# Finite Element Analysis of Proposed Self-Locking Joint for Modular Steel Structures
## 5 Parametric Study on the Proposed Connection
### Connection under Axial Tension  
The structural performance of the proposed connection under axial tensile load was influenced by the presence of spring pin and bolt, and it has been studied using model Cp2 (with spring pin and outer bolt) and Cp3 (without spring pin and outer bolt). The observation on the gap separation between lower columns and connection is the primary findings. Figure 8a shows the axial tensile load vs. vertical displacement (separation among columns) between models Cp2 and Cp3. Initially, both connections show a linear relationship up to 210 kN with a negligible separation. At this stage, the resistance to separation between lower and upper columns was due to the tensile resistance of long vertical bolts connecting both floor and ceiling beams. The perpendicular distance between long bolt and point of loading influences the separation between column and connection. The shorter the distance, the higher will be the resistance to separation [24]. After the load reached 250 kN, a significant difference in the direction of the curve was noticed. Shank of the outer bolt and spring pin in connection Cp2 at this stage came in contact with internal walls of bolt holes and started to resist further separation. The difference between curves increased with the increasing load, as shown in Figure 8a. The outer bolt and spring pins were under shear stresses while long bolts were under tensile stress. At a separation of 6 mm, as shown in Figure 8a model Cp2 was able to carry a tensile load of 405 kN, whereas model Cp3 carried a tensile load of 250 kN. This indicates that the presence of the spring pin and outer bolt provided a major contribution to the tensile capacity of connection by 62%, at the separation of 6 mm. This difference was increasing when the separation was kept increasing up to 9 mm. The separation between connection and the lower column was noticed, followed by the deformation of the long bolt and local deformation of the ceiling beam in connection Cp3, while in Cp2 connection, an additional shear deformation on outer bolt and pin occurred. Figure 7: (a) Classification of joint according to EC3. (b) Shear stresses on the wall of the adapter. Figure 8: (**a**) Gap between column and connection under axial tension. (**b**) Stress distribution on joint. (**c**) Boundary conditions in FE model. (**d**) Test setup of column specimen 01 and 02 in tension [24]. (**e**) Force–separation displacement curve comparison between proposed connection and vector bloc [24]. To evaluate the behavior of the proposed connection and effectiveness of spring pin, a comparison can be made with the behavior of existing inter-modular connection under axial tension reported in the literature. For the sake of comparison, the force vs. separation curve, as shown in Figure 8e, produced from proposed connection models Cp2 and Cp3 and two identical vector blocs, i.e., specimen 01 and specimen 02, were subjected to axial tensile load as reported in the experimental study of [24]. Each specimen consisted of upper and lower blocs; the upper bloc connected the ceiling beams to the column, whereas the lower bloc connected the column to the floor beams. The upper and lower blocs were connected by means of two high-strength socket head cap screws (SHCS), as illustrated in Figure 8d. In Figure 8e, it is illustrated that the proposed connection specimens showed an improved initial resistance by producing sharp stiffness in comparison to the selected existing inter-module connections. At a separation of 6 mm, Cp2 carried a higher load (410 kN) compared to Cp3 (350 kN), specimen 01(360 kN), and specimen 02 (335 kN). Reaching at the maximum load (450 kN), Cp2 and specimen 01 produced a separation between column and connection of 9 mm. The specimen 01 and specimen 02 were composed of solid cast-steel and did not show any local deformation in the connection.