# Seismic Upgrade of Steel Frame Buildings by Using Damped Braces
## 1 Introduction  
A major issue in seismically prone countries is the vulnerability of the building heritage to earthquakes. Considering the European scenario, the largest part of the building stock, built before the 1980s of the last century, was designed according to outdated codes to withstand gravitational loads only [1]. Italy, Greece and Romania are the European countries with the highest seismic risk and reinforced concrete (RC) frame structures are among the most recurrent typologies in these regions [1]. For this reason, seismic upgrading of RC buildings has emerged as a main research area [2; 3; 4; 5], and in recent years a number of technologies and design procedures have been investigated for the retrofit of RC structures, including the use of supplementary energy dissipation systems [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. However, also steel structures designed before the publication of modern regulations (e.g., AISC 341-16 [17], ASCE 7-16 [18], EN 1993-1-1 [19], EN 1998-1 [20]) have been reported to suffer local and global collapses as a consequence of earthquakes [21; 22; 23; 24; 25; 26; 27]. Braces equipped with energy dissipation devices have proved to be effective in reducing the seismic demand for both RC [6; 7; 8; 9; 10; 11; 12; 15] and steel structures [26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39], and the most updated codes (e.g., [17; 18; 20]) have incorporated general guidelines for the design of dissipative braces in new constructions, with the goals of limiting the lateral displacement and dissipating most of the seismic energy in auxiliary devices, avoiding any damage to the gravity-load resistant system [33; 39; 40; 41; 42]. Most of the procedures proposed in the literature [6; 7; 8; 9; 10; 11; 39; 43; 44; 45] for dimensioning dissipative braces are based on the Direct Displacement-Based Design (DDBD) method [45], in which a \"substitute\" single degree of freedom (SDOF) model is used to replace the real multi-degree of freedom (MDOF) structure. The design of the dissipating system is performed to achieve, for a given seismic intensity level, a specified performance objective, expressed for example as a specific target displacement [11]. An extensive review of the most significant procedures developed for RC frames can be found in reference [11]. [PERSON] and [PERSON] [46] proposed a DDBD procedure for steel frames with non-moment-resisting joints supplemented with buckling-restrained braces (BRBs). The procedure neglects the column deformability and consequently it is applicable to low-rise buildings only. [PERSON] et al. [39] presented a simplified procedure for steel frames with pinned beam-to-column connections and dissipative braces equipped with either steel hysteretic devices or viscoelastic dampers. The procedure, which accounts for the deformability of both the braces and columns, is based on the formulation of a continuous cantilever model equivalent to the discrete bracing system and provides analytical expressions to distribute the flexural and shear stiffness of the diagonal braces and columns at each floor. In order to have a single parameter in the design procedure, only the first vibration mode of the equivalent continuous cantilever system is considered. While the above procedures deal with the design of new constructions, other researches focused on the retrofitting of steel moment-resisting frames (MRFs) [28; 43; 44] according to old regulations which have been found in need of seismic performance upgrade. Some authors of this paper recently proposed a DDBD retrofit procedure [11; 12; 47; 48], aimed at upgrading RC structures, regular in plan and in elevation, by means of dissipative braces. The procedure uses a recursive algorithm based on the Capacity Spectrum Method [49; 50] to calculate the properties of the damped brace system, described by means of an equivalent SDOF system.