## 6 Application of PTMS  
The parametric study on the beneficial effect of the use of PTMSs is done on the model realized with C25 concrete. The poorest material among the one tested in the previous chapter is chosen in order to simulate a situation of bad casting that needed strengthening. Post-tensioned steel straps are added to the model, considering different layouts, and the resulting structural behavior is computed to identify the optimal retrofitting design to control the crack formation. Post-tensioned metal strap (PTMS) layouts are shown in Figure 13. The characteristics of the material used for the straps are presented in Table 8.  
Five different layout are studied: the first one is characterized by four straps placed around the thickest part of the chord close to the vertical element; the second one is equal to the first but an additional strap is placed in correspondence of the area where high principal stress are found; the third one is equal to the second but an additional strap is placed just beside the last one; the fourth one shows seven straps placed in the same position of the four of the first one; and the fifth one increases again, using all the available space to place eleven straps in the central zone. A friction interaction between belts and concrete with a friction coefficient of 0.5 and a nil cohesion has been established while the confinement effect has been simulated by a prestressing force equal to 10% of the yield force of the belt. The load corresponding to 35% of the one applied in the laboratory test is used in this section, it being the load that causes first cracking in the specimen. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Concrete Class**} & **Maximum Tensile Stress in Concrete** & **Minimum Compressive Stress in Concrete** & **Maximum Compressive Steel Section** & **Minimum Compressive Stress in Steel** \\  & **Section** & **Stress in Concrete** & **Steel Section** & **Stress in Steel** \\  & **[MPa]** & **Section [MPa]** & **[MPa]** & **Section [MPa]** \\ \hline C25 & 1.32 & \(-11.4\) & 205 & \(-342\) \\ C30 & 1.38 & \(-11.9\) & 198 & \(-329\) \\ C40 & 1.48 & \(-12.8\) & 190 & \(-303\) \\ C50 & 1.55 & \(-13.5\) & 184 & \(-285\) \\ C60 & 1.64 & \(-14.2\) & 178 & \(-265\) \\ \Figure 13: Layout of PTMSs and maximum stress [kN/m\({}^{2}\)] in the straps at 35% of the laboratory load. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Elastic** & **Ultimate Tensile** & **Yielding** & \\
**Modulus** & **Strength** & **Stress** & **Dimensions** \\
**[GPa]** & **fu** & **fy** & **[mm]** \\ \hline
230 & 1100 & 982 & 25 \(\times\) 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: PTMS material and geometrical characteristics. Analyzing the model with the PTMSs, the connection experiences tensile stresses close to the middle of the section, but due to the confinement given by the steel belts, the lower part of the concrete part remains almost unstressed. Thanks to the presence of steel belts, no cracks have been localized in the lower area even if an additional 10% of load increment has been achieved (from 35% to 45% of the laboratory test). The principal stresses in concrete under the different belt arrangements are presented in Figure 14.  
Figure 14: Principal stresses in C25 concrete specimen at 35% of laboratory load [kN/m\({}^{2}\)]. The behavior of the belts (PTMSs) becomes clear through the investigation of the distribution of stresses in the areas reinforced with the belts, particularly when examining different belt arrangements. For instance, when two belts are examined together, it can be observed that the sections where the belts are joined undergoes significantly reduced tensile stresses compared to other regions. The maximum stress generated in the belts in different arrangements (variable number of belts) are shown in Figure 13 and in Table 9.  
Moreover, the analysis reveals that the highest concentration of stress occurs in the thinner portion of the concrete structure.