“روش مستقیم پنج مرحله ای” برای طراحی لرزه ای اولیه ساختمان ها با میراگرهای ویسکوز اضافه شده A “direct five-step procedure” for the preliminary seismic design of buildings with added viscous dampers

1. Introduction For many years, since the early developments of modern earthquake engineering in the ‘60s, the seismic analysis and design of buildings have been carried out using methods essentially based on the concept of equivalent lateral forces. Nowadays, much more sophisticated analysis tools, such as nonlinear dynamic analyses, are available also in commercial software, and often professional engineers analyze and design building structures making use of such numerical tools. Nonetheless, actual seismic codes still admit the use of equivalent static analysis for the design of relatively regular and simple structures [10,22]. Furthermore, equivalent static analyses are particularly useful for preliminary design, since they permit a fast evaluation of the magnitude of the internal actions in the structural members and their pre-sizing necessary for the development of finite element models and for the computation of the detailed structural response with non-linear dynamic analyses. The use of dynamic analyses for major structures was first introduced in 1974 by the SEAOC Code [33] which recommended its use for “structures with highly irregular shapes, large differences in lateral resistance or stiffness between adjacent storeys” [15]. Later on, with the rapid development of computer programs, the use of dynamic analyses has been established as standard practice for the seismic design of building structures. As such, when in the ‘80s novel technologies for the seismic protection of buildings, such as seismic isolation and dissipative devices, were first adopted in the practice, the use of computer based simulations for the design of structures incorporating such new technologies appeared an obvious choice. Fundamental research works devoted to the development and evaluation of procedures for analysis and design of buildings with passive energy dissipation systems were carried out from the 1990s at the University at Buffalo [13,14,30,30,44]. The works are summarized in MCEER-00-0010 report [32] and ASCE 7-16, Chapter 18 [2] procedures, which are nowadays used in USA by professional engineers. Later on, most of the research works on viscous dampers [36–38,34,21,36,20] basically proposed sophisticated numerical algorithms for dampers optimization (i.e. dampers size and location), sometimes leading to complex design procedures. Alternative approaches leading to design procedures for the sizing of viscous dampers have been proposed in the last years: (i) LopezGarcia in 2001 [21] developed a simple algorithm for optimal damper configuration (placement and properties) in MDOF structures, assuming a constant inter-storey height and a straight-line first modal shape; (ii) Christopoulos and Filiatrault in 2006 [12] suggested a design approach for estimating the damping coefficients of added viscous dampers consisting in a trial and error procedure; (iii) Silvestri et al. in 2010 [35] proposed a direct design approach, referred to as the “five-step procedure”. In the present work, a simplified procedure for the sizing of viscous dampers and structural elements of framed structures equipped with inter-storey viscous dampers is presented. The procedure is grounded on some previous works by the authors [40,40,23,24,26] since it collects and exploits all fundamental results in the framework of the original “five-step procedure” [35]. The procedure, originally developed for elastic frames equipped with viscous dampers, is extended to the case of yielding structures making use of an overall reduction factor [23].