PERFORMANCE BASED DESIGN OF MR-FRAMES BY TPMC AND ENERGY APPROACH

The work herein presented is devoted to the development of a design procedure based on the combination of the Theory of Plastic Mechanism Control (TPMC) with the energy approach to satisfy both the performance requirements corresponding to different levels of the seismic intensity measure and the target plastic mechanism. To this scope, with reference to MR-Frames, the seismic design forces are directly derived by means of the energy balance equation. The earthquake input energy is evaluated according to the well-known Housner formulation. The maximum energy that the structure is able to absorb in elastic range is estimated by means of the Akiyama approach. As a result, the energy to be dissipated by means of hysteresis is obtained as the difference between the seismic input energy and the maximum stored elastic energy. The energy to be dissipated is related to the plastic collapse mechanism by means of the classical work equation by assuming an appropriate distribution of the seismic horizontal forces. The internal work is, therefore, strictly related, on one hand, to the collapse mechanism typology and, on the other hand, to the cumulated plastic rotation demand expected for a given level of the seismic intensity measure. As a result, the seismic design horizontal forces are derived as a function of the seismic intensity measure, i.e. the spectral acceleration value, and of the plastic rotation capacity. Regarding the beam dimensioning, two cases can be identified. The first case corresponds to beams whose size is governed by gravity loads. The second case corresponds to beams, parallel to the direction of the corrugation of the deck slab, whose size is governed by the seismic load combination. In this second case, the beams are preliminarily designed by assuming a distribution of their size according to the storey shear distribution and by imposing the prevention of storey mechanism at first storey. As a result, a system of two equations are derived where the unknowns are the plastic moment of beams at top storey and the plastic moment of columns at first storey. Finally, at all the other storeys, the column sections are designed by means of TPMC. The seismic performance of MR-Frames designed according to the above procedure are compared with those of frames designed according to codified rules by means of both push-over analysis and dynamic non-linear analyses.