Unconstrained Cross-Sectional Shape Optimisation of Cold-Formed Steel Beams and Beam-Columns

This paper is focused on optimising the cross-sectional shapes of simply-supported, singly-symmetric and open-section cold-formed steel (CFS) beams and beam-columns without manufacturing or assembly constraints. A previously developed Genetic Algorithm (GA) is used in this study. Fully restrained and unrestrained beams against lateral deflection and twist, as well as unrestrained beam-columns are optimised, of which the nominal member capacities are determined by the Direct Strength Method (DSM). The optimised cross-sectional shapes are presented and the evolution of the unrestrained cross-sectional shapes for various combinations of axial load and bending moment is analysed and discussed

Shape Optimisation of Cold-Formed Steel Profiles with Manufacturing Constraints - Part I: Algorithm

This paper presents a Genetic Algorithm optimisation method with manufacturing constraints for shape optimisation of cold-formed steel (CFS) profiles. Previous studies on unconstrained shape optimization of CFS crosssections, where the sole aim was to optimise the weight-to-capacity ratio of the profiles, yielded cross-sections that cannot be manufactured. Current coldforming processes, such as roll-forming and brake-pressing, have limited ability to form continuously curved surfaces without discrete bends. This paper defines simple manufacturing rules and introduces them into the evolutionary algorithm. Augmented Lagrangian constraint-handling technique, with equality and inequality constrained violations, is used to avoid ill-conditioned problems. The ability and accuracy of the algorithm to handle the defined manufacturing constraints are verified by implementing it to optimise the section capacity of bisymmetric closed thin-walled profiles, for which an analytical solution is known

Shape optimisation of manufacturable and usable cold-formed steel singly-symmetric and open columns

This paper aims at incorporating manufacturing and assembly features into a shape optimisation algorithm for cold-formed steel (CFS) profiles. Genetic algorithm (GA) is used as the search algorithm and is combined with the augmented Lagrangian constraint-handling method to avoid ill-conditioning. Manufacturable cross-sections are arbitrarily drawn in the initial generation and subsequently treated as an integral part of the GA. The assembly features considered in the study reflect the ones commonly encountered in the construction industry. They include fastening elements (horizontal flange and vertical web) and allowances for utilities, and are treated as constraints. The algorithm is applied to simply-supported singly-symmetric, free-to-warp open section columns with various numbers of manufacturing bends. Three assembly cases for half sections are investigated: (a) a horizontal flange, (b) a horizontal flange and a vertical web, and (c) a horizontal flange and a vertical web with a utility clearance. A two-step optimisation process is used to optimise the columns: (i) the optimum positions of the fastening elements (horizontal flange and vertical web) are determined first and (ii) the cross-sectional shapes are then optimised. The optimised columns are discussed and compared to the unconstrained optimised columns and the conventional lipped Cee-sections. The results demonstrate the robustness and efficiency of the algorithm

Shape optimisation of cold-formed steel columns with manufacturing constraints using the Hough transform

This paper introduces manufacturing constraints into a recently developed evolutionary algorithm for shape optimisation of CFS profiles. The algorithm is referred to as self-shape optimisation and uses Genetic Algorithm (GA) together with the Augmented Lagrangian (AL) method to avoid ill-conditioned problems. Simple manufacturing rules derived from the limitations of current cold-forming processes, i.e. a limited ability to form continuously curved surfaces without discrete bends, are described in the paper and incorporated into the algorithm. The Hough transform is used to detect straight lines and transform arbitrarily drawn cross-sections into manufacturable ones. Firstly, the algorithm is verified against a known optimisation problem and found to accurately converge to a manufacturable optimum solution. Secondly, the algorithm is applied to singly-symmetric CFS columns each of which is subject to an axial compressive load of 75kN and has a uniform wall thickness of 1.2 mm. The strength of the columns is evaluated by the Direct Strength Method (DSM) and all buckling modes are considered. Various column lengths (from 500 mm to 3000 mm) and numbers of roll-forming bends were investigated. The optimised cross-sections are presented and discussed

Shape Optimisation of Cold-Formed Steel Profiles with Manufacturing Constraints - Part II: Applications

This paper uses the Genetic Algorithm (GA)-based optimisation method for cold-formed steel (CFS) profiles with manufacturing constraints, developed in the companion paper, to shape-optimise simply-supported and singly-symmetric open-section columns. Having a uniform wall thickness of 0.047 inch (1.2 mm), the columns are subjected to a compressive axial load of 16,860 lbf (75kN) and optimised for yielding and global buckling. Column lengths ranging from 3.28 ft (1,000 mm) to 9.84 ft (3,000 mm) are investigated. The algorithm is run with and without considering the manufacturing constraints. Differences between the two types of cross-sections, i.e. manufacturable and non-manufacturable, are evaluated. The influence of the number of manufacturable flat segments on the optimised cross-sectional area is also investigated. Future developments of the method for strength optimisation under combined actions and practical applications are discussed

Shape optimisation of cold-formed steel profiles with manufacturing constraints - Part I: algorithm

This paper presents a Genetic Algorithm optimisation method with manufacturing constraints for shape optimisation of cold-formed steel (CFS) profiles. Previous studies on unconstrained shape optimisation of CFS cross- sections, where the sole aim was to optimise the weight-to-capacity ratio of the profiles, yielded cross-sections that cannot be manufactured. Current cold- forming processes, such as roll-forming and brake-pressing, have limited ability to form continuously curved surfaces without discrete bends. This paper defines simple manufacturing rules and introduces them into the evolutionary algorithm. Augmented Lagrangian constraint-handling technique, with equality and inequality constrained violations, is used to avoid ill-conditioned problems. The ability and accuracy of the algorithm to handle the defined manufacturing constraints are verified by implementing it to optimise the section capacity of bisymmetric closed thin-walled profiles, for which an analytical solution is known

Unconstrained shape optimisation of singly-symmetric and open cold-formed steel beams and beam-columns

This study aims to optimise the cross-sectional shape of singly-symmetric, open-section and simply-supported cold-formed steel (CFS) beams and beam-columns. No manufacturing or assembly constraints are considered. The previously developed augmented Lagrangian Genetic Algorithm (GA), referred to as the self-shape optimisation algorithm, is used herein. Fully restrained and unrestrained beams against lateral deflection and twist, as well as unrestrained beam-columns are optimised. Various combinations of axial compressive load and bending moment are analysed for the beam-columns. The Direct Strength Method (DSM) is used to evaluate the nominal member compressive and bending capacities. The accuracy of the automated rules, developed in the literature to determine the elastic local and distortional axial buckling stresses from Finite Strip signature curves, is verified herein to estimate the elastic bending buckling stresses. The optimised cross-sectional shapes are presented for all cases and the evolution of the unrestrained shapes from pure axial compression to pure bending is discussed