# Buckling Resistance of Tapered Steel Columns
###### Abstract
Similar concepts were introduced by [PERSON] [23], but they were more complex and not readily applicable to EN 1993. [PERSON] [24] further developed this procedure to include the possibility of encompassing columns with a variable axial force per length. More recent research on the design of tapered members related to flexural buckling was conducted by [PERSON] et al. [25] and [PERSON] et al. [26]. They proposed a design procedure for tapered members based on FEM parametric analyses and the general method available in EN 1993-1-1 [22]. [PERSON] et al. [27] proposed an approach which used the geometric and material nonlinearity, considering the imperfections, and defined the member's ultimate strength by either the strain limit or peak load factor. [PERSON] et al. [28] proposed a generalized imperfection shape function for the practical design of tapered I-section columns, and using this function, a new beam--column element was developed for tapered symmetric I-sections. [PERSON] et al. [29] proposed generalized line-element formulations for the geometrically nonlinear analysis of tapered steel members with nonsymmetric cross-sections. [PERSON] et al. [30] introduced an analytical model for the second-order direct analysis of steel structures with tapered members, allowing for symmetric and asymmetric variations. [PERSON] et al. [31] developed a stiffness reduction method for the in-plane design of web-tapered steel structures fabricated by welding individual plates. Other notable contributions included those by [PERSON] et al. [32] and [PERSON] et al. [33], where each introduced new design concepts for tapered members. [PERSON] et al. [34] developed an artificial neural network model to predict the critical buckling load of the web-tapered I-section steel columns, and the results of the proposed model were compared with approaches according to [8; 10; 21; 26]. The developed model predicted the critical buckling load of the columns more accurately than the existing equations. [PERSON] [35] and [PERSON] [36] proposed approaches though which it is possible to determine the buckling length of columns of variable cross-sections by multiplying the length by the K-factor. As a particular type of tapered structure, acoustic black hole (ABS) structures have been extensively studied recently [37; 38; 39]. Buckling analyses in structural engineering have seen applications beyond traditional materials and shapes. For instance, recent research [40; 41; 42; 43], presented the mechanical buckling and bending of stiffened functionally graded material (FGM) plates and beams. The studies focused on the influence of the material distribution, thickness-to-width ratio, and stiffener parameters on the buckling characteristics of the stiffened FGM plates and beams. Although this work differed in material composition and configuration, it highlighted the importance of considering various parameters in the buckling analysis, a theme central to the study of tapered steel members. The structural analysis of variable thickness plates with shear connectors has been a subject of interest in recent research. Despite being used for over 50 years, the design procedures for tapered members are not implemented in modern steel design standards (EN 1993 and AISC 360). Such a state can be attributed to the complexity of describing the stability compared to uniform members due to shifts in the bending, torsional, and axial stiffness with cross-section changes. Analytical solutions for buckling tapered compression members are only available in the elastic area for simple cases. The calculation of non-uniform members' buckling requires numerical and energy methods. There is a lack of research on practical structural design problems for non-uniform columns, and those that do exist often are not practical enough for everyday engineering use. Considering the complexity and engineering applicability, there is a need for further evaluation of the available design procedures.