## 4 Global Strengthening Requirements  
The strengthening of the existing building should consider whether the available effective stiffness, \(\rm K_{\rm eff}\), suffices to resist the seismic demand or if there is need to moderate, i.e., the drift demand. In the latter case, the retrofit solution should include global intervention measures to increase \(\rm K_{\rm eff}\) along with local interventions like FRP jacketing for alleviating brittle modes of failure (Figure 4a). Note that by increasing \(\rm K_{\rm eff}\) the demand may be reduced in two different ways: (a) a higher effective stiffness results in a lower predominant period tending towards the left in the displacement spectrum, and (b) through a more uniform distribution of deformation demand in the structure, which secures that the magnitude of deformation demanded by individual members is lowered. The necessary calculations for global measures are based on Appendix 8.2 of [4]. More specifically, the total building mass is M = 290 tonnes. The effective translational period \(\rm T_{\rm eff}\) is calculated based on the secant to yield sectional analysis for the definition of individual  
Figure 4: (**a**) Flowchart on the decision of implementing local and/or global interventions. For shear deflection shape (**b**) Storey stiffness ratios \(\rm k_{i}\) (\(=\rm K_{i}/K_{1}\)) and (**c**) corresponding stiffness to mass ratio for the first storey, \(\rm K_{1}/m_{1}\), versus period (note to obtain required \(\rm K_{1}\) values multiply the ordinate by the mass m, in tons). column translational stiffness K. By assuming that the building has a soft first storey (i.e., piltois-type), then practically all lateral translation is concentrated in the ground storey (K\({}_{\text{eff}}\) = \(\sum_{i=1}\)nK\({}_{\text{i}}\)\(\Delta\Phi_{1}^{\text{\,2}}\) = K\({}_{1}\)\(\times\) 1\({}^{2}\) = K\({}_{1}\)). Thus, the translational stiffness against seismic sway of the ground storey is (direction y-y): K\({}_{\text{eff}}\)\(\approx\) 38,690 kN/m. Note that column's C5 stiffness was taken conservatively as the least among the other two groups. Its reinforcement does not reach yielding due to the applied high axial load. Therefore, the effective period is T\({}_{\text{eff}}\) = 2\(\pi\)\(\surd\)(M/K\({}_{\text{eff}}\)) = 2 \(\times\) 3.14 \(\times\) \(\surd\)(290/38,690) = 0.54 s. The empirical reference value T\({}_{\text{ref}}\) in EN 1998-1 [35] is T\({}_{\text{ref}}\) = 0.075 H\({}_{\text{tot}}\)3\({}^{\text{\,4}}\) = 0.075 \(\times\) 93\({}^{\text{\,4}}\) = 0.39 s. Because T\({}_{\text{eff}}\)/T\({}_{\text{ref}}\) =0.54/0.39 = 1.4, T\({}_{\text{eff}}\) exceeds by more than 25% the empirical T\({}_{\text{ref}}\). Thus, K\({}_{\text{eff}}\) should be increased to lower T\({}_{\text{eff}}\) to an acceptable range of values, i.e., 0.4-0.45 s for a three-storey building. The target or improved period, T\({}_{\text{trg}}\), of the retrofitted structure may be selected based on experience, as a value between T\({}_{\text{ref}}\) and the initial T\({}_{\text{eff}}\). A note of caution is that the cost of the intervention increases as T\({}_{\text{trg}}\) is reduced getting closer to T\({}_{\text{ref}}\). Besides, an increase in K\({}_{\text{eff}}\) is required aiming at modifying the lateral deflection shape (fundamental response shape) due to localization of deformation at the ground floor columns (i.e., the assumed in Figure 5b). For the seismic assessment of the building, the peak ground acceleration was considered PGA = 0.24 g and the soil class as B.