1 INTRODUCTION 1.1 Generalities Under certain circumstances, beam-to-column joints can be subjected to the simultaneous action of bend- ing moments and axial forces. Although, the axial force transferred from the beam is usually low, it may, in some situations attain values that signifi- cantly reduce the joint flexural capacity. These con- ditions may be found in: vierendeel girder systems (widely used in building construction because they take advantage of the member flexural and compres- sion resistances eliminating the need for extra diago- nal members); regular sway frames under significant horizontal loading (seismic or extreme wind); irregu- lar frames (especially with incomplete storeys) under gravity/horizontal loading; and pitched-roof frames. On the other hand, with the recent escalation of terrorist attacks on buildings, the study of progres- sive collapse of steel framed building has been high- lighted, as can be seen in Vlassis et al. (2006). Ex- amples of these exceptional conditions are the cases where structural elements, such as central and/or pe- ripheral columns and/or main beams, are suddenly removed, sharply increasing the joint axial forces. In these situations the structural system, mainly the connections, should be sufficiently robust to prevent the premature failure modes that may lead to pro- gressive structural collapse. Unfortunately, few experiments considering the bending moment versus axial force interactions have been reported. Additionally, the availabe experi- ments are associated with a small number of axial force levels and associated bending moment versus rotation curves, M-φ. Nevertheless, a question still remains on how to incorporate these effects into a structural analysis. There is a need for M-φ curves, associated with numerous axial force levels, which accurately represent the joint rotational stiffness. This has led to the development of an approach to incorporate any moment versus rotation curve from tests including the axial versus bending moment in- teraction, as well as its evaluation and validation against experiments. This approach is not only re- stricted to the use of experiments, but can be applied to results obtained analytically, empirically, me- chanically, and numerically. As this approach is exclusively based on the use of M-φ curves, it can be easily incorporated into a nonlinear semi-rigid joint finite element formulation because the moment versus axial force interaction is associated with a specific M-φ curve. The nonlinear joint finite element formulation does not change. It only requires a rotational stiffness update procedure. This approach has been used to improve the joint fi- nite element model proposed by Del Savio (2004) and Del Savio et al. (2004, 2005), which was ini- tially based on the semi-rigid joint force independ- ence. 1.2 Component Method The component method consists of relatively simple joint mechanical models, based on a set of rigid and spring components. The component method, intro- duced in Eurocode 3 (2003), can be used to deter- mine the joint’s resistance and initial stiffness. Its application requires the identification of active com- Developments in semi-rigid joint moment versus rotation curves to incorporate the axial versus moment interaction A.A. Del Savio Imperial College London, London, United Kingdom & PUC-Rio, Rio de Janeiro, RJ, Brazil D.A. Nethercot Imperial College London, London, United Kingdom P.C.G.S. Vellasco UERJ – State University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil S.A.L. Andrade & L.F. Martha PUC-Rio – Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil ABSTRACT: Under certain circumstances, beam-to-column joints can be subjected to the simultaneous ac- tion of bending moments and axial forces. Although, the axial force transferred from the beam is usually low, it may, in some situations attain values that significantly reduce the joint flexural capacity. Few experimental tests are available and are usually described by their associated moment-rotation curves. An interesting ques- tion is how to incorporate these curves into a structural analysis, for the various required axial force load lev- els. The main aim of the present paper is the development of a consistent and simple approach to determine any moment versus rotation curve from experiments including the axial versus bending moment interaction.