In moment frame combined with dampers, the beam-to-column connection is subjected to not only bending moment but axial force in accordance with the damper arrangements. Previous investigation on existing steel passive controlled building structures [Ref. 1] pointed out that the beam axial force reaches up to 30% of its yield strength on entire beam cross section. For such beams, in addition to causing beam instability [Ref. 2], the presence of axial force tends to reduce the magnitude of plastic strength. Furthermore, Not only WF section but also RHS is commonly used for column in Japan. When the beam is connected to RHS column, it is well recognized that the strength of beam-to-column connection is significantly affected by out-of-plane bending strength of column flange (wall) and the lack of design consideration for this effect lead to decrease of plastic deformation capacity[Ref. 3 and 4]. The current recommendation for design of connections in steel structures [Ref. 5] specified the strength evaluation in consideration of this effect. However, the recommendation is only applicable to beam-to-column connection subjected to only bending moment.
 This paper presents strength evaluation of H-beam-to-RHS connection subjected to both bending moment and axial force. In order to derive the strength formulae, the limit analyses based on upper bound theorem were performed. Six collapse mechanisms of beam-to-column connection including the mechanism proposed by [Ref. 6] shown in Fig. 3 and Fig. 4 are considered in this study. All collapse mechanisms consist of axial yielding of beam flange, yielding of beam web along the beam depth and multiple out-of-plane yielding lines on the column flange. The best upper bound can be given by the lowest value of six collapse loads under axial force given. Therefore, the plastic strength of beam-to-column connection is defined by whichever is smaller of the upper bound solution aforementioned and plastic strength of beam.
 The axial force-moment interaction curves (N-M interaction curves) obtained by derived equations shown in Fig. 7, clearly indicated that when strength of beam-to-column connection were governed by collapse load of column flange, the strength of beam-to-column connection was significantly decreased with increase in axial force even if the plastic neutral axis exists within the beam web. Based on this observation, N-M interaction curves for the collapse load were approximated with bi-linear N-M interaction, as shown in Fig. 8. In response, the practical design equations for the yield strength and plastic strength were further developed ensuring a consistency with current design equations.
 In order to examine the validity of proposed design formulae, Finite element analyses were conducted with beam-column subassemblage models under bending moment and/or axial tensile force shown in Fig. 11, In the analysis, axial force ratio of beam, thickness of beam web and thickness of column were varied within the range of practical application. Additionally, the presence of weld access hole placed at beam ends was also examined. As shown in Fig. 15, the prediction by proposed design equations agreed with FEA results within the 8% error for the range of properties examined.