## 5 Local Strengthening through FRP Jacketing  
The objective is to remove, through FRP jacketing, brittle failure modes so that the flexural capacity of columns can be fully developed. The design methodology adopted follows the procedure described in Chapter 8 of [4; 5]. FRP confinement is applied as to enhance (i) displacement ductility, (ii) shear strength, and additionally, to prevent failure due (iii) buckling of steel longitudinal bars. For the needs of the current example, a generic carbon FRP fabric with the following mechanical properties was selected for column and beam retrofitting: thickness \(\mathrm{t_{0}}\) = 0.12 mm, modulus of elasticity: \(\mathrm{E_{f}}\) = 165,000 MPa, ultimate tensile stress: \(\mathrm{f_{fu}}\) = 2970 MPa and ultimate strain \(\mathrm{\varepsilon_{fuk}}\) = 0.018. The design tensile strain \(\mathrm{\varepsilon_{fu,h}}\) in the FRP layer shall not exceed the limit: \(\mathrm{\varepsilon_{fu,h}}\)= \(\mathrm{\eta_{1}}\)\(\mathrm{\eta_{2}}\)\(\mathrm{\eta_{3}}\)-\(\mathrm{\varepsilon_{fuk}}\)/\(\mathrm{\gamma_{f}}\) where \(\mathrm{\gamma_{f}}\) = 1.5 for fully wrapped FRP arrangement (i.e., the ground floor RC frames do not accommodate any masonry). Factors \(\mathrm{\eta_{1}}\), \(\mathrm{\eta_{2}}\), \(\mathrm{\eta_{3}}\) are considered as follows:  
* 2 \(\times\) 27) = 0.71 + 1 (h\({}^{\prime}\) is the straight part of the largest cross section side). * Factor \(\mathrm{\eta_{2}}\) = 1 accounts for the sufficiency of the wrap development length: the straight parts of the cross section sides h\({}^{\prime}\)\(\approx\) 300 mm and b\({}^{\prime}\)\(\approx\) 200 mm suffice to accommodate the minimum anchorage length of the external FRP layer \(\mathrm{l_{b}}^{\mathrm{min}}\) = 0.5\(\mathrm{\pi_{V}}\)(/E\({}_{\mathrm{f}}\)\(\times\)\(\mathrm{t_{0}}\)\(\times\)\(\mathrm{s_{o}}\)/\(\mathrm{\tau_{a}}\))= 0.5\(\mathrm{\pi_{V}}\)(/165,000 \(\times\) 0.12 \(\times\) 0.5/5) \(\approx\) 70 mm (\(\mathrm{s_{o}}\) and \(\mathrm{\tau_{a}}\) are slip and bond strength values, provided by the resin manufacturer); to this end the external layer of the FRP jacket can be anchored over the column's shorter side. * Factor \(\mathrm{\eta_{3}}\) = 1 for fully wrapped jacket (considers the redundancy of the jacket against debonding). Accordingly, the design tensile strain \(\mathrm{\varepsilon_{fu,h}}\) in the FRP layer is \(\mathrm{\varepsilon_{fu,h}}\) = \(\mathrm{\eta_{1}}\)\(\mathrm{\eta_{2}}\)\(\mathrm{\eta_{3}}\)-\(\mathrm{\varepsilon_{fu,h}}\)= 0.71 \(\times\) 1 \(\times\) 1 \(\times\) 0.018/1.5 = 0.0085. Given the required displacement ductility (\(\mathrm{\mu_{0}}\) = 1.25) from Section 4, the associated curvature ductility is \(\mathrm{\mu_{\phi}}\) = 2\(\mathrm{\mu_{\phi}}\) - 1 = 2 \(\times\) 1.25 - 1 = 1.5. The maximum compression strain demand is \(\mathrm{\varepsilon_{cu,c}}\) = 2.2\(\mathrm{\mu_{\phi}}\)\(\mathrm{\varepsilon_{sy}}\)\(\mathrm{\varepsilon_{Gd}}\) [form Equation (4a)]. For the corner columns (\(\mathrm{v_{Ed}}\) = 0.13) \(\mathrm{\varepsilon_{cu,c}}\) = 2.2 \(\times\) 1.5 \(\times\) 0.0025 \(\times\) 0.13 = 0.0011 \(<\) 0.0035 and for the peripheral columns (\(\mathrm{v_{Ed}}\) = 0.26) \(\mathrm{\varepsilon_{cu,c}}\) = 0.0021 \(<\) 0.0035. From these calculations, it is concluded that there is no need for confinement of concrete through closed FRP jackets to meet its strain demands in the compression zone resulting from the displacement ductility calculation. According to Section 3, flexural response dominates when the shear strength \(\mathrm{V_{Rd}}\) exceeds 1.5 \(\mathrm{V_{fl}}\). For the simplicity of the following calculations it is taken as 1.5 \(\mathrm{V_{fl}}\) = max(1.5 \(\mathrm{V_{fl,corner}}\),1.5 \(\mathrm{V_{fl,peripheral}}\)) \(\approx\) 128 kN and also the available \(\mathrm{V_{Rd,0}}\) = min(\(\mathrm{V_{Rd,0,corner}}\),\(\mathrm{V_{Rd,0,peripheral}}\)) = 60 kN.