Advances in Civil Engineering

Volume 2018, Article ID 3854620, 16 pages

https://doi.org/10.1155/2018/3854620

## Optimum Design of Braced Steel Space Frames including Soil-Structure Interaction via Teaching-Learning-Based Optimization and Harmony Search Algorithms

Correspondence should be addressed to Korhan Ozgan; moc.oohay@nagzonahrok

Received 19 August 2017; Revised 13 November 2017; Accepted 6 December 2017; Published 3 April 2018

Academic Editor: Moacir Kripka

Copyright © 2018 Ayse T. Daloglu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Optimum design of braced steel space frames including soil-structure interaction is studied by using harmony search (HS) and teaching-learning-based optimization (TLBO) algorithms. A three-parameter elastic foundation model is used to incorporate the soil-structure interaction effect. A 10-storey braced steel space frame example taken from literature is investigated according to four different bracing types for the cases with/without soil-structure interaction. X, V, Z, and eccentric V-shaped bracing types are considered in the study. Optimum solutions of examples are carried out by a computer program coded in MATLAB interacting with SAP2000-OAPI for two-way data exchange. The stress constraints according to AISC-ASD (American Institute of Steel Construction-Allowable Stress Design), maximum lateral displacement constraints, interstorey drift constraints, and beam-to-column connection constraints are taken into consideration in the optimum design process. The parameters of the foundation model are calculated depending on soil surface displacements by using an iterative approach. The results obtained in the study show that bracing types and soil-structure interaction play very important roles in the optimum design of steel space frames. Finally, the techniques used in the optimum design seem to be quite suitable for practical applications.

#### 1. Introduction

Optimum design of steel structures prevents excessive consumption of the steel material. Suitable cross sections must be selected automatically from a predefined list. Moreover, selected profiles should satisfy some required constraints such as stress, displacement, and geometric size. Metaheuristic search techniques are highly preferred for problems with discrete design variables. There are many metaheuristic techniques developed recently. Some of them are genetic algorithm, harmony search algorithm, tabu search algorithm, particle swarm optimization, ant colony algorithm, artificial bee colony algorithm, teaching-learning-based optimization, simulated annealing algorithm, bat-inspired algorithm, cuckoo search algorithm, and evolutionary structural optimization. In literature, there are many studies available for the optimum design of structures using these algorithms. For example, Daloglu and Armutcu [1] used the genetic algorithm method for the optimum design of plane steel frames. Kameshki and Saka [2] carried out the optimum design of nonlinear steel frames with semirigid connections using the genetic algorithm. Lee and Geem [3] developed a new structural optimization method based on the harmony search algorithm. Hayalioglu and Degertekin [4] applied genetic optimization on minimum cost design of steel frames with semirigid connections and column bases. Kelesoglu and Ülker [5] searched for multiobjective fuzzy optimization of space trusses by MS Excel. Degertekin [6] compared simulated annealing and genetic algorithms for the optimum design of nonlinear steel space frames. Esen and Ülker [7] optimized multistorey space steel frames considering the nonlinear material and geometrical properties. Saka [8] used the harmony search algorithm method to get the optimum design of steel sway frames in accordance with BS5950. Degertekin and Hayalioglu [9] applied the harmony search algorithm for minimum cost design of steel frames with semirigid connections and column bases. Hasancebi et al. [10] investigated nondeterministic search techniques in the optimum design of real-size steel frames. Hasançebi et al. [11] used the simulated annealing algorithm in structural optimization. Hasancebi et al. [12] investigated the optimum design of high-rise steel buildings using an evolutionary strategy integrated with parallel algorithm. Togan [13] used one of the latest stochastic methods, teaching-learning-based optimization, for design of planar steel frames. Aydogdu and Saka [14] used ant colony optimization for irregular steel frames including the elemental warping effect. Dede and Ayvaz [15] studied structural optimization problems using the teaching-learning-based optimization algorithm. Dede [16] applied teaching-learning-based optimization on the optimum design of grillage structures with respect to LRFD-AISC. Hasançebi et al. [17] used a bat-inspired algorithm for structural optimization. Saka and Geem [18] prepared an extensive review study on mathematical and metaheuristic applications in design optimization of steel frame structures. Hasançebi and Çarbaş [19] studied the bat-inspired algorithm for discrete-size optimization of steel frames. Dede [20] focused on the application of the teaching-learning-based optimization algorithm for the discrete optimization of truss structures. Azad and Hasancebi [21] focused on discrete-size optimization of steel trusses under multiple displacement constraints and load case using the guided stochastic search technique. Artar and Daloğlu [22] obtained the optimum design of composite steel frames with semirigid connections and column bases. Artar [23] used the harmony search algorithm for the optimum design of steel space frames under earthquake loading. Artar [24] used the teaching-learning-based optimization algorithm for the optimum design of braced steel frames. Carbas [25] studied design optimization of steel frames using an enhanced firefly algorithm. Daloglu et al. [26] investigated the optimum design of steel space frames including soil-structure interaction. Saka et al. [27] researched metaheuristics in structural optimization and discussions on the harmony search algorithm. Aydogdu [28] used a biogeography-based optimization algorithm with Levy flights for cost optimization of reinforced concrete cantilever retaining walls under seismic loading.

In literature, there are several researches available for optimum structural design, as mentioned above. On the other hand, there are a few researches on the optimum design of braced steel space frames including soil-structure interaction. So, this study investigates a 10-storey braced steel space frame structure studied previously in literature, which is investigated for four different bracing types and soil-structure interaction. These bracing types are X, V, Z, and eccentric V-shaped bracings. Optimum design solutions are obtained using a computer program developed in MATLAB [29] interacting with SAP2000-OAPI (open application programming interface) [30]. Suitable cross sections are automatically selected from a list including 128 W profiles taken from AISC (American Institute of Steel Construction). The frame model is subjected to wind loads according to ASCE7-05 [31] as well as dead, live, and snow loads. The analysis results are found to be quite consistent with the literature results. In this study, the vertical displacements on soil surfaces are also calculated. It is observed that minimum weights of space frames vary depending on the bracing type. Also, it can be concluded that incorporation of soil-structure interaction results in heavier steel weight.

#### 2. Optimum Design Formulation

The optimum design problem of braced steel space frames is calculated as follows:where is the weight of the frame, is the cross-sectional area of group , and are the density and length of member , is the total number of groups, and is the total number of members in group .

The stress constraints according to AISC-ASD [32] are defined as follows:

If , instead of using (2), the stress constraint is calculated as follows:where is the total number of members subjected to both axial compression and bending stresses, is the computed axial stress, is the allowable axial stress under axial compression force alone, is the computed bending stress due to bending of the member about its major , is the allowable compressive bending stress about major, is the Euler stress, is the yield stress of the steel, and is a factor. It is calculated from for the braced frame member without transverse loading between the ends and for the braced frame member with transverse loading.

The effective length factors of columns in braced frames are calculated as follows [33]:where and are the relative stiffness factors at the Ath and Bth ends of columns.

The maximum lateral displacement and interstorey drift constraints are defined as follows:where is the displacement of the *j*th degree of freedom under load case *l*, is the displacement at the upper bound, is the number of restricted displacements, and is the total number of loading cases.where is the interstorey drift of the *i*th column in the *j*th storey under load case , is the limit value, is the number of storeys, and is the number of columns in a storey.

The beam-to-column connection geometric constraint is determined as follows:where is the number of joints where beams are connected to the web of the column, is the flange width of the beam, is the depth of the column, is the flange thickness of the column, is the number of joints where beams are connected to the flange of the column, and and are flange widths of the beam and column, respectively (Figure 1).