Study of Elastic and Inelastic Buckling Behaviour of Plates Made with High-Strength Steel Under Shearing Stresses with Different Support Conditions

Abstract

The rising interest in the use of high strength steel (HSS) materials is justified by several advantages that they provide since their applications make the design with slender steel possible. In the civil engineering field, high-rise buildings and large span bridges can be designed with smaller foundations and less structural weight. Few researches work on buckling under pure shear are available in literature specially when it comes to the inelastic buckling behaviour. This dissertation investigates the analytical and the numerical simulation to predict the shear strength of the plates with different steel grades. The elastic local buckling stress τcr can be estimated using the plate stability theory. Critical load is usually calculated in eigenvalue linear buckling analysis and to find out the loads for which the model stiffness matrix becomes singular. The boundary conditions and the aspect ratio affect the local shear buckling coefficient. There are two steps of analysis carried out in this work. For the sake of comparison, the first step consisted of the linear elastic shear buckling analysis with three means: analytical procedure, EBPlATE software and ABAQUS package. Broadly speaking, results of the linear elastic buckling were as expected. The parametric study has shown once again the importance of the grade of the steel in the evaluation of the critical stress. In fact, as the steel grades grows, the smaller stress is given, showing that the mild steel has a better resistance against the elastic shear buckling than HSS cases with figures as twice as much for both the case of square or even rectangular plates simply supported. The aspect ratio plays an important role in elastic buckling under pure shear as it modifies the value of τcr by decreasing them as the ratio become larger. Changing the support conditions from simply supported to clamped one's has shown its importance namely by increasing the value of τcr for the particular case of square plate roughly twice as much for each studied case. The square plate shows better behaviour compared to the rectangular ones. And then, the numerical model by ABAQUS has been successfully validated for nonlinear buckling analysis. The second step consisted of the 2nd order non-linear analysis with the initial geometric imperfection obtained from the final deformed shape from the first step. Furthermore, nonlinear analysis was possible by a step realistic behaviour of the structure, which is programmed in ABAQUS/Standard. Incremental procedure based on RIKS algorithm is used to solve system of nonlinear equations is considered when a post-buckling behaviour is of interest this was possible by a step-by-step loading process. Also, the results show that the steel grades of the plate are of prime importance as it influences the elastic shear buckling of all studied plates by increasing the elastic buckling stress. The decrease of Vcr depends on the size of the geometry of the plates as well as the steel grade and boundary condition. The non-linear finite element method with initial geometric imperfection is compulsory to capture the shear buckling behaviour of the steel thin plates. Then, a comprehensive trial and error technique for the amplitude value of the initial geometric imperfection under shear was carried out to obtain the correct buckling load. The numerical simulation observed that the scaled magnitude of the imperfection required to match the buckling load was affected by the mesh aspect ratio, which eventually is affected by the mesh size. Finally, it can be asserted that the initial objectives of this study, which were to focus on the investigation of the elastic and inelastic behaviour of steel plates were generally achieved. Modelling the inelastic shear buckling has not been very successful because of the geometric imperfection for simply supported plate as it does not show the post-buckling behaviour which needs more effort to find out the true value of the geometric imperfection. While for clamped plate a more realistic model has been built-up giving much more valuables results.