# Seismic Upgrade of Steel Frame Buildings by Using Damped Braces
## 7 Conclusions  
The study investigated the viability of a displacement-based design procedure, originally conceived for the RC structures, for dimensioning the hysteretic dampers for the seismic rehabilitation of steel frame buildings. The procedure is applicable to low- and mid-rise buildings with regular distribution of masses and stiffnesses in plan and in elevation, for which the dynamic response is essentially governed by the first mode. Three case-study moment-resisting frames of two, four and eight stories, unable to meet the seismic performance requirements according to the current codes, have been investigated and the seismic retrofit has been designed examining two damper solutions, characterized by high and low ductility values (10 and 4, respectively). Eventually, the effectiveness of the design was verified by means of the NLSAs and NLDs. The main results of the study are summarized as follows. 1. The proposed procedure proved to be a viable means for proportioning the damped braces of the low- and mid-rise steel frames in order to achieve a target performance defined in terms of the maximum lateral displacement of the frame. 2. The design of an effective dissipation brace system for a steel frame must take into account also the ensuing increase in the internal forces of the structural members of the bays where the braces are introduced. For mid-rise buildings, an issue is represented by the increase in axial force and possible buckling of the columns for the seismic loads. For these buildings, it is recommended to explore different layouts for the brace system, especially at the lower stories. 3. In this study, two ductility factors, representing the upper and lower bounds for the conventional hysteretic dampers, were examined. For low-rise buildings, the performance of the upgraded structure was scarcely affected by the characteristic of  
Figure 16: (**a**) new plan layout of damped braces in the eight-story MRF; (**b**) buckling checks in column P3 of the retrofitted frame. the dampers, while for the mid-rise frame a non-negligible influence of the ductility factor of the damper system was highlighted from the NLDAs. 4. The analyses showed that the design procedure is conservative, and that the structural displacement calculated via the NLDAs is significantly smaller than the design target; this difference tends to increase as the ductility of the dampers increases. 5. Even though more cases need to be examined to validate these outcomes, the study provides some guidance to professionals who have to tackle with the seismic upgrading of steel frames with damped brace systems, by illustrating a handy procedure for the design and dimensioning of the damper layout and giving some practical suggestions for the assessment of the overall structural response. There are still some limitations in this study. Firstly, the procedure was applied to three archetypes of steel moment-resisting frames with an obvious non-symmetric distribution of strength and stiffness in the two main horizontal directions due to an unusual arrangement of column sections. Second, all the beam-to-column connections of the frame are moment resisting, which is a bit of an unusual approach according to the European practice. Finally, the procedure considers only structures that are regular in plan and in elevation. The future research will focus on the application to real low-rise and mid-rise steel structures, as well as will explore the extension of the procedure to in-elevation irregular frames and unsymmetric-plan arrangements. Conceptualization, E.B. and V.Q. ; methodology, E.B. and V.Q. ; software, E.B. and L.Z. ; supervision, V.Q. ; validation, V.Q. ; writing--original draft, E.B. ; writing--review and editing, V.Q. All authors have read and agreed to the published version of the manuscript. This work was funded by the Italian Department of Civil Protection (DPC) in the frame of the national Research Project DPC-ReLUIS 2022-2024, Work Package WP 15 \"Contributi normativi a isolamento e dissipazione\".