Principal axes of M-DOF structures part I: Static loading |
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Authors: | Zack?Liang Email author" target="_blank">George?C?LeeEmail author |
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Institution: | (1) Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, New York, USA;(2) Multidisciplinary Center for Earthquake Engineering Research, University at Buffalo, State University of New York, Buffalo, New York, USA |
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Abstract: | 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. |
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Keywords: | principal axes of M-DOF structures structural response couplings cross effect theoretical base |
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