Transverse stiffeners provide lateral support to slender webs along their span, enhancing the shear buckling resistance of steel plate girders. Moreover, intermediate transverse stiffeners are particularly crucial, because they anchor the forces generated by tension field action, mitigate out-of-web buckling, and support the edges of the web panel. The standard EN 1993-1-5 outlines three requirements for the design of intermediate transverse stiffeners: (1) strength verification, (2) a minimum elastic bending rigidity, and (3) a torsional rigidity check. However, research has demonstrated that applying the strength verification criterion often results in overly conservative designs due to assumed internal forces significantly exceeding those observed in numerical simulations and experimental studies. Consequently, US design standards have omitted this verification, focusing solely on the minimum bending rigidity requirement. A numerical study of 13,500 plate girders with diverse geometries and stiffener configurations was conducted to evaluate the minimum bending rigidity required for intermediate transverse stiffeners to ensure the ultimate shear resistance of steel plate girders. The analysis considered the effects of steel grade, web slenderness and aspect ratio, flange-to-web area ratio, and the presence of longitudinal stiffeners. The results indicate that the required minimum bending rigidity is particularly high for plate girders with slender webs, low aspect ratios, and high flange-to-web area ratios.

This paper presents a comprehensive review of the role of transverse, longitudinal, and diagonal web stiffeners in enhancing the shear buckling resistance of I-shaped steel plate girders. Over the past few decades, extensive laboratory experiments, analytical formulations, and numerical analyses have been conducted to better understand the shear behaviour of stiffened webs, supporting the development of more efficient and reliable design methods. The review summarises and critically compares the main design models for elastic buckling and ultimate shear resistance, as well as the essential design requirements for web stiffeners. Key investigations are compiled in detailed tables, and existing analytical expressions are examined in terms of their assumptions, boundary conditions, and accuracy. In addition, a finite element (FE) model is developed to evaluate the shear performance of girders with different stiffener configurations – including transverse, longitudinal, or diagonal – and its predictions are benchmarked against available design methods. The FE results complement the literature findings by highlighting general trends, verifying analytical formulations, and assessing the conservatism of current design rules. Overall, the study demonstrates that while existing models predict the shear buckling resistance of stiffened plate girders reasonably well, notable gaps remain regarding the interaction between stiffeners, the treatment of diagonal stiffeners, and the influence of torsional rigidity. The review identifies these challenges and outlines future directions for improving both the accuracy and efficiency of web stiffener design. • Transverse stiffeners boost shear by up to 35%, best in short girder panels. • Longitudinal stiffeners cut deflection, raise shear by 46% in long panels. • Diagonal stiffeners add up to 66% resistance; best when compression-aligned. • Web stiffener impact varies by panel slenderness, stiffness, and orientation. • Current models can be improved; updates needed for stiffener interaction effects.

In-plane normal and shear buckling analysis of bio-inspired helicoidal laminated composite annular sector plates on elastic support

A lattice sandwich panel has the potential for use in engineering structures to achieve weight reduction and thermal insulation. The high temperature distribution on the structure, formed by unilateral heating, is often nonuniform, exhibiting a temperature gradient along the panel thickness direction. This paper investigates the buckling behavior of lattice sandwich panels under nonuniform temperature using numerical simulations and experiments. The results indicate that high temperature significantly affects the load-bearing capacity and failure modes of lattice sandwich panels. At room temperature, the failure mode of a lattice sandwich panel is fracture rather than buckling. Under unilateral heating conditions, the lattice sandwich panel shows buckling failure, and the critical buckling load decreases significantly as the temperature increases. In comparison, under uniform temperature distribution conditions, the critical buckling load of the lattice sandwich panel is significantly lower, but the buckling mode remains similar.

Thermoelastic buckling and vibration analysis of shear and normal deformable three-phase bio-inspired composite beams under axially varying temperature fields

This study presents the buckling analysis of rectangular multiphase nanocomposite plates reinforced with alumina nanoparticles and discontinuous carbon fibers (DCFs), resting on an elastic foundation and subjected to different boundary conditions. A key contribution of this work is developing a multiscale computational framework that bridges microscale material modeling and macroscale structural analysis. The mechanical properties of nano-alumina/DCF/polymer nanocomposites are estimated using a micromechanical model considering important microstructures. The multiphase nanocomposite plate is modeled using the first-order shear deformation theory (FSDT), while the Winkler and Pasternak foundation models are employed to simulate the substrate. By constructing the system’s total potential energy functional and applying the p-Ritz method, numerical results are generated to investigate the influences of percentage, diameter and agglomeration of nano-alumina, size and stiffness of the nanoparticle/polymer interfacial layer, volume fraction and aspect ratio of DCFs, elastic foundation characteristics, and geometric parameters of the plate on the critical buckling loads. Three buckling cases namely uniaxial, biaxial, and shear buckling, are analyzed. It is observed that dispersing the alumina nanoparticles into the polymer matrix of DCFs increases the structural rigidity and elevates the critical buckling load. Larger nanoparticle diameters lead to a decline in buckling resistance of the multiphase nanocomposite plates.

Abstract Steel‐concrete composite plate girders are key structural elements used in loadbearing structures of high capacity or long spans. Despite lateral stiffeners, their slender webs remain prone to web out‐of‐plane shear buckling, especially under high temperatures, such as during fires. However, the shear buckling behaviour of these girders, both at ambient and elevated temperatures, requires further study. This research focuses on experimental and numerical study of shear buckling in steel‐concrete composite plate girders under fire exposure. Along with the largescale elevated temperature tests a computational framework using ABAQUS is developed and validated against experimental results, to analyse the structural fire response of composite plate girders as well as further influencing parameters. As a result of this integrated study, it is shown that higher web slenderness and panel aspect ratio, along with partial shear connection, reduced top flange rigidity, higher load ratio and lower material grade reduce the overall fire resistance. Furthermore, it is shown that thermal gradients and thermal expansion lead to accelerated web shear buckling. Finally, the concrete slab enhances stiffness and insulates the top flange, slowing its heating rate and taking 50% of the total shear force.

Abstract In most of the cases these steel girders with corrugated web are used in bridges, however, they are also applicable for industrial structures. Stability issues are important, as flange buckling and shear buckling can occur depending on the geometrical layout. Corrugated web girders have greater shear capacity than conventional I‐girders proved by previous investigations. In addition, the flange buckling behavior differs from that of conventional I‐girders. While there have been only a few studies on the bending‐shear (M‐V) interaction behavior, however, there is a lack of research on the M‐V interaction of hybrid trapezoidal web girders having different steel material grades for the flanges and the web. Previous international studies give proposal for M‐V interaction for those of girders having homogeneous steel grade (same for the flanges and web). EN1993‐1‐5 Annex D [1] gives a proposal for shear strength and flange buckling resistance. Besides it gives reduction factor for bending moment when accompanying shear force acts. Therefore, this paper focuses on the M‐V interaction behavior of hybrid steel trapezoidally corrugated web girders (different flanges and web steel grades).

Abstract The paper presents the results of an experimental program on welded steel I‐beams, consisting of ten two‐span plated girders with web stiffeners. By arranging transverse stiffeners on both sides, the web was divided into four or eight rectangular sections with an aspect ratio of a/h=2.5. The h/t ratios of the web were between 175 and 350, and the b/t ratios of the flanges were between 8 and 40. During the laboratory tests the girders failed by the tension field action at the internal support. In order to explore the shear buckling behavior of the tested girders geometrically and materially nonlinear analyses with imperfections were conducted on full‐shell finite element models. Based on the validated numerical model a parametrical study was conducted on two‐span beams with different geometrical parameters. With the results of the laboratory tests and the parametric study the accuracy of the shear strength formula and the interaction formula from the EN 1993‐1‐5:2024 is examined.

Abstract Thin‐walled channel sections are commonly used as structural beams subjected to bending and/or shear, with a variety of dimensional ratios between web depth, flange width, and lip size. The demand for customising the sectional element sizes in the cold‐forming process arises from different strength optimisation purposes. This results in a significantly wide range of flange width‐to‐web depth ratios, which in turn leads to major changes in the entire section's buckling capacity of buckling modes. This paper presents comprehensive numerical and analytical studies on the elastic buckling of thin‐walled channels subjected to shear, covering a full range of flange width‐to‐web depth ratios and various member lengths. Elastic buckling analyses of lipped and unlipped channels are conducted using both semi‐analytical and restrained semi‐analytical finite strip methods under different modelling conditions, and are benchmarked against finite element models. A new analytical solution for calculating the elastic shear buckling of channel sections across the full range of flange widths is proposed to provide the elastic buckling input for the ultimate capacity design of thin‐walled channel members in shear.

ABSTRACT This study targets stepwise 3D6d braided composites by establishing a constraint PSO‐SVM surrogate coupled with NSGA‐III optimization and TOPSIS selection to link true geometry and damage evolution with efficient multi‐objective design. A lift rod‐based densification route adjusts yarn insertion direction and preform density, fully parameterizing insertion density, density zone length, braiding pitch, and six directional yarn tension. Across 72 designs, the optimized architecture raises compressive strengths in X , Y , and Z by 26%, 19%, and 14% with concurrent increases in moduli. Measured strengths are 164, 224, and 268 MPa, and measured moduli are 5.9, 8.7, and 9.3 GPa, while coefficients of variation for modulus and strength are 2.5 × 10 −1 and 4 × 10 −1 , indicating improved near isotropy. Predictions for the experiment are below 5%. DIC and micro CT reveal a progressive failure governed by interfacial shear and fiber buckling, confirming the reliability of the model and the process strategy. The surrogate‐driven optimization framework offers practical guidance for integrated structure process design of high‐performance 3D braided composites.

Buckling is a key failure mode in aircraft structural design. Full wingbox buckling analyses are expensive to include in structural optimizations, so closed-form buckling predictions at the panel level are often used. However, these closed-form solutions are limited to special cases that are analytic, such as simply supported boundary conditions, thin-walled panels, and high aspect ratios for shear buckling. To improve buckling predictions while maintaining computational efficiency for structural optimization, the authors propose the use of machine learning to augment closed-form solutions. Their machine learning models are trained on finite element datasets of stiffened panel buckling with nondimensional parameters informed by closed-form solutions. The authors identify a log transform linear asymptote property from the closed-form buckling solutions. This property is included in the Gaussian process (GP) models to improve model extrapolation for low-aspect-ratio and highly stiffened designs. The custom GP model achieves a 99% R2 value for extrapolated data as compared to the closed form and provides accurate buckling predictions on a finite element dataset of mixed simply supported to clamped panels. With the mixed boundary condition dataset, potential weight savings are demonstrated of 3.12 and 11.7% on a subsonic wingbox and a supersonic wingbox, respectively.

Structural fire performance of steel-concrete composite girders in web shear buckling: Advanced numerical analysis

Fire performance of steel-concrete composite girders in web shear buckling: Large-scale tests

Elastic shear buckling analysis of infill panels in trapezoidal corrugated plate shear walls

Shear buckling resistance of sinusoidal corrugated web girders with stiffened openings: analysis, experiment, simulation and design guidance

Shear buckling resistance models for steel plate girders – Numerical investigation

Abstract Steel plate girders are widely utilised in steel bridges and long‐span buildings due to their versatility and strength‐to‐weight ratio. However, the slender web panels of such girders are susceptible to buckling under shear forces. To mitigate this, intermediate transverse stiffeners are commonly employed, serving primarily to restrain out‐of‐plane web deformations and increase post‐buckling resistance. Experimental investigations involving 10 plate girder specimens with varying web aspect ratios and stiffener configurations revealed that the measured forces in intermediate stiffeners were, on average, only 50 % of those prescribed by EN 1993‐1‐5 for design proposes. To build upon these findings, a complementary numerical study was conducted using finite element models calibrated against the experimental results. The simulations incorporated initial geometric imperfections, residual stresses and material nonlinearity. Calibration was achieved through comparison of load–displacement behaviour, internal stiffener forces and ultimate shear resistance. The numerical analyses offered further insight into the formation and spacing of plastic hinges in the compression flange and support the refinement of current design provisions for steel plate girders, promoting greater accuracy and efficiency in structural design.

Bamboo scrimber is an environmentally friendly biomass building material with excellent mechanical properties. However, it is susceptible to delamination failure of the transverse fibers under compression, which limits its structural performance. To address this problem, this study utilizes steel tubes to encase bamboo scrimber, forming a novel bamboo scrimber-filled steel tubular column. This configuration enables the steel tube to provide effective lateral restraint to the bamboo material. Axial compression tests were conducted on 18 specimens, including bamboo scrimber columns and bamboo scrimber-filled steel tubular columns, to investigate the effects of steel ratio and loading mode (full-section and core loading) on the axial compression performance. The test results indicate that the external steel tubes significantly enhance the structural load-bearing capacity and deformation capacity. Primary failure modes of the composite columns include shear failure and buckling. The ultimate stress and strain of the structure are positively correlated with the steel ratio; as the steel ratio increases, the ultimate stress of the specimens can increase by up to 19.2%, while the ultimate strain can increase by up to 37.7%. The core-loading specimens exhibited superior load-bearing capacity and deformation ability compared to the full-section-loading specimens. Considering the differences in the curves for full-section and core loading, the steel tube confinement coefficient was introduced, and the predictive models for the ultimate stress and ultimate strain of the bamboo scrimber-filled steel tubular column were developed with accurate prediction.

This paper investigates the potential to extend current design limits for transverse stiffener spacing and effective lateral unbraced lengths through experimental and numerical studies. The focus here is on noncompact and slender-web singly symmetric hybrid I-sections subjected to simultaneous high moment and high shear. The research presented in this paper is particularly pertinent to long-span bridge construction, where higher-grade flanges (hybrid sections) and singly symmetric girders with smaller compression flanges are becoming more common to optimize both material use and cost. Despite such optimization, a significant cost of long-span bridges is associated with the fabrication of intermediate transverse stiffeners necessary for shear strength and cross frames essential for the lateral stability of girders. Reducing the number of stiffeners or cross frames, especially in regions of high moment and high shear, could result in combined shear buckling and lateral torsional buckling. While moment–shear interaction is typically considered in cross-sectional capacities, few studies have explored the efficacy of the compression flange in anchoring the postbuckling tension field-induced stresses with the advent of lateral torsional buckling. Experimental findings and numerical analyses presented in this paper suggest that despite these conjoined instabilities, the current flexural and shear strength equations in the design codes are sufficiently conservative to warrant increasing the current allowances for unstiffened lengths for straight steel I-girders without any strength reduction. Finally, the authors show that the design shear strengths in codes can be enhanced by using a modified elastic shear buckling coefficient considering the flange and transverse stiffener contribution to the shear stability of steel I-girders.