A general procedure for the bending crush analysis of thin-walled members is proposed, where main emphasis is given to the estimation of collapse mode parameters and the prediction of post-collapse behaviours. Once the shape of local collapse is devised based on experiments, finite element buckling analyses or intuition and the collapse mode parameters are defined, plastic energy dissipation at the collapsing region can be formulated as a function of collapse mode parameters and a process control parameter by considering kinematically admissible displacement fields. Collapse mode parameters are estimated from the extremum principle of plastic energy dissipation. And the moment-angle relationship is obtained by differentiating the plastic energy with respect to the process control parameter.
In general, moment values calculated from the method of collapse mechanism are highly overestimated in the range of small deformation. Therefore, as an alternative solution for initial collapse, methods of predicting ultimate loads should be provided, which can be accomplished by extending the theoretical methods of calculating ultimate strength of compressive plates of the thin-walled beam constructions. Then the two solutions are combined by drawing a tangent from the ultimate load point to the load-deflection curve, and it would be an appropriate input data for a hybrid finite element analysis of collapsing beam structures.
Reliability and accuracy of the proposed method are examined by analyzing several typical bending collapse examples including angle strut, channel, trapezoidal tube and I-section beam. During the solution process, mode parameters corresponding to the folding wave lengths are assumed to be constant for the computational efficiency and those representing the radius of curvature of the traveling bending hinges are re-calculated at every step. Several collapse mechanisms are proposed for each example from intuitions, empirical observations or buckling mode shapes obtained from elastic finite element analysis. Comparing the predicted moment-angle curves with those from experimental results, they are in fairly good agreement and maximal deviation is shown to be approximately fifteen percent both in ultimate loads and deep collapse regions.
It is, therefore, concluded that the proposed method of predicting mode dimensions and post collapse behaviours are computationally effective and reasonably accurate. So the present method would be used as a design tool for the management of crush characteristics without real structural tests. But the present method might be somewhat complicated in describing mechanisms if the section would be complex. Some future works of developing hybrid technology will be expected. Those studies will be also needed which will improve accuracy and modeling flexibility such as taking account of multiaxial collapses and appropriate elastoplastic algorithms.
