The MDOF equivalent linear system and its applications in seismic analysis and design of framed structures

Abstract

This paper reviews the applications of the multi degree-of-freedom (MDOF) equivalent linear system in seismic analysis and design of planar steel and reinforced concrete framed structures. An equivalent MDOF linear structure, analogous to the original MDOF nonlinear structure, is constructed, which has the same mass and elastic stiffness as the original structure and modal damping ratios that account for the effects of geometrical and material nonlinearities. The equivalence implies a balance between the viscous damping work of the equivalent linear structure and that of the nonlinearities in the original nonlinear structure. This work balance is established with the aid of a transfer function in the frequency domain. Thus, equivalent modal damping ratios can be explicitly determined in terms of the period and deformation levels of the structure as well as the soil types. Use of these equivalent modal damping ratios can help address a variety of seismic analysis and design problems associated with planar steel and reinforced concrete framed structures in a rational and accurate manner. These include force - based seismic design with the aid of acceleration response spectra characterized by high amounts of damping, improved direct displacement-based seismic design and the development of advanced seismic intensity measures. The equivalent modal damping ratios are also utilized in the context of linear modal analysis for the definition and construction of the MDOF response spectrum. Furthermore, the equivalent modal damping ratios are employed in a seismic retrofit method for steel-framed structures with viscous dampers. Finally, it is demonstrated that modal behavior (or strength reduction) factors can be easily constructed based on these modal damping ratios for a more rational and accurate force-based seismic design, including the determination of inelastic displacement profiles.

Keywords

Seismic analysis / Seismic design / Steel-framed structures / Reinforced concrete-framed structures / MDOF equivalent linear system / Modal damping ratios / Modal strength reduction factors / Seismic intensity measures / MDOF response spectrum

CRediT authorship contribution statement

E.V. Muho: Writing - review & editing, Writing - original draft, Supervision, Software, Investigation, Formal analysis, Data curation. N.A. Kalapodis: Validation, Software, Investigation, Formal analysis, Data curation. G.A. Papagiannopoulos: Writing - review & editing, Writing - original draft, Supervision, Investigation. D.E. Beskos: Writing - review & editing, Writing - original draft, Supervision, Methodology, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Relevance to Resilience

The present work contributes to enhancing the resilience of building structures by providing advanced methods for the seismic analysis and design of framed structures. By developing an equivalent multi degree-of-freedom (MDOF) linear system that captures the mass, elastic stiffness, and modal damping ratios of the original nonlinear structure, this study offers a sophisticated approach to maintaining structural integrity under seismic events. The methods presented here allow for a detailed understanding of the behavior of steel and reinforced concrete frames during earthquakes, facilitating more accurate seismic designs that reduce the risk of catastrophic failures. The application of these findings in force-based seismic design, direct displacement-based methods, and retrofit strategies enhances the ability of buildings to withstand strong earthquakes, thus significantly contributing to the safety and resilience of building structures in earthquake-prone areas.

Funding Statement

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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