## 1 Introduction  
The present study focuses on two different methodologies (analytical and numerical) to be used in the analysis of the stability of columns with different sizes, lengths, and end constraints. Some studies have been used to assess the strength and deformation of columns as well as the failure modes [1] in mixed materials such as concrete filled with steel. These authors refer to the excellent interaction between steel and concrete, such as general application [2; 3]. Other authors tested different solutions of buckling in steel columns [4] where the influence of slenderness ratio, cross-section, and boundary conditions have a great influence on the behavior. Other studies focus on the analysis of columns with hollow cross-sections under pure compression through testing and finite element modeling using hybrid or simple materials [5; 6]. The main purpose was to obtain the bearing capacity which these columns support at different conditions. From the test results, some authors concluded that the axial compression for tubular columns is influenced by the material strength, section type, and section hollow rate [7]. Design methodologies have been developed in the past decades and employed in design standards, where Eurocode 3 is an example with different procedures that can be used for beam-columns analysis. This standard has the most advanced and precise beam-column formulae to be used [8]. According to the applications, circular, rectangular, and square cross-sections are commonly used in column construction, in mid- and high-rise buildings, bridges and piles, metro station columns, wind turbines, submarine pipelines, and other structures [9]. Someof them are concrete filled with steel tubes due to their high flexibility, stiffness, energy absorption, and seismic and fire resistance [9]. More recently, some studies have focused on analytical formulation to assess the axial capacity and compressive load of recycled concrete-filled steel tubular cross-sections [10]. Nevertheless, square and rectangular cross-sections are the most frequent in construction [11], due to the simpler design in column-beam connections applications, their considerable bending resistance, and aesthetic concerns. Recently, high-strength steel materials have also been used for these column types to define the axial load-carrying capacity, namely, in conjunction with the concrete to measure the compressive strength using the current design standards [12]. Also, welded thin-walled box sections have been studied because of their broad application in the industry, as they deal with economic and safe-scope projects [13]. Different approaches with numerical methodologies and experimental tests have been used to carry out typical applications on column buckling and to predict the behavior of these structures under applied loads in real situations [14; 15]. For example, buckling on composite columns has been a studied topic due to the requirements needed in the construction of large-span structures or even high-rise buildings and seismic areas [16]. Studies have been related to the application of numerical solutions as a good methodology in the study of failure modes that can be observed in columns [14]. Other studies experimentally evaluate the local buckling failure of columns when submitted to different loads as bending [15], where the circular hollow cross-sections are chosen due to being the most efficient and useful flexible structures. Other investigations focus on the presence of internal voids and opening cross-sections to study the effect on the ultimate load resistance and the web post-buckling as the predominant failure mode in the column [15; 17; 18]. In this study, the author uses the ANSYS(r) 2022 R2 program, with finite solid elements, to calculate the bearing capacity of different columns widely used in construction focusing on the study of the effective length, different sizes of square hollow cross-sections, and different end constraints.