## 4 Global Strengthening Requirements
For T\({}_{\text{eff}}\) = 0.54 s, the elastic spectral displacement demand is estimated from Equation (8) for T\({}_{\text{C}}\)\(\leq\) T \(\leq\) T\({}_{\text{D}}\) (from [35]):  
\[S_{\text{d}}\left(\text{T}\right)=a_{\text{g}}\,S_{\text{H}}\beta_{\text{o}} \left(T_{\text{C}}\text{T}\right)/40 \tag{8}\]  
where S = 1.2 (soil class B), T\({}_{\text{C}}\) = 0.5 s, T\({}_{\text{D}}\) = 2 s, \(a_{\text{g}}\) = 0.24 g, \(\eta\) = 1 (\(\xi\) = 5%) and \(\beta_{\text{o}}\) = 2.5, hence S\({}_{\text{d}}\) = 0.048 m. The elastic displacement S\({}_{\text{d}}\) will induce a lateral drift in the piltois \(\theta\) = S\({}_{\text{d}}\)/H = 0.048/2.7 \(\approx\) 1.8% which corresponds to drift or displacement ductility demand of \(\mu_{\text{o}}\) = \(\mu_{\Delta}\) = 1.8/0.64 = 2.8. According to Table 1, and after the implementation of only local measures to alleviate the brittle shear failure, the drift supply by considering the most conservative procedure a is lower than the demand for all columns. The reduction in the drift demand along with the improvement of the deflection shape of the piltois-type building requires the increase in piltois stiffness (i.e., adoption global intervention measures) before any application of FRP jacketing (local measures). The selection of a shear-type drift distribution along the building's height (Figure 5b) reduces the required intervention because a soft storey formation may be re-engineered towards this option for moderate improvement. By using the charts of Figure 4b,c result in the following target values for the storey stiffness ratios K\({}_{\text{i}}\)/K\({}_{\text{i}}\): K\({}_{2}\)/K\({}_{1}\) = 1.1 and  
Figure 5: (**a**) Stiffness distribution of the enhanced building and (**b**) its lateral displacement profile after performing Rayleigh iterative method. (**c**) Compressive strain ductility \(\mu_{cc}\) versus stirrup spacing s/D\({}_{\text{b}}\) for StIV. \(\rm K_{3}/K_{1}=1.6\) (see the dashed lines in Figure 4b, \(\rm K_{1}\) stands for the ground floor or first floor). For the chosen target period \(\rm T_{trg}=0.45\) s and by using Figure 4c, the required ground storey stiffness is \(\rm K_{1}/m_{1}=950\) kN/m, which once multiplied with storey mass \(\rm m_{1}=96.6\) tn results in \(\rm K_{1}=91,770\) kN/m, also, \(\rm K_{2}=1.1\)\(\times\) 91,770 \(\approx\) 100,950 kN/m and \(\rm K_{3}=1.6\)\(\times\) 91,770 \(\approx\) 146,830 kN/m for the 2 nd and 3 rd floor, respectively. The target stiffness value of the ground storey, \(\rm K_{1}=91,770\) kN/m, is much larger than the available \(\rm K_{eff}=38,690\) kN/m. Such a stiffness increase in ground storey may be achieved partly by the need to increase the central column cross section due to slenderness effect and by adding metallic cross bracings in the direction of the seismic action under consideration (here the direction is y-y). The central column of increased cross section (350 \(\times\) 450 mm) is assumed as being pinned at the base with elastic stiffness \(\rm K_{C5,new}=3 EI/H^{3}=11,748\) kN/m (the initial value was 3810 kN/m). The required cross braces stiffness is deduced as: \(\rm\Sigma K_{X}=K_{1}-K_{C5,new}-4\) corner columns \(\times\) 3810 kN/m \(-\) 4 peripheral columns \(\times\) 4910 kN/m \(\approx\) 45,140 kN/m. The span of each brace is \(\rm L=5\) m \(-\) 1.5 \(\times\) 0.35 m = 4.475 m and \(\rm\phi=arctanh(h_{std,L}/L)=0.6\) thus \(\rm\phi=31^{\circ}\) (\(\rm h_{std,L}\)=2.7 m). The length of the brace diagonals is \(\rm D=\sqrt{(4475^{2}+2700^{2})}=5226\) mm. The stiffness of braces is (modulus of elasticity for cast steel sections, \(\rm E_{g}=150,000\) MPa): \(\rm\Sigma K_{X}=45,140\) kN/m =2\(\rm E_{s}A_{br}/Dcos^{2}\phi=2\)\(\times\) 150,000 \(\rm A_{br}\)\(\rm\Sigma 5226\)\(\times\)\(\rm cos^{2}(31^{\circ})\) thus \(\rm A_{br}\approx 1100\) mm\({}^{2}\). By adding two boxes symmetrically (i.e., by connecting columns C1-C4 and C6-C9), then each brace should have total cross section \(\rm A_{br}=650\) mm\({}^{2}\).