Built-up steel I-girders are very commonly used in bridge construction. Their spans are typically very long, and they are susceptible to lateral torsional buckling if not enough lateral support is provided. This thesis includes guidelines for preventing lateral torsional buckling of steel I-girders under dead and wind load, accompanied with finite element analysis of double girder systems. The first portion includes capacity envelopes for single girders with single and double symmetric cross sections under various loading conditions and boundary conditions for double and single symmetric cross sections with double girders subjected to dead loads only. The second portion is dedicated to finite element analysis of double girders. Buckling analyses have been conducted on single symmetric double girders to verify their capacity equations and investigate the behavior of double girders subjected to wind load. The analyses focus on the weak axis bending of the double girder system as a whole and an evaluation of whether buckling of cross-bracing is an issue when lateral loads are present.

Structural wood design standards recognize lateral torsional buckling as an important failure mode, which tends to govern the capacity of long span laterally unsupported beams. A survey of the literature indicates that only a few experimental programs have been conducted on the lateral torsional buckling of wooden beams. Within this context, the present study reports an experimental and computational study on the elastic lateral torsional buckling resistance of wooden beams. The experimental program consists of conducting material tests to determine the longitudinal modulus of elasticity and rigidity modulus followed by a series of 18 full-scale tests. The buckling loads and mode shapes are documented. The numerical component of the study captures the orthotropic constitutive properties of wood and involves a sensitivity analysis on various orthotropic material constants, models for simulating the full-scale tests conducted, a comparison with experimental results, and a parametric study to expand the experimental database. Based on the comparison between the experimental program, classical solution and FEA models, it can be concluded that the classical solution is able to predict the critical moment of wood beams. By performing the parametric analysis using the FEA models, it was observed that loads applied on the top and bottom face of a beam decrease and increase its critical moment,respectively. The critical moment is not greatly influenced by moving the supports from mid-span to the bottom of the end cross-section.

The effect of initial out-of-straightness of steel beams with wide flange cross-sections on their elastic lateral torsional buckling strength is investigated analytically and numerically. A variational principle is first developed and then used to obtain the governing equilibrium conditions and associated boundary conditions for a beam with general patterns of initial out-of-straightness and initial angles of twist. The principle is then used to develop a finite element formulation to characterize the lateral torsional response of beams with initial out-of-straightness under general transverse loading. The validity of the finite element formulation is verified through comparison against results from models based thin-walled beam finite element and shell element models available in ABAQUS. Since the load lateral displacement responses do not exhibit a distinct point of loss of stability, two design criteria are proposed for the characterization of the failure. The first criterion is based on a threshold value for additional lateral displacement and the second criterial is based on a threshold value for the normal stresses. Both criteria are applied in conjunction with the analytical solution and finite element formulation in order to determine a moment resistance based on lateral torsional buckling that incorporates the effect of initial out-of-straightness. The moment capacity based on the displacement-based criterion is shown to solely depend on the ratio between the initial out-of-straightness component associated with the first buckling mode and the additional displacement threshold value specified. To the contrary, moment capacity based on the stress criterion, was found to depend upon the initial out-of-straightness magnitude, the normal stress threshold value and the geometry of the cross-section. The effects of the above parameters on the predicted moment capacity were investigated for beams with common sections in a systematic parametric study. Possible means of modifying the present provisions of CAN-CSA S16 relating to elastic lateral torsional buckling to incorporate the effect of initial out-of-straightness effects are discussed and illustrated through examples. The load-deformation plots for beams with initial out-of-straightens as predicted by the formulations developed in the present study are then used to extend the Southwell plot technique, originally developed for buckling of column with initial out-of-straightness, to the lateral torsional buckling of beams with initial out-of-straightness. The study shows that the plot, either experimentally or analytically obtained, of the applied load versus lateral displacement, at any point or angle of twist at any section, for a beam with initial out-of-straightness case can predict (a) the elastic critical moment of an analogous initially straight beam, and (b) the first buckling mode contribution to the initial out-of-straightness.

Structural wood design standards recognize lateral torsional buckling as an important failure mode, which tends to govern the capacity of long span laterally unsupported beams. A survey of the literature indicates that only a few experimental programs have been conducted on the lateral torsional buckling of wooden beams. Within this context, the present study reports an experimental and computational study on the elastic lateral torsional buckling resistance of wooden beams. The experimental program consists of conducting material tests to determine the longitudinal modulus of elasticity and rigidity modulus followed by a series of 18 full-scale tests. The buckling loads and mode shapes are documented. The numerical component of the study captures the orthotropic constitutive properties of wood and involves a sensitivity analysis on various orthotropic material constants, models for simulating the full-scale tests conducted, a comparison with experimental results, and a parametric study to expand the experimental database. Based on the comparison between the experimental program, classical solution and FEA models, it can be concluded that the classical solution is able to predict the critical moment of wood beams. By performing the parametric analysis using the FEA models, it was observed that loads applied on the top and bottom face of a beam decrease and increase its critical moment,respectively. The critical moment is not greatly influenced by moving the supports from mid-span to the bottom of the end cross-section.

The increased depth of castellated beams presents stability problems, specifically during erection. During erection the castellated beam must support the weight of an erector and self-weight until the continuous bracing of the floor deck is in place. The stability of the unbraced member is based on its resistance to lateral-torsional buckling. The cross-sectional properties that are related to lateral-torsional buckling, such as out-of-plane bending, warping constant, and torsional constant were calculated using three different approaches to model the unique geometry of castellated beams. These properties were used in various lateral-torsional buckling solutions to determine which procedure should be used to check for this mode of failure. Two specimens were tested to evaluate the results of the analytical unbraced length determination process. The tests results were used to better model the contribution of the web-to-column flange double angle connection on the stability of the castellated beam. / Master of Science

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / Thin-walled structures are major components in many engineering applications. When a thin-walled slender beam is subjected to lateral loads, causing moments, the beam may buckle by a combined lateral bending and twisting of cross-section, which is called lateral-torsional buckling. A generalized analytical approach for lateral-torsional buckling of anisotropic laminated, thin-walled, rectangular cross-section composite beams under various loading conditions (namely, pure bending and concentrated load) and boundary conditions (namely, simply supported and cantilever) was developed using the classical laminated plate theory (CLPT), with all considered assumptions, as a basis for the constitutive equations. Buckling of such type of members has not been addressed in the literature. Closed form buckling expressions were derived in terms of the lateral, torsional and coupling stiffness coefficients of the overall composite. These coefficients were obtained through dimensional reduction by static condensation of the 6x6 constitutive matrix mapped into an effective 2x2 coupled weak axis bending-twisting relationship. The stability of the beam under different geometric and material parameters, like length/height ratio, ply thickness, and ply orientation, was investigated. The analytical formulas were verified against finite element buckling solutions using ABAQUS for different lamination orientations showing excellent accuracy.

Structural steel design standards recognize lateral torsional buckling as a failure mode governing the capacity of long span unsupported beams with wide flange cross-sections. Standard solutions start with the closed form solution of the Vlasov thin-walled beam theory for the case of a simply supported beam under uniform moments, and modify the solution to accommodate various moment distributions through moment gradient expressions. The Vlasov theory solution is based on the assumption that cross-sectional distortional effects have a negligible effect on the predicted elastic critical moment. The present study systematically examines the validity of the Vlasov assumption related to cross-section distortion through a parametric study. A series of elastic shell finite element eigen-value buckling analyses is conducted on simply supported beams subject to uniform moments, linear moments and mid span point loads as well as cantilevers subject to top flange loading acting at the tip. Cross-sectional dimensions are selected to represent structural steel cross-section geometries used in practice. Particular attention is paid to model end connection details commonly used in practice involving moment connections with two pairs of stiffeners, simply supported ends with a pair of transverse stiffeners, simply supported ends with cleat angle details, and built in fixation at cantilever roots. The critical moments obtained from the FEA are compared to those based on conventional critical moment equations in various Standards and published solutions. The effects of web slenderness, flange slenderness, web height to flange width ratio, and span to height ratios on the critical moment ratio are systematically quantified. For some combinations of section geometries and connection details, it is shown that present solutions derived from the Vlasov theory can overestimate the lateral torsional buckling resistance for beams.

Structural steel design standards recognize lateral torsional buckling as a failure mode governing the capacity of long span unsupported beams with wide flange cross-sections. Standard solutions start with the closed form solution of the Vlasov thin-walled beam theory for the case of a simply supported beam under uniform moments, and modify the solution to accommodate various moment distributions through moment gradient expressions. The Vlasov theory solution is based on the assumption that cross-sectional distortional effects have a negligible effect on the predicted elastic critical moment. The present study systematically examines the validity of the Vlasov assumption related to cross-section distortion through a parametric study. A series of elastic shell finite element eigen-value buckling analyses is conducted on simply supported beams subject to uniform moments, linear moments and mid span point loads as well as cantilevers subject to top flange loading acting at the tip. Cross-sectional dimensions are selected to represent structural steel cross-section geometries used in practice. Particular attention is paid to model end connection details commonly used in practice involving moment connections with two pairs of stiffeners, simply supported ends with a pair of transverse stiffeners, simply supported ends with cleat angle details, and built in fixation at cantilever roots. The critical moments obtained from the FEA are compared to those based on conventional critical moment equations in various Standards and published solutions. The effects of web slenderness, flange slenderness, web height to flange width ratio, and span to height ratios on the critical moment ratio are systematically quantified. For some combinations of section geometries and connection details, it is shown that present solutions derived from the Vlasov theory can overestimate the lateral torsional buckling resistance for beams.

Lateral torsional buckling should be taken into account during the design of overhanging steel beams. One special type of overhanging beams is the crane trolley monorails. Lateral buckling of overhanging monorails under idealized loading and boundary conditions has been studied in the past using classical mathematical procedures. This thesis aims to present a detailed investigation of overhanging monorails using finite element analysis. Effects of different loading and boundary conditions were studied in detail. It was found out that the location of loading and supports on the cross section have significant effects on the buckling capacity. Beams having different warping and torsional properties were analyzed. The effects of cross section distortion on buckling capacity were investigated for beams with single and double overhangs. The reduction in capacity due to cross section distortion has been quantified. Based on the analysis results simple design recommendations were developed for lateral buckling of overhanging monorails and they are presented herein.

Structural steel design standards recognize lateral torsional buckling as a failure mode governing the capacity of long span unsupported beams with wide flange cross-sections. Standard solutions start with the closed form solution of the Vlasov thin-walled beam theory for the case of a simply supported beam under uniform moments, and modify the solution to accommodate various moment distributions through moment gradient expressions. The Vlasov theory solution is based on the assumption that cross-sectional distortional effects have a negligible effect on the predicted elastic critical moment. The present study systematically examines the validity of the Vlasov assumption related to cross-section distortion through a parametric study. A series of elastic shell finite element eigen-value buckling analyses is conducted on simply supported beams subject to uniform moments, linear moments and mid span point loads as well as cantilevers subject to top flange loading acting at the tip. Cross-sectional dimensions are selected to represent structural steel cross-section geometries used in practice. Particular attention is paid to model end connection details commonly used in practice involving moment connections with two pairs of stiffeners, simply supported ends with a pair of transverse stiffeners, simply supported ends with cleat angle details, and built in fixation at cantilever roots. The critical moments obtained from the FEA are compared to those based on conventional critical moment equations in various Standards and published solutions. The effects of web slenderness, flange slenderness, web height to flange width ratio, and span to height ratios on the critical moment ratio are systematically quantified. For some combinations of section geometries and connection details, it is shown that present solutions derived from the Vlasov theory can overestimate the lateral torsional buckling resistance for beams.