## 5 Design of FRP Strengthening
### FRP Anchors  
Anchors were provided at the ends of the U-wrap fabric and as close as possible to the bottom of the slab to maximize the effective depth of the strengthening scheme. The embedded anchors used on the first two specimens, S1A and S1B, were inserted into the slab at an angle of \(140^{\circ}\) to \(155^{\circ}\) with respect to the laminate to guarantee an effective load transfer to the top reinforcement. The inclination and slab thickness (\(12.2\) cm [\(4.8\) in]) limited the available embedment length to \(10\) cm (\(4\) in) for the \(4/5\) scale specimens (\(15.2\) cm [\(6\) in] for the in-situ beams). Anchor holes were drilled \(25\%\) larger than the anchor diameter (\(1.6\) cm [\(0.625\) in] holes for \(1.3\) cm [\(0.5\) in] anchors), which provided a hole area-to-anchor area ratio of \(1.6\), larger than the \(1.4\) limit recommended in [19]. Anchor hole edges, same as web corners, were rounded to a minimum \(1.9\) cm (\(0.75\) in) radius, exceeding the recommendation of \(1.3\) cm (\(0.5\) in) in \(\mathrm{ACI}\)\(440.2\)R and the Austin, Texas, report by [PERSON] et al. [19]. The goal was to minimize the risk of an anchor fracture due to stress concentrations at the bent, as this type of failure had been reported in [19] for their two-layer strip applications. The anchor fan geometries also satisfied and exceeded the recommendations by [PERSON] et al. [19], with splay lengths above the \(15.2\) cm (\(6\) in)-recommended minimum, full coverage of the FRP laminates, with overlap between adjacent anchors, and reduced fan angles below \(60^{\circ}\) to keep transverse stresses low. To prevent a bond failure at the splay, anchor fans were either sandwiched between two later of FRP or reinforced with a patch of the same FRP fabric, with the same fiber orientation as the main wrap.  
FRP anchors were designed using the model by [PERSON] and [PERSON] [24] for straight anchors, provided in Appendix B. To note, the concrete cone and dowel pullout failure modes are not applicable to the splice anchors on S5; their capacity was calculated for anchor rupture in tension only. All FRP anchors were designed to develop the maximum design strain in the FRP laminates of \(0.004\) permitted by \(\mathrm{ACI}\)\(440.2\)R. The design examples in [PERSON] et al. [33] use the same criteria, as opposed to designing for the rupture strain of the FRP laminate, as done by [19; 23; 32]. Arguments to support the adopted design approach are discussed later. DCRs for the anchors at the end-yielding region were \(0.92\) for S1B and \(0.87\) for S5, both controlled by anchor fracture (Table 7). The DCR for a bond failure for S1B was \(0.86\). On the other hand, the updated strength model by [PERSON] et al. [33] (Appendix B), not available at the time of design, predicts anchor fracture failures in both cases, with an overstress of \(63\%\) for S1B and \(8\%\) for S5 (Table 7). However, the FRP anchors at the hinging region of S1B did not fracture. As described in Section 6, the anchors closest to the main flexural crack were pulled out at around \(3\%\) drift, which could have been caused by a combination of an underprediction of the tensile capacity of the anchors (due to either or both the conservatism of the design equation or higher ultimate tensile strength of the anchors than that reported in Fyfe's technical brochures) and local strains in the FRP laminates higher than \(0.004\).