Many buildings located in earthquake-prone regions were not designed for seismic loadings. This paper shows how the energy-balance based methodology implemented in the forthcoming second generation of Eurocode 8 can be applied to seismic upgrade this type of frames located in high seismicity regions, so that they can endure the maximum considered earthquake with moderate (economically feasible to repair) damage. The seismic upgrading strategy applied is twofold. First, the beam- or column-ends, or the beam-column joints at risk of experiencing brittle failures are bonded with Fiber Reinforced Polymers. Next, new hybrid displacement-dependent dampers with recentering capability are installed at each story of the frame to dissipate most of the energy input by the earthquake and to control the maximum and the residual interstory drifts. The satisfactory performance of the seismically upgraded structure is demonstrated through many time history analysis.