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An algorithm for the optimum design of braced and unbraced steel frames under earthquake loading
Author(s) -
Gülay Gülten,
Boduroǧlu Hasan
Publication year - 1989
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290180111
Subject(s) - braced frame , linearization , structural engineering , linear programming , bracing , stiffness , simplex algorithm , rigidity (electromagnetism) , minification , mathematics , lagrange multiplier , mathematical optimization , displacement (psychology) , algorithm , computer science , engineering , nonlinear system , brace , frame (networking) , psychology , telecommunications , physics , quantum mechanics , psychotherapist
A solution technique based on the sequential linear programming (SLP) method is presented for the optimum design of braced and unbraced steel frames in seismic regions. First, the optimum rigidity distribution of the frames under static loading is computed, then the optimization procedure is repeated under the combined loading, setting lower bounds on the optimum static cross‐sectional areas and increasing allowable stresses. The stiffness, stress, displacement and side constraints are included in the optimization problem. As a result, a highly non‐linear mathematical programming problem is produced. A non‐linear programming algorithm is offered for the solution which is based on the successive linearization of non‐linear expressions and employs the simplex routine in an iterative manner. Design variables are chosen to be the free nodal displacements and the cross‐sectional areas of the members, while the objective function is taken to be the minimization of the total volume of the structure. As numerical applications, optimum weights of several frames (unbraced, concentrically and eccentrically braced) under static and combined loading cases are computed and the results are compared with those available in the literature.