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

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.