A Derivation of the Uniform Force Method for Analysis and Design of Gusset Plate Connections for Vertical Diagonal Bracing

The Uniform Force Method (UFM) for vertical diagonal bracing with gusset plate connections is a statically determinate analysis and design in which there are no moments at the interfaces between column, beam, and gusset, producing economical results. A derivation of force equations for a less constrained generalized case with only one gusset control point, rather than two, is given in Appendix A of AISC Design Guide 29, Vertical Bracing Connections (Muir and Thornton, 2014). By introducing the UFM constraint equation, the less constrained case in Design Guide 29 might be reduced to generate the UFM force equations, but that indirect proof has not been published, nor any proof until now. Herein, a short, simple, and direct derivation of the UFM force equations is presented.