Inverse mass matrix via the method of localized lagrange multipliers

An efficient method for generating the mass matrix inverse is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces, and constructs the free-free inverse mass matrix employing the standard FEM procedure. The various boundary conditions are realized by the method of localized Lagrange multipliers. Numerical experiments with the proposed inverse mass matrix method are carried out to validate the effectiveness proposed technique when applied to vibration analysis of bars and beams. A perfect agreement is found between the exact inverse of the mass matrix and its direct inverse computed through biorthogonal basis functions

Soil-structure interaction in the seismic vulnerability analysis of RC buildings. Application to a case study building located in southwestern Spain

Most seismic vulnerability analyses do not consider the Soil-Structure Interaction (SSI). However, it has been proved that SSI does not equally affect all types of structures and all types of soils. The analysis of the state of the art reveals that SSI especially affects the performance of mid/high-rise buildings under soft/inelastic soil conditions. This leads to overestimating the capacity of buildings and to obtaining unreliable results. This paper aims to assess the soil influence in the seismic vulnerability analysis of a reinforced concrete (RC) building. Three models of a real case study building have been determined (low-rise (real), mid-rise and high-rise). A pre-code 1970s case study building, located in Huelva, has been selected. This building shares typical constructive and structural characteristics with most RC buildings constructed during that period. The 3D continuum model of the soil has been carried out to simulate its nonlinear behaviour. The most probable soil profile has been defined, observing a clayey soil. Therefore, the analyses have been performed under undrained conditions. Nonlinear static analyses have been carried out to determine the seismic capacity of the models through the finite element method (FEM). The damage has been assessed by means of the local procedure, defined in the European seismic code, and the global fragility procedure. The results have shown that the soil does not significantly influence the behaviour of low-rise buildings. However, in the case of mid- and high-rise buildings, the maximum capacity can be reduced by up to 10% and 30%, respectively

A cost-effective retrofitting technique for URM buildings based on steel encirclements in openings: A case study

A project named PERSISTAH is being developed to study the seismic vulnerability of primary schools in Huelva (Spain) and the Algarve (Portugal). This area has a moderate seismicity but this is affected by a nearby area where earthquakes of large magnitude (Mw≥6) and longreturn periods happen. The seismic vulnerability of URM (UnReinforced Masonry) buildings has been observed and analysed in the last decades. The seismic retrofitting of these buildings is required in order to improve their seismic behaviour. Many retrofitting techniques have been developed for that purpose, most of them very complicated and expensive. Therefore, these are not appropriate to retrofit a large number of buildings. This is especially relevant in areas of moderate seismicity where the cost-efficiency ratio must be carefully considered. The aim of this paper has been to develop a simple, effective and affordable technique to retrofit these buildings. These buildings are characterised by numerous openings which causes a great weakness in the URM walls. Then, a technique that consists in installing a steel encirclement or a grille in the openings of the walls has been proposed. This is a specific retrofitting technique for URM walls since this technique substantially improves the seismic capacity of these structures. To test the technique a case study is proposed. The building under study is a primary school located in Huelva and built in 1961. Results have shown that the capacity of the building is notably increased. Also, the performance point and the damage level of the structure are decreased