Protection aims to ensure service continuity even upon failure by pre-computing backup paths. To save the network resources while providing protection, two strategies of resource sharing are defined in literature: (1) restrained sharing which limits the resource sharing to the backup paths and (2) global sharing which extends the resource sharing to the primary and backup paths. In this paper, we study the impact of resource sharing strategies on the resource utilization when the primary paths correspond to the shortest ones according to a strictly positive and static metric. With the single failure assumption, we show formally that the resource sharing between primary and backup paths is limited to some few links which cannot form a backup path. Thus, independently of the amount of resources (for instance: bandwidth) that can be shared between the primary and backup paths, the maximum number of backup paths is bounded. In our simulation, we comfort our formal result by showing that the two strategies have close rates of backup path rejection and backup bandwidth utilization.