A simplified method developed for the analysis of the mechanical behavior of a building is presented. This method is based on modal analysis of the structure. It relies on a mathematical expansion of the dynamical equations of the movement on the eigenshapes of the structure. The time-space loading is defined by empiric formulae which take into account the weight of equivalent TNT, the distance between the explosive and the structure, and allows to describe the propagation of the shock wave on the structure. Three typical loadings are investigated: long distance explosions (blast loading), medium and near distance explosions. The results concerning the movement of the structure given by the simplified method will be compared to those obtained by a direct time integration method. Particularly, the convergence of the simplified method towards the direct time integration method will be investigated in terms of displacements and stresses versus the explosive-structure distance. This method allows to identify the eigenshapes and eigenvalues of the structure which are important to be taken into account to predict the dynamical response of the building. This method is used as a pre-study (elastic mechanics) i.e. as a first step of a detailed dynamical analysis.

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