OPTIMUM DESIGN OF STEEL FRAMES WITH TAPERED MEMBERS

The design of steel tapered members for combined axial and flexural st rength is somewhat complex and tedious if no approximation is made. Ho wever, recent load and resistance factor design (LRFD) of the AISC cod e has treated the problem with sufficient accuracy and ease. In this s tudy, an algorithm is developed for the optimum design of steel frames composed of prismatic and/or tapered members. The width of an I-secti on is taken as constant, together with the thickness of web and flange , while the depth is considered to be varying linearly between joints. The depth at each joint in the frame where the lateral restraints are assumed to be provided is treated as a design variable. The objective function which is taken as the volume of the frame is expressed in te rms of the depth at each joint. The displacement and combined axial an d flexural strength constraints are considered in the formulation of t he design problem. The strength constraints, which take into account t he lateral torsional bucking resistance of the members between the adj acent lateral restraints, are expressed as an nonlinear function of th e depth variables. The optimality criteria method is then used to obta in a recursive relationship for the depth variables under the displace ment and strength constraints. These relationships are derived from th e Kuhn-Tucker necessary conditions. The algorithm basically consists o f two steps. In the first one, the frame is analysed under the externa l and unit loadings for the current values of the design variables. In the second, this response is utilized together with the values of Lag range multipliers to compute the new values of the depth variables. Th is process is continued until convergence is obtained. Numerical examp les are presented to demonstrate the practical application of the algo rithm. (C) 1997 Civil-Comp Ltd and Elsevier Science Ltd.