It has been demonstrated that the operation of industrial facilities in the Arctic zone and areas of Siberia and the North is associated with the increased hazard of the transition of their bearing elements from ductile to quasi-brittle and brittle states. In order to substantiate the safety and cold resistance in accordance with the up-to-date requirements of a risk-oriented approach in the conditions considered, a comprehensive deterministic and probabilistic identification of traditional strength margins considering the variability of standard properties of the material depending on temperature and margins for critical temperatures and critical stresses in ductile, quasi-brittle and brittle states has been proposed. At the same time, together with the assessment of probabilities of the occurrence of hazardous brittle fractures, it is required to determine the damages caused by them to implement the risk assessment of the occurrence of hazardous fractures. Notably, the further development and improvement of interconnected methods of justification of strength, lifetime, and safety in accordance with risk parameters will gain increasing importance. 

As a basis for such an analysis, it is proposed to use the normal law of probabilityof distribution of probabilities of low-temperature collapses of bridges, viaducts, power lines, and farms is proposed to be used as the initial for such an analysis. The distributions of times of fracture occurrences from the beginning of operation and fracture are nonlinear. The characteristics of strength and plasticity of structures are exponential depending on temperatures. For quantitative assessment of operability, two basic margins for critical stresses and critical temperatures are proposed to be used.