Fire-Resistant Steel Structures: Optimization Mathematical Model with Minimum Predicted Cost of Fire Protection Means

Steel structures quickly lose stability during a fire, which is why fire protection measures are used to increase their fire resistance limits. Structural fire protection in the form of boards or covers can achieve structural stability values ranging from 30 to 240 min under various fire conditions. Structural fire protection has certain advantages—it does not change its geometry during a fire, its behavior is predictable during testing (unlike intumescent fire protection), it has broad climatic applicability, and it can achieve high fire resistance limits. This article presents a mathematical model that calculates the minimum cost of structural fire protection while ensuring that the unexposed side of a steel column does not exceed 500 °C and achieves 180 min of standard fire resistance. Optimal values were extracted using genetic algorithms in the MS Excel environment and the “Solver” tool. The model was tested on a sample of 39 structural materials, such as cement boards, covers, and enclosures. The calculated coefficient of determination (R2) for the predictive model of the main component was 0.948. The predicted material cost was 6.83 $/m2. This study’s results can be used for preliminary cost estimation of fire protection treatments for steel structures in large design and operating companies.