Interactive optimization of nonprismatic girders

Abstract

An efficient and robust optimization algorithm is presented for minimum weight design of continuous multi-span nonprismatic steel plate girders using the General Geometric Programming technique. The nonlinear programming problem is formulated on the basis of the last editon of the American Institute of Steel Construction (AISC) Specification. The design variables are the flange width and thickness, the web depths and thickness, and the dimensions and spacings of the transverse stiffeners for stiffened plate girders. Each span is divided into one uniform and one or two nonuniform finite elements. The stiffness matrix of the nonuniform element is obtained through the Rayleigh-Ritz approach. The element stiffness matrices for each span are subsequently transformed into a superelement stiffness matrix through the condensation of internal degrees of freedom where a change of cross-section occurs. In the optimization algorithm, the nonlinear primal problem is transformed to an equivalent standard linear programming problem via double condensation. The algorithm is general and can be applied to stiffened or unstiffened, homogeneous or hybrid plate girders. The girder may be fully restrained against lateral torsional buckling or may have lateral supports only at selected locations along the length of the girder. The algorithm is implemented in FORTRAN 77 in an interactive computing environment with graphic capabilities.