Lateral stability analysis of steel tapered thin-walled beams under various boundary conditions

Document Type : Research


1 Assistant Professor, Department of civil engineering, University of Kashan, Kashan, Iran

2 Associate Professor, Civil Engineering Faculty, K.N.Toosi university of Technology, Tehran, Iran .

3 Associate Professor, Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, LabEx DAMAS, F-57000 METZ, France.


The lateral-torsional buckling of tapered thin-walled beams with singly-symmetric cross-section has been investigated before. For instance, the power series method has been previously utilized to simulate the problem, as well as the finite element method. Although such methods are capable of predicting the critical buckling loads with the desired precision, they need a considerable amount of time to be accomplished. In this paper, the finite difference method is applied to investigate the lateral buckling stability of tapered thin-walled beams with arbitrary boundary conditions. Finite difference method, especially in its explicit formulation, is an extremely fast numerical method. Besides, it could be effectively tuned to achieve a desirable amount of accuracy. In the present study, all the derivatives of the dependent variables in the governing equilibrium equation are replaced with the corresponding forward, central and backward second order finite differences. Next, the discreet form of the governing equation is derived in a matrix formulation. The critical lateral-torsional buckling loads are then determined by solving the eigenvalue problem of the obtained matrix. In order to verify the accuracy of the method, several examples of tapered thin-walled beams are presented. The results are compared with their counterparts of finite element simulations using shell element of known commercial software. Additionally, the result of the power series method, which has been previously implemented by the authors, are considered to provide a comparison of both power series and finite element methods. The outcomes show that in some cases, the finite difference method not only finds the lateral buckling load more accurately, but outperforms the power series expansions and requires far less central processing unit time. Nevertheless, in some other cases, the power series approximation has less relative error. As a result, it is recommended that a hybrid method, based on a combination of the finite difference technique and the power series method, be employed for lateral buckling analysis. This hybrid method simultaneously inherits its performance and accuracy from both mentioned numerical methods.


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