## 2 Materials and Methods
### Virgin Prototype RC T-Beam without Any External CFRP Strip Shear Reiforcement
The contribution of the various schemes of CFRP external shear reinforcement (V\({}_{\rm CFRP}\)) is added on the concrete contribution, as shown by the following Equations (1) and (2), where the cross-section of a single CFRP strip is equal to A\({}_{\rm CFRP}\) the CFRP Young's modulus is equal to E\({}_{\rm CFRP}\) and \(\varepsilon_{\rm CFRP}\) is the maximum tensile strain level assumed to develop at the CFRP strip being crossed by the diagonal shear cracks. Coefficient 2 at the front of the right part of Equation (2) accounts for the fact that the development of the diagonal shear crack is resisted by both sides of the hoop-shaped shear reinforcement surrounding the T-beam cross-section from both sides. \[\rm V_{p}=V_{c}+V_{CFRP} \tag{1}\]  
\[\rm V_{CFRP}=2\cdot A_{CFRP}\cdot E_{CFRP}\cdot\varepsilon_{CFRP} \tag{2}\]  
The provisions of the Greek guidelines [12] for retrofitting RC structural elements with externally attached FRP strips are utilized to calculate the CFRP external shear contributions. These guidelines provide upper acceptable limits for the tensile strain (\(\varepsilon_{\rm CFRP}\)) that such external shear reinforcement is allowed to develop. This tensile strain limit has a relatively low value for unanchored FRP strips, thus taking into account the debonding mode of failure. As indicated by Equation (1), the shear CFRP strip contribution is added to the shear contribution of the concrete resulting in the shear force predictions assuming _debonding_ limit-state which is denoted as strip \(\rm debV_{p}\) in Table 5 column 6. The presence of an anchoring system or closed hoop strips leads to accepting relatively higher tensile strain values (\(\varepsilon_{\rm CFRP}\)) than before, according to the same provisions. In this case, the presence of anchoring or the nature of closed hoops is assumed to lead to the tensile _rupture_ of the FRP material as limit-state. Again, applying Equation (2) and assuming as limit-state the rupture of the CFRP (either strip or rope) the corresponding shear capacity predictions are obtained which are denoted as either strip \(\rm rupV_{p}\) or rope \(\rm rupV_{p}\) (Table 5 column 6). In predicting the shear force or bending moment capacities, in the way described, the safety coefficients adopted in relevant design guidelines were set to be equal to 1. This way of obtaining the shear force capacity of RC beams strengthened by external FRP shear reinforcement is in line with the rationale followed by many relevant design guidelines [12; 59; 60; 61] with a varying degree of complexity. [PERSON] and [PERSON] [62] present an extensive review of a wide range of such design guidelines utilizing an extensive database of experimental results of RC beams strengthened with externally applied shear FRP retrofitting schemes. The following summarizes the main observations from comparing these predictions with the corresponding measurements. * The shear force capacity of the concrete, as found by the virgin beam results, is very well predicted. The concrete shear force resistance is also kept when predicting the total shear force resistance for the 2 nd, 3 rd, and 4 th strengthening scheme. This is due to the fact that the formation of diagonal cracking during the loading of the virgin T-beam at all subsequent stages did not reduce this shear resistance because the loading stopped before any significant widening of these diagonal cracks could take place. All the subsequent shear retrofitting schemes managed to prohibit any detrimental widening of these diagonal cracks till the last stage (last phase of loading during the 4 th strengthening scheme). This can be seen in Figure 23a,b. * For the 2 nd strengthening scheme, which exhibited flexural limit state, its measured flexural capacity of the tested RC T-beam is also very well predicted Therefore, the discrepancies between measured and predicted capacity values are limited to the CFRP shear contributions.