Developments in semi-rigid joint moment versus rotation curves to incorporate the axial versus moment interaction

Under certain circumstances, beam-to-column joints can be subjected to the simultaneous action 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 question is how to incorporate these curves into a structural analysis, for the various required axial force load levels. 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. ponents; evaluation of the force-deformation response of each component; and the subsequent assembly of the active components for the evaluation of the joint moment versus rotation response. The Eurocode 3 (2003) component method permits the evaluation of the semi-rigid joint’s rotational stiffness and moment capacity when subjected to pure bending. However, this component method is still not able to calculate these properties when, in addition to the applied moment, an axial force is also present. Eurocode 3 (2003) suggests that the axial load may be disregarded in the analysis when its value is less than 10% of the beam’s axial plastic resistance, but provides no information for cases involving larger axial forces. Even though, the Eurocode 3 (2003) component method has not considered the axial force, its general principles could be used to cover this situation, since it is based on the use of a series of force versus displacement relationships, which only depend on the axial force level, to characterize any component behaviour. 1.3 Background: Experimental and theoretical models The study of the semi-rigid characteristics of beam to column connections and their effects on frame behaviour can be traced back to the 1930s, Li et al. (1995). Since then, a large amount of experimental and theoretical work has been conducted both on the behaviour of the connections and on their effects on the complete frame performances. Despite the large number of experiments, they do not cover all possible connection ranges. As an alternative to tests, different methods have been proposed by researchers to predict bending moment versus rotation curves. These methods are usually classified as: empirical, analytical, mechanical (component-based approaches) and numerical (finite element). Recently, several researchers have paid special attention to joint behaviour under combined bending moment and axial force. The investigators concluded that the presence of the axial force in the joints modifies their structural response and, therefore, should be considered. A number of experimental works deserve mention: Guisse et al. (1997) performed tests on six prototypes of column bases with extended endplates with bolts placed outside of the beam height and six tests on flush endplates with bolts inside the beam height. In these tests, the compressive axial force was first applied and kept constant during the test while the bending moment was subsequently increased up to failure. Wald et al. (2000) conducted two tests on beamto-beam and beam-to-column joints. The loading system adopted a proportional increase of axial force and bending moment. However, a test without axial forces was not performed, making it difficult to assess the axial force influence on the joint response. Lima et al. (2004) and Simões da Silva et al. (2004) performed tests on fifteen prototypes, i.e. eight flush and seven extended endplate joints. All the tests adopted a loading strategy consisting of an initial application of the total axial force (tension or compression), held constant during the entire test, and the subsequent incremental application of the bending moment. Regarding the theoretical models recently developed to predict the behaviour of beam-to-column joints under bending moment and axial force, it is possible to mention: Jaspart (1997, 2000), Finet (1994) and Cerfontaine (2001, 2004) have applied the principles of the component method to establish design predictions of the M-N interaction curves and initial stiffness. Simões da Silva & Coelho (2001), based on the same general principles, have proposed analytical expressions for the full non-linear response of a beam-to-column joint under combined bending and axial forces. Sokol et al. (2002) proposed an analytical model to predict the behaviour of joints subjected to bending moment and axial force for proportional loading. Table 1 presents a summary of recent studies carried out to investigate joint behaviour when subjected to bending moment and axial force. Table 1. Summary of studies of joints subjected to bending and axial force, Lima et al. (2004). __________________________________________________ Authors Analysis type __________________________________________________ Finet (1994) AM* Jaspart (1997, 2000) AM* and ET** Cerfontaine (2001, 2004) AM* Simões da Silva & Coelho (2001) AM* Simões da Silva et al. (2001) AM* Lima (2003) ET** Wald & Svarc (2001) AM* Sokol et al. (2002) AM* _________________________________________________ * AM = Analytical model. ** ET = Experimental tests.