Optimum design of cold-formed steel beams subject to bending, shear and web crippling

Recently, cold-formed steel (CFS) members have become more prevalent within the construction industry. CFS beams can be optimised to increase their load carrying capacity. In this research, shape optimisation method is developed to obtain high structural resistance of cold-formed steel beams by taking into account the bending, shear and web crippling actions. First, the flexural strengths of the sections are determined based on the effective width method adopted in EC3, while the optimisation process is performed using the Particle Swarm Optimisation (PSO). Five different CFS channel cross-section are considered in the optimisation process. The flexural strengths of the optimised sections are then verified using detailed nonlinear finite element analysis. The results indicated that the optimised CFS beams provide a bending capacity which is up to 50% higher than the conventional CFS channel sections with the same amount of material. Shear, web crippling behaviours of five optimisedCFS beams were then investigated. Finally, innovative optimised CFS beam was proposed for lightweight forms of buildings and modular building systems to obtain high structural resistance

Experimental investigation of local-flexural interactive buckling of cold-formed steel channel columns

This paper presents the results of a comprehensive experimental programme aimed at studying the interaction of local and overall flexural buckling in cold-formed steel (CFS) plain and lipped channels under axial compression. The results were further used to verify the accuracy of the current design procedures in Eurocode 3, as well as to evaluate the effectiveness of a previously proposed optimisation methodology. A total of 36 axial compression tests on CFS channels with three different lengths (1 m, 1.5 m and 2 m) and four different cross-sections were conducted under a concentrically applied load and pin-ended boundary conditions. The initial geometric imperfections of the specimens were measured using a specially designed set-up with laser displacement transducers. Material tests were also carried out to determine the tensile properties of the flat parts of the cross-sections, as well as the cold-worked corner regions. A comparison between the experimental results and the Eurocode 3 predictions showed that the effective width approach combined with the P–M interaction equation proposed in Eurocode 3 to take into account the shift of the effective centroid consistently provided safe results. However, the Eurocode 3 procedures were also quite conservative in predicting the capacity pertaining to local-global interaction buckling, especially for plain channels. Furthermore, the experimental data confirmed the results of an optimisation study and demonstrated that the optimised CFS columns exhibited a capacity which was up to 26% higher than the standard channel with the same amount of material taken as a starting point

Optimum design of cold-formed steel portal frame buildings including joint effects and secondary members

In steel portal frames, cold-formed steel channel sections are increasingly used as the primary framing components, in addition to the secondary members e.g. purlins and side rails. For such framing systems, the stiffness of the joints at the eaves and apex affects the bending moment distribution, as well as the frame deflections. This paper investigates the influence of two joint configurations having full rigidity and semirigidity, respectively, on the optimum design of cold-formed steel portal frames. A real-coded genetic algorithm is used to search for the most cost-effective design. It is shown that through incorporating joint effects explicitly into the design process, a more appropriate balance between the joints and the member properties can be obtained, thus optimizing material use. The study then investigates the effect of secondary members on the optimum design. It is shown that incorporating the secondary members is important for portal frames having spans less than 12 m. For example, for a frame spacing less than 6 m, the material cost of the primary members can be reduced by up to 15%

The mechanics of composite corrugated structures: A review with applications in morphing aircraft

Corrugation has long been seen as a simple and effective means of forming lightweight structures with high anisotropic behaviour, stability under buckling load and energy absorption capability. This has been exploited in diverse industrial applications and academic research. In recent years, there have been numerous innovative developments to corrugated structures, involving more elaborate and ingenious corrugation geometries and combination of corrugations with advanced materials. This development has been largely led by the research interest in morphing structures, which seek to exploit the extreme anisotropy of a corrugated panel, using the flexible degrees of freedom to allow a structure’s shape to change, whilst bearing load in other degrees of freedom. This paper presents a comprehensive review of the literature on corrugated structures, with applications ranging from traditional engineering structures such as corrugated steel beams through to morphing aircraft wing structures. As such it provides an important reference for researchers to have a broad but succinct perception of the mechanical behaviour of these structures. Such a perception is highly required in the multidisciplinary design of corrugated structures for the application in morphing aircraft

Development of More Efficient Cold-Formed Steel Channel Sections in Bending

Cold-formed steel (CFS) cross-sections can be optimised to increase their load carrying capacity, leading to more efficient and economical structural systems. This paper aims to provide a methodology that would enable the development of optimised CFS beam sections with maximum flexural strength for practical applications. The optimised sections are designed to comply with the Eurocode 3 (EC3) geometrical requirements as well as with a number of manufacturing and practical constraints. The flexural strengths of the sections are determined based on the effective width method adopted in EC3, while the optimisation process is performed using the Particle Swarm Optimisation (PSO) method. To allow for the development of a new ‘folded-flange’ cross-section, the effective width method in EC3 is extended to deal with the possible occurrence of multiple distortional buckling modes. In total, ten different CFS channel cross-section prototypes are considered in the optimisation process. The flexural strengths of the optimised sections are verified using detailed nonlinear finite element (FE) analysis. The results indicate that the optimised folded-flange section provides a bending capacity which is up to 57% higher than standard optimised shapes with the same amount of material

An experimental and numerical investigation on strengthening the upright component of thin-walled cold-formed steel rack structures

Cold-formed steel (CFS) racking systems are widely used for storing products in warehouses. However, as commonly used structures in storage systems, thin-walled open sections are subjected to stability loss because of various buckling modes, including flexural, local, torsional and distortional. This research proposes a novel technique to increase the ultimate capacity of uprights, utilising bolts and spacers, under flexural and compressive loads. The proposed components are attached externally to the sections in certain pitches along the length. In this regard, axial tests were performed on 72 upright frames and nine single uprights with various lengths and thicknesses. Also, the impact of using reinforcing elements was evaluated by investigating the failure modes and ultimate load results. It was concluded that the reinforcement technique is able to restrain upright flanges and therefore improve the upright profiles' strength. For testing the flexural behaviour, 18 samples of three types were made, including non-reinforced sections and two types of sections reinforced along the upright length at different pitches. After that, monotonic loading was applied along both the minor and major axes of the samples. The suggested reinforcing method leads to increasing the flexural capacity of the upright sections about both the major and minor axes. Also, by using reinforcing system, the flexural performance was improved, and buckling and deformation were constrained. In addition, the reinforcement technique was evaluated by Finite Element (FE) method. Moreover, Artificial Intelligence (AI) and Machine Learning (ML) algorithms were deployed to predict the normalised ultimate load and deflection of the profiles. Following the empirical tests, the axial and flexural performance of different CFS upright profiles with various lengths, thicknesses and reinforcement spacings were simulated and examined. It was shown that the reinforcing technique improved the capacity of the samples. Consequently, the proposed reinforcements could be considered a highly effective and low-cost technique to strengthen the axial and flexural behaviour of open CFS sections considering a trade-off between performance and cost of utilising the approach

More efficient cold-formed steel elements and bolted connections

Modern society is challenged by economic and environmental issues, requiring engineers to develop more efficient structures. Using cold-formed steel (CFS) frame in construction industry can lead to more sustainable design, since it requires less material to carry the same load compared with other materials. However, the application of CFS structural systems is limited to low story buildings due to the inherent weaknesses of premature buckling behaviour of members and the low ductility of connections. Consequently, current design guidelines of CFS systems are very conservative especially in the case of seismic design. Furthermore, there is no generic optimisation framework for the CFS elements, capable of taking into account both manufacturing/construction constraints and post-buckling behaviour. This study aims to better understand, to predict, and to optimise CFS elements based on their strength and post-buckling behaviour. The optimised elements can be then included in full-structure modelling to develop more efficient CFS structural connections with high ductility and energy dissipation capacity, suitable for multi-story buildings in seismic regions. The geometrical dimensions of manufacturable CFS cross-sections were optimised regarding their maximum compressive and bending strength. All the sections were considered to have a fix coil width and thickness while the optimisation was performed based on effective width method suggested in EC3. The optimised solutions were achieved using Particle Swarm Optimisation (PSO) algorithm. The accuracy of the optimisation procedure was assessed using experimentally validated nonlinear Finite Element (FE) analyses accounting for the effect of imperfections To allow for the development of a new ‘folded-flange’ beam cross-section, the effective width method in EC3 was extended to deal with the presence of multiple distortional buckling modes. Improved strength were achieved for CFS elements by using the proposed optimisation framework. A non-linear shape optimisation method was presented for the optimum design of CFS beam sections based on their post-buckling behaviour. A developed PSO algorithm was linked to the ABAQUS finite element programme for inelastic post-buckling analysis and optimisation. The results also demonstrate that the optimised sections develop larger plastic area, which is particularly important in seismic design of moment-resisting frames. An experimental programme was carried out at the University of Sheffield to investigate the design and optimisation, considering interactive buckling in cold-formed steel channels under compression and bending. Both standard and optimised sections were tested. The specimen imperfections were measured using a specially designed set-up with laser displacement. Material tests were also carried out to determine the tensile properties of the flat plate and of the cold-worked corners. A total of 36 columns with three lengths and 6 back-to-back beams were completed. The column specimens were tested under a concentrically applied load and with pin-ended boundary conditions while the beams were tested in a four-point bending configuration. Based on the tests, numerical models were proposed and calibrated and the proposed optimisation framework was verified. A numerical study on the structural behaviour of CFS bolted beam-to-column connections under cyclic loading was presented. An innovative two node element which can take into account the slippage-bearing effects was proposed and implemented using an ABAQUS user defined subroutine. The connection performance in terms of strength, ductility, energy dissipation capacity and damping coefficient were investigated. The effects of bolt configuration, cross-sectional shapes and thicknesses on the connection performance were therefore examined. It is indicated that the proposed numerical model is robust and computationally efficient to simulate the failure modes and moment-rotation response of CFS bolted moment resisting connections

Development of optimum cold-formed steel sections for maximum energy dissipation in uniaxial bending

Cold-formed steel (CFS) elements are increasingly used as load-bearing members in construction, including in seismic regions. More conventional hot-rolled steel and concrete building structures are typically allowed by the design standards to exceed their elastic limits in severe earthquakes, rendering parameters indicating ductility and energy dissipation of primordial importance. However, insufficient research has yet been conducted on the energy dissipation of CFS structures. In the majority of previous optimization research on CFS sections the ultimate capacity, as typically controlled by local, distortional and/or global buckling modes, is considered to be the sole optimization criterion. This paper aims to improve the seismic performance of CFS elements by optimising their geometric and material highly non-linear post-buckling behaviour to achieve maximum energy dissipation. A novel shape optimisation framework is presented using the Particle Swarm Optimisation (PSO) algorithm, linked to GMNIA ABAQUS finite element analyses. The relative dimensions of the cross-section, the location and number of intermediate stiffeners and the inclination of the lip stiffeners are considered to be the main design variables. All plate slenderness limit values and limits on the relative dimensions of the cross-sectional components as defined by Eurocode 3, as well as a number of practical manufacturing and construction limitations, are taken into account as constraints in the optimisation problem. It is demonstrated that a substantial improvement in energy dissipation capacity and ductility can be achieved through the proposed optimization framework. Optimized cross-sectional shapes are presented which dissipate up to 60% more energy through plastic deformations than a comparable commercially available lipped channel

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

Structural behaviour of optimized cold-formed steel beams

Cold-formed steel (CFS) members have been used significantly in light-gauge steel buildings due to their inherent advantages. Optimizing these CFS members in order to gain enhanced loadbearing capacities will result in economical and efficient building solutions. This research presents the investigation and results of the optimization of CFS members for flexural capacity. The optimization procedure was performed using the particle swarm optimization (PSO) method, while the section moment capacity was determined based on the effective width method adopted in EN 1993-1-3 (EC3). Theoretical and manufacturing constraints were incorporated while optimizing the CFS cross-sections. In total, four CFS sections – lipped channel beam (LCB), optimized LCB, folded-flange and super-sigma – were considered in the optimization process, including new sections. The section moment capacities of these sections were also obtained through non-linear finite element (FE) analysis and compared with the EC3-based, optimized section moment capacities. The results show that, compared with a commercially available LCB with the same amount of material, the new CFS sections possess the highest section moment capacity enhancements (up to 65 %). In addition, the performance of these CFS sections when subjected to shear and web-crippling actions was also investigated using non-linear FE analysis