## 5 Local Strengthening through FRP Jacketing
#### Beam-Column Joint Strengthening
The horizontal shear force V\({}_{\mathrm{j}\mathrm{h}}\) acting in the joint is obtained from: \(\mathrm{V}_{\mathrm{j}\mathrm{h}}=\mathrm{V}_{\mathrm{j}\
u}\times\mathrm{h}_{ \mathrm{c}}/\mathrm{h}_{\mathrm{b}}\) =510.8 \(\times\) 250/400 = 319.2 kN with upper limit of: \(\mathrm{V}_{\mathrm{j}\mathrm{h}}\leq 80\%\times\mathrm{f}_{\mathrm{c}}/\mathrm{f}_{ \mathrm{c}\mathrm{m}}\sqrt{(1-\mathrm{v}_{\mathrm{Ed}}/\mathrm{\eta})\cdot \mathrm{b}}\mathrm{h}_{\mathrm{j}\
u}\) where \(\mathrm{\eta}\) = 0.6(1 \(-\mathrm{f}_{\mathrm{ck}}/\)250) = 0.58, \(\mathrm{b}\) = min[\(\mathrm{b}_{\mathrm{c}}\), \(\mathrm{b}_{\mathrm{b}}\)) + \(\mathrm{h}_{\mathrm{c}}/\mathrm{2}\)] = 250 mm and \(\mathrm{h}_{\mathrm{j}\mathrm{c}}\) = 250 \(-\) 2\(\cdot\)d\({}_{2}\)= 250 \(-\) 2 \(\times\) 27 =196 mm. Thus \(\mathrm{V}_{\mathrm{j}\mathrm{h}}\) = 319.2 kN \(<\) 334.4 kN. y-y direction--strong axis (C1-B7): The yield moment of beam B7-right is 134 kNm. The yield moments of the column below and above the joint are \(\sim\)90 kNm and 83 kNm: \(\Sigma\mathrm{M}_{\mathrm{yc}}\) = 83 + 90 = 173 kNm \(>\Sigma\mathrm{M}_{\mathrm{yb}}\) = 134 kNm. By being beams weaker than columns, they define the magnitude of shear stress in the joint. The horizontal shear force V\({}_{\mathrm{j}\mathrm{h}}\) is derived by following the Greek Code for Assessment and Retrofit [36], from Equation (14) as:  
\[\mathrm{V}_{\mathrm{j}\mathrm{h}}=\Sigma\mathrm{M}_{\mathrm{yb}}(1/\mathrm{jd}_{ \mathrm{b}}-1/\mathrm{H}_{\mathrm{n}}\times\mathrm{L}_{\mathrm{b,n}}/\mathrm{L }_{\mathrm{b}}) \tag{14}\]  
where \(\mathrm{j}\mathrm{d}_{\mathrm{b}}\)(=0.9 d; d = 370 mm) is the internal lever arm of the beam section, \(\mathrm{H}_{\mathrm{n}}\) is the theoretical storey height, \(\mathrm{L}_{\mathrm{b,n}}\) and \(\mathrm{L}_{\mathrm{b}}\) are the theoretical and clear half span of the beams, thus \(\mathrm{V}_{\mathrm{j}\mathrm{h}}\) =354.4 kN with upper limit of \(\mathrm{V}_{\mathrm{j}\mathrm{h}}\leq 80\%\)-\(\mathrm{\eta}\mathrm{f}_{\mathrm{cm}}\sqrt{(1-\mathrm{v}_{\mathrm{Ed}}/\mathrm{\eta})} \times\mathrm{b}_{\mathrm{j}\mathrm{h}_{\mathrm{j}\
u}}\), \(\mathrm{\eta}\) = 0.6(1 \(-\mathrm{f}_{\mathrm{ck}}/\)250), where \(\mathrm{b}_{\mathrm{j}}\) = 250 mm, \(\mathrm{\eta}\) = 0.58, \(\mathrm{h}_{\mathrm{j}\
u}\) = 350 \(-\) 2\(\cdot\)d\({}_{2}\) = 350 \(-\) 2 \(\times\) 27 = 296 mm. Thus, \(\mathrm{V}_{\mathrm{j}\mathrm{h}}\) = 354.4 kN \(<\) 505 kN. The horizontal shear force used for the calculation of the required FRP reinforcement, where fibers are oriented in the horizontal direction, is the maximum among 319.2 kN and 354.4 kN. For such a simple plan view of a building, one could deduce that the strong axis horizontal shear force apparently prevails. [Note: Alternatively, and with respect to the strong axis, the EN 1998-1 [35] for exterior beam-column joints proposes the simplified expression \(\mathrm{V_{jh}}=1.20\mathrm{A_{s1}f_{y}}-\mathrm{V_{col}}\), where \(\mathrm{A_{s1}}\) is the top reinforcement of beams as \(\mathrm{A_{s1}}=2\times\pi\times 10^{2}/4+2\times\pi\times 20^{2}/4\approx 785 \) mm\({}^{2}\) (see Figure 2b) \(\mathrm{f_{y}}=500\) MPa and \(\mathrm{V_{col}}\) the shear force in the column above the joint as \(\mathrm{V_{col}}=\mathrm{M_{y}}/L_{\mathrm{V}}=83/1.35\approx 62\) kN hence \(\mathrm{V_{jh}}\approx 410\) kN, which should be lower than \(80\%\cdot\eta\mathrm{f_{cm}}\surd(1-\mathrm{v_{Ed}}/\eta)\cdot\mathrm{b_{th} }\mathrm{f_{x}}=505\) kN. This approach increases the demand for FRP by almost 55 kN in comparison with what the most recent Code [36] deduces. Prefabricated Carbon Fiber Reinforced Polymer (CFRP) plates will be used for the beam-column joint strengthening. An essential requirement is the proper anchorage of the FRP plates, otherwise FRP strengthening should not be considered effective. Fib Bulletin 90 [2] in its Section 9.2.3 provides details about anchorage of FRP strengthening in beam-column joints.