## 1 Introduction
[PERSON] (1991) presented a one-dimensional theoretical modeling to study semi-rigid connection behavior [13]. [PERSON] and [PERSON] (1994) studied the behavior of semi-rigid and rigid connections under a seismic loading condition [14]. [PERSON] and [PERSON] (2017) used the member discrete element method to study the seismic behavior of steel frames with semi-rigid connections. Performing fracture analysis, they showed that semi-rigid and solid steel frames have more capacity compared to hard and rigid steel frames [15]. Furthermore, [PERSON] et al. (2015) performed nonlinear transient analysis on the planar steel frames with semi-rigid connections. They showed that the hysteresis curve of the connections has an important effect on the response of frames and is an important source for inhibition during structural vibration [16]. [PERSON] et al. (2015) evaluated the seismic behavior of two steel buildings with rigid and semi-rigid composite frames that resulted in the construction of semi-rigid internal frames that can lead to less shear and fewer columns and connections and increase the lateral bearing capacity of the building [17]. [PERSON] et al. (2015) compared the nonlinear seismic response of steel frames with semi-rigid and complete-rigid connections. [18]. [PERSON] et al. (2019) implemented the cloud analysis approach to evaluate the seismic reliability of a bending steel frame with two different ductility levels [19]. [PERSON] et al. (2017) investigated the performance of two conventional methods for seismic improvement of flexural strength concrete and steel structures. They implemented the force control method to achieve fragility curves using OpenSees software [20]. [PERSON] et al. (2015) investigated the formulation of incremental nonlinear dynamic analysis using an expanded overlay analysis mechanism under near-fault excitation [21]. [PERSON] et al. (2017) evaluated the accuracy of seismic analytical response using nonlinear numerical simulation by using the FAMA recommendation approach [22]. [PERSON] and [PERSON] (2017) explored seismic damage perspectives using incremental nonlinear analysis and fragility curves in high-rise structures [23]. [PERSON] et al. (2019) studied the ultimate strength of welded stiffened plates by using numerical modeling [24]. This study aims to investigate the linear and nonlinear behavior of semiconductor welded steel connections with a combination of static and reciprocating loads. The effect of semiconductor welded steel connections on the seismic behavior of three multi-story steel frames is investigated. The main innovations of the present study can be concluded as follows. First, as mentioned above, since steel bending frames with semi-rigid connections are one of the systems resistant to lateral loads such as earthquakes and wind, plastic connections are formed in several parts of the structure. Therefore, the role of connection strength in these frames remains a crucial and complex problem needing more in-depth investigation. Besides, in this study, a new type of RBS connection, namely, semi-rigid welded steel connection, is used for modeling, on which very few studies have been conducted before this. Furthermore, in this study, the analytical equation of semi-rigid connection (modified RBS connection) is expanded to estimate the energy absorption of this type of connection in relation to the moment-rotation relationship.