<div>The design of bridges prior to 1994 was carried out by either the Load Factor Design (LFD) or the Allowable Stress Design (ASD) methodologies. Load rating of these bridges was primarily conducted by Load Factor Rating (LFR). In 1994, the American Association of State Highway and Transportation Officials (AASHTO) developed and encouraged the use of a probabilistic-based method titled Load and Resistance Factor Design (LRFD) for carrying out bridge design. A new methodology consistent with LRFD was also developed and adopted for conducting load rating. Thus, a new Load and Resistance Factor Rating (LRFR) was adopted by AASHTO in 2001 for load rating. Today, the bridges that were designed by the old LFD methodology are rated by both LFR and LRFR. Continued development suggests that load rating in future will be based only on LRFR, therefore LRFR is the recommended method for carrying out load rating of bridges even if they were designed by LFD. </div><div><br></div><div>The Indiana Department of Transportation (INDOT) came across some LFD designed bridges which were adequate by LFR methodology, i.e., produced a rating factor of more than 1.0, but inadequate for LRFR. The load ratings were carried out using AASHTOWare Bridge Rating (BrR) software. These bridges belonged to five different limit states: lateral torsional buckling, changes in cross-section along the member length, tight stringer spacings, girder end shear and moment over continuous piers. </div><div><br></div><div>This research study explores the inherent differences between LFR and LRFR to justify the inconsistencies in the rating values. To find an explanation for these discrepancies, load ratings of these bridges were carried out extensively on AASHTOWare BrR. To verify the results produced by BrR, a separate analysis was also conducted using Mathcad and structural analysis results from SAP2000 for comparison purposes. Finally, the study also recommends some modifications in the BrR software that can be adopted for each of the above-mentioned limit states to resolve inconsistencies found between LFR and LRFR rating values. </div><div><br></div>

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.

The flexural capacity of the new hollow flange steel section known as LiteSteel beam (LSB) is limited by lateral distortional buckling for intermediate spans, which is characterised by simultaneous lateral deflection, twist and web distortion. Recent research based on finite element analysis and testing has developed design rules for the member capacity of LiteSteel beams subject to this unique lateral distortional buckling. These design rules are limited to a uniform bending moment distribution. However, uniform bending moment conditions rarely exist in practice despite being considered as the worst case due to uniform yielding across the span. Loading position or load height is also known to have significant effects on the lateral buckling strength of beams. Therefore it is important to include the effects of these loading conditions in the assessment of LSB member capacities. Many steel design codes have adopted equivalent uniform moment distribution and load height factors for this purpose. But they were derived mostly based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. In contrast LSBs are made of high strength steel and have a unique crosssection with specific residual stresses and geometrical imperfections along with a unique lateral distortional buckling mode. The moment distribution and load height effects for LSBs, and the suitability of the current steel design code methods to accommodate these effects for LSBs are not yet known. The research study presented in this thesis was therefore undertaken to investigate the effects of nonuniform moment distribution and load height on the lateral buckling strength of simply supported and cantilever LSBs. Finite element analyses of LSBs subject to lateral buckling formed the main component of this study. As the first step the original finite element model used to develop the current LSB design rules for uniform moment was improved to eliminate some of the modelling inaccuracies. The modified finite element model was validated using the elastic buckling analysis results from well established finite strip analysis programs. It was used to review the current LSB design curve for uniform moment distribution, based on which appropriate recommendations were made. The modified finite element model was further modified to simulate various loading and support configurations and used to investigate the effects of many commonly used moment distributions and load height for both simply supported and cantilever LSBs. The results were compared with the predictions based on the current steel code design rules. Based on these comparisons, appropriate recommendations were made on the suitability of the current steel code design methods. New design recommendations were made for LSBs subjected to non-uniform moment distributions and varying load positions. A number of LSB experiments was also undertaken to confirm the results of finite element analysis study. In summary the research reported in this thesis has developed an improved finite element model that can be used to investigate the buckling behaviour of LSBs for the purpose of developing design rules. It has increased the understanding and knowledge of simply supported and cantilever LSBs subject to non-uniform moment distributions and load height effects. Finally it has proposed suitable design rules for LSBs in the form of equations and factors within the current steel code design provisions. All of these advances have thus further enhanced the economical and safe design of LSBs.