Abstract :
[en] 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. • To explain the context of this study + final aim of this research
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-\delta 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 low-order 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. A dimensional analysis of the problem reveals that, under the considered assumptions, four dimensionless parameters mainly influence the required ductility of the beam. Two of them are related to the behavior of the indirectly affected part (the lateral restraint and mass). Another one is related to the mechanical properties of the investigated beam (i.e. the ratio of the bending to axial resistance). The last parameter incorporates scales of the geometry and of the deformed configuration at the onset of the plastic mechanism.
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-\delta 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). The dimensional analysis of the problem reveals that, under the considered assumptions, four dimensionless parameters mainly influence the dynamic stability of the beam-column. Two of them are related to the behavior of the indirectly affected part (the lateral restraint and mass). Another one is related to the critical load multiplier (i.e. the ratio of the axial compressive load to Euler elastic buckling resistance). The last parameter is the reduced slenderness of the beam-column.
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 case study shows that a very good agreement is achieved between the deflections predicted by the analytical and numerical models although a discrepancy is observed in the assessment of the axial force in the column due to the shape of the inertial force distribution of the beam assumed in the model. The second case study illustrates that, in both analytical and numerical models, the columns are predicted to fail by buckling due to the P-\delta effect although the axial force in the column is again inaccurately captured by the analytical model for the same reason.
