This paper presents an optimum design of statically indeterminate two-hinged steel portal frames under multiple loadings. An explicit formulation of the analysis equations using the Virtual Work Method is developed. Loading cases include both gravity loads and wind loads. Design equations involve local buckling, lateral torsional buckling, shear buckling, combined stresses and deflection constraints, as provided by Egyptian Code of Practice for Steel Construction and Bridges (ECP’01 2001) are included. The objective function is chosen as the minimum weight of the structure. The design variables are the cross-sectional dimensions of the built-up sections for rafters and columns. The design constraints cover all cases of discontinuity for compact prismatic sections. Ordinary mild steel and high tensile steel cases are considered. The optimization technique adopted in this research is the Modified Method of Feasible Directions. Several examples are presented to validate the efficiency of the formulation and to prove that the designs obtained in this work are more economical than those provided by other classical design approaches. Savings up to fifty percent of the weight of the frame are achieved for some cases.
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