Buildings 2023, 13, 328. https://doi.org/10.3390/buildings13020328 www.mdpi.com/journal/buildings Article An BESO Approach for Optimal Retrofit Design of Steel Rectangular-Hollow-Section Columns Supporting Crane Loads Rut Su, Sawekchai Tangaramvong * and Thu Huynh Van Department of Civil Engineering, Center of Excellence in Applied Mechanics and Structures, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand * Correspondence: sawekchai.t@chula.ac.th Abstract: In this paper, we propose a cost-effective optimal-topology retrofitting technique for hol- low-steel-section columns to sufficiently support industrial running cranes. A so-called bi-direc- tional evolutionary structural optimization (BESO) method was encoded within the MATLAB mod- eling framework, with a direct interface with an ANSYS commercial finite-element analysis pro- gram, to determine the optimal topology of double external steel plates connected to columns in a 3D space. For the initial ground structure, we have adopted standard uniform double U-shaped external stiffener plates located at the top and bottom flange layers of an I-beam to box-column connection (IBBC) area. The influences of inelastic materials and the incorporated nonlinear geom- etry can effectively describe the premature (local buckling) failures of the columns in an IBBC area. The applications of the proposed optimal-topology BESO-based stiffening method are illustrated through the retrofitting of three hollow-steel-section columns, characterized by non-slender and slender compression sections. Some concluding remarks are provided on the pre- and post-retrofit- ted responses of the columns, with the results showing both the accuracy and robustness of the proposed external stiffening schemes. Keywords: hollow steel column; retrofit; topology optimization; local bucking; elastoplastic mate- rials; stress intensity 1. Introduction Steel structures have been widely designed and constructed, not only in view of their engineering safety and integrity, but also because of their light weight and architectural aesthetics, thus providing more sustainable results and high performance in project de- velopment. Considering their superior strength, hollow-steel-section (HSS) members pro- vide a higher load capacity than open-steel sections [1]. Often, HSS members are suitably employed in engineering structures and infrastructures, particularly those with special requirements, such as the need for a long-span capability. One drawback underpinning the use of HSS members that limits their application is the occurrence of premature local buckling failures under concentrated forces (highly intensive stresses). A specific example involves the case of an HSS column connected to a corbel used under industrial running cranes (such as those employed in warehouses) [2]. The thin chord surfaces of HSS mem- bers are prone to premature failures under combined axial compression and flexural (ec- centrically applied) forces. Although many methods have been presented for the retrofitting of open-steel-sec- tion columns, few efforts have been made regarding the application of HSS columns, which invariably experience premature local failures, namely, inelastic column chord buckling. Applying lateral restraining materials (i.e., internal and external stiffeners) to the column members is a retrofitting approach that has been commonly adopted to pre- vent this special class of failure phenomena [3]. The stiffeners provide some additional Citation: Su, R.; Tangaramvong, S.; Van, T.H. An BESO Approach for Optimal Retrofit Design of Steel Rectangular-Hollow-Section Columns Supporting Crane Loads. Buildings 2023, 13, 328. https://doi.org/10.3390/build- ings13020328 Academic Editors: Bo Yang, Shan Gao, Hai-Ting Li and Kang Chen Received: 20 December 2022 Revised: 17 January 2023 Accepted: 19 January 2023 Published: 22 January 2023 Copyright: © 2023 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (https://cre- ativecommons.org/licenses/by/4.0/).