The focus of this thesis was to measure the relationship between the elastic chord stress and the eccentricity of a moment connection between two rectangular steel hollow structural sections (HSS) when subjected to out-of-plane bending. Two parametric studies were performed with a total of one-hundred-thirteen finite element models using ANSYS Student V18.2 (ANSYS 2017). A preliminary coarse parametric study of forty-seven finite element models was conducted to investigate the relationship between eccentricity and various parameters. The results of the preliminary study were then used to clarify which parameters should be examined more closely. A subsequent refined parametric study of sixty-six finite element models was performed to isolate the relationship between eccentricity and stiffness as well as the relationship between eccentricity and the von Mises stress in the chord wall, sidewall, and corner. Chord wall plastification appeared to control the design of eccentric connections, and a positive relationship between stress and eccentricity was generally observed. An inverse relationship was observed between the eccentricity of a connection and the relative stiffness of that connection. Further study should be conducted prior to recommending code design parameters or design guidance for eccentric connections. Eccentricity has been shown to have an overall negative effect on connection performance. Therefore, designers should take care when detailing eccentric tube connections.