Nonlinear SDOF Model for Progressive Collapse Responses of Structures with Consideration of Viscous Damping
Publication: Journal of Engineering Mechanics
Volume 143, Issue 9
Abstract
The effect of damping on progressive collapse responses of structures is typically ignored. However, the margin of conservatism resulting from ignoring damping is not well known. Therefore, in this paper, a nonlinear single-degree-of-freedom (SDOF) model is developed with a piecewise linear resistance function, viscous damping, and a loading function consisting of a ramp part and ensuing constant load. The closed-form analytical solutions are derived with Laplace transform techniques and verified with experimental results of steel beam-column assemblies under column-removal scenarios (CRS). The model is then used to investigate the damping effect on the dynamic displacement responses of structures under CRS with different initial conditions, structural resistance types, and levels of applied load. The results indicate that the effect of damping on displacement responses depends not only on the structural resistance but also on the level of applied load. For structural responses involving elastic and plastic hardening resistance, ignoring conventional global damping (e.g., a damping ratio of 3–5%) is reasonably conservative, but it is suggested that for structures with severe plastic softening resistance (e.g., softening stiffness greater than 10% elastic stiffness) and high damping ratio (e.g., more than 10%), the damping should be explicitly considered in the progressive collapse analysis; otherwise, it is too conservative, resulting in unnecessary cost.
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Acknowledgments
The work presented in this paper is supported by the National Natural Science Foundation of China (No. 51408189), Natural Science Foundation of Jiangsu Province of China (No. BK20140855), and the Fundamental Research Funds for the Central Universities (No. 2014B17914).
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jun 13, 2016
Accepted: Apr 19, 2017
Published online: Jul 13, 2017
Published in print: Sep 1, 2017
Discussion open until: Dec 13, 2017
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