Improving the static pushover analysis in the Italian Seismic Code by proper piecewise-linear fitting of capacity curves

Flavia De Luca¹, Dimitrios Vamvatsikos², Iunio Iervolino¹

¹Università degli Studi di Napoli Federico II

Via Claudio, 21, 80125 Napoli

flavia.deluca@unina.it, iunio.iervolino@unina.it

² National Technical University of Athens

9 Heroon Polytechneiou, 15780 Athens, Greece

divamva@central.ntua.gr

KEYWORDS: piecewise linear fit, Italian Seismic Code, oscillator, static pushover, incremental dynamic analysis

TOPIC - D - Criteri e Metodi di Progetto ed Analisi Strutturale

ABSTRACT

An improvement of the Italian Code bilinear fit for static pushover (SPO) curves is put forward aimed at significantly decreasing the error introduced in the conventional SPO analysis by the piecewise linear fitting of the capacity curve. While other issues, such as the MDOF - SDOF relationship, have been heavily examined in the last decades and improvements and changes to the original method [Fajfar, Fishinger,1988] have been proposed and introduced in codes and guidelines, the piecewise linear fit assumed has not been systematically investigated. The determination of an optimal multilinear fit has now become a more pressing issue, since new generation modeling approaches lead to highly curved pushover shapes with significant stiffness changes, especially when explicitly incorporating the initial uncracked stiffness of sections. In such cases, even determining the code-standard equivalent elastic stiffness and yield strength of the simple elastoplastic approximation can be greatly improved upon.

In the approach proposed herein, the error introduced by the piecewise multilinear fit of the force-deformation relationship is quantified by studying it at the single-degree-of-freedom (SDOF) level, away from any interference from multi-degree-of-freedom effects. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual curved backbones versus their piecewise linear approximations in terms of the spectral acceleration capacity for a continuum of limit-states, allowing an accurate interpretation of the results in terms of performance. An optimized elastoplastic bilinear fit is the first enhanced solution to decrease systematically the error introduced in the SPO analysis; moreover this fit employs the same R-m-T (strength reduction factor-ductility-period) relationship already prescribed by the Italian Code. A major further enhancement is the use of an optimized trilinear fit with an elastic, a positive and a negative stiffness segment; at the expense of requiring novel R-m-T relationships, such as SPO2IDA [Vamvatsikos and Cornell, 2005] or FEMA-440 [FEMA 2007], this step has far reaching implications by finally allowing a simple estimation of the global collapse capacity.

References

Fajfar P., Fischinger M., N2 - a method for nonlinear seismic analysis of regular buildings, Proceedings of Ninth World Conference on Earthquake Engineering, August 2-9, 1988, Tokyo - Kyoto, Japan.

Vamvatsikos D., Cornell A.C., Direct Estimation of Seismic Demand and Capacity of Multidegree-of-Freedom Systems through Incremental Dynamic Analysis of Single Degree of Freedom Approximation. Journal of Structural Engineering, 131(4): 589-599, 2005.

Federal Emergency Management Agency (FEMA) Improvement of nonlinear static seismic analysis procedures. Rep. No.FEMA-440, Washington, D.C, 2005.