Lateral Torsional Buckling Capacity Research Articles

Bracing systems for three-ribbed arch bridges against out-of-plane buckling

This paper is concerned with the design of bracing systems for three-ribbed parabolic arch bridges against out-of-plane buckling. Typical bracing systems for the three-ribbed arch bridges include K-bracing system and X-bracing system as well as transverse bracing system. The buckling criterion of the braced funicular three-ribbed arch bridge is derived from an exact matrix stiffness method (MSM) with a 14 × 14 s-order element stiffness matrix of three-dimensional beam-column elements that allows for torsional and warping deformations. The lateral torsional buckling load and mode are given by the lowest eigenvalue and eigenvector associated with the assembled structural stability stiffness matrix. A comparison study between different bracing system configurations suggests that the three-ribbed arches with the integral K- or X-bracing system (a K/X-bracing across the three arch ribs) have lower lateral torsional buckling loads than their arch counterparts with the independent K- or X-bracing system (the adjacent arch ribs are connected by K/X-bracing respectively), because the latter ones could provide more restraint on the middle arch rib to avoid early lateral torsional instability. Further, a bracing utilization efficiency index (defined as the normalized buckling capacity over material usage for bracing system) is proposed to quantify the effect of bracing systems in improving the lateral torsional buckling capacity of arch bridges. Highly efficient bracing systems that maximize the lateral torsional buckling load of three-ribbed arch structures with the lowest bracing material usage are then recommended.

Lateral-Torsional Buckling Modification Factors in Steel I-Shaped Members: Recommendations Using Energy-Based Formulations

Lateral torsional buckling (LTB) is of concern in long-span flexural members, particularly in the negative flexure regions of continuous-span, steel I-shaped members and during construction. While the elastic critical LTB capacity of a simply supported I-shaped member subjected to uniform moment has a closed-form solution, most LTB modification factors for beams subjected to moment gradients in the literature are empirical and work well only for specific loading and boundary conditions. This paper investigates the suitability of the different LTB modification factors in literature and design specifications for various loading and boundary conditions, accomplished via comparisons with analytical solutions using the Rayleigh-Ritz method and numerical solutions from finite element analyses. The analytical LTB modification factors are derived for doubly symmetric I-shaped members with different combinations of ideal flexural and torsional boundary conditions (simply supported and fixed) and subjected to different loading scenarios. The validity of the LTB modification factors determined using the Rayleigh-Ritz method and other formulae in the literature are also assessed for realistic intermediate restraint conditions, which are neither fully pinned nor fixed, by examining laterally continuous beams. Demonstrating that current design specifications for elastic critical LTB modifications are overly conservative

Effects of shear on the lateral torsional buckling of singly-symmetric I-beams

This paper presents an investigation on the negative effects of shear on the lateral torsional buckling (LTB) of singly-symmetric I-shaped beams due to web distortion associated with shear. Results from a parametric FEA study including eigenvalue buckling analyses and large-displacement analyses were utilized considering both stiffened and unstiffened webs to consider the impact of shear on the LTB resistance. Moment gradients caused by constant shear and a shear gradient were considered. The FEA solutions demonstrate that shear can significantly reduce the lateral-torsional buckling resistance. The FEA results were used to develop design equations that account for the reduction in the LTB capacity from shear. The solutions were compared with conventional methods proposed by Winter to account for the effects of web distortion on girders with slender webs. Results from the study show that (i) the average flange area should be used to account for the effects of shear of singly-symmetric beams; (ii) post-buckling strength has limited impact on the shear effects with regards to the LTB resistance; and, (iii) compared to Winter's approach, the proposed method can capture the variation of the moment reduction factor with the shear force in the unbraced length, and is able to predict moment resistances with reasonable accuracy compared to refined FEA solutions using both eigenvalue analysis and large-displacement analysis. Design examples are provided to demonstrate the calculation procedure.

Experimental Evaluation on Lateral Torsional Buckling Resistance of Continuous Steel Stringers

An extensive experimental study evaluated lateral torsional buckling resistance of two-span, continuous, steel beams in a test assembly that included three beam lines, an interior transverse support (floor beam), and transverse diaphragms at the end supports. Funded by the Louisiana Transportation Research Center (LTRC), this study was conducted to better understand continuous stringer behavior so that simplified analyses would better capture their lateral torsional buckling (LTB) behavior. Current practice produces Louisiana Department of Transportation and Development (LA DOTD) bridge ratings often conservatively controlled by stringer LTB capacity and, in many cases, necessitates posting; thereby imposing significant and often unnecessary operational restrictions. Forty-seven elastic tests were completed. The tests encompassed a variety of unbraced lengths and support conditions with steel diaphragms or timber ties acting as bracing members. The interior beam in the test assembly was loaded orthogonal to its strong axis at the middle of one or both spans using a spreader beam that minimized restraint and prevented the development of follower forces. Tests demonstrated that minimal bracing could significantly increase lateral torsional buckling resistance and justify a higher LTB resistance than what is currently used. Although the tests were conducted on assemblies used to represent a bridge floor system, the results provided an extensive set of valuable data that could be used by structural steel researchers interested in examining flexural resistance of continuous beams.

Multi-objective optimization of lateral stability strength of transversely loaded laminated composite beams with varying I-section

In this research, the lateral buckling analysis and layup optimization of the laminated composite of web and flanges tapered thin-walled I-beams based on maximizing lateral-torsional stability strength and minimizing mass/cost of the structure are investigated. The classical lamination theory and Vlasov’s model for thin-walled cross-section are adopted to establish the total potential energy for thin-walled symmetric balanced laminated beams with varying I-section. By implementing the Ritz method, an explicit formulation for the lateral-torsional buckling load of a double-tapered beam subjected to transverse loading is then derived in terms of the load height parameter and stiffness quantities. Subsequently, the optimal arrangements of layer sequences are obtained using the non-dominated sorting genetic algorithm (NSGA-II) and properly defined objective function. The critical factors of fitness function as lateral buckling strength and the mass of the structure with critical limitations as ply angle, number of layers for the web and flanges, and the thickness of all section walls are considered in this study. Finally, the optimal layer arrangement for the web and flanges are separately determined and discussed. The results show that the presented optimization procedure and layups patterns lead to increasing the lateral-torsional buckling capacity about 52% compared to the conventional angle-ply and unidirectional layups for the web and flanges, respectively.

Lateral torsional buckling capacity of corroded steel beams: A parametric study

Thickness reduction due to uniform corrosion increases the tendency of lateral torsional buckling (LTB) of open cross-sections and it reduces the moment capacity of the beam. The effect of the various corrosion cases on the LTB moment capacity (M b,rd) of the I-beams are investigated in this paper. An analytical framework for patch corroded I-beams is introduced to provide a guideline for simulating the nonlinear lateral torsional buckling behaviour of patch corroded simple beams. Hence the effect of different corrosion scenarios to reduce the buckling reduction factor (η LT) is investigated by conducting a parametric study. Twelve different beam lengths were considered to obtain different non-dimensional slenderness ratios (λ LT) in this parametric study. The degraded buckling curves were obtained for each corrosion scenarios.

Design equations for buckling strength of steel I-beam under non-uniform heating condition

This paper presents a numerical study on lateral-torsional buckling strength of the simply supported beam under fire subjected to general loading conditions. The influence of length to height ratio and the non-uniform temperature distribution in the steel beam was considered to evaluate the buckling strength of the beam. The numerical simulations were carried out by utilizing a commercial finite element program, ABAQUS. The buckling strengths of steel beams using buckling design curves at elevated temperature of Eurocode 3 Part 1–2 were also generated and compared. The results showed that the buckling resistance of the steel beam under fire using Eurocode 3 can give unconservative values for beams subjected to positive moment and give very conservative values for beams subjected to negative moment. The new correction factor was proposed to take into account the effect of length to height ratio and non-uniform heating condition on buckling strength. The proposal equation was suggested to determine the lateral-torsional buckling capacity of the steel beam under fire and general loading conditions.

Experimental study of 3-ply laminated glass beams subject to in-plane loads

In this study, nineteen 3-ply laminated glass beams of 1.0 m span with different glass and interlayer types were tested to failure. Annealed glass beams generally failed in shear facture, whereas beams of toughened glass displayed lateral-torsional buckling (LTB) response, with a bow-shaped out-of-plane deflected shape and significant out-of-plane bending. The experimental failure loads had significant scatter for nominally similar beams, highlighting the variability of glass as a material. The loads have been compared to design predictions for LTB from published design methods, and it was found that many of the existing methods consistently over-estimate the LTB capacity of the beams, in some cases by more than three times the experimentally determined failure load.

Behavior of laterally unsupported monosymmetric steel I-section beams at elevated temperature under non-uniform moments

The steel sections are subjected to instability and buckling failure due to the rapid degradation of flexural rigidity under fire-loading conditions. The behavior of monosymmetric hot-rolled steel I-section beams are studied in this paper under uniform and non-uniform moment conditions. Validated finite element models in ABAQUS is used for parametric study, considering 1500 linear and non-linear simply supported beam models. Behavior of monosymmetric I-beams is analyzed under different uniform temperature conditions having shorter, intermediate, and longer spans with a height-to-width ratio greater than two (h/b > 2). The collapse of beams with longer span is not much affected by the non-linear material behavior. Only up to 17% increase from elastic capacity is observed for such beam under inelastic capacity. The interaction curves for the degree of monosymmetry and moment gradient are provided that can be used for estimating inelastic lateral-torsional buckling (LTB) capacities. Further, statistical analysis and comparison of FE-results with design predictions from Eurocode 3 part 1.2 showed that a single design buckling curve is insufficient in predicting the collapse capacity of hot-rolled beams under different loading conditions at elevated temperatures. Eurocode 3 part 1.2 generally provide highly conservative predictions at higher temperatures for beams under single curvature; however, it may provide unsafe results under double curvature for intermediate to shorter span beams.

Characterization of residual stresses for LTB simulations of modern welded girders

A number of factors affect the lateral–torsional buckling (LTB) behaviour of steel members. Residual stresses are known to influence LTB in the inelastic range, with differing patterns between rolled and welded sections causing differences in inelastic LTB capacity between the two section types, even if geometry is identical. Finite element simulations can facilitate detailed investigation of this phenomenon; however, it is important that assumed initial residual stress distributions used in such simulations are accurate. While residual stress data are available for welded sections, existing proposed predictive models for these stresses are based on limited data sets, making it unclear if the models are appropriate for a broader range of sections. Therefore, to address the need for accurate LTB simulations in research, a new predictive residual stress model for modern welded girders is proposed in this study, based on recent residual stress measurements on welded sections. The proposed model takes section geometry and welding parameters into account and is calibrated with multiple data sets from the literature. Finite element simulations of LTB are carried out using the proposed model and an additional model proposed by Chernenko and Kennedy.

Limit states design of crane runway girders

Steel crane runway girders are subjected to torsion by their eccentric loads. The twist rotation of the principal axes caused by torsion induces additional bending moments, and reduces the resistance to lateral-torsional buckling. There is little guidance on how to design for torsion, and design procedures are often intuitive, with varying degrees of rationality and precision.This paper seeks to establish a logical procedure for designing crane runway girders which is based on an extension of the limit states methods of designing for biaxial bending. An additional term for the ratio of the design torque to the section torsion resistance is included in the interaction equations. Proposals are made for determining this section resistance. Research has shown that this addition can allow for the reduction in the lateral-torsional buckling resistance caused by the twist rotations. A linear elastic analysis of the twist rotations is used to determine the moment increases caused by torsion.An example of the proposed method is developed and illustrated by a design example. The design is governed by the member capacity, which is mostly affected by the lateral-torsional buckling capacity. Torsion has a very small effect, and the twist rotations are small. The twist rotations cause a significant increase in the minor axis bending moment, but this has only a minor effect on the member capacity.

The effect of slenderness on the lateral-torsional buckling and ultimate shear capacity of plate girders

Lateral torsional buckling and shear buckling are two of the most significant structural responses that should be considered during the design process of plate girders. Particularly the importance of lateral torsional buckling was once again witnessed during the reconstruction process of a bridge in Edmonton, Alberta, Canada when the plate girders failed due to insufficient bracing. This current study aims to acquire a better understanding of the effect of geometric parameters such as the web slenderness, flange slenderness and span-to-depth ratio on the critical buckling moment and ultimate shear strength of plate girders. To achieve this goal the critical buckling moment and ultimate shear strength of a plate girder were parametrically studied for a large number of geometries using a load case from an experimental study. The results of this parametric study clarified the effects of web slenderness, flange slenderness and span-to-depth ratio on the structural performance of a plate girder. The visualization of the results was used to identify the ranges of these geometric parameters where the structural performance is most sensitive to changing them.

Nonlinear Buckling Strength of Steel H-Beam under Localized Fire and Pure Bending

This paper presents a numerical simulation to assess lateral-torsional buckling (LTB) behavior of steel H-beams exposed to localized fire. The nonlinear buckling analysis was conducted using a finite element program, ABAQUS, to assess LTB of the beams. The steel beams were subjected to pure bending and localized fire. The location of the localized fire was applied below at a one-eighth point, a quarter-point and a half of the beam from the support. The combined effects of initial geometric imperfection and residual stress were also considered. The buckling strength of the beam under localized fire and ISO-834 standard fire were generated and compared. The results showed that the LTB strength degradation of the beam under localized fire was slower than that in ISO-834 standard fire. The fire source location and the length-to-height ratio of the beam have a significant effect on the LTB strength of the beam. The LTB capacity of beams using Eurocode 3 with the uniform heating assumption can give over-conservative results when the real fire scenario is localized fire. The buckling strength of steel beams using Eurocode 3 can give unconservative results when the fire scenario is ISO-834 standard fire.

Lateral Torsional Buckling Strengths of Stepped Beams at Midspan Exposed to Elevated Temperature

The American Institute of Steel Construction provides design equations for the lateral torsional buckling (LTB) of beams under fire. However, these equations are limited only to prismatic beams. Stepped beam factors are introduced by researchers that accounts the change in cross-sections of beams to determine capacities of stepped beams under normal temperatures. This paper assesses the validity of the stepped beam factors for the LTB capacities of stepped I-beams located at its midspans integrated to the AISC equation for beams under high temperatures. A set of numerical studies using finite element analysis program, ABAQUS, was conducted to assess the buckling behavior of stepped beams. The analysis is composed of heat-transfer analysis that evaluates the change in material properties of steel as heat propagates the material from 20 °C to 800 °C; and Static Riks analysis where the beams are applied with uniform end moments. Correlation between the results from the stepped beam equations and the simulated data from ABAQUS has been done. The comparison between data showed that the proposed equation generated conservative estimates with an average percentage difference of 11.48% for inelastic LTB, whilst, 2.07% for the elastic LTB. In addition, the ratio of the increase in strength and increase in volume of stepping of beams shows that the flange width of the stepped beam controls its efficiency in lateral torsional buckling capacity. Overall, the results of this research proved that the existing stepped beam equations can be used in calculating the structural capacity of stepped beams at midspan under both normal and elevated temperatures.

Lateral-torsional buckling behaviour of concrete-filled high-strength steel tubular flange beams under mid-span load

Lateral-torsional buckling (LTB) behaviour of concrete-filled high-strength steel tubular flange beams (HS-CFTFBs) is experimentally and numerically investigated. Six specimens are tested in simple support with a lateral unrestrained concentrated load in mid-span. Among them, two are failure controlled through flexural yielding (FY), whereas the remaining specimens are controlled through LTB. Finite-element (FE) models are then constructed and the comparison with the experimental results indicates that they could reliably and accurately evaluate failure modes, load–displacement relationship and ultimate capacities of HS-CFTFBs. These verified FE models are consequently used to investigate the effect of flange depth, concrete and steel with various span lengths. Results suggest that the ultimate moment capacity evidently decreases as the span length increased, particularly for the high-strength steel beams. The increasing flange depth remarkably improved the LTB strength but merely slightly increased the amount of steel. The infilled concrete could improve the resistance to flange distortion and thus increase the ultimate capacity. However, the strength of concrete exhibits a slight influence on ultimate capacity. Increasing fy could improve the LTB capacity when the span length is relatively small, but the improvements decrease with increasing span length. When the failure mode is elastic LTB, increased fy could substantially improve post-buckling stiffness and ductility

Stability performance of thin-walled pultruded beams with geometric web-flange junction imperfections

The current paper investigates the role of initial imperfections at web-flange junction on the lateral torsional buckling behavior of pultruded fiber reinforced polymeric beams. This study is based on experimental and numerical results, which are developed in two main steps: perfect beams and beams with initial imperfections at the web-flange junction. In the first step, small-scale tests are carried out to calculate the mechanical properties of the composite section. Perfect and imperfect pultruded I- and C- shaped beams are subjected to full-scale experimental tests under an applied four-point bending load with a total lengths varying from 1500 to 3000 mm, and 2500–3500 mm for the I- and C-beams, respectively. The end conditions of all beams studied are simply supported. Perfect beams are tested to investigate their dominant failure mode, as well as the impact of lateral bracing on the failure modes. While, imperfect beams are tested to determine the effect of initial imperfections on the lateral-torsional buckling capacity and failure mechanisms.

Experimental and numerical investigation of lateral torsional buckling behavior and capacity of welded Q460 beams

Compared to normal strength steel (NSS), high strength steel (HSS) has many advantages, such as high yield strength, high tensile strength, and high structural reliability. Recently, HSS beams have gradually been employed in practical engineering. In this investigation, eight tests and parametric analysis were carried out to study the lateral torsional buckling (LTB) behavior and capacity of welded Q460 beams. An effective loading system that released the lateral constraint of the loading point was developed. Totally eight tests of welded beams with lateral restraints at two end supports were conducted under a mid-span concentrated force. Among these eight welded beams, one Q235 beam was tested to compare with seven Q460 beams. The flange width-to-thickness ratio changed from 4.6 to 9.6, the web height-to-thickness ratio changed from 28.75 to 47.50, and the beam span was varied from 3 m to 5 m. In addition, a series of parametric analyses considering initial geometric imperfections were performed to evaluate and investigate the effects of key parameters on the LTB behavior of welded Q460 beams. The experimental and numerical results were compared with the LTB curves from Chinese design codes GB50017-2017 and GB50017-201X, Australian code AS4100, and Eurocode 3. The GB50017-201X, AS4100, and Eurocode 3 for general sections underestimate their LTB capacity. The current GB50017-2017 and Eurocode 3 for rolled and equivalent welded sections are unsafe for evaluating the LTB capacity of HSS beams. Modified design equations that are more appropriate for predicting the LTB capacity of welded Q460 beams are presented.

Optimisation of Shear and Lateral–Torsional Buckling of Steel Plate Girders Using Meta-Heuristic Algorithms

The shear buckling of web plates and lateral–torsional buckling are among the major failure modes of plate girders. The importance of the lateral–torsional buckling capacity of plate girders was further evidenced when several plate girders of a bridge in Edmonton, Alberta, Canada failed in 2015, because insufficient bracing led to the lateral buckling of the plate girders. In this study, we focus on the optimisation of the cross-sections of plate girders using a well-known and extremely efficient meta-heuristic optimisation algorithm called the harmony search algorithm. The objective of this optimisation is to design the cross-sections of the plate girders with the minimum area that satisfies requirements, such as the lateral–torsional buckling load and ultimate shear stress. The base geometry, material properties, applied load and boundary conditions were taken from an experimental study and optimised. It was revealed that the same amount of load-carrying capacity demonstrated by this model can be achieved with a cross-sectional area 16% smaller than that of the original specimen. Furthermore, the slenderness of the web plate was found to have a decisive effect on the cost-efficiency of the plate girder design.

Measurement and prediction of residual stresses in welded girders

Residual stresses can have a significant impact on the stability of structural members. In the case of I-section beam elements, such stresses can impact lateral–torsional buckling (LTB) capacity, particularly in the inelastic range. I-sections are typically fabricated by either rolling as a single shape or welding three plates together; residual stress distributions can differ considerably between the two section types. It is therefore possible for a built-up welded girder to have a different LTB capacity than that of a rolled one of identical cross-section. Concerns have been raised that such a difference may render North American steel design standards unconservative for welded girders. Because of the lack of recent physical LTB tests on welded girders, finite element modelling was used as a tool in making this assessment, and the assumed residual stress distributions were based on data from 1970 to 1980 that may not account for advancements in welding technologies and processes since the publication of these data. The paucity of recent residual stress data, however, prevents a direct assessment of these assumed distributions. In this study, residual stress measurements were carried out on a series of four welded steel test girders using the sectioning method. A comparison of the measured distributions with four existing models finds these models to be inaccurate in important ways; an updated model is therefore required for use in numerical simulations of LTB behaviour of welded girders used in industry today.

Lateral torsional buckling and section distortion of pultruded GFRP I-sections subject to flexure

Lateral torsional buckling (LTB) and local section distortion of pultruded glass fiber reinforced polymer (GFRP) I-sections subject to flexure are investigated. LTB behavior will dominate longitudinally slender beams having low flange slenderness. However, as the flange becomes more slender and/or the beam shorter, the effects of local section distortion (LSD) become significant, reducing the LTB capacity of the member. Using the energy method, an analytical study was conducted and explicit equations for predicting the critical LTB buckling moments of GFRP I-sections accounting for the effects of LSD are proposed. The proposed LTB equation was validated using experimental results and finite element analysis. Excellent agreement was observed between the proposed LTB equation and experimental results for sections expected to be dominated by LTB behavior. Extending the study using the same approach, an equation predicting LTB capacity as it is affected by LSD was also validated using experimental results. It is found that the proposed LTB equation captures the capacity reduction due to LSD and therefore, provides more accurate predictions for sections expected to be dominated by LSD behavior; those having small slenderness ratios and large flange slenderness ratios.