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Finite element formulation for distortional lateral buckling of I-beams
Highlights A family of finite elements was developed for the distortional lateral buckling of I beams. Web lateral displacement along height is a superposition of linear and Fourier modes. Classical lateral torsional buckling solution is recovered as a special case. Comparisons are conducted with classical solutions and shell finite elements. A parametric study investigated the effect of geometric parameters on the buckling resistance.
Abstract The present study develops a finite element formulation for the distortional buckling of I- beams. The formulation characterizes the distribution of the lateral displacement along the web height by superposing (a) two linear modes intended to capture the classical non-distortional lateral-torsional behaviour and (b) any number of user-specified Fourier terms intended to capture additional web distortion. All displacement fields characterizing the lateral displacements are taken to follow a cubic distribution in the longitudinal direction. The separation of variables is effectively achieved by exploiting the properties of the matrix Kronecker product. The finite element solution developed is shown to replicate accurately (a) the classical non-distortional lateral-torsional buckling solutions (b) previously developed distortional buckling solutions based on cubic interpolation of the lateral displacement, while (c) providing a basis to assess the effect to commonly omitted higher distortional modes on the predicted critical moments and buckling modes. The solution is then used to conduct a systematic parametric study of over 3900 cases to quantify the reduction in critical moments due to web distortion relative to the classical non-distortional predictions in the case of simply supported beams under uniform loads, point loads, and linear moment gradients, cantilevers, and beams with overhang.
Finite element formulation for distortional lateral buckling of I-beams
Highlights A family of finite elements was developed for the distortional lateral buckling of I beams. Web lateral displacement along height is a superposition of linear and Fourier modes. Classical lateral torsional buckling solution is recovered as a special case. Comparisons are conducted with classical solutions and shell finite elements. A parametric study investigated the effect of geometric parameters on the buckling resistance.
Abstract The present study develops a finite element formulation for the distortional buckling of I- beams. The formulation characterizes the distribution of the lateral displacement along the web height by superposing (a) two linear modes intended to capture the classical non-distortional lateral-torsional behaviour and (b) any number of user-specified Fourier terms intended to capture additional web distortion. All displacement fields characterizing the lateral displacements are taken to follow a cubic distribution in the longitudinal direction. The separation of variables is effectively achieved by exploiting the properties of the matrix Kronecker product. The finite element solution developed is shown to replicate accurately (a) the classical non-distortional lateral-torsional buckling solutions (b) previously developed distortional buckling solutions based on cubic interpolation of the lateral displacement, while (c) providing a basis to assess the effect to commonly omitted higher distortional modes on the predicted critical moments and buckling modes. The solution is then used to conduct a systematic parametric study of over 3900 cases to quantify the reduction in critical moments due to web distortion relative to the classical non-distortional predictions in the case of simply supported beams under uniform loads, point loads, and linear moment gradients, cantilevers, and beams with overhang.
Finite element formulation for distortional lateral buckling of I-beams
Arizou, Ramin (author) / Mohareb, Magdi (author)
Engineering Structures ; 262
2022-04-09
Article (Journal)
Electronic Resource
English
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