Review article

The «reverse» numerical-analytical method for definition the residual bearing capacity of steel frame elements after buckling is proposed. The method allows to take in consideration the post-critical behavior of plates making up the frame element and large plastic strain overflowing into the self-hardening stage.The solution is carried out by the reverse sequence: it is offered to define values of deformational and non-deformational internal forces by numerical unitless procedure according to a given post-limit deformed state of the most loaded cross-section of an element under compression and bending in one or two planes. Wherein deformational forces are assumed as actually acting forces, taking in consideration geometrical nonlinearity, and non-deformational forces are assumed as fictitious forces, compensating nonlinear material behavior and local buckling. The latter ones are considered to be the result of sequential symmetrical acting of two additional axial fictitious forces with one or two eccentricities on the elastic element. The first fictitious force compensates the initial stage of increase of plastic strains before element buckling, and the second one compensates local buckling and further increase of plastic strains in some part of element span after element buckling. The effect of the geometrical nonlinearity on internal forces is defined by «straight» unitless analytical solution of the problem, considering deformed state, using the elastic model of element compressed by actually acting and fictitious forces with their eccentricities. Evaluated internal forces are used in the reverse solution to define eccentricities of actually acting force on the ends of element. The proposed method has a sufficient accuracy for practical application and allows to reduce by orders the magnitude of computational time compared to numerical methods. The graphs showing how the post-buckling bearing capacity reduction coefficients depends on the value of the normalized strain of the most stressed fiber for some of the cross-sections most widely used in construction practice are presented.