Student: Vassilis Mpampatsikos
Supervisors: Dr Lorenza Petrini, Dr Roberto Nascimbene
ABSTRACT
In all Italian regions characterized by significant values of PGA, the assessment of the seismic response of the existing structures is a priority, since the majority of the building heritage was designed according to out-of-date or even non-seismic codes, possibly assuming values of PGA lower than those considered nowadays. The uncertainties about the nonlinear behaviour of the structures may be relevant, since the potential development and location of inelastic zone, as well as their ductility capacity, are, in general, unknown. It is, therefore, unlikely that a force-based assessment, obtained through an elastic analysis with the internal forces reduced by the behaviour factor, yields satisfactory results. The direct consequence is that the nonlinear behaviour of the structure should be faced directly, with corresponding strong increase of the complexity of the assessment process.
This issue was taken into account in this work; in particular, the assessment of R.C. frame buildings has been performed according to all the possible approaches proposed in both Italian Seismic Code [OPCM 3431] and Eurocode 8 [UNI EN 1998-3]. Both Codes consider the nonlinear methods of analysis as the normal way to evaluate the seismic demand, while they limit the use of linear analyses by strict conditions of applicability, in order to assure a uniform distribution of the nonlinearity. Concerning the assessment of the response, both Codes require a force- (strength-) based procedure for the brittle mechanisms (shear) and a displacement-based approach for the ductile ones (flexure). The evaluation of both shear and deformation (chord rotation) capacities of the structural members of a building subjected to a seismic input requires, in general, lengthy and not simple calculations.
On the base of these considerations, the aims of this work may be summarized as follows: I) checking the importance of considering, in linear analyses, the effective secant stiffness of the structural members instead of a fixed ratio of their gross stiffness. II) Checking the consistency of the results obtained applying the two Codes, in order to show if the simpler approach of the Italian Seismic Code may yield satisfactory results and testing if the two proposed formulas (empirical and theoretical) for computing the chord rotation capacity may yield results close to each other. III) Suggesting simplified approaches for the assessment procedure, concerning the evaluation of both seismic demand and capacity of the structural members. IV) Checking the importance of the definition of a bidimensional failure curve (which is not considered by the two Codes) in the assessment of the ductile mechanisms. In order to give answers to the above mentioned goals, four public R.C. frame structures, built according to out-of-date seismic codes, were examined. Considering that all buildings are irregular, characterized by different structural configurations and by a wide number of structural members, with different shapes, dimensions, lengths and reinforcement content, the conclusions valid for the four buildings were used to draw the following rules, that may be judged as general, although influenced by the considered numerical models
Concerning the assessment of the demand, the chord rotation may be simply evaluated as the drift, for the columns, and as the joint rotation, for the beams. Concerning the assessment of the ductile response: I) assuming, in linear analyses, the stiffness of the structural members equal to a ratio between 50% and 100% of their gross stiffness yields unconservative results compared to those obtained considering their actual secant stiffness at yielding. II) Both Codes yield close results when the chord rotation capacity is evaluated on the base of the empirical formula, while the Italian Seismic Code tends to underestimate the results when the theoretical formula is considered. The theoretical formula is very sensitive to the value of the shear span, while the empirical formula yields much stable results. III) The procedure based on the empirical formula can be sensibly simplified without any loss in the accuracy of the results, removing the dependency of the chord rotation capacity from the seismic demand. IV) The definition of a bidimensional failure curve may be crucial for buildings characterized by a significant torsional response and, in particular, for the dynamic linear analysis. Concerning the assessment of the brittle response: I) the Italian Seismic Code yields results which grossly underestimate those obtained through Eurocode 8 and, hence, the use of the procedure suggested in Eurocode 8 is recommended. II) Assuming, in linear analyses, the stiffness of the structural members equal to a ratio between 50% and 100% of their gross stiffness may be considered a suitable choice for simplifying the assessment. III) The procedure can be sensibly simplified without any loss in the accuracy of the results, removing the dependency of the shear capacity from the seismic demand.
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