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.

보의 고유진동수는 진동해석 뿐만 아니라 구조물의 동적특성을 파악하는데 중요한 역할을 한다 보의 단면이 불연속적으로 변하는 계단형 보의 고유진동수 해석은 복잡하다. 이런 계단형 보의 진동해석은 Rayleigh-Ritz법, FEM 등과 같은 근사해석법이 흔히 사용되는데 이들 해석의 정확성은 분할요소의 수, 계산의 반복수, 가정처짐곡선의 형상에 따라 좌우된다. 본 연구에서는 계단형 외팔보의 등가보 변환 방법을 이용한 기본고유진동수의 근사해석방법을 제시하고자 하였으며 여러 예제에 대하여 제안방법과 유한요소해석 결과를 비교하여 그 적용성과 신뢰성을 검증하였다.

보의 고유진동수는 보의 동적해석에서 중요한 역할을 한다. 보의 단면이 불규칙적으로 변하는 단형보의 고유진동수 산정은 해석상 복잡하고 어렵다. 이런 단형보의 해석은 주로 다자유도계 해석인 질량집중방법이 널리 사용되지만 이들 해석방법은 요소의 분할수나 계산의 반복수 또는 가정처짐곡선의 정확성 여부에 해석의 정밀성이 좌우된다. 본 연구는 대칭단형 단순보의 등가보 변환 방법과 그에 따른 고유치해석 방법을 제시하였으며 타 문헌의 예제와 여러 모델을 대상으로 그 타당성 및 실용성을 입증하였다.

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.

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.

비탄성 구간 내 비지지 길이가 존재하는 휨부재의 극한거동특성을 자세히 살펴보면, 단면 내 비균일 항복응력 도달로 인하여 초기의 이축 대칭단면이 일축대칭으로, 최종적으로는 비대칭단면의 특성을 보이게 된다. 이러한 극한거동에 대한 해석적 연구결과의 실험적 검토는 개발된 설계식의 상용화를 위해서 필연적으로 수행되어야 한다. 일반적으로 사용되는 구조용 강재를 이용한 실험연구는 재료비 및 실험장비 사용에 있어 많은 비용을 유발하므로 본 연구에서는 연구대상 구조부재의 거동특성을 파악할 수 있는 소규모의 경제적인 재료사용과 실험 상황을 구현하여 소규모 실험실에서 모형실험을 실시하였다. 유한요소해석프로그램인 ABAQUS를 사용하여 실험체의 극한강도를 산정하고, 기존에 개발된 제안식과의 비교를 통하여 I형 양단 스텝보의 비탄성 횡-비틀림 좌굴 강도 간편 설계식의 적용성을 평가하였다. 유한요소해석결과와 실험결과는 9%의 차이를 보이고 있으며, 제안식과 실험결과는 7%의 차이를 보이고 있다. 향후 추가적인 실험연구를 통하여 간편 제안식의 적절성을 추가적으로 평가할 예정이다.