Cross Correlations of Modal Responses of Tall Buildings in Wind-Induced Lateral-Torsional Motion

Recent trends towards developing increasingly taller and irregularly-shaped buildings imply that these complex structures are potentially more responsive to wind excitation. Making accurate predictions of wind loads and their effects on such structures is therefore a necessary step in the design synthesis process. This paper presents a framework for dynamic analysis of the wind-induced lateral-torsional response of tall buildings with three-dimensional (3D) mode shapes. The cross correlation reflecting the statistical coupling among modal responses under spatiotemporally varying dynamic wind excitations has been investigated in detail. The effects of intermodal correlations on the lateral-torsional response of tall buildings with 3D mode shapes and closely spaced natural frequencies are elucidated and a more accurate method for quantifying intermodal cross correlations is analytically developed. Utilizing the wind tunnel derived synchronous multipressure measurements, a full-scale 60-story asymmetric building of mixed steel and concrete construction is used to illustrate the proposed framework for the coupled dynamic analysis and highlight the intermodal correlation of modal responses on the accurate prediction of coupled building acceleration.     

Proper Orthogonal Decomposition-Based Modeling, Analysis, and Simulation of Dynamic Wind Load Effects on Structures

Multicorrelated stationary random processes/fields can be decomposed into a set of subprocesses by diagonalizing their covariance or cross power spectral density (XPSD) matrices through the eigenvector/modal decomposition. This proper orthogonal decomposition (POD) technique offers physically meaningful insight into the process as each eigenmode may be characterized on the basis of its spatial distribution. It also facilitates characterization and compression of a large number of multicorrelated random processes by ignoring some of the higher eigenmodes associated with smaller eigenvalues. In this paper, the theoretical background of the POD technique based on the decomposition of the covariance and XPSD matrices is presented. A physically meaningful linkage between the wind loads and the attendant background and resonant response of structures in the POD framework is established. This helps in better understanding how structures respond to the spatiotemporally varying dynamic loads. Utilizing the POD-based modal representation, schemes for simulation and state-space modeling of random fields are presented. Finally, the accuracy and effectiveness of the reduced-order modeling in representing local and global wind loads and their effects on a wind-excited building are investigated.     

Revisiting Multimode Coupled Bridge Flutter: Some New Insights

Better understanding of the bimodal coupled bridge flutter involving fundamental vertical bending and torsional modes offers valuable insight into multimode coupled flutter, which has primarily been the major concern in the design of long span bridges. This paper presents a new framework that provides closed-form expressions for estimating modal characteristics of bimodal coupled bridge systems and for estimating the onset of flutter. Though not intended as a replacement for complex eigenvalue analysis, it provides important physical insight into the role of self-excited forces in modifying bridge dynamics and the evolution of intermodal coupling with increasing wind velocity. The accuracy and effectiveness of this framework are demonstrated through flutter analysis of a cable-stayed bridge. Based on this analysis scheme, the role of bridge structural and aerodynamic characteristics on flutter, which helps to better tailor the structural systems and deck sections for superior flutter performance, is emphasized. Accordingly, guidance on the selection of critical structural modes and the role of different force components in multimode coupled flutter are delineated. The potential significance of the consideration of intermodal coupling in predicting torsional flutter is highlighted. Finally, clear insight concerning the role of drag force to bridge flutter is presented.     

Identification of Natural Frequencies and Dampings of In Situ Tall Buildings Using Ambient Wind Vibration Data

An accurate prediction for the response of tall buildings subject to strong wind gusts or earthquakes requires the information of in situ dynamic properties of the building, including natural frequencies and damping ratios. This paper presents a method of identifying natural frequencies and damping ratios of in situ tall buildings using ambient wind vibration data. Our approach is based on the empirical mode decomposition (EMD) method, the random decrement technique (RDT), and the Hilbert–Huang transform. Our method requires only one acceleration sensor. The noisy measurement of the building acceleration is first processed through the EMD method to determine the response of each mode. Then, RDT is used to obtain the free vibration modal response. Finally, the Hilbert transform is applied to each free vibration modal response to identify natural frequencies and damping ratios of in situ tall buildings. The application of the proposed methodology is demonstrated in detail using simulated response data of a 76-story benchmark building polluted by noise. Both the along-wind and across-wind vibration measurements have been illustrated. Simulation results demonstrate that the accuracy of the proposed method in identifying natural frequencies and damping ratios is remarkable. The methodology proposed herein provides a new and effective tool for the parametric identification of in situ tall buildings.     

Dynamic Modal Analysis and Stability of Cantilever Shear Buildings: Importance of Moment Equilibrium

The dynamic modal analysis (i.e., the natural frequencies, modes of vibration, generalized masses, and modal participation factors) and static stability (i.e., critical loads and buckling modes) of two-dimensional (2D) cantilever shear buildings with semirigid flexural restraint and lateral bracing at the base support as well as lumped masses at both ends and subjected to a linearly distributed axial load along its span are presented using an approach that fulfills both the lateral and moment equilibrium conditions along the member. The proposed model includes the simultaneous effects and couplings of shear deformations, translational and rotational inertias of all masses considered, a linearly applied axial load along the span, the shear force component induced by the applied axial force as the member deforms and the cross section rotates, and the rotational and lateral restraints at the base support. The proposed model shows that the stability and dynamic behavior of 2D cantilever shear buildings are highly sensitive to the coupling effects just mentioned, particularly in members with limited rotational restraint and lateral bracing at the base support. Analytical results indicate that except for members with a perfectly clamped base (i.e., zero rotation of the cross sections), the stability and dynamic behavior of shear buildings are governed by the flexural moment equation, rather than the second-order differential equation of transverse equilibrium or shear-wave equation. This equation is formulated in the technical literature by simply applying transverse equilibrium “ignoring” the flexural moment equilibrium equation. This causes erroneous results in the stability and dynamic analyses of shear buildings with base support that is not perfectly clamped. The proposed equations reproduce, as special cases: (1) the nonclassical vibration modes of shear buildings including the inversion of modes of vibration when higher modes cross lower modes in shear buildings with soft conditions at the base, and the phenomena of double frequencies at certain values of beam slenderness (L/r); and (2) the phenomena of tension buckling in shear buildings. These phenomena have been discussed recently by the writer (2005) in columns made of elastomeric materials.     

Challenges in the Application of Stochastic Modal Identification Methods to a Cable-Stayed Bridge

This paper presents an analysis of the data collected in the ambient vibration test of the International Guadiana cable-stayed Bridge, which links Portugal and Spain, based on different output-only identification techniques: peak-picking, frequency domain decomposition, covariance-driven stochastic subspace identification, and data-driven stochastic subspace identification. The purpose of the analysis is to compare the performance of the four techniques and evaluate their efficiency in dealing with specific challenges involved in the modal identification of the tested cable-stayed bridge, namely the existence of closely spaced modes, the perturbation produced by the local vibration of stay-cables, and the variation of modal damping coefficients with wind velocity. The identified natural frequencies and mode shapes are compared with the corresponding modal parameters provided by a previously developed numerical model. Additionally, the variability of some modal damping coefficients is related with the variation of the wind characteristics and associated with a component of aerodynamic damping.     

Vibration Studies of Tsing Ma Suspension Bridge

A three-dimensional dynamic finite element model is established for the Tsing Ma long suspension Bridge in Hong Kong. The two bridge towers made up of reinforced concrete are modeled by three-dimensional Timoshenko beam elements with rigid arms at the connections between columns and beams. The cables and suspenders are modeled by cable elements accounting for geometric nonlinearity due to cable tension. The hybrid steel deck is represented by a single beam with equivalent cross-sectional properties determined by detailed finite element analyses of sectional models. The modal analysis is then performed to determine natural frequencies and mode shapes of lateral, vertical, torsional, longitudinal, and coupled vibrations of the bridge. The results show that the natural frequencies of the bridge are very closely spaced; the first 40 natural frequencies range from 0.068 to 0.616 Hz only. The computed normal modes indicate interactions between the main span and side span, and between the deck, cables, and towers. Significant coupling between torsional and lateral modes is also observed. The numerical results are in excellent agreement with the measured first 18 natural frequencies and mode shapes. The established dynamic model and computed dynamic characteristics can serve further studies on a long-term monitoring system and aerodynamic analysis of the bridge.     

Investigation of Effects of Nonlinear Static Analysis Procedures to Performance Evaluation on Low-Rise RC Buildings

The aim of the study is to compare and evaluate structural response demands obtained from nonlinear static analysis procedures (NSPs) which are displacement coefficient method (DCM) recommended in FEMA 356 and capacity spectrum method (CSM) recommended in ATC 40. For these reasons, three of three-dimensional low-rise RC buildings with different characteristics are investigated. In order to determine nonlinear behavior of the buildings under lateral loads, the base shear-roof displacement relationships (capacity curves) are obtained by pushover analysis including P-delta effects. Then by considering four different seismic hazard levels, building performances are determined by using the CSM and by using from DCM results determined in a previous study. In order to determine performance levels of the buildings, maximum beam and column plastic rotation demands and maximum story drift demands are determined in the related maximum displacement demands. Plastic strains in the equivalent diagonal struts, representing the nonstructural infill walls, are also determined, similarly. Comparing structural response quantities (such as plastic rotations, story drifts, etc.) obtained from the NSPs for considered low-rise RC buildings, effects of different NSPs in performance evaluations of the buildings are investigated comparatively, as well.     

Wind-Induced Response Characteristics of Monolayer Cable Net

Monolayer cable net system supporting glass facades is structurally sensitive to wind excitations. At present, there are limited researches on its wind-induced vibration performance, therefore it appears imperative to understand the wind-resistant behavior of this type of cable net. The wind-induced response of the monolayer cable net subjected to fluctuating wind loads is investigated with frequency-domain method in this paper, when the cable net deforms to the balance position under the mean wind loads. Some critical factors to wind-induced response are highlighted, including participation property of the modes in the dynamic vibration, and coupling effect among modes. The response spectrum of the cable net is also intensively investigated. It is shown that the first mode dominates wind-induced response significantly in all the modes, and the modes contributing to the wind-induced responses prominently are distributed in a narrow band of low order modes. When some lower modes and coupling effects among these modes are considered, the results in frequency domain agree well with the corresponding results obtained from time domain method, which are adequate for engineering practice. The characteristics of response spectrum of the nodal displacements are similar to those of the cable forces. When the wind loads and structural parameters vary in practical ranges in engineering, the resonant component in the total response sometimes occupies larger part in the total fluctuating wind response of the cable net, while the background component dominates in the wind response more commonly. Nevertheless, the first mode makes the largest contributions, no matter the background or the resonant component dominates.     

New Static Sunshade Design for Energy-Efficient Buildings

Energy conservation inside the buildings is of utmost importance. To reduce the heating and cooling loads inside the energy-efficient buildings, solar entry regulation as per season can be attained with the use of specific sunshades. Although various static sunshades have been developed depending upon solar geometry, the efficiency with respect to control of solar entry inside the building is a major concern over the seasonal classification for a particular geographic location. The proposed work aims at the design development of a new static sunshade depending on solar angles, whose efficiency has been experimentally verified using a small-scale modeling technique. Three experimental models of insulating material were prepared with varying aspect ratio of windows and static sunshades. Sunlit area, which in turn controls the temperature inside the models, has been made the criteria for deciding the effectiveness of the proposed sunshade over existing horizontal sunshade. The proposed technique can be applied at any geographic location over the world for which sunshade can be designed as per the climatic requirements of the place.     

Mode Shape Corrections for Wind Load Effects

Traditionally, wind analysis procedures based on the “gust loading factor” approach and experimental techniques involving the high frequency base balance and the “stick-type” aeroelastic model test have assumed ideal structural mode shapes, i.e., linear lateral modes and uniform torsional modes. The influence of nonideal mode shapes manifests itself through modifications in the generalized wind load, the structural displacement, the equivalent static wind load (ESWL), and the attendant influence function. This has led to the introduction of several correction procedures, each focusing on an individual feature of the overall response analysis framework. This paper presents a systematic development of correction procedures in terms of correction factors (CFs) to account for nonideal mode shapes in the formulation of generalized load, analysis of structural response, and the derivation of the ESWL. A parameter study is conducted to examine the significance of CFs in estimating various load effects. It is observed that the influence of a nonideal mode shape is actually negligible for the displacement response and the base bending moment, but not so for other load effects, e.g., the base shear and the generalized wind load. Although the existing procedures are effective in correcting the intended response component, they should not be used indiscriminately for other load effects. This paper also presents a correction procedure for the influence of mode shapes on the ESWLs, a loading format that is very attractive for implementation in codes and standards and design practice as well as for the correct interpretation of wind tunnel measurements.     

Free Vibrations of Cylindrical Storage Tanks: Finite-Element Analysis and Experiments

This note summarizes a theoretical and experimental study undertaken to provide a deeper understanding of the effect of different parameters on the coupled modal characteristics of circular cylindrical tanks. First, the most common case of clamped-free tanks resting on rigid foundations is investigated by using finite-element (FE) modeling and holographic experiments. A good agreement between experimental and numerical results is a basis to draw a number of conclusions. For both tank geometries investigated, the frequencies for modes of circumferential parameter n = 1 (the “beam” modes) are found to be reduced most significantly by the presence of liquid. Very significant dependence of the radial shell mode shapes on the filling ratio is confirmed both by the FE and experimental results. In addition, nonclassical vibration patterns for radial shell modes were extracted numerically and recorded experimentally. Special attention is paid to the pairs of shell modes. Second, the effects of a flexible foundation and axial compression are investigated using holographic interferometry. The modal responses of this shell–liquid system are found to be different from those of the existing theoretical models.     

桥梁模态频率与运营环境作用的相关性

桥梁模态频率随运营环境作用的变化规律是结构健康监测的研究主题之一.根据东海大桥6 a监测数据的周期变化特性,识别了运营条件下主梁竖弯、侧弯、扭转基频变化的影响因素,采用偏相关系数和周期平均法对比了各因素的影响程度.研究发现,东海大桥的模态频率存在1 a、1周、1 d、12.42 h等变化周期,与结构温度、交通荷载、风荷载、海面高度等的变化周期相吻合;结构温度和交通荷载是引起该桥频率变化的最主要因素,它们在各周期上的相对影响大小不同;周期平均法可有效分离监测数据中的年、周、天周期成分,揭示不同运营环境作用与频率变化的相关性.研究结果有助于加深对桥梁运营期频率变化的理解,从而更准确地评估结构性能.      

Glass Breakage Tests under Fluctuating Wind Loads

The current North American design codes for wind loads have dealt with the unique characteristics of glass using the observed failure mechanism of static fatigue, which is based on the concept of damage accumulation as described by Brown’s integral. However, both the load resistance and the design loads have aspects that have not been fully validated because of available but limited experimental results, particularly with regard to fluctuating load patterns. With the recent development of a sophisticated pressure-loading device, precise, time-varying wind loads as well as conventional ramp loading were applied to annealed glass plates in this study. The measured results were consistent with Brown’s integral, confirming the conversion method from realistic wind-load time histories to equivalent static loads.     

Frequency Spectrum Analysis of Impact-Echo Waveforms for T-Beams

Numerical and experimental studies were performed to assess the transient impact response of 11 T-beams with various dimensions and aspect ratios. Numerical modeling was performed using a three stage finite-element modeling procedure which included modal analysis, resonant analysis, and three-dimensional transient dynamic analysis. The response at impact locations on both the top centerline of the flange and the bottom centerline of the web was investigated. Physical models of three of the beams were constructed in the laboratory to determine the physical response of the beams when subjected to a transient impact and to verify the numerical results. Relationships between the fundamental frequencies and the frequencies of higher cross-sectional modes of vibration were established for the various aspect ratios. Shape factors were derived from the numerical and experimental results. The practical significance of the results is demonstrated for a project where impact-echo testing was used to nondestructively assess the condition of a decommissioned concrete T-shaped girder.     

Building Orientation and Wind Effects Estimation

The methodology for estimating wind effects presented in this paper is based on the database-assisted design approach. It accounts for the effects of wind directionality, for the effects of the uncertainties in the parameters that determine wind effects, and for the effects of building orientation. The methodology yields estimates of wind effects that are far more realistic than those based on the conventional building code approach, which disregards uncertainties in those parameters, as well as the effects of wind directionality and building orientation, or accounts for these effects through the use of a blanket reduction factor. The pilot software on which the calculations presented in this paper are based is a first step toward modern computer-intensive electronic standards wherein wind loads can be calculated by using database-assisted reliability-based calculations of wind effects. We believe such standards will go a long way toward achieving significantly safer and more economical buildings in regions affected by strong winds.     

Wind Pressures on Parapets of Flat Roofs

A wind-tunnel study has been carried out to assess wind pressures acting on parapets, including their top surfaces. Local and area-averaged pressure coefficients were measured on parapets of flat-roof models with a length to height ratio (L/H) of 1:1, 2:1, and 3:1. The results were obtained for full-scale equivalent parapet heights of 1 and 2 m and for wind directions ranging from zero to 315°. The local wind load on the parapet was found to be approximately 30% larger at the windward corner of the building than at the midspan location. Maximum parapet loads for the low building model were approximately 30% larger than those for the cubical model. Parapet height did not significantly affect the peak local load on the parapet except in the corner region, where the inward load (toward the roof) for the 1 m parapet was 25% higher than that for the 2 m parapet.     

Bivariate Quasi-Steady Model for Prediction of Roof Corner Pressures

Extremely high-suction pressures generated beneath the conical vortex flow in the roof-corner region have a devastating effect on the building roofs in high-wind events. The application of quasi-steady theory near the roof corners of low-rise buildings deserves careful investigation for the appropriate assessment of the design wind loads. A synchronized incident wind and pressure data acquisition system was set up on the full-scale experimental building at Texas Tech Univ. Experiments were conducted systematically to simultaneously collect the incident wind and roof-corner pressure data under the influence of cornering winds. By using a conditional sampling technique, a bivariate quasi-steady model was established to incorporate the influence of both horizontal and vertical wind directional variations on the roof-corner pressures. Comparison between the measured pressures and the model-predicted pressures has shown that the quasi-steady theory in the suggested form is applicable in the roof-corner separated flow region where vortices are present. This conclusion further justifies the application and codification of quasi-steady approach for wind load assessment of low-rise buildings and other structures.     

Wind Damage to Masonry Buildings

An examination has been made of the methods of construction of masonry‐walled buildings, and their performance in severe windstorms. Particular emphasis was placed on low‐rise buildings using unreinforced concrete block walls and light roofs, which suffer the majority of wind damage. It is shown that traditionally built, nonengineered buildings have become more wind sensitive in recent years as the result of a reduction in the number of internal walls and a lowering of roof weights. Empirical design procedures regarding wall height‐to‐thickness ratios and roof anchorage have not changed to reflect this increased sensitivity, leaving many modern, nonengineered buildings with insufficient wind resistance. Professionally designed structures often have a similar structural form to traditionally built structures, since the same empirical design rules are often used to size walls and roof anchors. The longer roof spans in these buildings render them even more sensitive to wind uplift loads, and subject to progressive collapse. The inadequacies of present building code requirements are discussed and recommendations for improvements are made.     

Uniform Shear Buildings under the Effect of Gravity Loads

Gravity loads play an important role in the linear and nonlinear behavior of buildings during earthquakes. They can also be the cause of ultimate collapse of the structures. In this study, the governing equation of continuous uniform shear buildings under the effects gravity loads is derived and eigenfrequencies, displacement, and drift mode shapes are obtained by eigenanalysis. It is shown that how the geometric properties of the structure affect the fundamental oscillation period and response of the building. Inclusion of the effects of the gravity loads makes the solution of the governing differential equation dependent on the Bessel functions of the first and second kind. The modal load and mass equations are solved using the orthogonality relations of Bessel functions. Effects of gravity on displacement and drift behavior of shear buildings on soft soils and rock subjected to limited near-fault earthquake excitations are shown.