Purpose. Development of a computer model for the study of fire resistance of steel structures protected by fire-resistant coatings, using the example of a fire-resistant steel beam created in the LIRA-SAPR software complex (Ukraine). Methods. Finite element method, application of computational methods of numerical modelling of the LIRA-SAPR software complex, mathematical modelling of thermal processes of non-stationary thermal conductivity. Results. A computer model was developed in the LIRA- SAPR software complex, with the help of which thermal engineering calculation of the beam was carried out. The model makes it possible to evaluate the fire resistance of both unprotected and fire-protected steel beams, to take into account the properties of the beam material and the material of the fire-resistant coating. The peculiarity of modelling the non-stationary heating of a fire-resistant steel beam is to specify the thermophysical characteristics of the fire-resistant coating when solving the problem of non-stationary thermal conductivity. The results of the calculated determination of the fire resistance of the fire-resistant steel beam were compared with experimental data. As a result, a satisfactory convergence of the results of the calculation and experimental study of fire resistance was established (the error is no more than 12%). The results of the experimental determination of the fire resistance of unloaded beams under fire conditions of the standard fire temperature regime were analysed. The accuracy of the developed computer model was evaluated with the results of the experiment. Scientific novelty. A finite-element model of a fire-resistant steel beam has been developed in the LIRA- SAPR software complex, which allows calculating the fire resistance limits of beams protected by fire-resistant coatings with scientifically justified parameters with sufficient accuracy for engineering calculations. Practical significance. It consists in creating the basis for the calculated assessment of fire resistance of building structures protected by fire-resistant coatings by creating computer models capable of performing fire resistance calculations. Due to this, there should be a significant reduction in the cost of work on fire resistance assessment and, as a result, an increase in the effectiveness of measures to increase the fire resistance of building structures.

Building structures are very diverse in their purpose and application. The reliability and safety of their operation depends on many factors: geometric dimensions, materials used, acting external loads and their combinations, etc. All these parameters determine the internal forces, stresses and strains that arise in structures, which determine their strength, rigidity and stability. In order to ensure the strength, rigidity and stability of buildings and their structural elements, appropriate calculations are performed. In the field of the theory of calculation of building structures, there is a constant refinement of the actual work of these structures, i.e. such design schemes are created that most accurately correspond to the actual operating conditions. The more optimally the design scheme is drawn up, the less time-consuming will be the stages of calculation and design of the corresponding structure. Therefore, the solution of the problem of optimization of design schemes is of great scientific and practical importance. One of the existing approaches to finding optimal solutions is discussed in the course "Operations Research". Operations Research deals with the development and application of methods for finding optimal solutions based on mathematical modeling. The operation model is an analytical dependence of the objective function on dependent (controlled) variables, which, within certain limits, we can choose at our discretion and set the range of their change. Solver is a Microsoft Excel add-in that can be used in Structural Analysis problems. With its help, you can find the optimal value (maximum or minimum) of the formula contained in one cell, called the target, taking into account restrictions on variable values in other cells. Simply put, with the Solver add-in, you can determine the maximum or minimum value of one cell by changing other cells. Most often, the add-on "Search for a solution" is used in solving optimization problems of the economy (simplex method, transport problem, etc. There are practically no results of using this approach in the calculations of building structures.

Розроблено структурно-логічну схему забезпечення вогнестійкості вогнезахищених залізобетонних конструкцій на основі запропонованої математичної моделі та розрахунково-експериментального методу оцінювання вогнестійкості вогнезахищених залізобетонних конструкцій. Розроблено математичну модель оцінювання вогнестійкості вогнезахищених залізобетонних конструкцій, яка включає в себе виконання таких етапів: вибір апарату формалізації, побудова зовнішнього опису, перевірка працездатності моделі, побудова внутрішнього стану, перевірка працездатності та ідентифікація параметрів. Сформульовані початкові та граничні умови при побудові зазначених моделей, які дозволяють з достатньою для інженерних розрахунків точністю прогнозувати вогнестійкість вогнезахищеної залізобетонної конструкції. Розроблено комп’ютерну модель напружено-деформованого стану вогнезахищеного багатопустотного залізобетонного перекриття в програмному забезпеченні «ЛІРА-САПР» для підвищення рівня пожежної безпеки будівель та споруд. Проведено статичний розрахунок вогнезахищеної залізобетонної багатопустотної плити перекриття, в результаті якого отримано напружено-деформований стан перекриття при сумісній дії силових і температурних навантажень. Проведено порівняння результатів чисельного моделювання з результатами експериментального дослідження вогнестійкості. Перевірено точність розробленої комп’ютерної моделі для оцінювання вогнестійкості вогнезахищених залізобетонних конструкцій. Встановлено нелінійні закони деформування матеріалів конструкцій, а саме: експоненціальний та кусково-лінійний, які враховують модуль пружності бетону, коефіцієнт лінійної температурної деформації бетону, граничну відносну деформацію бетону, які дозволяють з достатньою для інженерних розрахунків точністю (до 5 %) оцінювати вогнестійкість вогнезахищених залізобетонних конструкцій.

Purpose. Design a dugout made in factory conditions for further implementation in the system of ensuring reliable protection of soldiers in combat conditions, taking into account quick installation and ease of use on the front line. Methods. Analysis and synthesis, generalisation, theory of probability, theory of decision-making. Results. Based on the analysis of foreign experience in the construction of fortifications, the construction of a cylindrical dugout made of reinforced concrete is presented, aimed at reducing the time of their deployment, increasing mobility and strength, ease of manufacture, and the possibility of multiple use in various places of hostilities. Scientific novelty. The structure of the dugout is a reinforced concrete pipe (barrel, container, bunker) with a diameter of 2.5÷3.0 m, a length of 4.0÷6.0 m and a wall thickness of 150÷200 mm with transverse walls at its edges that hold armoured doors . In the cavity of the pipe, a metal frame for fastening the shelves for rest is mounted, which can be turned in the pipe and fixed in the appropriate position using spacer screws. In a similar way, round armoured doors are turned and fixed in the transverse walls, around which 6÷8 holes with a diameter of 120-150 mm are provided for ventilation, lighting and observation. The further direction of the research is the formation of calculated combinations of forces for solving problems of dynamics in time, namely group D1 – calculation for emergency load, explosion, impact, failure of elements when calculating for progressive collapse with the help of LIRA-SAPR software. Practical significance. Implementation of the development results into the system of ensuring reliable protection of soldiers in combat conditions will allow to minimise losses among the military due to the use of reinforced concrete structures of cylindrical shape, manufactured in factory conditions.