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Time derivative of earthquake acceleration

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Earthquake Engineering and Engineering Vibration 2005年第1期4卷 1-16页

作者： george c. lee Multidisciplinary center for Earthquake Engineering Research University at Buffalo Buffalo NY 14261-0025 USAProfessor

Unlike acceleration, velocity, and displacement, the time derivative ofacceleration (TDoA) of ground motion has not been extensively studied. In this paper, the basiccharacteristics of TDoA are evaluated based on records from the 1999 chi-chi, earthquake (Mw 7.6)and one of its aftershocks (Mw 6.2). It is found that the maximum TDoA at a free-field station wasover 31,200 cm/s3 (31.8 g/s); and the duration of 'strong' TDoA, between the first and the last timepoints exceeding 2,000 cm/s3 (2 g/s), was almost one minute near the epicenter area. Since groundTDoA sensors are not commonly available, the time series are calculated by direct numericaldifferentiation of acceleration time series. Relative error analysis shows that the error isnon-transitive and total error is within 4%. The density function of TDoA amplitude, frequencycontent and spatial distribution of peak ground jerk (PGJ) are evaluated. The study also includesexamination of some TDoA responses from a seven-story building and comparison of ground TDoA withthe limit TDoA used in the transportation industry for ride comfort. Some potential impacts of TDoAon humans have also been reviewed.

关键词： time derivation of acceleration peak ground jerk acceleration time series earthquake ground motion earthquake effect on human activities

Towards multiple hazard resilient bridges:a methodology for modeling frequent and infrequent time-varying loads Part I,comprehensive reliability and partial failure probabilities

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Earthquake Engineering and Engineering Vibration 2012年第3期11卷 293-301页

作者： Zach Liang george c.lee Department of Mechanical and Aerospace Engineering University at Buffalo Department of civil Structural and Environmental EngineeringUniversity at Buffalo

The current AASHTO load and resistance factor design （LRFD） guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads （also referred to as multiple hazard or MH loads） can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions：（1） formulate the failure probabilities; （2） normalize various load distributions; and （3） establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.

关键词： multiple hazards bridge probability-based design comprehensive reliability partial failure probability

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Towards establishing practical multi-hazard bridge design limit states

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Earthquake Engineering and Engineering Vibration 2013年第3期12卷 333-340页

作者： Zach Liang george c.lee Department of Mechanical and Aerospace Engineering Unidersity at Buffalo Depart of civil Structural and Environmental Engineering University at Buffalo

In the U.S., the current Load and Resistance Factor Design （LRFD） Specifications for highway bridges is a reliability-based formulation that considers failure probabilities of bridge components due to the actions of typical dead load and frequent vehicular loads. Various extreme load effects, such as earthquake and vessel collision, are on the same reliability-based platform. Since these extreme loads are time variables, combining them with not considered frequent. non- extreme loads is a significant challenge. The number of design limit state equations based on these failure probabilities can be unrealistically large and unnecessary from the view point of practical applications. Based on the opinion of AASHTO State Bridge Engineers, many load combinations are insignificant in their states. This paper describes the formulation of a criterion to include only the necessary load combinations to establish the design limit states. This criterion is established by examining the total failure probabilities for all possible time-invariant and time varying load combinations and breaking them down into partial terms. Then, important load combinations can be readily determined quantitatively,

关键词： multi-hazards load and resistance factor design re.liability based bridge design specifications design limit state equations

From the editors:special issue announcement

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Earthquake Engineering and Engineering Vibration 2009年第2期8卷 251-261页

作者： Wang Zhiqiang george c. lee Department of Bridge Engineering Tongji University Shanghai 200092 China Department of civil Structural and Environmental Engineering University at Buffalo State University of New York USA

A comparative study of selected bridge damage due to the Wenchuan, Northridge, Loma Prieta and San Fernando earthquakes is described in this paper. Typical ground motion effects considered include large ground fault displacement, liquefaction, landslide, and strong ground shaking. Issues related to falling spans, inadequate detailing for structural ductility and complex bridge configurations are discussed within the context of the recent seismic design codes of china and the US. A significant lesson learned from the Great Wenchuan earthquake, far beyond the opportunities to improve the seismic design provisions for bridges, is articulated.

关键词： bridge damage Wenchuan earthquake Northridge earthquake Loma Prieta earthquake San Fernandoearthquake ground motion liquefaction landslide

Bridge pier failure probabilities under combined hazard effects of scour, truck and earthquake. Part Ⅰ: occurrence probabilities

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Earthquake Engineering and Engineering Vibration 2013年第2期12卷 229-240页

作者： Zach Liang george c. lee Department of Mechanical and Aerospace Engineering Unidersity at Buffalo Depart of civil Structural and Environmental EngineeringUniversity at Buffalo

In many regions of the world, a bridge will experience multiple extreme hazards during its expected service life. The current American Association of State Highway and Transportation Officials （AASHTO） load and resistance factor design （LRFD） specifications are formulated based on failure probabilities, which are fully calibrated for dead load and nonextreme live loads. Design against earthquake loads is established separately. Design against scour effect is also formulated separately by using the concept of capacity reduction （or increased scour depth）. Furthermore, scour effect cannot be linked directly to an LRFD limit state equation, because the latter is formulated using force-based analysis. This paper （in two parts） presents a probability-based procedure to estimate the combined hazard effects on bridges due to truck, earthquake and scour, by treating the effect of scour as an equivalent load effect so that it can be included in reliability-based bridge failure calculations. In Part I of this series, the general principle of treating the scour depth as an equivalent load effect is presented. The individual and combined partial failure probabilities due to truck, earthquake and scour effects are described. To explain the method of including non-force-based natural hazards effects, two types of common scour failures are considered. In Part 11, the corresponding bridge failure probability, the occurrence of scour as well as simultaneously having both truck load and equivalent scour load are quantitatively discussed.

关键词： multi-hazards load and resistance factor design bridge scour

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On similitude law of sub-systems

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Earthquake Engineering and Engineering Vibration 2006年第1期5卷 133-142页

作者： Zach Liang george c.lee Department of civil Structural and Environmental Engineering University at BuffaloState University of New YorkBuffaloNew YorkUSA Multidisciplinary center for Earthquake Engineering Research University at BuffaloState University of New YorkBuffaloNew YorkUSA

Based on Buckingham＇s π-Theorem, dimensional analysis has achieved considerable success over the past near-century. Model testing has long been a powerful tool in both scientific studies and engineering applications. However, the prototype objects are becoming more and more complicated nowadays, and many of the prototype systems can contain several sub-systems. The conventional theories on model-prototype similarity and dimensional analysis have only limited application since the π-Theorem itself does not distinguish between the original system and subsystems. This is particularly true in the field of structural dynamics, where the structure is often modeled as a multi-degree-of-freedom system. In this paper, we attempt to show that, if a system can be decoupled into several nontrivial subsystems, then, in each subsystem, the number of π-terms will be reduced and therefore simplify the model testing. On the other hand, if a system cannot be decoupled into subsystems, then using model testing with reduced π-term analysis, both experimentally and theoretically, may introduce severe errors.

关键词： similitude law Buckingham's π-theorem model testing sub-systems

Principal axes of M-DOF structures Part I:Static loading

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Earthquake Engineering and Engineering Vibration 2002年第2期1卷 293-302页

作者： Zack Liang george c.lee Department of civil Structural and Environmental EngineeringUniversity.at BuffaloState University.of New YorkBuffaloNew YorkUSA Multidisciplinary center for Earthquake Engineering Research University at BuffaloState University of New YorkBuffaloNew YorkUSA

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.

关键词： principal axes of M-DOF structures structural response couplings cross effect theoretical base

Experimental study of hollow rectangular bridge column performance under vertical and cyclically bilateral loads

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Earthquake Engineering and Engineering Vibration 2013年第3期12卷 433-445页

作者： Han Qiang Du Xiuli Yihui Zhou george c. lee Key Laboratory of Urban Security and Disaster Engineering of MOE Beijing University of Technology McEER University at Buffalo State University of New York

To investigate the seismic performance of hollow reinforced concrete （Rc） bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending, five specimens were tested. A parametric study is carried out for different axial load ratios, longitudinal reinforcement ratios and lateral reinforcement ratios. The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity, which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns. Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations, and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance. However, the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design. The hollow Rc rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations, and may be considered as a substitute for current hollow Rc rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges （JTG/T B02-01-2008）. The length of the plastic hinge region was found to approach one sixth of the hollow Rc rectangular bridge column height for all specimen columns, and it was much less than those specified in the current JTG/T. Thus, the length of the plastic hinge region is more concentrated for Rc rectangular hollow bridge columns.

关键词： bridge columns hollow section cyclic loading test biaxial bending seismic performance

Acomparative study between china and *** seismic design philosophy and practice of a long span arch bridge

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Earthquake Engineering and Engineering Vibration 2006年第1期5卷 61-69页

作者：徐艳 george c lee 范立础胡世德 Multidisciplinary center for Earthquake Engineering Research University at Buffalo Buffalo NY 14260 USA State Key Laboratory for Disaster Reduction in Civil Engineering Tongji University Shanghai 200092 China Multidisciplinary center for Earthquake Engineering Research University at Buffalo Buffalo NY 14260 USA Department of Bridge Engineering Tongji University

This paper presents the first of a series of case studies on the seismic design of long span bridges （cable-stayed bridges, suspension bridges and arch bridges） under a cooperative research project on seismic behavior and design of highway bridges between the State Key Laboratory for Disaster Reduction in civil Engineering, Tongji University and the Multidisciplinary center for Earthquake Engineering Research, University at Buffalo. The objective of this series of case studies is to examine the differences and similarities on the seismic design practice of long span bridges in china and the U.S., to identify research needs and to develop design guidelines beneficial to bridge engineers in both countries. Unlike short to medium span bridges, long span bridges are not included in most seismic design specifications, mainly because they are location dependent and structurally unique. In this paper, an available model of a steel tied half through arch bridge with a main span of 550m in china is discussed. Analysis is focused on comparisons of the seismic responses due to different ground motions. Seismic design criteria and seismic performance requirements for long span bridges in both countries were first introduced and compared, and then three near field earthquake records with large vertical components were selected as the excitations to examine the seismic behavior and seismic vulnerability of the bridge. Results show that （1） the selected near field ground motions cause larger responses to key components （critical sections） of the bridge （such as arch rib ends） with a maximum increase of more than twice those caused by the site specific ground motions; （2） piers, longitudinal girders and arch crowns are more vulnerable to vertical motions, especially their axial forces; and （3） large vertical components of near field ground motions may not significantly affect the bridge＇s internal forces provided that their peak acceleration spectra ordinates only appear at periods

关键词： long span arch bridge seismic design practise seismic vulnerability near field ground motion vertical motion