The principles of a new approach to the problem of brittleness of structural steel products subjected to loading in presence of stress concentrators (SC) or cracks are outlined in this article. The results of testing to uniaxial tension and three-point bending, as example, the samples with SC show that the ductility characteristics ($\psi_K$) do not allow the unambiguous determining of the fragility threshold. It is proposed to additionally introduce a strength quality parameter $B_{rNF}$ to the complex of mechanical characteristics of metals and alloys. The strength quality parameter $B_{rNF}$ relates to the bearing capacity $\sigma_{NF}$ of a product or specimen with SC. At a critical value of $B_{rNF}$ ≤ 1, it indicates the brittleness threshold and meets the criterion of brittleness under condition of $\sigma_{NF}$ ≤ $\sigma_{0.2}$. As shown, the $B_{rNF}$ parameter is more informative than the traditional mechanical characteristics of ductility and toughness. It is uniquely relates to the loading conditions of such products and can be obtained by calculations based on the data of basic mechanical characteristics of metals, which eliminates complicated and expensive full-scale tests of products.