Development and analysis of low-order models of frame structures under blast loads

The main aim of this thesis is to propose an easy-to-apply tool to assess the level of damage of a structure in which one compartment is subjected to blast loading. This compartment is extracted from the structure accounting for the interaction with the part of the structure surrounding the loaded compartment, which is assumed to be elastic. Before studying the whole frame structure, the structural elements (i.e. the beam and its adjacent columns) are firstly studied separately taking into account the lateral restraint and mass offered by the indirectly affected part (IAP) of the structure. Secondly, the dynamic behaviour of a simple compartment made of pinned members and laterally braced is investigated. The material laws are assumed to be elastic-perfectly plastic, neglecting the effect of strain rate on the yield strength. The out-of-plane instabilities of the structural members are disregarded. Two analytical models are developed to predict the dynamic response of the frame beam subjected to blast loading, including the elastic lateral restraint and inertia offered by the IAP of the structure, the development of nonlinear membrane action (P − δ effect) and also, the interaction between bending moment and axial force in the plastic hinges. The first model is based on a single degree of freedom (SDOF model) which is the transverse mid-span deflection of the beam while the second model is a two-degree-of-freedom (2-DOF) model which also includes the axial elongation of the beam. The accuracy of these two loworder models is assessed with finite element simulations. This validation stage shows that the proposed low-order models capture the physics of the problem in most cases of practical interest. Concerning the columns, an analytical model is proposed to assess its dynamic response under constant axial compressive load and lateral blast loading. It accounts for large displacement (P − δ effect), bending moment-axial force (M-N) plastic interaction as well as its interaction with the indirectly affected part (IAP) of the structure. This model is non-smooth piecewise linear and involves two degrees of freedoms (2 DOFs) in each regime of the motion of the column (related to the possibilities of development of plastic hinges). Subsequent to a parametric study, it is demonstrated that a good correlation is found between the results provided by the analytical model and a richer FEM model, despite some little discrepancies observed for some intermediate values of stiffness of the lateral restraint and lateral mass. As a possible improvement, adjustments to the analytical model are suggested. Finally, the dynamic behaviour of a simple frame under constant compressive loads and lateral blast loading is studied with a last 2-DOF analytical model. A multi-layer model of the cross-section of the beam is used to derive the bending moment-axial force (M-N) plastic interaction instead of the Lescouarc’h formula and normality rule. The coupling between the beam and the adjacent columns is ensured through appropriate boundary conditions. For the studied frame, two blast scenarios are contemplated, the first one corresponds to a quasi-static blast loading while the second one refers to a dynamic blast loading. The first