## 5 Local Strengthening through FRP Jacketing
The difference \(\Delta\)V = 1.5 \(\mathrm{V_{fl}}\) - \(\mathrm{V_{Rd,0}}\) = 68 kN will be resisted by FRP closed-type jacketing as \(\Delta\)V = \(\mathrm{V_{Rd,f}}\) = (2\(\mathrm{f_{f}}\)/b) \(\times\) bh \(\times\) EF \(\mathrm{\varepsilon_{fu,h}}\), which it results to \(\mathrm{t_{f}}\) = 0.07 mm \(<\) t\({}_{0}\) = 0.12 mm. A single layer suffices for shear strengthening along the column's height. For the lap-splices, even if the available bond strength \(\mathrm{\tau_{b}}\) = 2.82 MPa [from Equation (7)] due to cover and stirrups contributions suffices for bar yielding [\(\mathrm{\tau_{b}}\) = 2.82 MPa \(>\)\(\mathrm{\tau_{cd}}\)D\(\mathrm{\tau_{fsy}}\)/(4l\({}_{\mathrm{o}}\)) = 2.3 MPa], however it is reduced after that milestone because cover is cracked [term 2\(\mathrm{\varepsilon_{ctck}}\) in Equation (7) is set equal to 0]. The contribution of FRP jacketing in restoring the bond strength to the yielding limit is given by Equation (10):  
\[\mathrm{\tau_{b}}=2\mathrm{\mu_{fr}}/(\mathrm{\tau D_{b}})[0.33A_{\mathrm{st}} \mathrm{f_{y,st}}/(\mathrm{N_{b}},\mathrm{s})+2\mathrm{t_{f}}\,\mathrm{E_{f}} \mathrm{\varepsilon_{f,sl}})/\mathrm{N_{b}}] \tag{10}\]  
thus, for D\(\mathrm{b}\) = 14 mm, \(\mathrm{\mu_{fr}}\) = 1, \(\mathrm{N_{b}}\) = 3, \(\mathrm{\varepsilon_{f,sl}}\) = 0.0015, \(\mathrm{t_{f}}\) = \(\mathrm{nt_{o}}\), \(\mathrm{A_{st}}\) = 2 \(\times\)\(\mathrm{\pi}  
the buckling curve of Figure 5c (case StIV-f\({}_{y}\) = 500 MPa and sideway buckling) and for \(\rm{s}/\rm{D}_{b}\) =150/14 \(\approx\) 11, the strain at which the bar will become unstable is \(\mu_{\rm{c}c}\)\(\approx\) 2 = \(\epsilon_{\rm{s,crit}}/\epsilon_{\rm{s,y}}\) thus \(\epsilon_{\rm{s,crit}}\) = 2 \(\times\) 0.0025 = 0.005. Hence, for the estimation of the required jacket confinement, it must be ensured that \(\epsilon_{\rm{cu,c}}\)\(\geq\) max(\(\epsilon_{\rm{cu,c}}\) = 0.0035, \(\epsilon_{\rm{s,crit}}\) = 0.005) = 0.005. Equation (11a-c) correlate term \(\epsilon_{\rm{cu,c}}\) with the FRP jacketing:  
\[\epsilon_{\rm{cu,c}}=\epsilon_{\rm{cu}}+0.075[\zeta\times(\alpha_{\rm{f}}\, \rho_{\rm{fv}}\rm{E}_{\rm{f}}\,\epsilon_{\rm{fu,h}}+\alpha_{\rm{w}}\rho_{\rm{sv }}\rm{f}_{\rm{yst}})/\rm{f}_{c}-0.1]\geq\epsilon_{\rm{cu}} \tag{11a}\] \[\alpha_{\rm{f}}\approx 1-((\rm{b}-2\rm{R})^{2}+(\rm{h}-2\rm{R})^{2})/ (3 bh)\] (11b) \[\rho_{\rm{fv}}=2\rm{t}_{\rm{f}}(\rm{h}+\rm{b})/(hb) \tag{11c}\]  
with \(\epsilon_{\rm{cu}}\) = 0.0035, \(\zeta\) = 1 (for \(\epsilon_{\rm{cu,c}}\) \(\leq\) 0.01), \(\alpha_{\rm{f}}\) = 0.56, \(\alpha_{\rm{w}}\) = 0.15, \(\rho_{\rm{sv}}\) = 0.00314 and \(\epsilon_{\rm{fu,h}}\) = 0.0085 (as previously calculated); thus Equation (11a) results to \(\rho_{\rm{fv}}\) = 0.0023 and \(\rho_{\rm{fv}}\) = 2\(\rm{t}_{\rm{f}}\) (\(\rm{b}+\rm{h}\))/(bh), which in turn corresponds to n = 2 layers along the critical regions of all columns, top and bottom, of length l\({}_{\rm{pl}}\) = 615 mm (for simplicity of the intervention this length is rounded to 600 mm). Given the above calculations for elimination of premature buckling and splice failure, the applied jacketing (2 layers result to t\({}_{\rm{f}}\) = 0.24 mm and thus to \(\rho_{\rm{fv}}\) = 0.0033) offers a limited displacement ductility. This is testified through Equation (12):  
\[\mu_{\rm{A}}=1.3+12.4\times(0.5\times\alpha_{\rm{f}}\rho_{\rm{fv}}\rm{E}_{ \rm{f}}\epsilon_{\rm{fu,h}}/\rm{f}_{c}-0.1)\geq 1.3 \tag{12}\]  
Its implementation results to \(\mu_{\rm{A}}\) = 1.06 \(\geq\) 1.3 thus \(\mu_{\rm{A}}\) = 1.3. This supply suffices against the required value (as previously calculated \(\mu_{\rm{A}}\) = 1.25). The FRP strengthening of the ground storey columns (except C5) is summarized as follows: a single CFRP layer is wrapped along the height of each column to alleviate shear failure, one additional CFRP layer is wrapped at the lower 700 mm of each column to strengthen the splice region, one additional CFRP layer is wrapped at the upper 600 mm of each column to alleviate compressive bar buckling (Figure 6a).