Interactive Buckling Research Articles

Experimental Study and Design Method of Cold-Formed Thin-Walled Steel Unequal-Leg Angles under Axial Compression

An experimental study of cold-formed thin-walled steel unequal-leg angles (CFTWS-ULAs) under axially oriented pressure is presented in this paper. Firstly, the initial imperfections and material properties of the angle specimens were measured in detail. The angle specimens were tested under fixed-ended conditions. The results of the experiments showed that the angle specimens with small slenderness ratios were susceptible to local buckling, the angle specimens whose legs had high slenderness ratios and low width–thickness ratios were found to easily suffer from the occurrence of flexural buckling, and the angle specimens whose legs had high width–thickness ratios were found to easily suffer from the occurrence of interactive buckling between local buckling and flexural buckling. The finite element analysis of the ULAs was conducted using ABAQUS6.14 finite element software by creating a model. The buckling modes and ultimate bearing capacities of the test specimens were compared, and the finite element analysis verified that the established model built using the finite element is credible and subsequent parametric analysis was performed. The slenderness ratio had the most significant impact on the ultimate bearing capacities of the unequal-leg angles, as indicated by the analysis results. When the width–thickness ratio and the width ratio of the legs fell within a specific range, the ultimate bearing capacities of the unequal-leg angles increased as the width–thickness ratio and the width ratio of the legs increased. Finally, the comparison results showed that the design strengths predicted by the specifications were very conservative, because the local buckling and torsional buckling were calculated at the same time. Therefore, a recommendation was proposed that the calculation of the load-carrying capacity of an unequal-leg angle should ignore torsional buckling.

A Review of the Mechanical Properties of and Long-Term Behavior Research on Box Girder Bridges with Corrugated Steel Webs

Based on an analysis of the extant literature, this paper summarizes the research progress on the mechanical properties and long-term behavior of corrugated steel web (CSW) box girder bridges. First, the research results of CSW box girder bridges in terms of the shear buckling performance (local shear buckling, overall shear buckling, and interaction buckling), bending performance, bending capacity, torsional capacity, and coefficient of internal force increase are summarized, along with the main factors affecting the mechanical performance of CSW box girder bridges. Second, based on research on the self-oscillation characteristics and dynamic response of CSW box girder bridges, the influence of structural parameters on the self-oscillation characteristics is analyzed. Finally, the long-term mechanical behavior of the CSW box girder bridges is analyzed in terms of fatigue, creep, and temperature effects. The existing research results demonstrate that there still exist deficiencies in the mechanical properties and long-term behavior of CSW box girder bridges, and this paper thus suggests a future research focus on CSW box girder bridges to provide a reference for further improving their basic theoretical system.

Seismic Design and Ductility Evaluation of Thin-Walled Stiffened Steel Square Box Columns

This paper investigates the seismic performance of thin-walled stiffened steel square box columns, modeling bridge piers subjected to unidirectional cyclic lateral loading with a constant axial load, focusing on local, global, and local-global interactive buckling phenomena. Initially, the finite element model was validated against existing experimental results. The study further explored the degradation in strength and ductility of both thin-walled and compact columns under cyclic loading. Thin-walled, stiffened steel square box columns exhibited buckling near the base, forming a half-sine wave shape. The research also addresses discrepancies from different material models used to analyze steel tubular bridge piers. Analysis using a modified two-surface plasticity model (2SM) yielded results closer to experimental data than a multi-linear kinematic hardening model, particularly for compact sections. The 2SM, which accounts for cycling within the yield plateau and strain hardening regime, demonstrated enhanced accuracy over the multi-linear kinematic hardening model. Additionally, a parametric study was conducted to assess the impact of key design parameters—such as width-to-thickness ratio (Rf), column slenderness ratio (λ), and magnitude of axial load (P/Py)—on the performance of thin-walled stiffened steel square box columns. Design equations were then developed to predict the strength and ductility of bridge piers. These equations closely matched experimental results, achieving an accuracy of 95% for ultimate strength and 97% for ductility.

Stability of hot-finished and cold-formed steel hollow section columns: A comparative study

A comparative study into the buckling behaviour of hot-finished and cold-formed steel hollow section members subjected to axial compression is presented in this paper. The main differences between hot-finished and cold-formed hollow sections are initially discussed. An experimental programme conducted to investigate the local, global and local-global interactive buckling of hollow section columns is then described. Three S355 normalised hot-finished and three S355/S420 (dual certified) cold-formed profiles, covering circular, square and rectangular hollow sections (CHS, SHS and RHS respectively), were studied. The stress-strain characteristics of the examined materials were obtained through tensile coupon tests. 3D laser scanning was utilised to determine the distribution of geometric imperfections in selected SHS test specimens and a consistent approach to characterise different forms of geometric imperfections from the scan data is put forward. A stub column test was carried out on each cross-section to examine its local buckling behaviour, and a series of long column tests were performed on all test profiles. In total, 21 tensile coupon tests, six stub column tests and 40 long column tests were conducted in this programme. Finite element models were also developed, validated and used for parametric studies to generate supplementary numerical datasets. The obtained test and numerical data, along with the existing experimental results collected from the literature, were used to evaluate the accuracy and reliability of the Eurocode 3 (EC3) stability design provisions for hot-finished and cold-formed hollow section columns; aspects requiring improvements are highlighted to guide future studies.

Eccentric compressive performance and design of asymmetric steel columns with complex edges

Box-type houses often use asymmetric cold-formed thin-walled steel columns with complex edges to meet structural requirements. However, there is a need to clarify the mechanical properties of eccentric loading in this section of the steel column. This study conducted eccentric compression tests on 24 asymmetric cold-formed thin-walled steel columns with complex edges, clarifying the specimens' ultimate load-bearing capacity and buckling mode. The results showed that the resistance to pressure provided by the corner was higher than that provided by the two crimped edges. Subsequently, a finite element model was established, and its accuracy was verified by comparing it with experimental results. Finally, based on the formula for calculating the nominal axial strength in AISI, the direct strength method formula for the stable bearing capacity of asymmetric cold-formed thin-walled steel columns with complex edges under in-plane eccentric compression was proposed. This method takes into account the local-global interactive buckling and distortional-global interactive buckling. The comparison between the theoretical calculation results and numerical simulation results demonstrated that the design method proposed in this study is effective and conservative. It can provide a reference for future engineering applications.

Interactive buckling behaviour of Q420–Q960 steel welded thin-walled H-section long column

Considering the broad application prospect of high-strength steel (HSS) in engineering structure, and the limitations present in existing studies on interactive buckling of HSS welded thin-walled box-section long column, both test and finite element analysis were employed to investigate the interactive buckling behavior exhibited by 12 specimens fabricated from Q420–Q960 steels. The detailed analysis considered various aspects, including the failure mode, axial deformation, interaction of local and overall buckling deformation, and the ultimate bearing capacity. Observations revealed that the utilization rate of steel strength diminished with an escalation in both the plate width–thickness ratio and steel strength. An increase in the plate width–thickness ratio correlated with an earlier onset of local buckling, and the influence of steel strength was found to be negligible. More importantly, the limit of the plate width–thickness ratio for columns undergoing interactive buckling increased with a rise in column slenderness and decreased with an increase in steel strength. Taking into account the influence of column slenderness and steel strength, a novel calculation formula for determining the limit of the plate width–thickness ratio was derived. It is noteworthy that Eurocode 3 and JGJ/T 483–2020 were found too conservative for calculating the ultimate bearing capacity, while ANSI/AISC 360–22 was found suitable. Additionally, a calculation method for the ultimate bearing capacity of Q420–Q960 steel welded thin-walled H-section long column was proposed based on the direct strength method.

Stability of Prestressed Stayed Steel Columns Under Eccentric Compression

Prestressed stayed steel columns (PSSCs) are structural components notable for their exceptional stability and load capacity. However, their behavior under eccentric compression remains poorly understood compared to their performance under axial compression. This study conducted tests and finite element analysis (FEA) to investigate the stability of PSSCs under eccentric compression loading. The study focused on examining the overall stability, buckling modes, and ultimate load capacity of PSSCs under various scenarios. The findings revealed that PSSCs exhibit significantly higher stability and load capacity than conventional columns. However, when subjected to eccentric compression, they experience a substantial decrease in stability. The results of the linear and nonlinear buckling analyses suggest that interactive buckling may occur under certain conditions, thereby influencing the buckling load. These findings clarify the correlation between stability and eccentric compression, offering valuable insights for future research and practical engineering applications.

Monte Carlo Simulations for Global and Local Interaction Buckling of Welded Box-sections

The present study focuses on investigating the interaction behavior of local and global buckling resistance of welded box-section columns by using stochastic analysis. Previous studies mainly investigated this failure mode using experimental or numerical investigations but using deterministic approaches. The current research employs Monte Carlo simulations as a robust numerical tool to estimate the interaction buckling resistance. Stochastic variables are defined, encompassing variabilities in geometrical and material properties, as well as local and global imperfections. To facilitate these simulations, a rigorously validated numerical model is employed, utilizing geometrical and materially nonlinear analysis with imperfections (GMNIA). This advanced modeling approach accounts for the complex nonlinearities inherent in the behavior of welded box-section columns. The characteristic resistance derived from the Monte Carlo simulation is compared to 1. test results, 2. analytical buckling resistance according to the Eurocode design approach, and 3. previously proposed deterministic approaches. Within the research program, an improved generalized design formula is developed to estimate the buckling resistance for pure local, global, and interaction buckling modes. The new design equation is compatible with the design rules of the Eurocode and enhances the ease of use of the standard regulations.

Global interactive-mode imperfection generation for K6 single-layer latticed shell using generative adversarial networks

The worst imperfection shape of K6 single-layer latticed shells corresponding to the lowest nonlinear load-carrying capacity is difficult to be obtained in design owing to significant multi-modal interaction. The global interactive buckling of the K6 single-layer latticed shell is investigated numerically, and the intelligent model for generating its worst global interactive-mode imperfection is developed via generative adversarial networks (GAN). For the cases vulnerable to interactive buckling, the load-carrying capacity is found to be reduced significantly up to 35% with two-mode interaction considered, and unstable behaviour, such as the dominant mode changing due to the deformation evolution of different modal components, is observed at the post-buckling stage. Moreover, the GAN model for generating the worst imperfection shape and the artificial neural network for evaluating the corresponding ultimate load are developed based on the data obtained from numerical analysis. The time of training model to converge is less than 30 min, and the generating process using the trained model only takes a few seconds. It is demonstrated that for the K6 single-layer latticed shells, the developed models can give the worst imperfection and the corresponding ultimate load accurately and efficiently with interactive buckling considered well. This work can be used to develop the programming module for the intelligent design of latticed shells in future.

Local–overall buckling behavior of corroded intermediate compression-bending H-section steel columns

The primary aim of this paper is to assess the impact of corrosion damage on intermediate H-section steel columns subjected to combined compression and bending about the strong axis. The study conducted a comprehensive investigation into the corrosion-induced transition in the buckling behavior of steel columns through experimental and numerical analyses. Six H-section Q355 steel intermediate columns were designed, with five undergoing an artificial spray-accelerated corrosion process. The three-dimensional scanning technology was employed to quantify the general corrosion and corrosion pits. Eccentric compression tests were carried out on intermediate H-section steel columns to investigate the effect of the different corrosion levels on the failure mode and load-displacement curves, as well as to determine local buckling load based on the load-strain curves. The test results showed that the corrosion characteristic parameters of each cross-section of the steel column exhibited irregularity and variation in all locations, reflecting the heterogeneity of corrosion. The density of corrosion pits exhibited a decreasing trend with increased corrosion duration. Corrosion remarkably reduced both the ultimate carrying capacity and local buckling capacity, with the most severely corroded specimen exhibiting an average cross-sectional area loss rate of 37 %, resulting in a 43 % and 51 % reduction in ultimate load and buckling load compared to the uncorroded specimen. Furthermore, the corrosion features substantially influenced the failure mode, resulting in a transition from overall buckling to local buckling or local-global interaction buckling. A numerical methodology was developed to incorporate the actual surface morphology of corrosion, and the reliability of the modeling method was validated through comparison with experimental results, further revealing the failure mechanism of corroded intermediate H-section steel columns under compression and bending about the strong axis.

Unified machine-learning-based design method for normal and high strength steel I-section beam–columns

High strength steel is regarded as a promising construction material due to its superior mechanical properties. However, the codified failure load predictions for high strength steel welded I-section beam–columns are not accurate in some cases owing to the lack of relevant design codes for high strength steel structures. In addition, current design codes ignore the interaction effect of the cross-section plate elements, leading to the inaccuracy of codified predictive ultimate resistances for both normal and high strength steel beam–columns. In this paper, a unified and accurate design method was proposed based on machine learning for both normal and high strength steel welded I-section beam–columns failing by different failure modes. Firstly, a total of 812 experimental and numerical data on welded I-section beam–columns with various steel grades, geometric dimensions, including cross-section dimensions and member lengths, and failure modes, including global buckling, local buckling and local–global interactive buckling were collected to establish a database. Seven machine learning algorithms, including Decision Tree, Random Forest, Support Vector Machine, K-Nearest Neighbour, Adaptive Boosting, Extreme Gradient Boosting and Categorical Boosting were applied to develop regression models to predict failure loads. Based on the established database, each machine learning model was then trained and key hyperparameters were optimised. The model performance was evaluated through a series of statistical indicators and the feature importance analysis, and the evaluated results indicated that the XG-trained regression model had the highest level of accuracy. Finally, the predictions given by the XG-trained regression model were compared with those of the existing codified design provisions, as given in Eurocode and American codes. The evaluation results indicated that the codified predictive bearing capacities of I-section beam–columns were scattered and inaccurate, while the XG-trained regression model provided substantially improved failure load predictions.

CFRP strengthening of web perforated CFS lipped channel short columns: An experimental study

Web perforations provided in the columns or studs of light-gauge steel buildings to meet the functional requirements, decrease the axial capacity and lead to localized failure. Hence, the aim of this study is to experimentally investigate the influence of carbon fiber reinforced polymer (CFRP) strengthening on the stability, axial strength, and stiffness of the CFS web-perforated lipped channel short columns (of 600 mm length) subjected to monotonic axial compression. A total of 20 specimens, provided with circular perforation at mid-height and at the centre of the web, were tested by adopting different CFRP skin-strengthening configurations, considering Uni-Directional CFRP (CF_UD) and Bi-Directional CFRP (CF_BD) laminas or laminates. From the tests conducted, it was observed that CF_UD and CF_UD / UD were found to result in an increase in axial capacity of 11.12% and 22.23% for the cases of single- and double-layered CFRP, respectively. Similarly, the axial stiffness increased by 9.23% and 26.07%, respectively. However, the only considered triple-layered laminate, CF_UD / UD / BD has outperformed among the entire adopted strengthening configurations, with an increase in axial strength and stiffness of 28.90% and 38.33%, respectively, in comparison to the bare steel specimens. Notably, a local-distortional interactive buckling mode of failure was noticed in the cases of both bare steel and CFRP-strengthened specimens.

Enhanced buckling reduction factors using amplified imperfections for existing steel structures

The topic of the paper is the buckling analysis of existing structures having enlarged imperfections, which might reduce the buckling capacity during the reuse of steel structures. The research aims to develop global and local buckling reduction factors that take into account the presence of enlarged imperfections, which often are observed in existing steel structures. GMNI analyses are conducted on I- and box-section columns subjected to pure compression, incorporating accurate local and global imperfections treated as non-amplified imperfections. Multiple amplification ratios are used to enlarge the value of these imperfections within the numerical parametric study. The local and global buckling formulas specified in EN1993-1-5 and EN1993-1-1 were previously calibrated against GMNI analysis that considers the effect of residual stresses and geometrical imperfections. A calibration process is performed within the current study by modifying the value of the factor α in the global and local buckling formulas to obtain the buckling resistances determined by enlarged imperfections. The developed formulas are subsequently evaluated against the interaction buckling resistance of local and global buckling behaviour. Statistical measures are also employed to assess the resistances derived from the developed formulas against GMNI results for pure local, global, and interaction buckling resistances. This paper provides a tool for designers to estimate the buckling capacity when existing imperfections surpass those assumed during the design phase.

Experimental investigation of global-distortional interaction buckling of stainless steel C-beams

This work reports the test data for press-braked stainless steel C-beams subjected to global-distortional (G-D) interaction. The chemical constituents of austenitic S30408 used in the tests were proved to meet the European (EN 10088–1:2014) and Chinese (GB/T 3280–2015) codes. The tensile test of the material was performed to determine the mechanical properties of the flat and corner areas of the press-braked C-beams. Initial imperfections of each specimen were assessed before conducting the bearing capacity tests. A total of 10 specimens consisting of 20C-beams were subjected to four-point bending. All specimens first underwent distortional buckling and then global buckling. The vertical displacement at the mid-span and the loading points, support rotation, distortional deformation, lateral deformation, strain at the boundary of the upper flange as well as strain of the lower flange were meticulously recorded and analyzed. Based on the observed test phenomena, the recorded displacement and strain data, the failure mechanism of G-D interaction and the development of the buckling waves were unveiled. The test data was employed to evaluate the accuracy of the design methods in accordance to the Direct Strength Method (DSM), EN 1993-1-4, AS/NZS 4673 and ASCE 8–22. All codes are found to account for distortional buckling by employing the Effective Width Method (EWM) to reduce the compression plate area. The evaluation results revealed that DSM could safely and stably make a prediction of the ultimate capacity for G-D interaction in stainless steel beams, while EWM have a lower performance in prediction.

Experimental and numerical study on hysteretic behaviour of corrugated steel plate shear walls under lateral loads

This paper presents experimental and numerical investigations of the hysteretic performance of the corrugated steel plate shear wall (CSPSW) subjected to lateral loads, and proposes an effective hysteretic model for the CSPSW with interactive buckling or yielding of the corrugated steel plate (CSP). First, a cyclic loading test for a CSPSW with interactive buckling was conducted. The CSPSW test specimen exhibited high strength, lateral stiffness, and good energy dissipation capacity. In accordance with the cyclic test, a numerical model was developed to simulate the hysteretic behaviour of the CSPSW. Subsequently, extensive parametric analyses were performed to investigate the effects of the concerned geometry parameters on the hysteretic performance of CSPSWs, such as the height–thickness ratio, aspect ratio, corrugation angle, horizontal subpanel width and surrounding frame stiffness. The available limits of the height–thickness ratio, aspect ratio and surrounding column stiffness for CSPSWs were suggested. Based on the experimental and numerical results of the hysteretic curves and theoretical derivations, a hysteretic model for a CSPSW with interactive buckling or yielding of the CSP was proposed and verified by tests and finite element models. The results showed that the proposed hysteretic theoretical model can reproduce the hysteretic performance of CSPSWs with reasonable accuracy.

Equivalent geometric imperfection for interaction buckling of welded box-section columns - Stochastic analysis

The current paper investigates recently developed GMNIA-based equivalent global and local imperfections to be applicable in the FEM-based design of welded box-section columns. While these imperfections were developed independently for the local and global buckling problems, their applicability to coupled instability problems has not yet been investigated. Therefore, this study addresses this gap by investigating the effectiveness of these imperfections in predicting pure local, global and interaction buckling capacities by comparing them against accurate stochastic analyses using Monte Carlo simulations. The current simulations take into account the variations in geometrical and material properties as well as the imperfections, leading to a highly accurate estimation of the buckling capacity of welded box-section columns. Statistical measures are used to assess the accuracy of each imperfection type and imperfection combination. The discrepancy in deterministic resistance resulting from the application of imperfections and combinations is assessed by comparing them with the accurate buckling resistance. Based on the statistical evaluation, the numerical model uncertainty is also evaluated, serving as the input data of the model factor calculation. The present paper gives a unique introduction to the calculated model factors and presents its calculation methodology for local and global buckling problems.

A dimensionless analytical analysis for buckling and lateral buckling interaction of thin-walled beams with open cross sections

This paper investigates the interaction between buckling and lateral buckling of thin-walled beams with arbitrary open cross-section using nonlinear modeling in large rotation and with warping. First, the equilibrium equations have been transformed into dimensionless ones, and within a nonlinear stability model, various dimensionless parameters are introduced to control the interaction between buckling and lateral buckling. In comparison to a reference of literature, this work focuses on the case of arbitrary sections and includes a greater number of higher-order terms in our analysis. These additions have an impact on the coefficients of the stability formula by expanding its applicability to non- symmetric sections. Then, the effect of the different dimensionless parameters, thus introduced on the stability curve, has been studied. The proposed solutions are validated and compared to numerical solutions obtained by a general finite element package including the warping developed by the authors using Asymptotic Numerical Method (ANM) to solve the initial nonlinear equations.

Local–flexural interactive buckling behaviour and design of press-braked stainless steel slender Z-section columns

The present paper reports an experimental and numerical study on the local–flexural interactive buckling behaviour and resistances of press-braked stainless steel slender Z-section columns. A testing programme adopted two press-braked stainless steel slender Z-sections and included material testing, initial geometric imperfection measurements and twelve fixed-ended column tests, with the experimental setups, procedures and results fully reported. The testing programme was accompanied by a numerical modelling programme, with finite element models developed and validated against the fixed-ended column test results; upon validation, parametric studies were conducted to generate additional numerical data over a wide range of cross-section dimensions and member lengths. The obtained test and numerical data were adopted to evaluate the relevant design rules for press-braked stainless steel slender Z-section columns susceptible to local–flexural interactive buckling, as set out in the American specification and European code. It was revealed from the evaluation results that the American specification led to accurate interactive buckling resistance predictions, while the European code resulted in relatively conservative interactive buckling resistance predictions. Finally, a revised Eurocode design approach was developed and provided more accurate and consistent interactive buckling resistance predictions for press-braked stainless steel slender Z-section columns than its original counterpart.

Fiber–Based Model for Simulating Inelastic Interaction Buckling of Rectangular CFST Slender Columns with Unequal Wall Thickness

Rectangular concrete-filled steel tubular (RCFST) columns can be designed to have unequal wall thickness to maximize their resistance to combined axial and uniaxial bending loads. However, there is very little published research on their local–global interaction buckling behavior. This paper presents an efficient fiber-based simulation model for analyzing the inelastic interaction buckling of eccentrically loaded RCFST slender columns with unequal wall thickness. The model considers the progressive local–global interaction buckling, distributed plasticity, concrete cracking and crushing, second-order effects, and geometric imperfections. The mathematical model is programmed to compute not only the axial load–displacement responses but also the interaction curves of axial load and moment of slender RCFST columns. The simulation modeling is validated by experimentally measured data. The validated computer model is used to parametrically study the interaction local–global buckling responses of RCFST columns while the range analysis is conducted to identify the relative significance of key parameters. It is demonstrated that the proposed computer model accurately simulates experimentally measured responses. Hence, it can be used with confidence in practice to analyze and design RCFST slender columns fabricated with steel plates of unequal thickness. The existing design standard AS/NZS 2327:2017 provides acceptable strength predictions of RCFST slender columns and beam-columns while the procedure specified in Eurocode 4 overestimates their capacities.

Tests, numerical simulations and design of G550 high strength cold-formed steel lipped channel section columns failing by interactive buckling

This paper presents the experimental and numerical investigations into the structural performance and strengths of G550 high strength cold-formed steel (CFS) lipped channel section columns failing by interactive buckling. A testing program was first conducted, comprising material testing, measurements of initial local, distortional and global geometric imperfections and ten pin-ended column tests. The interaction between different buckling modes was observed and discussed for all the examined specimens upon testing. A numerical modeling program was subsequently performed, where numerical models were created and verified with reference to the test results and afterwards utilized to conduct parametric analysis to produce more numerical data over an extensive spectrum of cross-section geometries and effective member lengths. The effective width method (EWM) codified in the European code and direct strength method (DSM) specified in American and Australian standards were evaluated, based on the combined set of numerical and test data, for their suitability to G550 high strength CFS lipped channel section columns susceptible to interactive buckling. The evaluation results indicated that (i) the EWM yielded scattered and conservative ultimate strengths for columns with small and intermediate slenderness ratios, but relatively accurate results for those of large slenderness ratios and (ii) the DSM led to more consistent and accurate strength predictions for G550 high strength CFS lipped channel section columns failing by interactive buckling, though a number of strength predictions were on the unsafe side.