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.     

Analytical modelling of multi‐mass flexible rocking structures

This paper presents a new analytical model for describing the large rocking response of an elastic multi‐mass structure resting on ideally rigid ground. Using the experimental results from a rocking steel column, the ability of the proposed analytical model to estimate the rocking and translational acceleration response under free vibration, pulse and earthquake excitations is evaluated. It is observed that the classical treatment of impact may result in an unrealistically large transfer of energy to vibrations. Therefore a new Dirac‐delta type impact model that spreads the effects of impact over time and space is proposed. The use of a Dirac‐delta model and accurate restitution factors play a pivotal role in prediction of rocking and acceleration responses. In order to characterize the nonlinear response better, a modal analysis of the linearized system is proposed. With this approach, the vibration mode frequencies and shapes during rocking action were determined. A comparison of analytical and experimental modal estimations suggests good agreement. The results emphasize that the vibration characteristics of several vibration modes are affected by rocking action, and these modes may be excited at impact. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian probabilistic damage detection of a reinforced‐concrete bridge column

A Bayesian probabilistic approach for damage detection has been proposed for the continuous monitoring of civil structures (Sohn H, Law KH. Bayesian probabilistic approach for structure damage detection. Earthquake Engineering and Structural Dynamics 1997; 26 :1259–1281). This paper describes the application of the Bayesian approach to predict the location of plastic hinge deformation using the experimental data obtained from the vibration tests of a reinforced‐concrete bridge column. The column was statically pushed incrementally with lateral displacements until a plastic hinge is fully formed at the bottom portion of the column. Vibration tests were performed at different damage stages. The proposed damage detection method was able to locate the damaged region using a simplified analytical model and the modal parameters estimated from the vibration tests, although (1) only the first bending and first torsional modes were estimated from the experimental test data, (2) the locations where the accelerations were measured did not coincide with the degrees of freedom of the analytical model, and (3) there existed discrepancies between the undamaged test structure and the analytical model. The Bayesian framework was able to systematically update the damage probabilities when new test data became available. Better diagnosis was obtained by employing multiple data sets than just by using each test data set separately. Copyright © 2000 John Wiley & Sons, Ltd.     

Rosenblueth's modal combination rule for systems with non-classical damping

A simple rule is derived to combine, within the framework of a complex mode superposition, the maximum modal responses of systems such as soil-structure and structure-equipment systems, for which closely spaced natural frequencies are likely, and for which, because of the large difference in the damping values of their various components, the assumption of an orthogonal damping matrix may lead to significant errors. The rule constitutes the generalization of Rosenblueth's rule for systems with closely spaced natural frequencies and classical modes, and is expressed in terms of their complex mode shapes and natural frequencies. Its derivation is based on the theory of a complex modal analysis for systems with non-classical modes of vibration and on Rosenblueth's original derivation. As in this original derivation, earthquake ground motions are modelled as a stationary white noise process, but the formulae obtained under this assumption are modified later on to account for the transient nature of actual earthquakes. A numerical example is presented to illustrate the application of the rule, and a comparative study with numerical integration solutions is performed to assess its accuracy. In this comparative study, it predicts the numerical integration solutions with an average error of 0.3 per cent.     

Numerical study of characteristics of underground blast induced surface ground motion and their effect on above-ground structures. Part II. Effects on structural responses

Studies of structural responses and damage to high-frequency blast motion are very limited. Current practice uses some empirical allowable ground vibration limits in assessing structural performance. These empirical limits overlook the physical parameters that govern structural response and damage, such as the ground motion characteristics and inherent structural properties. This paper studies the response of RC frame structures to numerically simulated underground blast-induced ground motions. The structural response and damage characteristics of frame structures to ground motions of different frequencies are investigated first. The effects of blast ground motion spatial variations and soil–structure interaction on structural responses are also studied. A suitable discrete model that gives accurate response prediction is determined. A damage index defined based on the accumulated plastic hinge rotation is used to predict structural damage level. Numerical results indicated that both the low structural vibration modes (global modes) and the first elemental vibration mode (local) might govern the dynamic structural responses depending on the ground motion frequency and structural response parameters under consideration. Both ground motion spatial variations and soil–structure interaction effects are prominent. Neglecting them might yield inaccurate structural response prediction. The overall structural response and damage are highly ground motion frequency dependent. Numerical results of structural damage are also compared with some test results obtained in a previous study and with code specifications. Discussions on the adequacy of the code allowable ground vibration limits on RC frame structures are also made.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 2: Complex modes

A method, based on the Hilbert–Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency–time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Research on mode localization of reticulated shell structures

Reticulated shell structures (RSSs) are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features: some modal vectors of the structure change remarkably when the values of its physical parameters (mass or stiffness) have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS, and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.     

岩溶区砌体建筑环境振动特性分析

当前地震动速度时程时域特性分析方法,仅能分析岩溶区地震动速度时程的振动周期、强弱程度与时间变动的问题,但未能准确计算岩溶区砌体建筑物自振频率,导致砌体建筑环境振动特性分析结果存在误差。深入研究岩溶区砌体建筑环境振动特性分析方法,构建混凝土损伤塑性模型,分析岩溶区砌体建筑材料的屈服(受压)应力-非弹性应变关系、开裂(受拉)应力-非弹性应变关系和损伤因子;采用贝叶斯方法检测岩溶区砌体建筑受压受拉时的自振频率,通过L-M神经网络法消除自振频率后,使用振动特性分析方法准确分析岩溶区砌体建筑环境振动特性。实验结果表明,所提方法分析准确率高达0.99,分析16栋岩溶区砌体建筑环境振动特性耗时仅有5 ms,具有较高的分析精度和效率。     

Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures, usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings. The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response, which is called the higher-mode effect. The modal analysis approach, however, may not be directly applied to the dynamic analysis of viscoelastically damped buildings. This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency. Therefore, the structural stiffness and damping contributed from those dampers would be different for each mode. In this study, the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes. Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect. Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response. Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings. The higher-mode effect on base shear is less significant than on story acceleration response. Maximum difference of the seismic response usually occurs at the top story. Also, the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers. For practical application, it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence, is on the conservative side. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

An efficient,adaptive algorithm for large-scale random vibration analysis

An efficient, adaptive and robust algorithm is proposed to reduce the cost of large-scale stationary and transient random vibration analysis of structures excited by multiple partially correlated nodal and or base excitations. The cost saving is accomplished by computing integrals selectively, and yet attempting to maintain a level of accuracy desired by the analyst. Recently, proposed closed-form solutions for fully coherent propagating band-limited white-noise excitation are used to rank approximately the terms in the modal covariance matrix. Terms are then evaluated starting from the most important one, and the computations are terminated in such a way that the accuracy level requested by the user is satisfied in an approximate sense. Two variations of the algorithm are proposed: the first one is more robust and is preferred, and is recommended when computing a relatively small number (hundreds) of response quantities; the second one is more efficient when computing a very large number (thousands) of response quantities. Both variations are adaptive, and consider the closeness, damping and participation of all modes explicitly, while the first method also considers the mode shapes. The efficiency and accuracy of the algorithm is investigated by using it to compute the stationary and transient seismic response of the Golden Gate suspension bridge.     

System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes

Based on the Hilbert–Huang spectral analysis, a method is proposed to identify multi‐degree‐of‐freedom (MDOF) linear systems using measured free vibration time histories. For MDOF systems, the normal modes have been assumed to exist. In this method, the measured response data, which are polluted by noises, are first decomposed into modal responses using the empirical mode decomposition (EMD) approach with intermittency criteria. Then, the Hilbert transform is applied to each modal response to obtain the instantaneous amplitude and phase angle time histories. A linear least‐square fit procedure is proposed to identify the natural frequency and damping ratio from the instantaneous amplitude and phase angle for each modal response. Based on a single measurement of the free vibration time history at one appropriate location, natural frequencies and damping ratios can be identified. When the responses at all degrees of freedom are measured, the mode shapes and the physical mass, damping and stiffness matrices of the structure can be determined. The applications of the proposed method are illustrated using three linear systems with different dynamic characteristics. Numerical simulation results demonstrate that the proposed system identification method yields quite accurate results, and it offers a new and effective tool for the system identification of linear structures in which normal modes exist. Copyright © 2003 John Wiley & Sons, Ltd.     

Structural health monitoring of long-span suspension bridges using wavelet packet analysis

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage. This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform (WPT). The WPT- based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum (WPES) has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices VD reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index VD is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.     

Combined analysis and test of earthquake-resistant circuit breakers

Following the severe earthquake damage at San Fernando in 1971, it became of technical and perhaps psychological importance to demonstrate that properly re-designed electrical equipment is able to withstand even worse transient vibration phenomena which can be produced in an earthquake simulator laboratory. This has been accomplished for one column of a 500 kV gas circuit breaker and the test results are used to qualify the much larger original 3-column assembly by means of a computer-aided structural analysis. Since the equipment exhibited some closely spaced, cross-coupled modes of vibration, a valuable comparison could be obtained between the effects produced by El Centro 1940 ground acceleration and those for a more purposeful sine beat vibration input. The latter can be adjusted to produce definite stresses and fatigue effects in specific parts of the equipment due to quasi-resonance response.     

钢筋混凝土建筑在连续震动下的壁板结构破坏程度分析

计算连续震动下钢筋混凝土建筑的壁板结构破坏程度需要对大量数据进行回归计算,不能快速、有效地确定壁板承载力,因此提出一种新型钢筋混凝土建筑在连续震动下的壁板结构破坏程度分析方法。通过确定混凝土建筑材料、钢筋材料、壁板截面与单元材料等属性参数,完成钢筋混凝土壁板结构有限元建模;通过对连续震动下破坏壁板结构的内、外力分析,确定壁板结构总体破坏程度。设计对比实验结果表明,应用新型壁板结构破坏程度分析方法能有效确定壁板抗剪承载力和抗弯承载力,避免因壁板结构失去支撑力,而造成建筑损坏现象发生。     

含软弱夹层岩质边坡的模态分析及其对边坡地震动力响应影响的初步研究

本文以含软弱夹层岩质边坡作为研究对象,基于数值软件ANSYS的模态分析给出了含不同倾角与厚度软弱夹层边坡的前5阶固有频率与振型,并分析了夹层倾角和厚度对边坡固有模态的影响。接着,结合已有的大型振动台模型试验结果,在小应变范围内讨论了边坡的固有模态与其动力响应特性之间的关系。结果表明:(1)在夹层倾角相同时,含较厚软弱夹层边坡固有频率低于含较薄软弱夹层边坡;(2)在夹层厚度相同时,随着倾角增加,夹层从反倾变化到顺倾,低阶(1、2)固有频率也逐渐增加,而高阶(3、4、5)固有频率则呈下降趋势;(3)从第3、4阶开始,边坡变形受夹层影响增强;(4)基于加速度傅里叶谱比分析得出的边坡响应放大频率与边坡前5阶固有频率范围接近,加速度和位移响应在夹层及以上部位响应强烈,与边坡前5阶振型较为一致,预示了边坡的共振响应。需要指出的是,本文得出的结论尚且不能用于准确解释边坡在大变形及破坏阶段的动力响应特征,但可为边坡动力特性及共振响应的深入研究提供思路。     

重力坝大孔口坝段抗震试验研究

以景洪水电站重力坝大孔口坝段为研究对象,通过输入没特性地震波的振动台模型试验和三维有限元分析,定量、定性地研究了大孔口坝段地震反应的特性。结果表明,对于大孔口坝段使用现行抗震规范反应谱曲线乍得的结果偏小;用振型迭加计算大孔坝段地震响应,参与迭加的振型不应少于五阶;应充分考虑不同地震特性的影响。     

Response spectrum analysis for floor acceleration

The peak floor acceleration (PFA) is a critical parameter influencing the performance of non‐structural elements in buildings. This paper develops a response spectrum analysis method based on the complete quadratic combination (CQC) rule to estimate the PFA. The method accounts for the rigid contribution of truncated higher modes and the cross‐correlations between all pairs of modes. The approximation is introduced in the time domain and then formulated in the frequency domain by CQC. Application of the method to a continuous cantilever beam idealizing a building with shear walls is presented and compared with alternative formulations. The proposed method is able to provide a consistent estimation of the PFA along the entire structure, not only where the PFA is principally influenced by the first few flexible modes but also where the PFA is mainly related to the rigid response of the structure, for example, near its base. Copyright © 2015 John Wiley & Sons, Ltd.     

Damage identification of structures with uncertain frequency and mode shape data

A statistical method with combined uncertain frequency and mode shape data for structural damage identification is proposed. By comparing the measured vibration data before damage or analytical finite element model of the intact structure with those measured after damage, the finite element model is updated so that its vibration characteristic changes are equal to the changes in the measured data as closely as possible. The effects of uncertainties in both the measured vibration data and finite element model are considered as random variables in model updating. The statistical variations of the updated finite element model are derived with perturbation method and Monte Carlo technique. The probabilities of damage existence in the structural members are then defined. The proposed method is applied to a laboratory tested steel cantilever beam and frame structure. The results show that all the damages are identified correctly with high probabilities of damage existence. Discussions are also made on the applicability of the method when no measurement data of intact structure are available. Copyright © 2002 John Wiley & Sons, Ltd.     

Permanent deformation estimates of dynamic equipment foundations: Application to a gas turbine in granular soils

Permanent displacements of a gas turbine founded on a fine, poorly graded, and medium density sand are studied. The amplitudes and modes of vibration are computed using Barkan´s formulation, and the “High-Cycle Accumulation” (HCA) model is employed to account for accumulated deformations due to the high number of cycles. The methodology is simple: it can be easily incorporated into standard mathematical software, and HCA model parameters can be estimated based on granulometry and index properties. Special attention is devoted to ‘transient’ situations at equipment´s start-up, during which a range of frequencies – including frequencies that could be similar to the natural frequencies of the ground – is traversed. Results show that such transient situations could be more restrictive than stationary situations corresponding to normal operation. Therefore, checking the stationary situation only might not be enough, and studying the influence of transient situations on computed permanent displacements is needed to produce a proper foundation design.     

嘉峪关光化楼残损变形现状及抗震性能分析

中国木结构建筑是我国宝贵的物质文化遗产和文化瑰宝，具有悠久的文化历史。以嘉峪关光化楼为依托，对光化楼进行实地调研，分析光化楼主要残损变形。采用ANSYS软件建立考虑光化楼残损变形的三维有限元精细模型，并进行模态分析与时程分析。研究结果表明，光化楼主要残损变形为油饰脱落、墙体剥蚀开裂、柱偏移等，极个别柱产生较大偏移；光化楼刚度相对稳定，前20阶振型自振频率均在10Hz以内；光化楼动力放大系数与层间位移角均较小，仍具有良好的抗震减震性能。