This study focuses on a new strengthening method of continuous bridges with several spans that present extensive damage in their foundation/piers due to scour and erosion. The method consists on the construction of a new upper steel arch with a network hanger's arrangement over the original deck with the aim to hang the existing deck to the new arch. The deck is acting as a tie in the new structural configuration. This allows to remove the damaged foundations/piers, deriving on an arch bridges with an span-length similar to the total length of the strengthened bridge and avoiding future problems related to scouring. The paper discusses about the resisting mechanisms that control the structural optimization process and therefore defines the design criteria. The main target of this process is different for each case, namely: the optimization of the arch in traditional network bridges; the limitation of maximum and minimum stresses in the deck in the case of strengthened bridges. Finally, it allows the comparison of each case, setting the differences between them and providing a new line of research on the topic of the tied arch method.