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Structural Engineering and Mechanics   Volume 38, Number 2, April25 2011, pages 195-210
DOI: https://doi.org/10.12989/sem.2011.38.2.195
 
Exact dynamic stiffness matrix for a thin-walled beam-column of doubly asymmetric cross-section
A. Shirmohammadzade, B. Rafe*1 and W.P. Howson

 
Abstract     [Buy Article]
    Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.
 
Key Words
    coupled flexural-torsional motion; thin-walled beams; exact dynamic stiffness matrix; transcendental eigenvalue problem.
 
Address
A. Shirmohammadzade and B. Rafe: Sahand University of Technology, P.O. Box 51335/1996, Tabriz, Iran
W.P. Howson: Cardiff School of Engineering, Cardiff University, The Parade, Cardiff, CF24 3AA, UK
 

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