The use of damage functionals in earthquake engineering: A comparison between different methods

Abstract

SUMMARYThe behaviour of the EPP-SDOF model under seismic actions is analysed herein by different 'damage functionals' to define collapse under cyclic loading. In particular, the damage functionals based on the concept of maximum ductility and dissipated plastic energy are first compared. Afterwards the methods of Banon and Veneziano, Park and Ang and the linear cumulative law of plastic fatigue are reviewed and extensively analysed. Comparisons in the case of simple cyclic histories and in terms of acceleration collapse spectra are carried out with reference to significant earthquake records. In particular, it is shown in which cases the damage functionals of Banon and Veneziano, Park and Ang and the linear cumulative law of plastic fatigue, completely defined by the value of a single parameter, degenerate in the limit methods of ductility or dissipated energy and in which cases they provide similar results.

Probabilistic Evaluation of Seismic Performance for a Steel Moment Frame Using Damage Indices

“…Five damage indices are selected for this study: Ductility Ratio [26,2], Modified Flexural Damage Ratio (MFDR) [12], Park and Ang [16], Krawinkler and Zohrei [15], and Final Softening [27]. Selection of these indices were based on two criteria: Firstly, they are well known amongst researchers and have been used in a numerous studies.…”

“…'Damage Indices', or in mathematical terminology, 'Damage Functionals' are functional relationships that synthetically represent the damage imposed on structure with a real number [2]. In a normalized form, output of these functions is a number between 0 and 1, which 0 represents no damage and 1 represents rupture or complete failure.…”

Bridge Seismic Retrofit Measures Considering Subduction Zone Earthquakes

“…It is recognized a direct relationship between the number of inelastic cycles and damage (Krawinkler et al 1983), (Stephens & Yao 1987). Various models have been developed to quantify this relationship (Cosenza et al 1993) (Ghobarah et al 1999); two well-known relationships describing the cumulative damage are the normalized cumulative ductility and the Coffin-Manson law for low-cycle fatigue in conjunction with the Miner's rule of linear damage accumulation. Both models show a direct relationship between structural damage and the number and amplitude of damaging cycles.…”

“…A direct relationship between the number of inelastic cycles and damage can be assumed (Krawinkler et al 1983), (Stephens and Yao 1987). Various models have been developed to quantify this relationship (Cosenza et al 1993) (Ghobarah et al 1999). In order to capture the behavior under ground motion excitations, most of current testing protocol developments and experimental studies have been conducted based on a general cumulative damage concept using the CoffinMason model and the Miner's rule of linear damage accumulation as a baseline (Krawinkler et al 1983).…”

Seismic damage estimation of in-plane regular steel moment resisting and x-braced frames

“…The most commonly used parameter of the first class is ductility, which relates damage only to the maximum deformation and is still regarded as a critical design parameter by codes. To account for the effects of cyclic loading, simple rules of stiffness and strength degradation have been included in various noncumulative indices [4,5,6], mainly referred to reinforced concrete members. Cumulative-type indices can be divided in deformation based [7] or hysteresis based [8,9] formulations and methods that consider the effective distribution of inelastic cycles and generalize the linear law of low-cycle fatigue of metals through a hypothesis of linear damage accumulation [10].…”