Abstract
Lateral Torsional Buckling of Welded Wide Flange Beams 
Md. Imran Kabir
Lateral Torsional Buckling (LTB) can be defined as a combination of lateral displacement and twisting due to an application of load on an unsupported beam. Design specifications of Canada CSA S16-14 provides solutions for LTB of welded and rolled beams that were derived for constant moment situation. Same equations have been used over the years for design of rolled and welded shape beams. A recent study has shown that the current code equations might overestimate the capacity of the welded wide shape beams, which make them unsafe to use. Thus a detailed study is required to evaluate the existing LTB equations for welded wide flange (WWF) shapes. This thesis evaluates the performance of current equations in providing LTB capacities of WWF shape beams. A nonlinear finite element (FE) model is developed to investigate the LTB capacity of WWF shape beams. The validated FE model is used to analyze a series of simply supported WWF shape beams with varying unbraced lengths and subjected to equal end moments. Four different patterns of residual stresses and a constant initial imperfection of L/1000 are considered for the analysis. In total, 320 FE models are analyzed, and it is observed that current code overestimates the LTB capacity of WWF shape beams as much as of 37% mainly using the measured residual stress of Lehigh University. 
 Later, LTB capacity of WWF shape beams subjected to other loading configurations i.e. linear and non-linear moment gradient is investigated. Three types of linear moment gradient are considered i.e. end moment ratio of 0.5, 0.0, -1.0 while for non-linear moment gradient, two types of transverse loading i.e. concentrated load at mid span and uniformly distributed load along the length of the beam are considered in this research. In addition, for transverse loading, the effect of load height is taken into account by changing the position of load at top flange, centroid and bottom flange. Thus, in total 123 and 228 FE models are developed for linear and non-linear moment gradient respectively. From the parametric study conducted for linear moment gradient, it is observed that current CSA S16-14 strength curve overestimates significantly for end moment ratio of 0.5 (40.1%) and 0.0 (34.57%) while it essentially coincides with FE results for end moment ratio of -1.0. 
In the case of transverse loading, CSA S16-14 strength curve overestimates by 17% and 33% for concentrated load and distributed load respectively when the load is applied at the top flange of the beam. Unlike the top flange loading, CSA S16-14 strength curve underestimates by 64% and 44% for concentrated and distributed load applied at bottom flange respectively. However, in both cases, CSA S16-14 reasonably matches with the FE results when the load is applied at shear center of the cross-section. In addition, the mean value of equivalent moment factor, ω2 provides good agreement with recommended values by CSA S16-14. In all cases, FE results are compared with other standards i.e. AISC, Eurocode as well as with latest equation proposed by the researchers in University of Alberta. Although, Eurocode is found to be conservative in every cases but proposed equation by the researchers at University of Alberta shows good agreement only in the case of unequal end moment and transverse loading condition. Hence, this equation can be used with a lower resistance factor for LTB strength calculation of WWF beams.