A nonlinear model for gusset plate connections

• Model accounts for all members attached to gusset plate connection.
• In linear range, each member has 6 × 6 stiffness matrix.
• In nonlinear range, each member has six load–displacement and moment–rotation curves.
• Verified against NTSB model of I-35 W Bridge.
• Most useful for structures with repeated similar connections and multiple load cases.

The investigation of the 2007 collapse of the I-35 W Highway Bridge in Minneapolis, Minnesota, used very detailed nonlinear finite-element (FE) analysis. On the other hand, the Federal Highway Administration (FHWA) provided simple guidelines for the load rating of gusset plates, but load rating was never intended to capture the actual behavior of gusset plates. The approach proposed here combines the accuracy of the first method with the simplicity of the second. From the detailed FE analysis of a single joint, the stiffness matrix of semi-rigid equivalent springs (linear in a simple model, nonlinear in a more advanced model) was derived by applying forces and moments to the free end of each portion of member (hereafter called stub member) that framed into the joint, one action at a time, while keeping the ends of the other stub members fixed. The equivalent springs were then placed in a global model, which was in turn verified against a global, detailed FE analysis of the I-35 W Highway Bridge. The nonlinear equivalent spring model was able to predict the correct failure mode. The approach was applied to a Howe truss bridge as an example of performance prediction of bridges with semi-rigid connections, most of them of one type. As the simplified spring model was developed from a detailed FE analysis of the joint considered, this approach would not be justified if all joints had to be modeled in detail. Examples where the approach can be used include: structures where only specific joints need to be investigated (e.g., joints subjected to concentrated loads), and structures where the same joint model can be used repeatedly at multiple locations. In some cases, the effort required in performing detailed FE analyses of many joints in order to develop simplified models can be justified if the simplified models can be used in subsequent multiple load cases, thus leading to overall computational savings. Under these circumstances, the nonlinear connection model proposed here provides a simple and affordable way to account for connection performance in global analysis.