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Structural Engineering and Mechanics
  Volume 35, Number 5, July30 2010 , pages 555-570
DOI: https://doi.org/10.12989/sem.2010.35.5.555
 


Energy approach for dynamic buckling of shallow fixed arches under step loading with infinite duration
Yong-Lin Pi, Mark Andrew Bradford and Weilian Qu

 
Abstract
    Shallow fixed arches have a nonlinear primary equilibrium path with limit points and an unstable postbuckling equilibrium path, and they may also have bifurcation points at which equilibrium bifurcates from the nonlinear primary path to an unstable secondary equilibrium path. When a shallow fixed arch is subjected to a central step load, the load imparts kinetic energy to the arch and causes the arch to oscillate. When the load is sufficiently large, the oscillation of the arch may reach its unstable equilibrium path and the arch experiences an escaping-motion type of dynamic buckling. Nonlinear dynamic buckling of a two degree-of-freedom arch model is used to establish energy criteria for dynamic buckling of the conservative systems that have unstable primary and/or secondary equilibrium paths and then the energy criteria are applied to the dynamic buckling analysis of shallow fixed arches. The energy approach allows the dynamic buckling load to be determined without needing to solve the equations of motion.
 
Key Words
    dynamic buckling; energy conservation; escaping-motion; lower dynamic buckling load; nonlinear equilibrium path; step loading of infinite duration; upper dynamic buckling load.
 
Address
Yong-Lin Pi: School of Civil and Environmental Engineering, Faculty of Engineering and Information Technology,
University of Technology, Sydney, Broadway, NSW 2007, Australia
Mark Andrew Bradford: School of Civil and Environmental Engineering, Faculty of Engineering and Information Technology,
University of Technology, Sydney, Broadway, NSW 2007, Australia
Weilian Qu: Key Laboratory of Roadway Bridge and Structural Engineering, Wuhan University of Technology, Wuhan 430070, China
 

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