The behavior of hinged support at the ends of the rack with initial bending under the action of load is considered. Spring rods are arranged symmetrically. The rack has an initial bend, compressed by forces constant in time. All real elements have one or another imperfections in the form of technological bends, therefore, they begin to bend from the very beginning of the load. The load, when it is exceeded even by an infinitesimally small amount, there is a loss of stability of this type of deformation, is called critical. In the calculation of stability under the long-term action of external forces, it is necessary to determine the load, at which the rate of movement in time monotonically decays. Solving the problem in such a setting is acceptable for systems, the development of movements of which in time leads to a change in the stress state. This condition for a compressed rack is fulfilled only in the presence of initial imperfections (initial bending, off-center application of compressive force, etc.). When solving the problems of the theory of stability, taking into account the creep of the material plays an important role. Creep can be limited in time or unlimited. When solving the problem of the stability of racks with initial imperfections, made of a material that has creep and reinforced with elastic rods, the following assumptions are made: 1) the hypothesis of flat sections is considered valid; 2) the deformations of the creeping material and the elastic rods at the points of contact are the same; 3) the modulus of deformations during stretching and compression are equal; 4) the creep material works in the stretched zone without the appearance of cracks. The relationship between deformations and elasticities in the material of the rack is established by a formula based on the linear relationship between deformations and elasticities. The creep rate of concrete is based on the hereditary theory of aging. In the work, an integro-differential equation was obtained - the equation of slow motion of the rod, expressions were obtained for the study of bends in any at what point in time, the formula for determining the critical force with long-term load action is derived.
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