Derivation and analysis of methods for calculation of axially loaded steel compression members based on different building codes

The article presents the physical significance of the study of axially loaded steel compression members and the origin of accepted analytical models, which are the basis for the methods of their calculation in current building codes of CIS and European countries. An approximate solution of the problem of eccentrically loaded elastic compression member is given and analytical relationships for determining the buckling coefficient as a result of solving an analytical problem and as a result of applying building codes are obtained. Based on the results from solving the structural analysis problem, a solution for axially loaded compression member buckling coefficient, which is the ratio of such stress value from axial compression to the yield stress of steel at which the outermost fibers of the cross section yield, is given. When obtaining the solution of the buckling coefficient for axial compression, it is justified that the clarity of obtaining a solution is achieved by introducing the number Pi in place of the numerical values. It is indicated that the reason for shifting relative eccentricity from the ideal value of 0.2 is the impossibility of buckling at small slenderness ratios. It is justified that the calculation methods described in Eurocode and the building code of Russia (SNiP), despite the difference in the definition of nominal slenderness ratio, have common physical significance and their difference is only in approaches to the definition of random eccentricity. The building code approaches to calculating relative eccentricity included in buckling coefficient are stated and analyzed and their physical significance is described. The significance of relative eccentricity which is included in European and Russian codes is unfolded and the relationship between relative eccentricity and imperfections in the shape and type of cross-section is indicated. The significance of the imperfection factor in accordance with EN 1993-1-1: 2005 which depends on initial imperfections, the shape of the cross-section and the technology of member manufacture is explained and the application of approximating linear function, which reflects the technological factor of precision of manufacturing and inevitably arising imperfections, is justified. The significance of the coefficients of imperfection α and β, which are included in the Russian building code for steel structures, is unfolded.