## 2 Materials and Methods
### Design Procedure and Geometry of the Connection
This force must include the factor \(C_{\rm pr}\) and the maximum probable moment of the beam at the face of the column \(M_{\rm f}\), which is calculated as follows [4]:  
\[M_{\rm f}=C_{\rm pr}R_{\rm y}Z_{\rm x}F_{\rm y}+VS_{\rm h} \tag{2}\]  
where \(Z_{\rm x}\) is the plastic module of the beam section; \(V\) is the shear force at the plastic hinge; and \(S_{\rm h}\) is the location of the plastic hinge measured from the center of the column. The factor \(C_{\rm pr}\), which is provided by AISC 358, considers the maximum probable resistance in the connection, including the effect of hardening by deformation of the material, and is calculated as follows [4]:  
\[C_{\rm pr}=\min\left(\frac{F_{\rm y}+F_{\rm u}}{2\;F_{\rm y}},\;1.2\right) \tag{3}\]  
In addition to the previous requirements, the bolts must be pretensioned to at least 70% of \(F_{\rm u}\). (4) The geometry of the diaphragm must be defined as a function of the diameter of the column. More precisely, the external diameter of the diaphragm \(\phi_{\rm e}\) must be equal to 1.5 times the diameter of the column \(d_{\rm c}\) and the tangent length \(l_{\rm dg}\) must be equal to 25% of the diameter of the column \(d_{\rm c}\). These dimensions were evaluated by means of numerical modeling, considering even the influence of the angle \(\theta\) on the flow of efforts and levels of plastic deformation in the diaphragm. As a result, a value of 30 degrees was established for \(\theta\). (5) The thickness of the diaphragm \(t_{\rm p}\) must be obtained from the stress states of coarse area creep, net area fracture and shear block, considering the maximum capacity force, \(F_{\rm pr}\). In turn, \(F_{\rm pr}\) is obtained by decomposing the maximum probable moment of the beam located on the face of the column between the web of the beam \(d_{\rm b}\) and including the thickness of the diaphragm:  
\[F_{\rm pr}=\frac{M_{\rm f}}{d_{\rm b}+t_{\rm p}} \tag{4}\]  
The thickness of the diaphragm must coincide with a commercial plate thickness. Thus, the iteration must be started with a preliminary thickness and its compliance with the mentioned stress states must be verified. For the resistance of the diaphragm, a resistance reduction factor for ductile limit state, \(\phi_{\rm d}=1\), must be considered according to AISC 358 [4]. (6) Diaphrags must be connected to the column wall using full penetration welds. For this, it must be ensured that the edges are provided with 45-degree levels. For this work, the AWS TC-U4b-GF type welding detail with preheating of parts according to AWS D1.1 was utilized [32]. (7) Joining the shear plate to the column can be done using full penetration welds or fillet welds. If fillet welds are implemented, they must be calculated to resist the probable maximum shear \(V_{\rm p}\). Figure 2 shows the components and main dimensions of the connection obtained from the design process described above. The action of the maximum capacity force \(F_{\rm pr}\) and the maximum probable moment \(M_{\rm f}\) are also illustrated. As shown in the figure, the column is made of ASTM A500 grade C steel and has a circular section with an outer diameter of 323.9 mm and a nominal wall thickness of 9 mm. The beam corresponds to an IPE360  
rolled profile and is made of ASTM A572 grade 50 steel. The actual strengths of the steel were estimated according to the ASTM E8-11 standard [33]. For the column, the values of 410 MPa and 563 MPa were obtained for the yield and ultimate limit of the material respectively, whereas for the beam, the corresponding values were 386 MPa and 540 MPa. The column was filled with concrete of 21 MPa compressive strength. The diaphragm thickness was 19 mm, and the number of bolts per diaphragm was 16 with a bolt diameter of 5/8 inches (15.875 mm) and made of ASTM A490 steel. Table 1 shows all the relevant values of the connection.