A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

Abstract

SUMMARYThe seismic response of elasto-plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto-plastic structure can be computed as the mean of the responses to a certain number of spectrum-ÿtting generated accelerograms. A more e ective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predeÿned non-exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto-plastic structural system and the results are compared with those obtained applying current code recommendations.

Probabilistic estimate of seismic response design values of RC frames

“…In [5] it has been already verified that the proposed method does not depend on the spectral shape (subsoil class) assumed for the accelerograms generation. Herein the EC8 [4] spectrum for subsoil class B-medium stiff soil (average shear wave velocity Vs = 360−800 m/s) is assumed as target elastic response spectrum in the accelerogram generation.…”

“…The comparison of Figures 11 and 12 shows that the differences among the scattering of the global and the local response parameters are not significant. The actual response distribution of both the global and local response parameters can be modeled with a lognormal distribution [2,5,12,13], as confirmed by the performed 2 tests, whose results are not reported here for the sake of brevity. The obtained results allow to apply to the MDOF systems the probabilistic method proposed in [5,12] using the amplification coefficients obtained from the analysis of the ESH SDOF systems.…”

“…The actual response distribution of both the global and local response parameters can be modeled with a lognormal distribution [2,5,12,13], as confirmed by the performed 2 tests, whose results are not reported here for the sake of brevity. The obtained results allow to apply to the MDOF systems the probabilistic method proposed in [5,12] using the amplification coefficients obtained from the analysis of the ESH SDOF systems. To compare the results obtained with the proposed method with those deriving from the application of EC8 [4] provisions, modified estimators Z = ·Y of the considered global and local response parameters are also calculated assuming the minimum number of accelerograms, that is three.…”

“…A safe design value of the response should be characterized by a significantly large probability of not being exceeded by any response. As already shown in [5], predefined non-exceedance probability levels can be ensured only if amplified values of the estimates, Z = ·Y , are used. Obviously, also the PDF of the Z 's population is Lognormal.…”

“…The non-exceedance probability, W ( ), of the defined design value is calculated as reported in [5]. W versus T curves for assigned values of have been determined for all the possible parameters combinations.…”