Beam bracing is applied to prevent the relative displacement of the top and bottom flanges or to effectively control the twisting of the section, and the lateral stability of the beams are provided by lateral bracing, torsional bracing or a combination of both. Modular steel I-girders are laterally interconnected by torsional bracings that are installed to increase the resistance to lateral torsional buckling. In this paper, numerical parametric study was carried out by varying the crossbeam web height to examine the effects of the web torsional stiffness. Three-dimensional finite-element analysis using the commercial finite element software ABAQUS was obtained for the parametric numerical analyses of a series of feasible two-girder models, and the failure mode, lateral-torsional buckling strength and the moment-displacement behavior of the main girders was determined.

Over the years, several studies have been made for the improvement of the design criteria of stepped beams. However, studies on lateral-torsional buckling of stepped beams located at the midspan have been very limited. Hence, this study aims to evaluate the elastic lateral-torsional buckling strength of doubly symmetric singly stepped I-beam at midspan subjected to pure bending along the entire span. The I-beam measurements and specifications are in accordance with the AISC standards. For the analysis of stepped beams, the parameters α, β and γ are used. In this paper, singly stepped beams are defined as beams having an increased cross section at midspan. The unbraced length used for the simply supported stepped I-beams are 13.59m, 18.12m, and 22.65m while the parameters α, β and γ for the cross section varies from 0.167~0.333, 1.0~1.4, and 1.0~1.8, respectively. To model and perform the analysis for the I-beams, a universal finite element analysis program, ABAQUS, will be used. S4R elements will be used to model the simply supported beams and to check the accuracy of the models guide design specifications are used. The results from the finite element analysis will be shown in tables and plotted into graphs. Based from the obtained results, conclusions and new design guidelines are proposed.

This study aims to give a brief summary of the development in the series of studies that have been made regarding the lateral-torsional buckling (LTB) capacity of beam spans with increased cross section at one end, also known as singly stepped beam (SSB), and at both ends, also known as doubly stepped beam (DSB). A three-dimensional program ABAQUS was used to analyze buckling through finite element method, while a statistical regression program MINITAB was used in developing and proposing simple design equations. The following topics discussed in this study include: (1) proposed design equation that account for change in cross section of stepped beams under uniform moment; (2) proposed design equation, with a corresponding moment gradient factor equation, of stepped beams under general loading conditions; (3) proposed design equation for stepped beam with continuous top flange lateral bracing; (4) proposed design equation for monosymmetric stepped beam subjected to uniform moment and to general loading conditions; (5) effect of inelastic buckling of stepped beams subjected to pure bending and general loading conditions considering combined effects of residual stress and geometrical imperfection; and (6) determination of LTB strength of monosymmetric stepped beam by conducting destructive test of subjecting a beam to concentrated load. The summary presented provides researchers information in understanding the subject matter; moreover, this provides a meaningful contribution to futures researches.

This study is all about the presentation of the results of the analyses made to determine the inelastic lateral torsional buckling strength of singly symmetric singly stepped I-beam with constant depth subjected to basic loading condition. A finite element program ABAQUS and a regression program MINITAB are used to analyze the simply supported singly symmetric singly stepped I-beams having singly symmetric ratio, ρ, of 0.1 to 0.9 and a Lb/h ratio of 4.5. Using the results of the analyses made, a design equation is suggested that can easily calculate the stepped beam correction factor Cist which then can be used to determine the inelastic lateral torsional buckling strength of singly symmetric singly stepped I-beams subjected to pure bending moment. Then, the results from the equation proposed are compared with the results obtained from the finite element analysis. The results obtained show acceptable results for singly stepped beams having a ρ of 0.3 to 0.9 and a very conservative result for a ρ of 0.1.

본 논문에서는 횡비틀림좌굴을 고려하는 2차 소성힌지해석법을 이용하여 3차원 강뼈대구조물의 설계기법을 개발하였다. 본 해석은 구조시스템 및 개별부재의 재료적 기하학적 비선형 거동을 고려한다. 더욱이, 종래의 2차 소성힌지해석에서 횡비틀림좌굴효과에 의한 휨강도 감소효과를 고려하지 못한 문제를 해결하였다. 강뼈대구조물의 잔류응력과 휨에 의한 비선형성 및 기하학적 불완전성에 의한 점진적인 소성화효과를 고려하는 효율적인 방법을 기술하였다. 횡비틀림좌굴효과를 고려하기 위하여 비지지장 및 단면 형상으로 구성되는 침강도 감소모델을 사용하였다. 개발된 2차 소성힌지해석법을 LRFD 설계방법과 비교함으로서 검증하였다. 예제해석을 통하여 횡비틀림좌굴효과는 2차 소성힌지해석법에 고려해야 할 중요한 요소임을 알 수 있었다. 본 해석은 실제 설계에 활용할 수 있는 효율적이고 신뢰성 있는 방법이다.

反復혜重올 받는 짧은 I 보 (Beam) 의 慣-비틀림 座때(Lateral-Torsional Buckling) 에 대한 흩윌뼈한 Parametric Study 를 逢行하여 보의 座맴現象올 좀 더 깊이 考흉하고자 한다. 有限한 비틀림햇形의 뒤틀림 (Warping) 이외에 m 少한 맺톨JTft形의 뒤틀립도 고려한 幾何學적 (完全) 非綠形의 一次7ê 보를 껴￥析的 모델 로 사용하고， 또한 金!홉의 周期的뺑性(Cyclic Plasticity) 쌓:tJJ을 보다 잘 나타내기 위해 多빼 週期的뿔性 모 덴올 Consistent Return Mapping Algorithm과 결합시켜 遭用한다. :한ì.ffI때 단방에서 아래와 갇은 여러가지 Parameter Study를 끊行함으로써 反復휴重을 받는 짧은 I 보의 함 -비블립 座며의 -압的 應홈을 ι~.흉한다 : 材料의 降ik~옳度， 降ik플래토 (Yield Plateau) , 뿔形率硬化，U-:tJJ 硬化(Kinematic Hardening) , 웰留應力， 作用倚重의 f.1端中心에 대 한 {f，í ι、率， 作用倚훌의 보 톰面에 대 한 높 이， 作用혜훨의 보 김이방향의 位置， 보 뻐f 面의 置f!{， 作用倚重으로 부터 멀리 떨어진 支持端의 固定度.

Recently, as the level of market competition in the structural engineering field continues to rise, structural designers are finding other ways to make their designs stand out. One way of doing that is to make the designs more economical without sacrificing efficiency. As a result, the use of stepped beams and the studies involving it has become more common. Stepped beams are beams that have a sudden increase in cross section along its length. The change in cross section is made by increasing the width and/or the thickness of the flanges along a certain length while maintaining the dimensions of the web. Most of the studies involving lateral torsional buckling of stepped beams are focused on developing equations and studying the effects of symmetry. However, the studies involving actual test experiments are still very limited. Thus, this study has three main objectives. The first objective of this study is to give a brief historical overview on the series of studies involving the lateral torsional buckling capacity of stepped beams and give an idea on its current state of the art. The second objective is to determine if the intuitive expectation that the lowest critical moment always corresponds to uniform bending moment holds true for stepped beams. The degree of symmetry is varied and several loading conditions are observed. The third objective of this study is to determine the actual inelastic lateral torsional buckling capacity of doubly stepped singly symmetric I-beams having compact and non-compact flange sections subjected to two point loading condition and to use the results obtained to determine the applicability of previously proposed equations in predicting the buckling strength of stepped beams. The results are obtained by conducting actual destructive tests on doubly stepped I-beams using a universal testing machine and running simulation tests using the finite element program, ABAQUS. The main factors that are considered for the experimental and finite element analysis are the degree of beam symmetry, the loading condition, the supports, the stepped beam factors and the unsupported length. The degree of symmetry of all the stepped beams analyzed is fixed at 0.7. The unsupported lengths of the beams analyzed are 3 meters and 4 meters. The results obtained from the analysis are compared with the results from design specifications to determine the effects of steps and from proposed design equations to determine the equations’ applicability and safety. Finally, the results revealed that the stepped beams did have an increase in lateral torsional buckling capacity in comparison with the prismatic beams and that the proposed equations are suitable to be used in predicting the strength of stepped beams having compact flanges under the observed loading condition. However, for beams having non-compact flanges, the previously proposed equations produced over conservative results. Further study can also be made on stepped beams with varying degree of symmetries, loading conditions, boundary conditions and stepped beam parameters.

This study focuses on the effects of load height on the inelastic lateral buckling of doubly stepped I-beams. The effects of having compact and non-compact flanges are also covered by this study. Two sections are analyzed: one having compact flanges and web while the other section has a compact web and non-compact flanges. The loadings are limited to those having an inflection point of zero. Also, the three main locations for the loads analyzed would be at the top of the flange, at the shear and at the bottom flange. The nonlinear analysis is done using the finite element program, ABAQUS. Also, to take into consideration the effect of inelastic buckling, residual stresses and geometric imperfections are applied to the models made. The results of the analysis would then determine if the location of the loads has significant effects on the buckling strength of the stepped beams. Also, the results are compared to the results of previous studies involving the effects of load-height on prismatic beams. The final results are tabulated and conclusions and new design methods are provided.

This parametric study investigates the effect of significant parameters on the elastic global lateral torsional buckling capacity of horizontally curved twin I-girder systems. Included are the effect of curvature and the effect of girder spacing. Twin I-girder systems analyzed in this study are those which are interconnected by intermediate cross frames and are subjected to uniform moment. The finite element analysis software, ABAQUS, is used to model the horizontally curved twin I-girder system and conduct the buckling analysis. To see the significant effect of curvature and girder spacing, the results from the finite element analysis of horizontally curved twin I-girder systems are compared to the results of a closed form solution for straight twin I-girder systems. The findings of this parametric study will be shown using illustrative figures and tabulated data and conclusions are made.

Several studies concerning the lateral torsional buckling of horizontally curved I-beams have been made by different researchers. However, these studies are mostly limited to linear analysis and involving only single girders having single span. Nonlinear analysis of horizontally curved I-beams have been very limited or almost none. The aims of this study are to give a brief summary of the studies that have been made involving several factors concerning the lateral torsional buckling capacity of horizontally curved I-beams and to show several analyses that focused on determining the behavior of the horizontally curved I-beams that experience lateral torsional buckling failure. Subjects discussed in this study include: (1) different design provisions involving LTB of curved I-beams; (2) different equations that can be used concerning LTB of curved I-beams; (3) effect of cross frames; (4) effects of cross frame spacing; and (5) analysis results and trends comparing LTB strength of curved I-beams to straight beams. The summary of these studies will be essential in determining the future studies that has to be made involving the lateral torsional buckling of horizontally curved I-girder bridges which should cover single girder and multi girder systems as well as single span and multi span curved bridge systems.

It has been proven in recent studies that for monosymmetric I-section beams, in considering bending moment diagrams caused by any combination of applied end moments and transverse loads acting at the shear centre, the lowest critical lateral torsional buckling moment does not necessarily correspond to uniform bending. This finding is different from the intuitive expectation that researchers have that for lateral torsional buckling of thin walled beams, the lowest critical lateral torsional buckling moment always corresponds to a uniform bending moment diagram. To determine the applicability of the findings stated, considering stepped beams, this study will be focusing on the comparison of the lateral torsional buckling strength trends in monosymmetric I-beams having doubly stepped and compact cross section. Several loading conditions will be applied to see the effect of different moment diagrams having different inflection points on the lateral torsional buckling strength of stepped beams. The study will be made using the finite element program, ABAQUS. The study will investigate stepped beams having monosymmetric ratios ranging from 0.5 to 0.9. These ratios correspond to varying bottom flange width while keeping the top flange width unchanged. Both elastic and inelastic analysis will be carried out for this study. Finally, the findings for this study will be shown using illustrative figures and conclusions will be made.

본 연구에서는 비탄성 영역 내 비지지 길이가 존재하고 양단 및 일단 계단식 단면을 가지는 일축대칭 변단면 I형보의 해석적·이론적 연구를 토대로 하여 비탄성 횡-비틀림 좌굴 강도 해석을 실시하였다. 하중조건으로는 비지지 길이 내 모멘트가 0인 지점이 개수에 따라 모델을 구분지어 적용시켰으며, 플랜지 길이방향 비, 너비 방향 비, 두께의 비로 변단면 I형보를 나타내었다. 비선형 횡-비틀림 좌굴 해석을 위해 단순직선분포를 잔류응력으로 가정하였으며, 국내 I형강 표준 치수 허용치에 근거하여 부재 길이의 0.1%를 초기 최대 횡변위로 적용하여 초기변형으로 고려하였다. 유한요소해석에 사용된 프로그램은 ABAQUS(2009)이며, 회귀분석프로그램인 MINITAB(2006)을 이용해 간편한 설계식을 제안하고 있다. 본 연구 결과에서 개발·제안된 식은 향후 비탄성 횡-비틀림 좌굴 강도에 대한 연구에 많은 도움이 될 것이다.