• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.275-289
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• 2013

The cross sections of multi-span beams are sometimes suddenly increased at the interior support of continuous beams to resist high negative moment. An earlier study on elastic lateral torsional buckling of stepped beams was conducted to propose new design equations. This research aims to continue the earlier study by considering the effect of inelastic buckling of stepped beams subjected to pure bending and general loading condition. A three-dimensional finite element-program ABAQUS and a statistical program MINITAB were used in the development of new design equations. The inelastic lateral torsional buckling strengths of 36 and 27 models for singly and doubly stepped beams, respectively, were investigated. The general loading condition consists of 15 loading cases based on the number of inflection point within the unbraced length of the stepped beams. The combined effects of residual stresses and geometrical imperfection were also considered to evaluate the inelastic buckling strengths. The proposed equations in this study will definitely improve current design methods for the inelastic lateral-torsional buckling of stepped beams and will increase efficiency in building and bridge design.

• Steel and Composite Structures
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• v.4 no.1
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• pp.23-36
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• 2004

The inelastic lateral-distortional buckling of doubly-symmetric hot-rolled I-section beam-columns subjected to a concentric axial force and uniform bending with elastic restraint which produce single curvature is investigated in this paper. The numerical model adopted in this paper is an energy-based method which leads to the incremental and iterative solution of a fourth-order eigenproblem, with very rapid solutions being obtained. The elastic restraint considered in this paper is full restraint against translation, but torsional restraint is permitted at the tension flange. Hitherto, a numerical method to analyse the elastic and inelastic lateral-distortional buckling of restrained or unrestrained beam-columns is unavailable. The prediction of the inelastic lateral-distortional buckling load obtained in this study is compared with the inelastic lateral-distortional buckling of restrained beams and the inelastic lateral-torsional buckling solution, by suppressing the out-of-plane web distortion, is published elsewhere and they agree reasonable well. The method is then extended to the lateral-distortional buckling of continuously restrained doubly symmetric I-sections to illustrate the effect of web distortion.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.7
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• pp.3495-3501
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• 2013

The cross-sections of continuous multi-span beams are sometimes suddenly increased or stepped at the interior supports of continuous beams to resist high negative moments. This paper investigates inelastic lateral-torsional buckling of monosymmetric stepped I-beams subjected to pure bending. A three-dimensional finite-element program ABAQUS and a regression program were used to analytically develop new design equation. The flange thickness ratio, flange width ratio and stepped length ratio were considered as parameters of this study. The combined effects of residual stresses and geometric imperfection on inelastic lateral-torsional buckling of beams are considered. The proposed solution can be easily used to calculation for inelastic lateral torsional buckling strengths of monosymmetric beams with doubly stepped cross sections and to develop new design equations for inelastic lateral-torsional buckling resistances of stepped beams.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.6A
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• pp.399-409
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• 2012

The flexural behavior of HSB plate girder with a non-slender web, due to inelastic lateral-torsional buckling, under uniform bending was investigated by the nonlinear finite element analysis. Both homogeneous sections fabricated from SM570-TMC, HSB600 or HSB800 steel and hybrid sections with HSB800 flanges and SM570-TMC web were considered. The flanges and web of selected noncomposite I-girders were modeled as thin shell elements and the geometrical and material nonlinear finite element analysis was performed by the ABAQUS program. The steel was assumed as an elasto-plastic strain hardening material. Initial imperfections and residual stresses were taken into account and their effects on the inelastic lateral-torsional buckling behavior were analyzed. The flexural strengths of selected sections obtained by the finite element analysis were compared with the nominal flexural strengths from KHBDC LSD, AASHTO LRFD, and Eurocode and the applicability of these codes in predicting the inelastic lateral torsional buckling strength of HSB plate girders with a non-slender web was assessed.

• Journal of Korean Society of Steel Construction
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• v.24 no.2
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• pp.217-231
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• 2012

The flexural behavior of HSB I-girder with a non-slender web attributed to inelastic lateral-torsional buckling under uniform bending was investigated using nonlinear finite element analysis of ABAQUS. The girder was assumed to have a compact or noncompact web in order to prevent premature bend-buckling of the web. The unbraced length of the girder was selected so that inelastic lateral-torsional buckling governs the ultimate flexural strength. The compression flange was also assumed to be either compact or noncompact to prevent local buckling of the elastic flange. Both homogeneous sections fabricated from HSB600 or HSB800 steel and hybrid sections with HSB800 flanges and SM570-TMC web were considered. In the FE analysis, the flanges and web of I-girder were modeled as thin shell elements. Initial imperfections and residual stresses were imposed on the FE model. An elasto-plastic strain hardening material was assumed for steel. After establishing the validity of the present FE analysis by comparing FE results with test results in existing literature, the effects of initial imperfection and residual stress on the inelastic lateral-torsional buckling behavior were analyzed. Finite element analysis results for 96 sections demonstrated that the current inelastic strength equations for the compression flange in AASHTO LTFD can be applied to predict the inelastic lateral torsional buckling strength of homogeneous and hybrid HSB I-girders with a non-slender web.

• Steel and Composite Structures
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• v.5 no.4
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• pp.305-326
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• 2005

The inelastic buckling behaviour of continuously restrained two and three-span continuous beams subjected to concentrated loads and uniformly distributed loads are studied in this paper. The restraint type considered in this paper is fully restrained against translation and elastic twist applied at the top flange. These types of restraints are most likely experienced in industrial structures, for example steel-concrete composite beams and half through girders. The buckling analysis of continuous beam consists of two parts, firstly the moment and shear distribution along the member are determined by employing force method and the information is then used for an out-of-plane buckling analysis. The finite element method is incorporated with so-called simplified and the polynomial pattern of residual stress. Owing to the inelastic response of the steel, both the in-plane and out-of-plane analysis, which is treated as being uncoupled, extend into the nonlinear range. This paper presents the results of inelastic lateral-torsional and lateral-distortional buckling load and finally conclusions are drawn regarding the web distortion.

• Journal of Korean Society of Steel Construction
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• v.16 no.1 s.68
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• pp.155-167
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• 2004

In this paper, the inelastic buckling behavior of the beam under uniform bending was investigated using the energy-based method, which can tackle problems in fourth order eigenvalue. The pattern of residual stress was not available to satisfy the I-sections manufactured in Korea. however; therefore, the well-known polynomial and simplified pattern of residual stress was adopted in this study. The inelastic lateral-distortional buckling behavior of the beam with I-sections manufactured in Korea was investigated. The study was then extended to the inelastic lateral-torsional buckling of the beam by minimizing the out-of-plane web distortion. The inelastic lateral-torsional buckling results obtained in this paper were compared with the prediction of allowable bending stress given in the Korean steel designers' manual (1995). Results showed that the importance of inelastic lateral-distortional buckling did not arise for beams under uniform bending. Likewise, the design method in KSDM (1995) was proven to bo too conservative for intermediate and short spans of beams without intermediate bracing.

• International journal of steel structures
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• v.18 no.4
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• pp.1440-1463
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• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

• Journal of the Korean Society of Hazard Mitigation
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• v.8 no.6
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• pp.53-60
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• 2008

The cross-sections of continuous multi-span beams sometimes suddenly increase, or become stepped, at the interior supports of continuous beams to resist high negative moments. The three-dimensional finite-element program ABAQUS (2007) was used to analytically investigate the inelastic lateral-torsional buckling behavior of stepped beams subjected to linear moment gradient and resulted in the development of design equations. The ratios of the flange thickness, flange width, and stepped length of beam are considered for the analytical parameters. Two groups of 27 cases and 36 cases, respectively, were analyzed for doubly and singly stepped beams in the inelastic buckling range. The combined effects of residual stresses and geometrical imperfection on inelastic lateral-torsional buckling of beams are considered. First, the distributions of residual stress of the cross-section is same as shown in Pi and Trahair (1995), and the initial geometric imperfection of the beam is set by central displacement equal to 0.1% of the unbraced length of beam. The new proposed equations definitely improve current design methods for the inelastic lateral-torsional buckling problem and increase efficiency in building and bridge design.

• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.4
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• pp.1-9
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• 2009

This paper investigates inelastic lateral-torsional buckling of stepped beams subjected to uniformly distributed load and end moments. A three-dimensional finite-element program ABAQUS (2007) and a regression program MINITAB(2006) were used to analytically develop new design equation for singly and doubly stepped beams with simple boundary condition. The flanges of the smaller cross-section in the stepped beams were fixed at 30.48 by 2.54 cm, whereas the width and thickness of the flanges of the larger cross-section varied. The web thickness and height of the beams were kept at 1.65 cm and 88.9 cm, respectively. The ratios of the flange thickness, flange width, and stepped length of beam are considered with analytical parameters. Two groups of 27 cases and 36 cases, respectively, were analyzed for doubly and singly stepped beams in the inelastic buckling range. The combined effects of residual stresses and geometrical imperfection on inelastic lateral-torsional buckling of beams are considered. The distributions of residual stress of the cross-section is same as shown in Pi and Trahair (1995) and the initial geometric imperfection of the beam is set by central displacement equal to 0.1% of the unbraced length of beam. The comparisons between results from proposed equations and the results from finite element analyses were presented in this paper. The maximum differences of two results are of 13% for the doubly stepped beam and 10% for the singly stepped beam. The proposed equations definitely improve current design methods for the inelastic lateral-torsional buckling problem and increase efficiency in building and bridge design.