# Seismic Design of Steel Moment-Resisting Frames with Damping Systems in Accordance with KBC 2016
## 1 Introduction  
There were no seismic design provisions for the application of damping systems in the Korean Building Code (KBC) 2009, therefore, Korean engineers encountered many difficulties in the practical application of damping devices [1]. The KBC was revised in 2016 with the addition of design criteria for structures with damping systems [2]. The design provisions for structures with damping systems in KBC 2016 adopted only nonlinear response history procedure. In the case of ASCE 7, both equivalent lateral force procedure and response spectrum procedure are allowed. However, the use of those two procedures is restricted for strict conditions and nonlinear response history procedure is adopted major design procedure in ASCE 7-16 [3].  
In spite of being adopted as a major design procedure, nonlinear response history analysis procedure requires much more computational efforts compared to linear analysis. It is difficult to design damping devices by trial and error using nonlinear response history analysis. Therefore, many design procedures adopt equivalent linearization technique to take into account the nonlinear characteristics of either damping device or building structure [4; 5; 6; 7; 8; 9; 10]. Some design procedures adopt nonlinear static analysis to take into account the inelastic behavior of the structure more directly [11; 12], which utilizes the equivalent linearization technique to determine the performance point. Many equivalent linearization techniques for different nonlinear damping devices have been proposed [13; 14; 15]. Most of them utilize damping correction factors, which represent response reduction for a specified amount of damping ratio developed for linear or nonlinear systems [13; 14; 16; 17]. However, those design procedures based on equivalent linearization technique have limitations inthat they assume deformed shape based on elastic analysis and are difficult to identify localized nonlinear behavior of a structure, such as weak story mechanism and force or deformation demands on structural components and damping devices with sufficient accuracy for detailed design. Besides, proposed optimization procedures have been developed. Some of those procedures adopt stochastic analysis [18; 19] or linear response history analysis [20]. The others make use of nonlinear response history for evaluation of objective function or boundary conditions [21; 22; 23]. However, the latter methodologies repeat nonlinear response history analysis for every iterative step during optimization and, as a result, are computationally demanding in the case of actual building structures with many degrees of freedom  
This study is to propose and validate an efficient and systematic design procedure for inelastic multi-degree-of-freedom (MDOF) structures with damping systems complying with KBC 2016, which requires nonlinear response history analysis but does not provide methodology for detailed design. Two design examples for steel moment frames using nonlinear response history analysis are presented. The proposed design procedure makes use of nonlinear response history analysis of an MDOF structure directly to determine design parameters of damping devices and captures complex inelastic behavior of building structures more realistically. Differently from the existing optimization procedure, the design procedure performs only a small number of nonlinear response history analyses, which is usually three to five times. As a result, the proposed design procedure requires only a small amount of computational efforts compared to the existing optimization-based design procedures that perform nonlinear response history analysis repeatedly until convergence. The proposed design procedure can be implemented using commercial structural analysis software and can be applied to design code except for KBC 2016.