Lateral Torsional Buckling Strength Research Articles

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.

Assessing lateral torsional buckling of stepped steel I beams using finite element method

The use of steel beams with variable sections along their length is getting more attention in recent years. These variable sections can vary gradually along the beam or change abruptly as a drop or a step. The current study investigates the lateral torsional buckling (LTB) of stepped steel beams with flanged I section subjected to uniformly distributed pressure on the top flange. The studied parameters are the step height, the step length, and the boundary conditions of the beam. The finite element method is used to carry out a linear buckling analysis of the beams’ models. The results show significant degradation in beams LTB strength due to the jump of the beam's section. Reducing the simply supported beam depth by 25 % reduces LTB strength by about 40–50 %, while reducing the fixed beam depth by 25 % reduces LTB strength by about 30–40 %. Further reduction in depth showed no significant additional reduction in simply supported beams strength, while the fixed beams showed another 30–40 % reduction in strength with another 25 % reduction in beam total depth. The step made the compressive stress transfer between the two flange parts through the web.

Lateral torsional capacity of steel beams in different loading conditions by neural network

Lateral torsional buckling (LTB) is a common mode of failure in steel structures due to instability. However, current standard recommendations have limitations in accurately determining the ultimate capacity of members subjected to LTB. To address this issue, an in-depth parametric study using finite-element analysis (FEA) was conducted to investigate the effects of major parameters, including various types of loading, on the strength of steel I-beams. Additionally, the artificial neural network (ANN) technique was used to find a reliable procedure for assessing the LTB strength of steel I-beams using a generated database. To demonstrate the efficacy of the developed formulation, it was compared against predictions using existing equations. The presented formula demonstrated strong accuracy, making it an effective tool for engineers designing I-beams to resist LTB. This research makes significant contributions to the structural engineering field and has important implications for the creation and evaluation of steel structures.

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.

Full beam formulation for the lateral torsional buckling analysis of elastic frames by considering the structural detail of beam-to-column joint

The total potential energy formulation plays an essential role in investigating the flexural–torsional instability of elastic plane frames composed of thin-walled members. However, the work conjugateness between the internal moments and rotation variables of typical frame member cannot be restored completely when applying the conventional potential energy approaches. This paper aims to fully consider the virtual work done by the induced conservative and nonconservative moments in the planar frame prone to lateral buckling. The proposed full beam formulation can help identify those neglected moments that are necessary for fulfilling the equilibrium at the critical state no matter which potential energy formulation is concerned. It has been found that the relative significance of the virtual work done by the neglected moments with respect to the first variation of total potential energy is served as an indicator as whether the conventional potential energy equation can be used for investigating the lateral torsional buckling behavior of the frame. In the out-of-plane buckling investigation of benchmark elastic frames, it has been demonstrated in cases where the neglection of non-zero virtual work done by the nonconservative moment or an approximate account of the induced bimoment through the kinematic warping model may result in incorrect critical load. The lateral torsional buckling strength of the elastic frames can only be correctly determined by taking into account the structural configuration of beam-to-column joint.

New formulas for predicting the lateral–torsional buckling strength of steel I-beams with sinusoidal web openings

Lateral torsional buckling (LTB) of steel I-beams is characterized by simultaneous lateral deflection and twist. LTB is an instability failure mode that has been intensively investigated. However, existing standard procedures and formulations still have limitations in determining the LTB ultimate moment, especially when considering the use of perforated beams. Consequently, in the current paper, by conducting an extensive parametric study, it was tried to investigate the effect of all main parameters as well as the effect of different loading conditions on the ultimate LTB resistance of steel I-beams with sinusoidal web openings. Then, based on the provided database, the artificial neural network (ANN) method was employed, and based on it, a high-precision formulation was proposed to predict the ultimate LTB strength of steel I-beams. In addition to the ANN method, a regression-based formula was also developed as a classical method to examine the differences between the two methods. Finally, the proposed formulas were compared with other existing formulas for estimating the LTB strength. The results showed that the proposed formula based on ANN not only present a reasonable accuracy compared to the existing formulations but also can be used by engineers as practical equations in the design of I-beams with sinusoidal web openings.

Lateral-torsional buckling strength of corrugated web girders – Experimental study

Current standards and specifications do not provide specific design methods to determine the lateral-torsional buckling (LTB) strength of girders with trapezoidally corrugated web. In the international literature there are some previous investigations available focusing on the LTB strength of corrugated web girders. Based on numerical calculations analytical solutions have been derived in the past, however, there is a lack of experimental test results to prove or improve these design proposals. The authors performed an extensive experimental research program including eleven large-scale test specimens. All the test girders have different flange sizes, beside, having the same corrugation profile. The test specimens are loaded by pure in-plane bending having simply supported boundary conditions. The tested specimens have limited warping and rotational restraint at the supports. No web distortional type failure is observed. During the tests the longitudinal strains are captured in characteristic cross-sections and the displacements in vertical and lateral directions are measured as well as the rotation of the mid-span cross-section. The measured LTB strength of the test specimens is compared with existing analytical proposals regarding corrugated web girders and the differences are evaluated. It is observed that the imperfections have key role in the LTB behavior. Based on the experimental results buckling curve “b” from Eurocode 3 is preliminary proposed for the determination of the lateral-torsional buckling strength of trapezoidally corrugated web girders. The executed test program gives useful background to further numerical studies.

Small-scale laterally-unrestrained corrugated web girders: (II) Parametric studies and LTB design

As shown in the companion paper, innovative tests of corrugated web girders (CWGs) were performed followed by validation of the finite element (FE) model. Accordingly, this paper continues investigating the lateral–torsional buckling of small-scale corrugated web girders through parametric studies. This is to expand the available data required to unveil their behaviour and strength. The layout of the tested girders is considered herein, where the webs of small corrugation dimensions are under pure bending moment with symmetrical boundary conditions. This study deals with the linear and nonlinear buckling analyses of the lateral–torsional buckling (LTB) of CWGs using ABAQUS software. Accordingly, 108 models are conducted, considering the effects of the girder length, web overall dimensions, corrugation dimensions, flange dimensions and different steel grades. The results show that increasing the girder length decreases consequently the ultimate flexural strength and stiffness of CWGs. With regard to the web overall dimensions, increasing the web depth is found to have a significant effect on the strength of CWGs in contrast to the effect of the web thickness value, which has insignificant effect on strength. Furthermore, the results revealed that increasing the flange dimensions increases subsequently the strengths of CWGs. In addition, it is noted that the lower the steel grade, the more effectively the material is used especially for girders failing elastically. Additionally, the critical and design LTB strengths of small-scale CWGs with small corrugation dimensions are evaluated. The comparisons show that the critical LTB stress requires modifications to accord well with FE results. Furthermore, comparisons of the ultimate FE strengths with those of Lindner’s equation (1990), EC3 (2004) and AISC (2010) are provided. The comparisons exhibit that the predictions of Lindner’s equation (1990) are suitable, while the predictions of EC3 (2004) and AISC (2010) are highly conservative. Therefore, modifications are made for EC3 (2004) and AISC (2010) design models to provide more appropriate design strengths for CWGs with small corrugation dimensions for use in buildings.

Efficient elastic buckling assessment algorithm for steel members with random non-uniform corrosion

This paper developed an efficient algorithm to study the elastic buckling strengths of non-uniformly corroded steel members. The algorithm is derived based on the authors’ previous work on buckling strength assessment for the steel members by further introducing random non-uniform corrosion damage to the cross-section along member. In the algorithm, the random nature of the corrosion is captured by the Monte Carlo simulations. Moreover, the non-symmetric section effects, including the noncoincidence of section shear center and centroid and Wagner effects, caused by the non-uniform corrosion are considered in the algorithm. The proposed algorithm permits more than ten million times of Monte Carlo simulations being completed efficiently, which greatly reduces the computational expense compared with the existing finite element analysis algorithms. The effects of corrosion depth, corrosion ratio, and corrosion location on the flexural buckling (FB), lateral-torsional buckling (LTB), and axial-torsional buckling (ATB) strengths of the steel member are studied. It is found that corrosion has the most adverse effect on ATB than LTB and FB strengths of the member. When the corrosion distributes more compactly through the section, its adverse effect on the buckling strength of the member could be more significant. Even for the same corrosion ratio, corrosion depth, and total corrosion region number, the reduction factor of the buckling strength can be varied by up to more than 20% due to the difference of the corrosion locations. The reduction factor of the FB strength is generally linear against the corrosion depth. While for the LTB and ATB strength, the reduction factors show nonlinear as per the corrosion depth.

New AISC and EC3 design for S690 plate girders at elevated temperatures

Recently, the determination of the strengths of bridge girders exposed to fire has become of great importance as a result of the failure of some famous bridges for the same reason (e.g. Birmingham and MacArthur Maze Bridges (USA)). On the other hand, S690 high strength steel is widely examined and used in bridges all over the world, such as Mttådalen Bridge in Sweden. With respect to the effect of elevated temperatures on the strength of flexural members, stocky I-section beams have been studied in the literature. On the opposite, the lateral-torsional buckling (LTB) strengths of laterally-unrestrained plate girders with slender webs, which are used extensively in bridges such as those of Birmingham and MacArthur Maze Bridges (USA), and particularly formed from S690 at elevated temperatures have not been addressed. Additionally, AISC (2016) and EC3–1-2 (2005) do not neither cover S690 steel elements nor IPGs with slender webs. Therefore, these girders are simulated in this paper using ABAQUS programme. Currently, the simplified finite element method used successfully by Chen and Young (2008) and Fang and Chan (2019), which utilises the reduced material properties of S690 above the room temperature, is used, which means assuming a balanced structure and a uniform temperature range. The parametric studies consider the variations of the cross-sectional radius of gyration and elastic section modulus. Since the main focus of this paper is strength predictions, strengths are first compared to design models initially proposed according to AISC and EC3–1-2, which are found to yield very conservative predictions. Then, modified AISC and EC3–1-2 design models are recommended, which can safely predict the strengths of S690 IPGs with slender webs at elevated temperatures.

Lateral–torsional buckling strength of corrugated web bridge girders: EC3 and AISC modified design methods

Due to the growing number of used corrugated webs in structural members such as buildings and bridges, their behaviour and strength should extensively be investigated. Accordingly, this paper is an extension to the experimental study recently conducted by the authors on trapezoidally corrugated web girders (CWGs) under pure bending moment (PBM). In particular, this paper focuses on the flexural strengths of CWGs, for highway bridges, under the effect of elastic and inelastic lateral–torsional buckling (LTB). Currently, ABAQUS programme is employed to generate linear and nonlinear finite element (FE) analyses. Firstly, verified FE models using the above mentioned experimental data are adopted to generate parametric studies using large corrugation dimensions (used in actual bridges). Girder length, defined by the number of the corrugation waves, changes from 4 to 36 waves with an increment of 4 waves. Furthermore, changes in the corrugated web height, web thickness, flange thicknesses, flange widths and corrugation angle have been considered. The elastic FE results are compared with available prediction equations in the literature, which calculate the critical LTB stress using different warping constants. The results show that the calculations using Nguyen et al’s method (2010) is the best. With regard to the design strength, the comparisons exhibit that original predictions of Lindner equation (1990), EC3-1-1 (2004) and AISC (2010) are highly conservative. Hence, modified versions for Lindner equation (1990), EC3-1-1 (2004) and AISC (2010) are suggested to provide more suitable design strengths for CWGs.

Assessment of lateral–torsional buckling in steel I-beams with sinusoidal web openings

Beams with sinusoidal web opening are alveolar beams manufactured from a single web cut, which lead to the production of higher I-sections and with a better strength-to-weight ratio when compared to the I-sections from which they originated. There are few studies in the literature about this I-section type, especially in relation to their behavior regarding global stability and Lateral Torsional Buckling (LTB) strength. Bearing in mind the importance of understanding the behavior of alveolar beams with sinusoidal openings in relation to LTB, an extensive parametric study was carried out through numerical analysis in the commercial finite element software ABAQUS. The study was performed with 10 I-sections of the IPE type, with lengths ranging from 6 m to 32 m. In addition, initial imperfections were considered, such as residual stresses and geometric imperfections. With the parametric study results, it was possible to evaluate the main existing analytical procedures, both for the determination of the LTB elastic critical moment, as well as the LTB ultimate moment. The adequacy of standard procedures (AISC; Eurocode 3 and AS4100) was evaluated, as well as analytical procedures present in the scientific literature for determining the LTB ultimate moment. Through the achieved results, it was possible to analyze the behavior of different adaptation methods for the calculation of the elastic critical moment in sinusoidal alveolar beams, as an alternative to the traditional double-T approach. Furthermore, it was found that the AISC-360 standard is unsafe in the case of actions applied to the upper flange, even though this is the most common condition in engineering projects.

Nonlinear imperfect analysis of corrugated web beams subjected to lateral-torsional buckling

In this paper the lateral-torsional buckling (LTB) behavior of steel trapezoidally corrugated web girders is studied by advanced nonlinear finite element (FE) analysis in order to develop new computer-based design method for the determination of the LTB strength of such innovative members subjected to pure bending. Due to the low number of previous investigations the rules of FE modelling for strength determination is not unified nor regulated in the case of corrugated web girders. In addition, standards and specifications do not provide any prescriptions on how to determine the LTB strength of corrugated web girders. The required imperfections have key role in the LTB strength determination. The paper discusses the FE modelling issues on the basis of own test results. Advanced FE model is developed, mathematically verified, and validated by experimental test results. Standards provide equivalent geometric imperfections for conventional flat web I-girders. These proposals have not been, however, investigated for the application to corrugated web girders. Thus in this paper a detailed imperfection sensitivity studies are performed and finally modelling prescriptions and required imperfections – including residual stresses and initial geometric imperfections – are developed and proposed to promote a novel FE analysis based design method for these innovative structures.

Design and analysis of concrete-filled tubular flange girders under combined loading

This paper is concerned with the behaviour of concrete-filled tubular flange girders (CFTFGs) under the combination of bending and tensile axial force. CFTFG is a relatively new structural solution comprising a steel beam in which the compression flange plate is replaced with a concrete-filled hollow section to create an efficient and effective load-carrying solution. These members have very high torsional stiffness and lateral torsional buckling strength in comparison with conventional steel I-girders of similar depth, width and steel weight and are there-fore capable of carrying very heavy loads over long spans. Current design codes do not explicitly include guidance for the design of these members, which are asymmetric in nature under the combined effects of tension and bending. The current paper presents a numerical study into the behaviour of CFTFGs under the combined effects of positive bending and axial tension. The study includes different loading combinations and the associated failure modes are identified and discussed. To facilitate this study, a finite element (FE) model is developed using the ABAQUS software which is capable of capturing both the geometric and material nonlinearities of the behaviour. Based on the results of finite element analysis, the moment–axial force interaction relationship is presented and a simplified equation is proposed for the design of CFTFGs under combined bending and tensile axial force.

A Simplified Design Method for Lateral–Torsional Buckling of GFRP Pultruded I-Beams

This paper provides a simplified design approach for estimating the lateral–torsional buckling (LTB) strength of the pultruded glass fiber-reinforced polymer (GFRP) composite I-beams. A detailed finite element (FE) model based on ABAQUS incorporating more realistic parameters for pultruded GFRP I-beam is developed and verified against the test results available in the relevant literature. After achieving a reliable FE model (through high degree of accuracy in the numerical validation), detailed parametric studies were undertaken by varying the section geometries as well as the span of pultruded I-beams. The selection of the sectional dimensions was based on the composite manuals available in the market, to ensure ease in the practical application of the outcomes of this study. In this analysis, simply supported beam with a uniform bending moment is considered. In accordance with the results of the FE parametric analysis, the accuracy of the theoretical LTB strengths predicted by the equations proposed for pultruded GFRP beams available in the literature is assessed. This comparison indicates that the existing method results in an over-conservative LTB strength estimates for pultruded GFRP I-beams, especially in the low and medium slenderness range. This is primarily due to a comparatively lesser impact of section imperfections on LTB resistance than high slenderness range. Therefore, to address this shortcoming, new simplified design formulations were proposed to have high accuracy of the LTB strength predictions for pultruded GFRP I-beams especially in the low and medium slenderness range. The proposed equations have been provided that might aid the structural engineers in economically designing the pultruded GFRP I-beams in the future.

The influence of structural imperfections on the LTB strength of I-beams

The structural imperfections, namely, the residual stresses, are generated during most manufacturing processes involving material deformation, heat treatment, machining or processing operations. The intensity and distribution of residual stresses are dependent on the techniques used in the production of steel sections (welding, rolling or cold formed techniques) and their dimensions. An appropriate evaluation of residual stress is of great importance for the structural performance of steel I-beams. 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) strength, particularly in the inelastic range. For the development of post buckling numerical analyses, the consideration of residual stress distribution models is fundamental for the correct determination of the LTB strength of I-beams. However, there are several models that attempt to represent the distribution and intensity of residual stresses. These models have a different influence on the LTB behavior of I-beams in numerical analysis. Therefore, this paper aims to investigate, through the development of post buckling numerical analyses with the ABAQUS software, the influence of the different residual stress distribution models on the LTB strength of I-beams. Seven different residual stress models were analyzed on simply supported I-beams subject to uniformly distributed loading applied in the shear center and in the upper flange. The results were compared with standard procedures. It was verified considerable divergences in LTB strength depending on the residual stress model applied. In addition, this paper presents a synthesis of the main residual stress distribution models. The analyses showed in this work shall help the choice of the residual stress distribution model on future numerical simulations.

Numerical study and strength model of concrete-filled high-strength tubular flange beam under mid-span load

High-strength steels (HSS) have been increasingly used in building and bridges due to their advantages, such as lightening the self-weight and reducing the carbon emissions. However, these benefits cannot be fully utilised for long-span flexural members because of lateral–torsional buckling (LTB). For an improved buckling resistance, a new concrete-filled high-strength tubular flange beam (HS-CFTFB) is formed, and its strength is theoretically and numerically studied. Theoretical models of the HS-CFTFB are derived to estimate the full plastic strength and the elastic LTB strength. The finite-element models are then built to determine the buckling factor in the inelastic LTB strength model. The FE models are validated and found to be in good agreement experimental results. With these verified numerical models, a comprehensive parametric study is conducted to investigate the effect of geometric and material properties of HS-CFTFBs. Finally, the design formula of HS-CFTFBs and its scope of application are determined on the basis of a parametric study.

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 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

Lateral torsional buckling of ultra-high-performance fibre-reinforced concrete girders

Ultra-high-performance fibre-reinforced concrete (UHPFRC) is a relatively newly developed construction material that not only has high compressive strength (greater than 150 MPa), but also high tensile strength (10–20 MPa). The use of UHPFRC enables the design of slender structural members; hence, instability could become a major governing failure mode. However, the estimation of buckling strength for a concrete structure is not easy, owing to its material characteristics. In this paper, the lateral torsional bucking behaviour and strength of ultra-high-performance concrete I-beams are discussed. A methodology is introduced to obtain the effective moment of inertia of UHPFRC I-beams, considering tensile cracks. By using the effective moment of inertia, the linear elastic buckling strength can be calculated. In addition, the inelastic lateral torsional buckling behaviour is investigated through finite-element analysis. A generalised buckling strength curve with a slenderness parameter is discussed. As a result, the limitations for classification of compact and non-compact members are defined, and lateral torsional buckling strength equations are suggested for a simply supported UHPFRC I-girder subjected to centre point loading. Several experimental studies were also conducted, and the results are applied to verify the final results.