This thesis presents the development and results of an iterative method for obtaining a minimum weight structural design, called an optimum design. The optimum design iteration is based on a sequence of fully stressed designs, each intermediate design possessing a distinct set of allowable stresses that force the desirable design changes to occur. The test for the optimum state is based on the Kuhn-Tucker conditions, where negative Lagrange multipliers in the set identify element parameters that can be changed to produce a lighter weight structure. Five case studies are presented to demonstrate the algorithm.