Lateral Distortional Buckling Research Articles

Critical load for shear-induced lateral-distortional buckling in I-section steel beams considering flexural stiffness ratio

In prefabricated buildings, lateral-distortional buckling (LDB) of I-section steel beams is a common failure mode that has garnered considerable attention. However, existing studies and design methods for lateral-distortional buckling primarily focus on members subjected to in-plane flexure and do not take into account the influence of shear forces. In this paper, a study on the elastic lateral-distortional buckling behavior of I-section steel beams under in-plane shear loads was conducted. Firstly, refined finite element (FE) models of beam webs under shear loads were established and validated against theoretical formulas for different boundary conditions. Subsequently, by combining with analytical solutions and numerical results, an accurate buckling load formula for the beam web with a free bottom edge was obtained, which can be used for further study. Based on the parametric analysis results, a formula was obtained to determine the critical flexural stiffness ratio of flange to web. When the flexural stiffness ratio exceeds the critical value, the lateral-distortional buckling of I-section steel beams can be effectively avoided. Finally, a formula that incorporates both the critical flexural stiffness ratio and the span to height ratio was proposed to calculate the elastic critical lateral-distortional buckling loads of I-section steel beams solely under in-plane shear loads.

Data-driven design approach for the lateral-distortional buckling in steel-concrete composite cellular beams using machine learning models

Composite steel-concrete beams are presented as an interesting solution for covering long spans. These profiles are characterized by the existence of sequentially spaced openings along the beam web. A very common particular use of this type of structure is in continuous or semi-continuous floors, in which the existence of intermediate supports in the span of the structural member leads to the occurrence of points with negative bending moment. Steel structures in this condition can present different types of instability due to the compression of the bottom flange, such as lateral-distortional buckling and web-post buckling. In this context, a comprehensive parametric study was carried out through finite element simulation aiming to obtain the resistance capacity of this type of structural system. It was observed that different analytical procedures aimed at calculating the ultimate moment of this type of structure fail to predict the bearing capacity of the elements successfully. Thus, aiming to promote more precise design approaches, the modeling of the resistant load of these structures was performed using different supervised machine learning techniques. It was found that machine learning techniques have the potential to correctly predict the bearing capacity of the studied members, having a better agreement with the numerical data obtained, when compared to the approaches presented by analytical procedures described in the literature and design codes. Different machine learning algorithms were trained based on a dataset obtained via FEM: artificial neural networks, support vector machines, XGBoost and Random Forest. All models showed considerable effectiveness, with statistical determination coefficients (R²) higher than 0.9. Among these, the best prediction capacity was obtained with the XGBoost model in terms of correlation coefficient and Mean Square Error, presenting itself as the model that came closest to the set of numerical data used as reference.

A Parametric Study on the LDB Strength of Steel-Concrete Composite Beams

Lateral distortional buckling (LDB) is an instability phenomenon characteristic of steel-concrete composite beams (SCCB) that occurs in the presence of hogging moments in regions close to internal supports. The LDB behavior in SCCB is not yet fully understood. The procedures for determining the LDB strength are based on the classic lateral torsional buckling theory or on the inverted U-frame model. In addition, the standard procedures make use of the classic design curves of the SSRC (Structural Stability Research Council) and ECCS (European Convention for Constructional Steelwork) developed to analyze the stability behavior of steel elements. However, studies indicate that the use of the same empirical curves obtained for the analysis of steel elements leads to the conservative results of the LDB strength in SCCB. Therefore, this article aims to assess the LDB strength in SCCB through the development of post-buckling numerical analysis using the ABAQUS software. In the parametric study, four types of steel with different mechanical properties were analyzed. In addition, the I-section, the unrestrained length, and the reinforcement rate in the concrete slab were varied. The results showed the influence of the steel type on the LDB strength and deviations from the standard procedures. A small influence of the longitudinal reinforcement area variation was verified in the LDB strength in the FE analyses; however, this factor is significantly important in the standard procedures, causing considerable divergences. These results can provide a reference for future research and specification reviews.

Nonlinear Inelastic Stability Behavior of High-Strength Stainless Steel I-Beams with Sinusoidal Web Openings

Perforated beams can bring countless benefits compared to traditional plain-webbed beams. However, steel beams with sequential web openings are more susceptible to instabilities, and special care must be taken in a design concerning the failure modes these structures can present. The study presented herein explicitly dealt with the stability behavior of perforated beams with sinusoidal openings. This type of perforated member features smooth-lined openings constructed from a single thermal cut in conventional plain-webbed steel profiles. A broad study was carried out through numerical simulation using the ABAQUS software, in which perforated profiles manufactured with S600E high-strength stainless steel were studied. The use of high-strength steels in perforated profiles is a little explored topic in the literature, despite having a significant impact on the behavior of these elements. With the study carried out, a broad overview of the stability behavior of these members was obtained, especially concerning global stability. A total of 5940 FE models were developed, considering the application of different types of loads. In these models, linear buckling analysis (LBA) and geometrically and materially nonlinear analysis with imperfections (GMNIA) were performed. The results obtained were compared with international design codes, and it was found that some codes fail to represent the behavior of members that present lateral-distortional buckling (LDB) and interactions between local and global failure modes. This behavior is a significant design concern since the studied members had high yield strength, making them more susceptible to interaction-governed failure modes than usual-yield strength members. Additionally, the study found that some design codes do not accurately represent the behavior of members loaded outside the shear center due to the destabilizing effect of loading on these structures.

Lateral distortional buckling of continuous composite beams in fire situation: Experimental and numerical analyses

In continuous steel-concrete composite beams, hogging moments may occur near the internal supports. This type of bending causes compression in the bottom flange, which may buckle laterally in an ultimate limit state known as lateral distortional buckling. Despite the consideration that continuity may result in an economic design, no research had yet been conducted on the possibility of lateral distortional buckling in continuous composite beams in fire situation. This paper presents an experimental and numerical study on the lateral distortional buckling of steel concrete composite beams. Four real scale fire tests were conducted and proved that it may indeed occur. A parametric study was also developed. It has been shown that this buckling mode may lead to a reduction in the strength of composite beams of up to 50% when compared to the plastic moment. It was also noted that this buckling mode is usually accompanied by local buckling, which may occur even in compact sections, leading to a decrease in bearing capacity. These results indicate a need of reviewing the design codes to consider the possibility of lateral distortional buckling at high temperatures, as it may be more than at ambient temperature.

Three-Dimensional Numerical Simulation for Lateral Distortional Buckling Behaviour of Steel-Concrete Composite Beams

Lateral Distortional Buckling (LDB) is a mode of instability in Steel-Concrete Composite (SCC) beams that is yet to be fully understood by the structural engineering research and design community. This work investigated numerical methods to understand the LDB behavior of SCC beams under negative moments that exhibit nonlinear behavior. Focus of the study was to develop and validate 3-Dimensional finite element (FE) models which capture the LDB behavior of SCC beams precisely. Detailed 3-Dimensional FE models of the SCC beams were developed using ABAQUS. For modeling concrete, a nonlinear damage plasticity model was considered. A quad-linear curve was used to describe the stress-stain relationship for the steel beam. The stress-stain relationship for the rebar was described using a bi-linear curve while an elastic perfectly plastic model was assigned to the headed stud shear connectors. Steel hardening behavior was simulated using an isotropic hardening model. The interaction between the concrete slab, steel beam, and studs was described using appropriate interface elements combined under suitable constraints. The FE model’s accuracy was validated by results obtained from previous experiments found in literature together with a brief description of the experiments done by previous researchers to ensure completeness. Validation of the model was done by comparing Moment-Rotation curves obtained from the experimental tests, lateral displacements of the bottom flange along the axial direction and comparison of the failure modes between the numerical model and experimental test specimens. It was observed that the maximum relative error for the ultimate moment capacity of the composite beams from FE analysis and the experimental tests was less than 2% which shows that the FE model was in strong agreement with the experimental results. Accordingly, the numerical model developed herein proves to be capable of accurately representing the LDB phenomenon.

Lateral Distortional Buckling Resistance Predictions of Composite Alveolar Beams: A Review

Few studies have investigated the structural behavior of steel-concrete composite alveolar beams in hogging bending regions. Their resistance can be reached by lateral distortional buckling (LDB), coupling LDB and local failure modes, or limit states of cracking or crushing in the concrete slab. This case is characteristic of continuous or cantilever elements. Another critical issue is that the design and calculation recommendations only address the LDB verification on steel-concrete composite beams without web openings, thus disregarding the interaction between the buckling modes. Furthermore, it is necessary to use adaptations of these formulations for beams with web openings. This review paper aims to evaluate the different approaches for standard code adaptations to verify the LDB resistance of the beams in question and to highlight the investigations that addressed this issue. The addressed adaptations consist of different approaches which determine the cross-section geometric properties in the central region of the openings, the so-called double T section, in the region of the web posts (solid section), and the averages between the solid section and double T section. The accuracy of the formulations in question is verified against experimental results from the literature. Furthermore, discussions and suggestions for further studies are presented.

Investigations of horizontal rotation at the support of bending beams as proof of global distortional buckling mode

Presented research aims to prove the appearance of lateral-distortional buckling mode by observing the beams' deflection characteristics. Eight-layer channel and lip-channel cross-section glass fibre reinforced polymer (GFRP) beams subjected to pure bending in the web plane were discussed. The Finite Element Method and the Semi-Analytical Method were used to perform all calculations. Deflection angles at the beams' ends show that the lateral deflection sharply increases from load close to critical one and in the post-buckling range. It was observed that for simply supported beams subjected to bending, the lateral-distortional global buckling mode is accompanied by rotation at support in the flange plane.In the FEM approach, the lowest buckling mode is usually considered in beams subjected to bending, and the angle of rotation in the load plane corresponding to the critical bending moment is only analysed. However, in the interactive buckling analysis, the horizontal rotation at the supports is accompanied by the global mode, and its impact is often neglected due to its high bifurcation value compared to the lowest mode. Moreover, in the paper, the influence of this mode on the equilibrium paths, the critical buckling load, the load-carrying capacity, distributions of internal membrane forces, and vertical and horizontal angle of rotation was investigated.

A New Formula for Predicting Lateral Distortional Buckling Strength of I-Beams Subjected to Different Loading Conditions

Lateral distortional buckling (LDB) mode has been investigated as one of the failure modes in steel I-beams. The LDB mode in such beams is known by simultaneous lateral deflection, twist, and cross-sectional change due to web distortion. However, many studies have been conducted to investigate the behavior of this failure mode; so far, no formula has been found to calculate the ultimate LDB resistance of I-beams, which also takes into account the effect of different loading conditions. 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 LDB resistance of I-shaped beams. 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 LDB 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 LDB strength. The results showed that the proposed formula based on ANN not only presents a reasonable accuracy compared to the existing formulations but also can be used by engineers as practical equations in the design of I-beams.

Lateral-distortional buckling of steel-concrete composite beams: Kinematics, constrained-mode GBT and analytical formulae

This paper investigates and sheds fresh light on the kinematics and mechanics involved in the lateral-distortional buckling (LDB) behaviour (involving web single or double curvature) of simply supported I-section steel beams elastically restrained by concrete slabs under uniform negative (hogging) bending. The findings obtained are used to derive and illustrate the application of analytical formulae to calculate LDB moments of the steel-concrete composite beams considered. The study is based on a Generalised Beam Theory (GBT) approach to perform buckling analyses using constrained deformation modes that incorporate the displacement/rotation restraints, thus making it possible to obtain accurate buckling results with only a few deformation modes. The formulae provide the solution of the LDB equilibrium equation when only one or two constrained deformation modes are involved. Their merits and accuracy are assessed through the application to problems of practical interest – the LDB moments determined are compared with values (i) provided by other available formulae and/or (ii) obtained from conventional GBT, finite strip and/or Ansys shell finite element analyses. It is found that (i) the proposed constrained-mode GBT clearly outperforms the conventional one, both in structural insight and computational efficiency, and (ii) the derived analytical formulae consistently yield accurate LDB moment estimates.

New predictive equations for LDB strength assessment of steel–concrete composite beams

Lateral distortional buckling (LDB) mode has been investigated as one of the failure modes in steel–concrete composite beams (SCCB). The LDB mode in such beams is known by lateral displacement accompanied by rotation of the compressed bottom flange that occurs due to the web distortion. However, many studies have been conducted to investigate the behavior of this failure mode, no equation has yet been found that can accurately calculate the ultimate LDB resistance of SCCB. Consequently, in the current paper, by conducting an extensive parametric study including 475 finite element models (FEM), an attempt was made to provide a reliable database. Then, based on the provided database, two methods of artificial neural network (ANN) and multiple regression (MR) were employed, and based on them, high-precision equations were proposed to predict the ultimate LDB strength of SCCB. Finally, the proposed formulas were compared with the existing formulas for estimating the LDB strength of SCCB. The results showed that the proposed formulas not only present a reasonable accuracy compared to the existing formulations but also can be used by engineers as practical equations in the design process of SCCB.

Numerical investigation on behaviour of castellated steel beam in lateral distortional buckling

The construction sector makes extensive use of steel because of its flexibility, corrosion resistance, and lightweight. Castellated I-shaped steel beams have a more comprehensive range of applications than typical type steel beams. Castellation ensures that structural stability is improved and can be used in steel structures. Previous investigations have shown that lateral distortional buckling (LDB) is the primary cause of apparent failure in castellated steel beams. Here in this study, a numerical investigation was carried out using a finite element model developed in commercial software ABAQUS®. Then using a validated numerical model, parametric studies were conducted. The effect of eccentric loading, the partition of web castellation, and the effect on lateral distortional buckling (LDB) failure mode under vertical stiffener in the web are evaluated. The present study shows that LDB exists in the case of eccentric loading and web partitions. Eccentric loading led to a 5% decrease in ultimate load capacity. The addition of web partition enhanced the ultimate load-carry capacity by 7%. Higher load capacity was observed for specimens with vertical stiffeners, which helps mitigate lateral distortional buckling of castellated steel beams.

Effect of web stiffeners on the lateral distortional buckling of channel section with hollow flanges

Hollow Flange Channels (HFC) have been known for their higher capacity when compared to open flange C-sections. On the other hand, the small stiffness of HFC slender web compared to their flanges limits the bending capacity to the lateral distortional buckling (LDB) strength. Welding web stiffeners can limit the web distortion and enhance the bending capacity. This paper investigates how to alleviate LDB capacity of HFCs using transverse web stiffeners. Stiffener’s spacing, depth and thickness are the parameters, modeled with different beam lengths. It is found that using the right spacing and depth of stiffeners can greatly increase the HFC capacity. Adding full depth stiffener to 4000 mm span increases the capacity by 32%. However, this percentage decreases for longer spans with partial depth stiffeners. Increasing the stiffener thickness have been found insignificant in enhancing the performance. A new formula is proposed to predict the bending capacity of stiffened HFC.

Stepwise regression approach for lateral-distortional buckling capacity assessment of cellular steel beams

Stepwise regression approach for lateral-distortional buckling capacity assessment of cellular steel beams

Stability behavior of Steel–concrete Composite Beams subjected to hogging moment

The behavior of Steel–concrete Composite Beams (SCCB) under the action of hogging moment is not yet fully understood. In this condition, these structural elements may be subjected to local buckling or Lateral Distortional Buckling (LDB). LDB is a mode of stability in which the web must distort in order for the compression flange to displace and twist during buckling. The classic LDB standard procedures start from the determination of the elastic critical moment and subsequently use empirical curves to determine the LDB strength. However, investigations show that there is no consensus in determining the LDB elastic critical moment. In addition, studies indicate that the use of the same empirical curves obtained for the analysis of steel I-beams leads to the conservative results of the LDB strength in SCCB. In this context, this paper investigates the behavior of SCCB under the action of hogging moment through the development of buckling and post-buckling numerical analyses with the ABAQUS software. In the parametric study, the effects of the I-section, the unrestrained length, the reinforcing ratio, the concrete slab height and the slab topology were investigated. The investigations showed divergences between the elastic critical moment and ultimate moment when compared with classic procedures. In addition, the influence of the analyzed parameters is presented. These results can provide a reference for future research and specification reviews.

Evaluation of lateral-distortional buckling strength of castellated steel beams using regression models

The effects of web distortion on the buckling behavior of castellated steel beams have rarely been studied; and so far, no exact formula has been proposed to predict the lateral-distortional buckling (LDB) capacity of such beams. Therefore, in the following paper, an attempt has been made to propose new formulas for predicting the LDB capacity of castellated beams using two regression models. To do this, at the first, an extensive parametric study including 480 finite element (FE) models was performed. Both material nonlinearities and initial geometric imperfections were carefully applied to the models and they were also well validated against experimental results. The next, based on the parametric study, nine non-dimensional parameters that affect the LDB behavior of castellated beams were considered, and using them as input parameters, two predictive models including stepwise regression (SR) and multiple regression (MR) were developed. The models were then used to provide new formulations for estimating the LDB strength of castellated steel beams. In the end, the proposed formulas were compared with the existing design guides available for estimating the buckling strength in AS4100, EC3, and AISC codes. The results showed that the proposed formulas for use by practical engineers are accurate enough.

The influence of structural and geometric imperfections on the LDB strength of steel–concrete composite beams

The behavior of structural steel frames is significantly influenced by the presence of structural and geometric imperfections. The structural imperfections, namely, the residual stresses, are generated during most manufacturing processes involving material deformation, heat treatment, machining or processing operations. As the residual stresses, the geometric imperfections are fundamental in the analysis of critical buckling and post-buckling behavior of thin-walled structures. These initial imperfections can be captured using the second order inelastic analysis, also known as advanced analysis. In the modern steel design codes, e.g., European code EC3, Australian code AS4100, North American Code AISC360-16 and Chinese code GB50017 the development of advanced numerical analyses is allowed to predict the behavior of steel and composite frames. However, the random nature of the shapes and magnitudes of the initial imperfections results in difficulties in developing these analyses. Therefore, this paper presents an assessment of the influence of structural imperfections, namely, the residual stresses, and geometric imperfections on the Lateral Distortional Buckling (LDB) strength of steel–concrete Composite Beams (SCCB). The basis of the research is a thorough comparison between numerical and experimental results. Several residual stress patterns found in the literature have been implemented in numerical simulations of four different tests on SCCB subjected to uniform hogging moment. In addition, a sensitive analysis of the geometric imperfection values, namely, the initial bending, was developed. The post buckling numerical analyses were developed with the ABAQUS software. The analysis shown in this work shall help the choice of the initial imperfections on future numerical simulations on SCCB.

Finite element modelling of castellated steel beams under lateral-distortional buckling mode

This paper examined the effects of web distortion on the buckling behavior of castellated steel beams. To this purpose, a series of nonlinear finite element (FE) models was constructed and well verified against an experimental work on the distortional buckling of castellated beams; both material nonlinearities and initial geometric imperfections were carefully applied to the models. Next, an extensive parametric study was performed using the finite element models to investigate the effects of beam length, steel grade and cross-section dimensions on the ultimate buckling load and buckling modes of castellated steel beams. The results showed that the use of low grade steel and thick flanges makes an economical design in the castellated steel beams. Moreover, it is concluded that lateral-distortional buckling (LDB) mode is more common in the castellated beams with intermediated overall slenderness, thick flanges and slender web. Finally, the ultimate loads obtained from finite element analysis (FEA) were compared with the results predicted by AS4100, EC3 and AISC codes. It was concluded that all three Specifications provide unsafe estimates for most specimens in this study.

New predictive equations for lateral-distortional buckling capacity assessment of cellular steel beams

Assessment of the ultimate capacity of the cellular steel beams subjected to the lateral-torsional buckling containing web distortion (lateral-distortional buckling) was rarely investigated. So far, there is no accurate formula to predict the lateral-distortional buckling (LDB) capacity of such members. Here, extensive simulations (660 specimens) based on the nonlinear finite element analysis (FEA) were carried out to simulate the cellular steel beams in distortional-buckling mode. The influence of eight parameters that may affect the LDB capacity was deeply investigated. Then, gene expression programming (GEP) and nonlinear multiple regression (NMR) algorithms progressed as predictive models to obtain formulae for measuring the failure moment capacity of the cellular steel beams. The used data for the GEP and NMR models development, obtained from the FEM simulations that were done initially. It was attempted to derive exact enough formulae, which considers all the variables that may affect the LDB capacity of cellular steel beams. The validation of the GEP and NMR models have been further verified by several statistical criteria. Finally, a comparison was performed between the proposed formulae and the predictions obtained from AS4100, EC3, and AISC codes. It was shown that the proposed formulae are enough exact and applicable to use by practicing engineers.

Elastic Critical Moment of Lateral Distortional Buckling of Castellated Composite Beams under Uniform Hogging Moment

AbstractContinuous and semicontinuous castellated composite beams can present a global buckling mode in the hogging-moment regions known as lateral-distortional buckling. In this mode, the lower po...