The decrease of the nominal strength with the increase of the structural dimension is a wellknown occurrence in fracture, named ‘size effect’. Size effects are usually dealt within the framework of linear elastic fracture mechanics, mainly in situations where structural failure is driven by unstable crack propagation. This condition may not be fulfilled by large concrete structures such as gravity dams, in the presence of significant stabilizing contributions due, e.g., to self weight. An efficient numerical scheme, apt to relate nominal strength and characteristic size of any brittle and quasi-brittle structure, leads to a finite dimensional complementarity problem, which depends on a load amplification factor that has to be maximized to return the sought nominal strength. This approach is illustrated here with the aid of some reference examples.