• Computational Structural Engineering
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• v.5 no.1
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• pp.119-132
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• 1992

The objective of this study is to perform extensive parametric studies of the lateral-torsional buckling of short 1-beams under repeated loadings, and to gain a further insight into the lateral-torsional beam buckling problem. A one-dimensional geometrically (fully) nonlinear beam model is used, which includes superposed infinitesimal transverse warping deformation in addition to finite torsional warping deformation. A multiaxial cyclic plasticity model is also implemented to better represent cyclic metal plasticity in conjunction with a consistent return mapping algorithm. The general response for the lateral-torsional buckling of short I-beams under repeated loadings is examined through several parametric studies around the standard case : the material yield strength, the yield plateau, the strain hardening, the kinematic hardening, the residual stresses, the load eccentricity with respect to the shear center, the height of the load with respect to the cross-section of the beam, the location of the load along the length of the beam, the dimensions of the cross-section of the beam and the fixity of the supported end remote from the load.

• Steel and Composite Structures
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• v.39 no.5
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• pp.599-614
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• 2021

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young's and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

• 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.

• Steel and Composite Structures
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• v.46 no.5
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• pp.709-718
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• 2023

The absence of an important portion of the web plate in steel beams with multiple circular perforations, cellular beams, causes the web plate to undergo distortions prior to and during lateral torsional buckling (LTB). The conventional LTB equations in the codes and literature underestimate the buckling moments of cellular beams due to web distortions. The present study is an attempt to develop analytical methods for estimating the elastic buckling moments of cellular beams. The proposed methods rely on the reductions in the torsional and warping rigidities of the beams due to web distortions and the reductions in the weak-axis bending and torsional rigidities due to the presence of web openings. To test the accuracy of the analytical estimates from proposed solutions, a total of 114 finite element analyses were conducted for six different standard IPEO sections and varying unbraced lengths within the elastic limits. These analyses clearly indicated that the LTB solutions in the AISC 360-16 and AS4100:2020 codes overestimate the buckling loads of cellular beams within elastic limits, particularly at shorter span lengths. The LDB solutions in the literature and the Eurocode 3 LTB solution, on the other hand, provided conservative buckling moment estimates along the entire range of elastic buckling.

• Steel and Composite Structures
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• v.4 no.4
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• Journal of Korean Society of Steel Construction
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• v.23 no.6
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• pp.647-657
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• 2011

This paper describes the moment capacity of flexural members with local buckling based on a series of FE and experiment results. Thin-walled flexural members undergo local, lateral-torsional, or interactive buckling according to the section geometries and lateral boundary conditions. Flexural members with large width-to-thickness ratios in the flanges or the web may undergo local buckling before lateral-torsional buckling. Local buckling has a negative effect on the flexural strength based on the lateral-torsional buckling of flexural members. This phenomenon should be considered in the estimation of the flexural strength of thin-walled sections. Flexural members with various width-to-thickness ratios in their flanges and web were analyzed. Initial imperfections in the local buckling mode, and residual stresses, were included in the FE analyses. Simple bending moment formulae for flexural members were proposed based on the FE and test results to account for local and lateral-torsional buckling. The proposed bending moment formulae for the thin-walled flexural members in the Direct Strength Method use the empirical strength formula and the grosssection modulus. The ultimate flexural strengths predicted by the proposed moment formulae were compared with the AISC (2005), Eurocode3 (2003), and Korean Highway Bridge Design Specifications (2010). The comparison showed that the proposed bending moment formulae can reasonably predict the ultimate moment capacity of thin-walled flexural members.

• 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.

• Steel and Composite Structures
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• v.12 no.3
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• pp.183-205
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• 2012

This paper presents an investigation of the effect of inclined stiffeners on the load-carrying capacity of simply-supported hot-rolled steel I-beams under various load conditions. The study is carried out using finite element analysis. A series of beams modeled using 3-D solid finite elements with consideration of initial geometric imperfections, residual stresses, and material nonlinearity are analyzed with and without inclined stiffeners to show how the application of inclined stiffeners can offer a noticeable increase in their lateral-torsional buckling (LTB) capacity. The analysis results have shown that the amount of increase in LTB capacity is primarily dependent on the location of the inclined stiffeners and the lateral unsupported length of the beam. The width, thickness and inclination angle of the stiffeners do not have as much an effect on the beam's lateral-torsional buckling capacity when compared to the stiffeners' location and beam length. Once the optimal location for the stiffeners is determined, parametric studies are performed for different beam lengths and load cases and a design equation is developed for the design of such stiffeners. A design example is given to demonstrate how the proposed equation can be used for the design of inclined stiffeners not only to enhance the beam's bearing capacity but its lateral-torsional buckling strength.

• Steel and Composite Structures
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• v.30 no.5
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• pp.483-492
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• 2019

In the current study, the influence of the initial lateral (sweep) shape and the cross-sectional twist imperfection on the lateral torsional buckling (LTB) response of doubly-symmetric steel I-beams was investigated. The material imperfection (residual stress) was not considered. For this objective, standard European IPN 300 beam with different unbraced span was numerically analyzed for three imperfection cases: (i) no sweep and no twist (perfect); (ii) three different shapes of global sweep (half-sine, full-sine and full-parabola between the end supports); and (iii) the combination of three different sweeps with initial sinusoidal twist along the beam. The first comparison was done between the results of numerical analyses (FEM) and both a theoretical solution and the code lateral torsional buckling formulations (EC3 and AISC-LRFD). These results with no imperfection effects were then separately compared with three different shapes of global sweep and the presence of initial twist in these sweep shapes. Besides, the effects of the shapes of initial global sweep and the inclusion of sinusoidal twist on the critical buckling load of the beams were investigated to unveil which parameter was considerably effective on LTB response. The most compatible outcomes for the perfect beams was obtained from the AISC-LRFD formulation; however, the EC-3 formulation estimated the $P_{cr}$ load conservatively. The high difference from the EC-3 formulation was predicted to directly originate from the initial imperfection reduction factor and high safety factor in its formulation. Due to no consideration of geometric imperfection in the AISC-LFRD code solution and the theoretical formulation, the need to develop a practical imperfection reduction factor for AISC-LRFD and theoretical formulation was underlined. Initial imperfections were obtained to be more influential on the buckling load, as the unbraced length of a beam approached to the elastic limit unbraced length ($L_r$). Mode-compatible initial imperfection shapes should be taken into account in the design and analysis stages of the I-beam to properly estimate the geometric imperfection influence on the $P_{cr}$ load. Sweep and sweep-twist imperfections led to 10% and 15% decrease in the $P_{cr}$ load, respectively, thus; well-estimated sweep and twist imperfections should considered in the LTB of doubly-symmetric steel I-beams.

• Steel and Composite Structures
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• v.18 no.3
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• pp.603-621
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• 2015

In this study, theoretical models and design procedures of the behavior of thin-walled simply supported steel beams with an open cross section under a large torsional effect are presented. I-sections were chosen as the cross section types. Firstly, the widely used differential equations for the lateral buckling for the pure bending moment effect in a beam element were adopted for the various moment distributions along the span of the beam. This solution was obtained for both mono-symmetric and bisymmetric sections. The buckling loads were then obtained by using the energy method. When using the energy method to solve the problem, it is possible to locate the load not only on the shear center but also at several points of the section depth. Buckling loads were obtained for six different load types. Results obtained for different load and cross section types were checked with ABAQUS software and compared with several standard rules.