## 4 Description of the Experimental Campaign
### Design and Detail of Steel Jacketing  
The steel jacketing was designed to restore 100% of the strength of the damaged dapped end of each specimen. The resisting model of the strengthening system is the same as a slip-resistant connection between two steel members. In fact, the strengthening system must be able to carry the ultimate load of the undamaged dapped end without slipping at the interface with the web surface. For this reason, it is calculated according to [33] as follows:  
\[F_{s,Rd}=\frac{k_{s}\cdot\mu\cdot\mu}{\gamma_{M3}}.F_{p,C} \tag{1}\]  
where \(F_{s,Rd}\) is the design slip resistance of a single preloaded bolt; \(k_{s}\) is a coefficient that depends on the type of hole, here considered equal to 1; \(n\) is the number of sliding surfaces, in this case, equals to 2; \(\gamma_{M3}\) is a partial safety factor, considered equal to 1 to calculate mean resistance; \(F_{p,C}\) is the preload force of the bolts equal to 0.70\(\cdot f_{ub}\cdot A_{s}\), where \(f_{ub}\) is the ultimate strength of the bolt and \(A_{s}\) is the cross-section.  
M20 class 8.8 bolts are used. Each bolt is pre-loaded with a force of 137 kN. Considering a friction coefficient between concrete and steel \(\mu=0.3\), the slip resistance of the single bolt is \(F_{s,Rd}=75\) kN. With the bolt arrangement shown in Figure 8, a maximum vertical load of 240 kN can be applied to each couple of steel plates, jacketing the web.  
The resistance of the slip-resistant connection between concrete web and steel plates (240 kN) is about 60% higher than the resistance obtained for the sound-dapped ends using the strut and the method (150 \(\div\) 160 kN). This choice was conducted because strut and tie models generally underestimate the ultimate load (solution on the safe side) and it is easy to find real laboratory resistances that are 20% to 30% higher than the one supposed using STM. On the contrary, the friction coefficient to be applied to the interface between steel and concrete was unknown as the surface was not prepared and, therefore, irregular.  
The authors were expecting a real slip resistance lower than 240 kN and a sound saddle resistance higher than 160 kN. The difference between these values was intended to obtain a fair margin of safety to avoid slipping on the interface.  
The resistance of the steel plates was calculated in order to be able to carry the saddle load without superposing to the STM mechanism. Therefore, no sum-up was taken into account. Steel plates are by far stiffer than cracked concrete, therefore they work before the STM mechanism can rise. The concrete under the plates was completely uncracked at the end of the test showing that the steel jacketing was carrying most of the load.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Beam Type** & **Dapped-End Status** & **Failure STM Load [kN]** \\ \hline Orthogonal reinforcement & Sound & 150 \\ Damaged & 65 \\ Inclined reinforcement & Sound & 160 \\ Damaged & 70 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Ultimate load according to STM.  
The geometry of the steel strengthening system is shown in Figure 8. The base steel plate is 5 mm thick, its extension inside the beam depends on the extension of the damaged area; in fact, it extends until it is firmly anchored within an area of the beam whit sound shear reinforcement, as can be seen in Figure 9. SP1 elements are squared solid steel 15 mm thick with a side of 60 mm and have the function of diffusing the preload force of the bolt to avoid local failure of concrete under high compression. IR1, IR2, IR3, IR4, IR5, and IR6 elements are 5 mm thick and 15 mm deep. Their function is to avoid instability of the steel plate in the area where the half-joint load is applied directly to it.