# On inelastic local flange buckling

Sammanfattning: This thesis deals with inelastic local buckling of I-beam flanges made of steel. The main focus is on the theoretical description of the buckling process, and the influence of various parameters, e.g. the plastic modulus, yield plateau, yield stress etc., on the buckling process. In the thesis, discussion on the relevancy of different constitutive models for the inelastic behaviour of steel are discussed, and a theoretical model for the inelastic local flange buckling is presented. In the theoretical models of the inelastic local buckling problem presented in the past, there has been quite some confusion about what constitutive model is applicable. The incremental theory has been applied by some, the deformation theory of plasticity has been used by others also relatively recently, and the theory of Lay has been used by others. In this thesis, it is concluded that the incremental theory of plasticity based on an isotropically hardening von Mises yield surface in combination with the associated flow rule is applicable for the modelling of inelastic local flange buckling. The theory of Lay is concluded nonvalid. A simple slip plane theory which in distinction to the mathematical theory of plasticity is based on the physical mechanism of plastic deformation, and in its present form valid for a subspace of stress containing shear and normal stress, has been developed in the thesis. This slip plane theory is in good agreement with the incremental theory of plasticity. For the modelling of the flange buckling, the buckling process is assumed to consist of three phases without any distinct borders in between. The first phase is considered related to mainly torsional deformations and can hence be seen as a torsional buckling phase. The second phase is associated with progressively lesser shear stiffness of the material and plate bending is introduced. In the third phase, the shear stiffness is wiped out and plate bending is assumed to resist the buckling entirely. The first phase is modelled as the inelastic torsional buckling of a thin plate, restrained so as to avoid any other instability mode. This includes the description of the inelastic torsion of a thin plate. For that purpose, the plate is assumed to be composed of an infinite number of rectangular hollow cross sections. This first phase mainly governs the buckling stress and the ductility of the flange. Herein, the term ductility is used for deformation capacity in general, and hence by ductility of a compressed flange is ment the amount of axial shortening during which the flange is able to resist a compressive mean stress equal to or exceeding the yield stress. The second phase is not considered in the modelling. Instead, the first phase is directly followed by the third phase in the model. In this third phase, the flange buckle is considered as a yield line mechanism. In this yield line buckle model, the effect of stress redistribution is accounted for. The two models are linked together to a unified model and hence this model is able to approximately describe the mean stress-mean strain relation of a locally buckling flange. Using this model, a parametric study is performed in order to investigate the dependence of the flange buckling behaviour on various parameters. It is concluded that parameters like the plastic modulus, length of yield plateau, initial imperfections, and residual stresses have only a relatively moderate effect on the buckling process. Quite naturally, the parameters that has the most effect on the buckling behaviour is the width to thickness ratio and the yield stress. However, according to the procedure in the codes, these parameters are combined in the definition of a so called slenderness parameter, defined as the square root of the yield stress over the critical stress. Hence this parameter is in the codes assumed as the only governing parameter with respect to local buckling. The parameter study however reveals this approach as not entirely correct. From the theoretical model, it seems like this approach is unfavourable to high strength steel. In order to verify the conclusions from the theoretical modelling, experiments were made on crusiform stub columns. In all 22 specimen were compressed and the specimen were made of two materials, namely Weldox 700, with a nominal lower yield strength of 700 MPa and hence representing high strength steel, and SS 1312, with a nominal lower yield strength of 220 MPa thereby representing the ordinary steel grades. Hence for each material 11 stub columns with varying slenderness with respect to flange buckling were tested. The experimental results agreed fairly well with the results from the theoretical model.

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