Peter Jiki
University of Agriculture
Nigeria
Title: Lateral Stability of Damaged Open Thin-walled Beams using Lyapunov’s Second method
Biography
Biography: Peter Jiki
Abstract
Lateral buckling of damaged thin-walled beams of open sections is studied in this work using Lyapunov’s direct method of stability analysis. First, a damaged stiffness reduction parameter α is calculated, following which a metric and an energy type Lyapunov functional (function) are proposed for the solution of the stability problem. It is shown that without the use of deflection functions for u, v and β in the equilibrium equations, a simple manipulation of the eigen-value inequalities yields familiar expressions for the lateral buckling loads(moments) for simply supported and fixed beams. The lateral bucklibng moments obtained using this method compare well with those in the literature using deflection functions. When the damaged parameter is applied to these expressions, the reduced lateral buckling loads or moments are obtained. Numerical examples demonstrate the application of the method proposed in the present work. It is concluded that the method is accurate and when combined the proposed load reduction parameter, the extent of damage to the beam can be obtained rapidly.