An algorithm for the optimum design of braced and unbraced steel frames under earthquake loading

Abstract

SUMMARYA 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.

A New Genetic Algorithm Methodology for Design Optimization of Truss Structures: Bipopulation-Based Genetic Algorithm with Enhanced Interval Search

“…Vanderplaats and Sugimoto [11] developed a design technique "automated design synthesis" utilizing the approaches of SLP and SQP. Automated design synthesis method was proposed for minimizing the weight of frames with various bays and stories under static and seismic loadings by Karihaloo and Kanagasundaram [12], and Gülay and Boduroglu [13]. The optimization techniques based on nonlinear programming were used for generation of optimal designations for steel structures under different loading conditions and design requirements (Lassen [14], Wang and Grandhi [15], Salajegheh [16], Hernández [17]).…”

“…The position numbers corresponding to optimal design for example 3 are [10,14,13,14,6 17, 8, 19, 23, 23, 4, 7, 20, 9, 8, 4, 9, 7, 7, 12, 16, 15, 6, 16, 14, 1, 14, 6, 3, 16, 12, 20, 18, 15, 7, 3, 2, 6, 11, 3, 15, 10, 22, 8, 17, 14, 19, 17, 3, 18, 11, 15, 5, 17, 8, 20, 8, 18, 8, 4, 8, 20, 21, 6, 12, 3, 19, 16, 7, 17, 15, 11, 13, 13, 11, 11, 23, 22, 10, 18, 22;] …”

Graph theoretical implementation of memetic algorithms in structural optimization of frame bracing layouts

“…Since, the pioneering works of Maxwell (1890) and Michell (1904) for dealing with structural topology optimization, numerous attempts are made for similar problems and have proven the efficiency of diagonal members in resisting transversal loads (Majid and Elliott, 1971; Taranath, 1998; Kaveh and Kalatjari, 2003; Gulay and Boduroglu, 1989; Kameshki and Saka, 2001; Di Sarno and Elnashi, 2004; Mijar et al , 1998; Liang et al , 2000; Mueller et al , 2002). Such a superior efficiency with respect to beams and columns has enforced the use of diagonal bracings for optimal resistant systems against lateral loads in building frames.…”

Equation for achieving efficient length of link-beams in eccentrically braced frames and its reliability validation

“…Great optimization attempts in the previous works devoted to design phase of the EBF systems, like optimizing maximum dissipating energy in the link beams subjected to some design specifications like section of link beams, section of stiffeners in link beams, location of stiffeners and … [3][4][5] mainly depends on engaged design code or minimizing frame weight based on the geometry of the eccentrically braced frames or other design specifications [6][7][8]. In this paper, the only specification of the frame that is going to be determined by the optimum amount is the length of link-beam which is a preliminary presumed parameter in design phase of EBF frames and it is not reliant on presumed design provisions.…”