M. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / Though aluminium (Al) is justifiably described as a green metal with an increasing rate of application in structures, designers still restrain themselves from its applications as a load-bearing skeleton in structure due to insufficient design guidelines. This insufficient information is more with channel sections that might experience lateral-torsional buckling (LTB) when used as a load-bearing skeleton in structures. This study investigates the effects on imperfections on LTB load-carrying stability for 6061-T6 Al alloy channel section arches and proposed design guidelines. The case study focused on freestanding circular fixed end arches subjected to a transverse point load at the shear centre. The software package Abaqus was used to study a total of 110 arch models from three separate channel sections with an additional 16 arch models for validation. Sixty-six channel arches were developed at a constant length, while the remaining 44 arches were formed at constant slender ratios using 11 discrete included angles. The FE analyses methods used for the investigation were validated with existing analytical methods and showed good agreement, despite the assumptions of the bilinear curve used for material nonlinearity, initial geometric imperfections and residual stresses that presented the imperfections of the models. The different investigated factors include slender ratios, change in cross-section area, imperfections, and angles. These factors were found to have substantial impacts on the prebuckling state, which turns to impact LTB behaviour and load-carrying capacity. From arches developed at constant span length, the arches with moderately included angles (50°≤2𝛼≤90°) were found suitable for the designs against LTB, followed by the shallow (2𝛼<50°) and deep arches (90°<2𝛼≤180°) respectively. For arches developed at constant slender ratios, the deep arches were found to be more suitable in the design against LTB, followed by the moderate and shallow arches, respectively. In addition, it was realised that the change in web-flange thickness, section depth and slender ratios, had significant effects on the LTB loads magnitudes and very insignificant effects on the general behaviour across the included angles. The same occurrence was also observed on the prebuckling analyses. All the investigated channel section arches showed the imperfections to have significant impacts on the LTB loads. Arches developed at constant span length showed the maximum elastic LTB loads to have overestimated the expected real LTB loads by approximately 48 percent. While the maximum elastic LTB loads of arches developed at 𝑆𝑟𝑥⁄= 60 and 90 showed that the real LTB loads were overestimated by about 39 and 14 percent, respectively. That said, the elastic LTB loads on average overestimated the real LTB loads by over 50 percent for the arches developed at the constant span length and by only 18 percent for arches developed at the constant slender ratios.

The aging infrastructure worldwide and the typical increase in service loads relative to original design loads make it essential to develop effective techniques for strengthening and rehabilitating existing structures, to enhance their resistance. An effective method for strengthening existing steel I-beams is to weld either one or two cover plates to the flange(s). In many cases, it is not feasible to completely unload the beam before carrying out the strengthening procedure. In these conditions, operators resort to strengthen beams while under loading. In such scenarios, it becomes a challenging task to assess the lateral torsional buckling (LTB) capacity of the member under present steel design standards (e.g., CAN/CSA-S16 2019 and ANSI/AISC360 2022) which do not consider the effect of pre-strengthening loads on LTB resistance. Within this context, the present study investigates the effects of pre-strengthening loads on the critical moment capacity by developing a series of solutions, ranging from elaborate and accurate to simplified but approximate, to predict the elastic LTB capacity of beams strengthened with cover plate(s) while under load. In this respect, the study contributes to the existing body of knowledge through four aspects: In the first contribution, a shell-based finite element (FE) study is developed to analyze the effect of various geometric and loading parameters on the LTB capacity of doubly symmetric beams strengthened symmetrically with two cover plates. The study carefully simulates the entire history, including the application of pre-existing loads, clamping forces to align the initially straight steel cover plates with the bent beam configuration, the rebound effect arising after clamping force removal, the contact at the interfaces between cover plates and flanges induced by welding, and the application of post-strengthening loads up to the point of elastic LTB initiation for the strengthened system, as determined by eigenvalue analysis. A simplified design equation is then proposed to quantify the post-strengthening critical moment capacity. The validity of the equation is assessed against FE results and its merits and limitations are discussed. The study shows that web distortional effects play a crucial role in reducing the elastic critical moment capacity. Practical recommendations are provided to mitigate such distortional effects and hence maximize the elastic critical moment capacity of the strengthened beams. The second contribution formulates a variational principle for the LTB analysis of doubly symmetric beams strengthened symmetrically with identical steel cover plates. The formulation considers the full sequence of loading and strengthening and captures the effects of pre-strengthening loads and the beneficial effects of pre-buckling deformation (PBD). The study examines the effect of geometry, partial strengthening schemes, presence of different pre- and post-strengthening load patterns, and load height effects. The variational principle is subsequently used to develop a FE formulation, culminating in a quadratic eigenvalue problem. The validity of the FE formulation is assessed through comparisons with other numerical techniques predictions as well as experimental results by others, and subsequently used to conduct a parametric study to characterize the gain in elastic critical moment capacity attained by cover plate strengthening. For beams partly strengthened with cover plates along their spans, the study identifies the optimum locations for cover plates that maximize the critical moments. The third contribution builds upon the variational principle developed by formulating a simple and approximate energy-based design-oriented solution to quantify the LTB resistance of simply supported I-beams strengthened with cover plates. The solution captures the detrimental effect of loads acting on the beam before strengthening and the beneficial effects resulting from PBD, pre- and post-strengthening load heights, as well as moment gradient effects. The potential use of the equations developed in practical applications involving beam strengthening is illustrated through design examples. The fourth contribution expands the variational formulation to include beams with monosymmetric cross-sections and/or symmetric beams with unsymmetric cover plate geometries. The modified variational principle is used to develop a thin-walled beam FE formulation, which is subsequently employed to predict the non-distortional LTB capacity of monosymmetric strengthened beams. Comparative analyses with shell models confirm the validity of the proposed solutions, and practical design recommendations for suppressing web distortion are provided. The effects of various design parameters on the total elastic critical moment capacity are evaluated in a systematic parametric study. The study identifies the loading conditions under which the magnitude of pre-strengthening loads significantly influences the predicted total critical moments. The solutions developed in the present study equip structural designers and analysts with novel techniques that reliably quantify the LTB strength of steel beams strengthened with cover plates, thus enabling them to optimize strengthening strategies for beams whose strengths are governed by LTB modes of failure.