Lateral Torsional Buckling Resistance Research Articles

A new finite element formulation for the lateral torsional buckling analyses of orthotropic FRP-externally bonded steel beams

Abstract The present study develops a new finite element (FE) formulation for the lateral torsional buckling (LTB) analyses of steel beams exteriorly bonded with orthotropic fiber-reinforced polymer (FRP) layers. The formulation considers shear deformations, partial material interaction, local and global warping deformations, and orthotropic FRP properties. The buckling responses of multispan FRP-bonded steel beams predicted by the present solutions are excellently validated against experiment and numerical solutions. As observed, the FRP strengthening is highly effective for the LTB resistance of steel beams. However, the LTB responses are strongly dependent on the orthotropic properties and strengthening lengths of FRP layers. The effects of shear deformations, span ratios, and loading conditions on the LTB responses are also quantified in the present study.

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.

Proposed Improvements to AISC 360-22 Chapter F for Built-Up I-Section Members

Recent analytical and experimental data has shown that the AISC 360–22 Ch. F lateral-torsional buckling (LTB) resistance equations significantly overpredict the strengths of a wide range of built-up I-girders. These overpredictions are mainly attributed to unaccounted-for yielding effects and an insufficient characterization of the plateau strengths by the AISC 360–22 compact- and noncompact-web limits. The objective of the current study is to present and justify the implementation of a new set of recommended AISC 360 Ch. F provisions (AISC 360 Rec.) for built-up I-girders. These recommended provisions were developed by making six targeted improvements to AISC 360–22, which consist of changes to the web classification limits, the inelastic/elastic LTB strength threshold, the handling of moment gradient, and the representation of the LTB strength curve itself. Two independent studies evaluate the performance of the AISC 360 Rec. equations. In the first study, professional factors (Mtest/Mn) were calculated and statistically evaluated using a newly updated LTB experimental database. The second study compares the LTB strength curves for targeted cross sections to the results from nonlinear shell finite element analysis (FEA) test simulations. The findings demonstrate that the recommended approach provides accurate-to-conservative strength predictions that meet or exceed a targeted minimum reliability index of 2.6, which AISC 360–22 does not achieve for a range of I-section member characteristics. The development of the AISC 360 Rec. provisions is significant as it fixes the strength overprediction problems recently observed for built-up I-girders while maintaining good accuracy for members where the AISC 360–22 equations perform well.

Lateral-torsional buckling resistance of non-prismatic and prismatic mono-symmetric I-section steel beams based on stress utilization

The lateral-torsional resistance of prismatic double-symmetric I-section beams is accurately predicted using a mechanically consistent Ayrton-Perry approach, combined with a calibrated generalized imperfection. The corresponding design formulation was recently adopted in the revised version of Eurocode 3. However, for prismatic mono-symmetric I-section beams, the General Case shall be used while for non-prismatic beams only the General Method is available. Both methods present a very large scatter and highly underestimate the lateral-torsional buckling resistance. This paper proposes an extension to the General Formulation for non-prismatic beams with arbitrary boundary conditions, partial lateral restraints, and arbitrary loading for mono-symmetric I-sections. Using an advanced numerical model calibrated with experimental test results, a large parametric study is undertaken, and its results are used to assess the available design methodologies and the proposed method. It is concluded that the General Formulation provides excellent safe-sided estimates of the LTB resistance, and it is confirmed the very poor performance of the General Case and the General Method.

Proposition of a modified formulation to predict the lateral-torsional buckling resistance of steel beams: meta-analysis of test data

Proposition of a modified formulation to predict the lateral-torsional buckling resistance of steel beams: meta-analysis of test data

Behaviour of concrete filled rectangular tube girders in bending

A detailed study of the behaviour of concrete-filled rectangular tubular flange girders (CFRFGs) was undertaken. The CFRFGs were steel beams in which the top flange plate is replaced with a concrete-filled steel section, resulting in greater load-carrying capacity and lateral torsional buckling resistance compared with a regular steel beam of similar proportions. They are complex members and their behaviour is governed by several interrelated parameters, which were studied in this work. Using the Abaqus program, a three-dimensional finite-element (FE) model was developed to investigate the flexural behaviour of simply supported CFRFGs. Using available experimental results, the computational model was validated and then used to study the influence of the most salient properties on the overall response. Based on a fundamental assessment of the behaviour, a simplified analytical model was developed to predict the capacity of these types of section in a way that is suitable for designers. The results were compared with those from the FE analysis and it was found that the analytical model is capable of providing an accurate depiction of the behaviour and the bending moment capacity.

Lateral torsional buckling of I‐section simply supported beams with stepped height

AbstractVariable cross‐section beams are widely used, especially I‐section stepped beams with variable height, which have benefits such as saving materials to match the moment diagrams, reducing the structure height, and access for technical services. However, lowering the beam height also leads to a significant decrease in lateral torsional buckling resistance. Currently, the standards do not provide calculation rules for this type of beam yet, and some studies on lateral torsional buckling of beams have only focused on those with varying flange width and thickness while keeping the beam height constant. This article introduces an approximate formula to determine the critical moment of simply supported I‐section beams when the height varies. The proposed formula is validated by comparing with finite element simulation results obtained by COMSOL Multiphysics 5.6. The evaluation shows that the formula has a low coefficient of variation and high coefficient of determination, ensuring its reliability.

Influence of transverse stiffening on the lateral-torsional buckling resistance of built-up I-girders

Recent studies have shown that the AISC 360 Specification substantially overpredicts the strength of certain built-up steel I-girders subjected to high moment gradient. These strength overpredictions have been attributed to various effects, including (1) the direct scaling of the uniform bending lateral-torsional buckling (LTB) strength curve by the elastically-derived moment gradient factor, Cb, without considering the yielding induced at the larger predicted strengths, (2) reduction in the elastic LTB strength due to web shear and corresponding elastic distortional buckling effects, (3) compression flange lateral bending due to amplification of the initial flange sweep, and (4) intensification of the compression flange lateral bending due to web distortion. This paper scrutinizes the impact of transverse stiffening on the elastic and inelastic LTB resistance of a suite of I-girders previously evaluated experimentally and numerically without transverse stiffening through full-nonlinear shell finite element analysis test simulations. The results provide further insight into the sources of the AISC Specification overpredictions and the practical aspects of adding transverse web stiffeners to increase the LTB strength.

Lateral-torsional buckling resistance of corrugated web girders

AbstractThere is currently no accurate calculation procedure for determining the lateral-torsional buckling resistance of trapezoidally corrugated web girders. Therefore, a detailed investigation is performed in the frame of an experimental and numerical research program at the Department of Structural Engineering of the Budapest University of Technology and Economics. Based on the previous experimental results, a numerical model is developed to be used to determine the lateral-torsional buckling resistance by using deterministic method. The effect of flange size, corrugation geometry and boundary conditions are investigated. An improved design method is developed for the determination of the lateral-torsional buckling resistance of trapezoidally corrugated web girders.

Novel formula for the elastic critical moment of beams with corrugated web

AbstractThis paper presents a novel analytical expression to determine the elastic lateraltorsional buckling resistance of I‐beams with corrugated web. The corrugated web beams have higher torsional stiffness than the flat web beams; therefore, the self‐weight of the beam can be reduced. The appropriate hand calculation methods to determine the elastic critical moment of corrugated web beams are based on the modification of warping constant of the cross‐section. In this paper, instead of modifying the warping constant the approximate expression is derived from the total potential strain energy of the beam using an energy method. During the solution, the beam is separated into three parts. The flanges are modelled as thin‐walled beams and the corrugated web is modelled as a thin equivalent orthotropic plate with uniform thickness. To assess the accuracy of the proposed analytical formula full shell finite element models were created in Abaqus software. The accuracy of the proposed expression is examined for sinusoidal and trapezoidal corrugation also. The results of the parametric study showed that the derived formula is accurate and applicable for elastic lateral‐torsional buckling analysis of I‐beams with web corrugation.

BENDING RESISTANCE OF HIGH STRENGTH HOT-ROLLED STEEL UNIVERSAL COLUMN SECTION

The most commonly found steel grades in the market are S 275 and S 355 However, recent advancement in the welding techniques allows for the development of high-strength steel for higher grades up to S 700 with reasonable cost and quality to construct heavy-loaded and long spanned structures. To facilitate the selection of the section sizes in accordance to Eurocode 3 Standard, this research focusses on investigate and validate the bending resistance, Mc,Rd and lateral torsional buckling resistance, Mb,Rd of a hot-rolled steel universal column section (UKC) from common steel grades (S 275 and S 355) up to high strength steels (S 460, S 550 and S 650). This study employed Microsoft Excel spreadsheet to develop a program for design calculation for UKC in accordance with Eurocode 3 Standard and compared with the available results provided in SCI P363. The validated program was further applied to develop selection data for high strength UKC steels (S 460, S 550 and S 650). The study outcome suggests that the classification, Mc,Rd and Mb,Rd of the steel is greatly affected by the steel grade. The parametric study in this research also shows that C1 factor, section size and span length can also affect the Mc,Rd and Mb,Rd of the steel, aside from steel grade. Further analysis of high strength UKC steels was done and tabulated since the program developed was validated and employed in the study

Impact of the fabrication process on the lateral–torsional buckling of welded I-section beams

The buckling behaviour of a steel member is greatly dependent on the residual stress distribution, which is affected by the fabrication process. Indeed, residual stresses in welded steel members are significantly influenced by possible flame-cuts at the flange tips commonly used in practice. However, the Eurocode 3 rules do not account for the beneficial effects of the flame-cuts. Experimental data on commonly used slender members are limited, and therefore to gain further insight an experimental test campaign involving eight slender welded members is carried out. The influence of the flange dimensions and fabrication process was investigated. A new residual stress model is proposed for welded I-sections made of flame-cut flanges integrating results from the literature. Moreover, the actual buckling behaviour of welded members made of flame-cut flanges and/or with a cross section that is not uniform and doubly symmetric is studied. A literature overview of past experimental works highlights the lack of results on common mono-symmetric and/or tapered members, especially for welded members made of flame-cut flanges. An experimental study was thus conducted including lateral–torsional buckling tests on four beams: two uniforms and two tapered. Both types of beams comprised a doubly symmetric and a mono-symmetric I-section. The benefits resulting from tapering and/or increasing the compression flange thickness of an I-section beam are highlighted. The experimental results validate the use of a finite element model for studying the impact of the flange fabrication process on the lateral–torsional buckling resistance. Flame-cuts present at both flange ends increase the ultimate resistance.

Experimental and Analytical Studies of Continuous Steel-Stringer Lateral-Torsional Buckling Resistance

In the 1950s and 1960s, some Louisiana’s bridges were constructed using steel twin-girder or truss systems, in which floorbeams are carried by the main members and continuous (spliced) stringers are supported by the floorbeams. The main members are either two-edge (fascia) girders or trusses. One of the byproducts of this type of design is that stringer bottom flanges are in compression in the negative moment region over the floorbeams, which could result in lateral torsional buckling (LTB) should inadequate lateral bracing be provided. When the continuous stringers are load-rated using AASHTOWare Bridge Rating analysis software (BrR 7.1), their LTB resistance is calculated in accordance with American Association of State Highway Officials (AASHTO) LRFD Bridge Design Specifications, which do not account for potential bracing provided by a noncomposite deck and could underestimate flexural strength. As a result, the rating may be low enough to require restrictive load posting or even bridge closure. This paper summarizes extensive experimental and numerical studies investigating the behavior of this type of floor system by testing two-span, continuous, steel stringers in a grillage that included three stringer lines, an interior transverse support (floorbeam), and transverse diaphragms at the end supports. The tests and finite-element analysis studies encompassed a variety of unbraced lengths and support conditions with steel diaphragms or timber ties acting as bracing members. The findings demonstrated that, for the systems examined, minimal bracing could substantially enhance LTB resistance and supported the use of higher flexural strengths than those currently predicted using AASHTO Specifications. This paper illustrates the use, challenges, and successes in LTB modeling beams with various support and bracing conditions. The most flexible cases were the most difficult to achieve close agreement with experimental results.

A new proposal for the design of laterally unrestrained cellular steel beams under moment gradient at elevated temperatures

The laterally unrestrained cellular steel beams (CB) are more susceptible to buckling failure and collapse early due to the material degradation that occurs in a fire situation. The lateral-torsional buckling (LTB) resistance design proposed by Eurocode 3 pt. 1–2 is relatively conservative for both uniform and non-uniform bending cases and hence needs to be improved. This paper aims to investigate the influence of single and double curvature bending on the LTB resistance of cellular steel beams subjected to elevated temperatures. To carry out the present numerical study, the finite element (FE) models are first validated with a set of numerical and experimental data available from the existing literature. Extensive parametric FE analyses are performed by considering different sizes and spacing of the opening, and various beam slenderness for hinge and roller boundary conditions. Based on parametric research, a new design proposal for LTB buckling resistance of CB at elevated temperatures for various moment gradients is presented. Compared with the analytical results provided by Eurocode 3 pt. 1–2, the proposed design method is safer and conservative. The proposed approach provides better agreements than existing procedures. Moreover, a statistical analysis of the results is performed, and the accuracy of a new proposal is presented in this paper.

Lateral-torsional buckling assessment of I-beams with sinusoidally corrugated web

This paper assesses the elastic and inelastic lateral-torsional buckling resistance of I-beams with sinusoidal corrugated web through an extended 22 degrees of freedom thin-walled beam-column finite element method. The appropriate hand calculation methods to determine the elastic critical moment of corrugated web beams are based on the modification of the warping constant of the cross-section. Instead of modifying the warping constant, the corrugated web is modelled as a thin, equivalent orthotropic plate with uniform thickness. An approximate expression is also derived from the total potential strain energy of the beam using the Ritz method. The result of the parametric study showed that the developed finite element is accurate and applicable for linear buckling analysis of beams with sinusoidal web corrugation. With the results of the linear buckling analysis the plastic resistance of the corrugated web beam can also be determined. Based on advanced finite element simulations' results the parametric study showed that the standard-based imperfection factor leads to conservative results to predict the inelastic lateral-torsional buckling resistance of sinusoidally corrugated beams, so a more precise but still safe imperfection factor is proposed for sinusoidally corrugated web beams.

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.

Noncomposite concrete deck bracing effects on continuous steel stringer lateral torsional buckling resistance

Louisiana’s bridges used two-girder or truss systems in the 1950 s and 1960 s, in which floorbeams are carried by main members and continuous stringers are supported by the floorbeams. The main members are either two edge (fascia) girders or trusses. Continuous span stringer bottom flanges are in compression in their negative moment regions, which could result in lateral torsional buckling (LTB). When these stringers are load rated using AASHTOWare Bridge RatingTM analysis software, lateral torsional buckling (LTB) resistance is calculated in accordance with the AASHTO LRFD Bridge Design Specifications, which the authors have determined may not adequately account for bracing effects provided by a noncomposite deck, and therefore could underestimate the flexural strength. Resulting ratings may be low enough to require restrictive, and possibly unnecessary, load postings or even bridge closures. This issue affects more than 20 significant bridges that are key parts of Louisiana’s highway system. To address the challenge of underestimated stringer LTB resistance and assess bracing effects provided by a concrete deck, experimental and analytical studies were performed on a two-span, continuous, steel stringers in a grillage system, which included three stringer lines, an interior transverse support (floorbeam), and transverse diaphragms at the end supports. The tests encompassed a variety of configurations, with and without a concrete deck. This paper describes laboratory testing setups and discusses experimental results, focusing on bracing effects on LTB resistance due to the presence of a noncomposite concrete deck. Finite element models using ANSYS were calibrated, validated using test results and used to simulate stringer behavior in Louisiana’s representative bridges. Finite element analyses of various tests showed generally comparable results to test data, and provided a feasible approach to load rate continuous stringers if a refined analysis is deemed necessary. The studies showed that stringer LTB resistance could possibly be tripled when noncomposite deck bracing effects are considered.

Experimental and analytical assessment of LTB resistance of built-up steel I-section members

Analytical and experimental research investigations conducted subsequent to the development of the unified AISC 360–05 Section F4 and F5 and AASHTO [3] LRFD provisions for built-up I-section members have identified several areas where improvements are needed. However, the experimental data is relatively scarce within the design space for inelastic lateral-torsional buckling (LTB) of these member types. This study presents the results of eight experimental tests of doubly symmetric built-up I-section members and a large number of full-nonlinear shell finite element analysis (FEA) simulations validated against the experimental results. The study was conducted to supplement existing data and to evaluate three recommended changes to the AISC 360 Specification: (1) reduction of the ordinate at the transition between the elastic and inelastic LTB equations to ML = 0.5RpgMyc for the base uniform bending case, where Rpg is the web bend-buckling strength reduction factor and Myc is the yield moment to the compression flange; (2) use of the more general equation in AISC 360–16 Table B4–1 Case 16 for the compact-web limit, λpw; and (3) use of a variable crw factor from the current AASHTO LRFD Specifications for the calculation of the noncompact-web limit, λrw. Comparisons were also made to the predictions from the first generation of Eurocode 3. Results from the study support the recommended changes to the AISC 360 Specification and confirm the significant impact of flange lateral bending from the amplification of initial compression flange sweep for members with LTB slenderness close to the noncompact bracing limit associated with ML.

Numerical analysis and prediction of lateral-torsional buckling resistance of cellular steel beams using FEM and least square support vector machine optimized by metaheuristic algorithms

This study presents an advanced framework for modeling the lateral-torsional buckling behavior of cellular steel beams, which combines hybrid intelligent models with numerical simulation. The proposed hybrid intelligent models employ a large dataset-based finite element method (FEM) for training and validation the framework, as well as metaheuristic algorithms for optimal auto-hyper-parameters selection. A total of 1535 numerical models are examined in order to evaluate the lateral-torsional buckling behavior. Following that, the least square support vector machine (LSSVM) optimized using four metaheuristic algorithms (ME): particle swarm optimization (PSO), ant lion optimization (ALO), grey wolf optimizer (GWO), and Harris hawks optimization (HHO) algorithms, is utilized to estimate accurately the lateral-torsional buckling resistance. According to the findings of a comprehensive performance evaluation utilizing statistical and graphical comparing criteria, the suggested LSSVM-ME predicts the lateral-torsional buckling behavior with excellent accuracy. LSSVM-HHO, in particular, outperforms the other hybrid intelligence models, with an RMSE of 41.72 kN.m and an NSE of 0.99. Overall, the results indicate that the proposed framework has a great potential for use as a practical tool for estimating the lateral-torsional buckling behavior of cellular steel beams.

A Critical Evaluation of Moment Gradient (Cb) Factror Calculation Procedures for Singly Symmetric I-Section Members

This paper explores the manual calculation of the elastic lateral-torsional buckling resistance of prismatic singly symmetric I-section members having a variation in the bending moment between the brace points. The paper shows that the quarter-point moment gradient factor, Cb, equation in the AISC Specification (2016), as modified by its Commentary, is inaccurate for reverse-curvature bending of singly symmetric I-section members. In addition, the paper explains that the Cb equations in the current AASHTO Specifications (2020) provide some accounting for the different patterns of compression in the separate flanges for cases involving moment reversal. To rectify the limitations of the ASC and AASHTO methods, the paper recommends a modified form of an alternative quarter-point Cb equation proposed by Wong and Driver (2010). For singly symmetric cases involving moment reversal, the terms in the quarter-point equation are replaced by the ratio of the moments to the corresponding elastic buckling moment based on Cb = 1, considering which flange is in compression at each of the locations where the moments are sampled. The studies show that the Wong and Driver equation, with this modification, provides substantially improved accuracy compared to the existing AASHTO and ASC equations for reverse-curvature bending with slightly less calculation effort. In addition, the paper demonstrates the accuracy of the direct application of the Wong and Driver equation for single-curvature bending cases.