The subject of the study is the roof slabs, made of profiled sheetings, supported by bottom truss systems. The profiled sheet, being the upper belt of these structures, experiences longitudinal-transverse bending under the distributed transverse load and a longitudinal eccentric compressive force. Analytical and numerical studies determined the stress-strain state of the profiled sheeting. The dependences of the limiting value of the distributed load on the compressive longitudinal force and the eccentricity of its application are revealed. A technique for optimizing the design parameters of roof slabs have been developed. The studied roof slabs made of profiled sheeting, supported by a truss system, have a rather complicated design with many parameters, on which the performance criteria depend. Studies of the ties between these parameters are quite laborious. Therefore, it is not possible to solve the problems of optimizing these structures by known analytical and numerical methods. To find the rational parameters of the studied slabs, we used the method of phased numerical experiments using simplex optimization. Using this technique, the optimal structural parameters of the slabs with spans of 6-12 m were determined for a given efficiency criterion.
The analytical expressions and graphs for determining a limiting load have been obtained using the methods of the theory of limiting balance. The processes of strain of the beams after formation of a plastic hinge until their complete destruction have been investigated. The dependences of a bearing capacity of the beam on its parameters and characteristics of the foundation soils have been obtained. The regularities of formation of plastic hinges have been revealed depending on a place of application of the load. The limiting values of the load have been calculated analytically, and the forms of deformation of the beam have been established at the time of the appearance of the first plastic strains and in the limiting state. The comparative analysis of the research results of the adopted model with the numerical studies of the elastoplastic beam has been carried out.
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