This study investigates how the plastic redistribution of internal forces can be exploited to obtain an improved balance between structural form and the utilization of material capacity, leading to increased material efficiency. Both the external load and the material parameters that govern resistance are treated as random variables. Random variables and their distributions describing yield strength, post-yield behavior and ultimate strength are supported by tensile-test data. The tests indicate a material capacity substantially higher than assumed in current design standards. A set of experimental results for a rectangular one-story, one-bay steel frame with a rectangular cross-section subjected to horizontal loading is used as a benchmark. Effects of uncertainty are assessed by varying the external load and the material parameters in a nonlinear structural model and propagating them with a Monte-Carlo simulation. First-order and second-order reliability methods are applied to the same problem, and the results are compared with the Monte-Carlo estimates and experimental results. The model captures geometric and material nonlinearities and is used to evaluate the capacity of the frame after it reaches yield stress and when plastic hinges form in the members. The cross-sectional geometry is taken as the design variable and is characterized by its second moment of area and section modulus, the latter influencing the plastic moment capacity and structural response after yield stress is reached. By optimizing cross-section design considering the moment redistribution in the structure after formation of a plastic hinge the material efficiency can be increased.