A convex relaxation formulation for a minimum weight design problem of steel frame structures is proposed in this paper. The non-convexity of this kind of problem usually results in only local optimal solutions. Further, although the global optimal solution is not always necessary, a better local optimal solution is always preferred. To measure the accuracy of a local optimal solution, we use branch and bound approach with reformulation-linearization technique. We propose a new region partitioning technique for this approach. The effectiveness of the formulation is investigated with two numerical examples.
