## 2 Materials and Methods
### Design Procedure and Geometry of the Connection  
To guarantee ductility in SMFs, design by capacity must be considered, which requires preparing the column and the elements that are part of the connection to resist the maximum forces that the steel beam can develop when entering the inelastic range. In addition, the damage must be concentrated at a specific location called the plastic hinge [4]. Analytical and experimental considerations indicate that an excellent structural response can be achieved if the formation of a strong column-weak beam mechanism is induced through the design. In this mechanism, plastic hinges at the ends of the beams avoid excessive local ductility while the columns remain in the elastic range with the exception of the base of the columns. Additionally, the columns are subjected to variable axial loads due to seismic effects, which affects their resistance and ductility. In addition, the failure of a column can cause partial or total collapse of the building. These are the main reasons why the columns of the SMF are protected, which is based on the condition that they remain in the elastic range. To achieve this objective, it is of fundamental importance to apply the concepts of capacity design. In this way, a ductile response will be obtained in which the plasticization of the beams occurs progressively, and the system is capable of developing an adequate response [1; 4; 30; 31]. In addition, the column and beam selection for the frame must comply with the seismic requirements of AISC 341-16, section E3 [5], which provides the specifications for SMF with special energy dissipation capacity. The analyses performed in this work allowed us to show that a strong column-weak beam relationship is guaranteed and that the plasticization mechanism is verified according to AISC 358 [4]. In this work, the value of the moment ratio defined in AISC 341 which quantifies the column to beam strength ratio was equal to 1.26. This value was based on the actual materials strengths and was calculated by considering the actual expected maximum strength of the beam and the summation of the maximum probable moments. In addition, the design of bolts, external diaphragms, welding and connection to shear stresses were also guaranteed according to AISC 358, AISC 360 and AWS D1.1 [4; 6; 32]. To comply with the above, several conditions were met in the design stage. These conditions are described as follows:  
(1) The transverse section of the beam and the column must comply with the width-thickness relationship required to be classified as seismically compact. Likewise, it must be ensured that the beam skids are located laterally to avoid loss of capacity due to torsional lateral buckling. (2) The strong column-weak beam hierarchy must be fulfilled, which is greater than unity. In addition, the sum of the probable moments in the beams and columns must be calculated from the centerline of the column and must consider the shear force located at the plastic hinge. (3) The diameter and number of bolts must be obtained by considering the state of shear and crushing stresses in the diaphragm and the beam. The maximum bolt diameter,  
Figure 1: Research framework utilized to evaluate the seismic behavior of the steel beam-to-CFST column connection using external diaphragms. \(d_{\rm bmax}\), needed to control brittle failure in the beam flange, is determined by the following expression in millimeters [4]:  
\[d_{\rm bmax}=\frac{b_{\rm f}}{2}\left(1-\frac{R_{\rm y}F_{\rm y}}{R_{\rm t}F_{\rm u }}\right)-3 \tag{1}\]  
where \(b_{\rm f}\) is the dimension of the flange of the beam; \(R_{\rm y}\) is the overstress factor, which depends on the material of the beam; \(F_{\rm y}\) is the creep resistance; and \(R_{\rm t}\) is the ratio of the expected tensile strength to the specific minimum tensile strength \(F_{\rm u}\). The magnitude of the shear force \(V\) to which the group of bolts is subjected must also be considered.