Brazier Effect of Thin Angle-Section Beams under Bending

Zhiguang Zhou,Songtao Xue,Chaoxin Sun,Liuyun Xu

doi:10.3390/su10093047

Zhiguang Zhou, Songtao Xue + Show 2 more

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https://doi.org/10.3390/su10093047

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Abstract

Thin-walled section beams have Brazier effect to exhibit a nonlinear response to bending moments, which is a geometric nonlinearity problem and different from eigenvalue problem. This paper is aimed at investigating the Brazier effect in thin-walled angle-section beams subjected to pure bending about its weak axis. The derivation using energy method is presented to predict the maximum bending moment and section deformation. Both numerical analyses and experimental results were used to show the validity of the proposed formula. Numerical results show that the boundary condition can influence the results due to the end effect, and that the influence tends to be negligible when the length of angle beam goes up to 30 times as the length of beam side. When the collapse in experiments is governed by Brazier flattening, the moment vs. curvature curve deviates significantly from the linear beam theory, but coincides well with the proposed formula in consideration of the restraint due to limited span of experimental setup. It can be concluded that the proposed formula shows good agreement with numerical results and experimental results.

Highlights

When an initially straight thin-walled circular cylindrical shell is subjected to bending, there is a tendency for the cross section to become progressively more oval as the curvature increases.The moment–curvature response deviates significantly from the linear beam theory
The collapse is not controlled by the plate curvature curve is different from the linear beam theory, but well coincides with the flattening theory buckling, but by Brazier flattening, crippling, ridge-line buckling.collapse, The collapse in consideration of the end effect
This paper mainly aims at presenting a theoretical analysis for Brazier effect in thin-walled angle-section beams

Summary

Introduction

The moment–curvature response deviates significantly from the linear beam theory. This nonlinear bending response phenomenon is due to geometric nonlinearity and was first investigated by Brazier [1]. The main characteristic of Brazier flattening is the reduction of flexural stiffness of the shell with the increase of curvature. Under steadily increasing curvature, the bending moment has a maximum value that is defined as the instability critical moment, which is given by employing the well-known energy method. Reissner [2] reconsidered Brazier’s theory and demonstrated that Brazier’s solution is a first-order approximate solution. Reissner derived the second-order approximate solution and found the maximum moment is 8% lower than the value

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