The methods show that shake table control in testing large near-field seismic events is often a trade off between accurate tracking and nonlinear velocity saturation of the hydraulic valves that can result in severe acceleration spikes. Control methods are developed to improve performance and include both acceleration and displacement feedback to reduce the acceleration spikes, and record modification, where the reference signal is modified to conform to the shake table's operational parameters. Results show record modification gives exact tracking for near-field ground motions, and optimal system response for reference signals with velocity components greater then the system capabilities. Overall, the research presents a methodology for simple effective identification, modelling, diagnosis and control of structural shake table systems that can be readily generalised and applied to any similar facility.     

A NON-PARAMETRIC APPROACH TO ATTENUATION RELATIONS

Abstract

A non-parametric multidimensional regression method is proposed for the prediction of seismic ground motion parameters. The main features which distinguish the method from standard regression procedures are: (1) The relationship between the input and output variables is not selected a priori by a prediction law, (2) an arbitrary number of input variables Can be taken into account, provided that an appropriate data base exists, and (3) the computational procedure is very simple. The results can be easily updated when new information becomes available. The method has been applied for the derivation of attenuation relations by using a combination of databases compiled by other researchers. In the majority of the cases discussed in this paper, the method was used for the prediction of horizontal peak ground acceleration as a function of magnitude and distance. In some cases, ground conditions were also taken into account. Some results on the attenuation relations of peak ground velocity and displacement, as well as Arias intensity, are also presented.     

Shake Table Test and Numerical Analysis of a Bridge Model Supported on Elastomeric Pad Bearings

Elastomeric pad bearings are widely applied in short- to medium-span girder bridges in China, with the superstructure restrained by reinforced concrete (RC) shear keys in the transverse direction. Field investigations after the 2008 Wenchuan earthquake reveal that bearing systems had suffered the most serious damage, such as span falling, bearing displaced, and shear key failure, while the piers and foundations underwent minor damage. As part of a major study on damage mechanism and displacement control method for short- to medium-span bridges suffered in Wenchuan earthquake, a 1:4 scale, two-span bridge model supported on elastomeric pad bearings were recently tested on shake tables at Tongji University, Shanghai. The bridge model was subjected to increasing levels of four seismic excitations possessing different spectral characteristics. Two restraint systems with and without the restraint of RC shear keys were tested. A comprehensive analytical modeling of the test systems was also performed using OpenSees. The experimental results confirmed that for the typical bridges on elastomeric pad bearings without RC shear keys, the sliding effect of the elastomeric pad bearings plays an important role in isolation of ground motions and, however, lead to lager bearing displacement that consequently increases the seismic risk of fall of span, especially under earthquakes that contain significant mid-period contents or velocity pulse components. It is suggested from the test results that RC shear keys should be elaborately designed in order to achieve a balance between isolation efficiency and bearing displacement. Good correlation between the analytical and the experimental data indicates that the analytical models for the bearing and RC shear key as well as other modeling assumptions were appropriate.