This paper is devoted to the frameless coverings – special-type arch coverings extended to territories of Ukraine. This type of coating is essentially folded open type cylindrical ribbed shells are based on an arched structural element – the thin-walled, cold-deformed profile. Based on accepted hypotheses and assumptions, in particular, on the assumption of the compatibility of deformations of arched structural elements, finite-element models of these coatings were constructed. The research of influence of existence of face and intermediate diaphragms on the stress-strain state of the shell models of special type arch systems is conducted, considering various lengths of compound covers. During the research, assessment of the impact of existence of diaphragms of rigidity on stability of the shells was also executed. The first forms of buckling and stability safety factors (critical parameter of buckling) corresponding to them were defined. The components of the stress-strain state obtained in the research are presented in the form of isofields of the main tensile stresses σ1 and the main compressive stresses σ3 and also in the form of isofields of vertical movements, and stability safety factor in the form of the relative chart, for each of these shells. From the analysis, it is noted that the diaphragms of rigidity contribute significantly to the intense deformed condition of the investigated structures. The analysis of isofields of the main stresses σ1 and σ3, shows redistribution of efforts. In total, the above described clearly demonstrates the necessity of installation of diaphragms for and necessitates further research in the considered direction. Also it is noted that for the investigated arch systems, the main measure of the exhaustion of bearing capacity is buckling. Taking into account the above, it is noted that the scientific interest is attracted by rationalization of length of the block between diaphragms as prospect of further the main criterion of which should be buckling resistance of the special-type arch coverings.

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