Intermediate Stiffeners Research Articles

Simulation and cross-section design of steel beams under moment gradients

A systematic study into the effect of moment gradients on the cross-section resistance of hot-rolled steel square hollow section (SHS), rectangular hollow section (RHS) and I-section beams has been conducted and is presented in this paper. Finite element (FE) models were first developed and validated against test results from the literature; parametric studies covering different steel grades, cross-section geometries and moment distributions were then carried out. It was found that cross-section bending resistances increase with increasing moment gradient in the low to intermediate range, despite the necessary rise in the level of co-existent shear. Under high moment gradients, the negative impact of the high co-existent shear outweighs the positive influence of the moment gradient, and cross-section bending resistances fall. It was found that the benefits from moment gradients vary with the cross-section slenderness and the aspect ratio of the cross-section, and increase when intermediate web stiffeners are present. A new design method that captures the observed behaviour is devised, featuring a new parameter to describe the local moment gradient in beams under different loading conditions. The proposed design equations are shown to be more accurate than existing provisions in EC3 and to meet the reliability requirements set out in EN 1990. The new method is therefore deemed to be suitable for implementation within the EC3 framework.

Shear buckling resistance and intermediate transverse stiffeners internal forces of full-scale steel plate girders – Experimental tests and numerical investigation

This paper presents the results from two full-scale transversally stiffened plate girder’s load tests in shear and bending. The plate girder’s internal stiffener forces and shear buckling resistance are estimated using the web and stiffener measured strains. These results show that the reported axial compression and bending moment of the intermediate transverse stiffeners for the tested plate girder are 70% of the FprEN 1993–1-5: 2022 [1] design force. The two full-scale plate girders fail due to buckling shear. Nonlinear FEM analyses based on the test girder geometry, measured initial geometric imperfections, and the material properties from the tensile tests, show excellent agreement with the test results, with less than 5% on the maximum applied forces and related displacements. The principal membrane stresses path that triggers the failure of the web plate are investigated based on numerical results and compared with the test measurements. Contrary to the assumption of a rotated stress field model, the principal compression stress obtained in the experimental test was higher than shear buckling stress in the vicinity of the intermediate transverse stiffener.

Improving the local and distortional resistance of CFS trapezoidal self-supporting roof members

This paper reports the development, numerical implementation and application of a methodology to perform the multi-objective optimisation, with respect to local and distortional failures, of cold-formed steel (CFS) trapezoidal cross-section shapes used in members belonging to self-supporting roof systems and manufactured by bending the steel sheets with roll-forming machines. Initially, a brute-force approach is adopted to search for optimal unstiffened cross-section shapes of members subjected to positive (sagging) and negative (hogging) bending moments. Next, an optimisation procedure based on a Genetic Algorithm (GA) is employed to find stiffened cross-sections that (i) outperform the original (plain/unstiffened) ones, as far as the resistance against local and distortional failures is concerned, and (ii) can be fabricated with minimal additional cost, through the sole addition of small intermediate stiffeners, whose possible locations are pre-defined in accordance with a map of executable fold-line positions – the original cross-section typology, overall dimensions and wall angles are retained. The design approach adopted to estimate the member ultimate strengths is based on the Direct Strength Method (DSM), and Generalised Beam Theory (GBT) is used to calculate the elastic buckling stresses due to bending. The application and capabilities of the proposed methodology are illustrated, by means of numerical results presented in terms of cross-section families belonging to optimal Pareto Fronts – an excellent performance of the procedure was found in all cases.

Flexural capacity and local buckling half-wavelength of high strength steel tubular beams under moment gradients: An experimental study

An experimental investigation into the effect of moment gradients on the flexural behaviour of hot-rolled high strength steel square hollow section (SHS) beams is presented in this paper. In total, 20 beam specimens in steel grades S690 and S770, and with cross-sections spanning from Class 2 to Class 4 based on the Eurocode 3 slenderness limits, were tested under three- and four-point bending. In the three-point bending tests, the beam spans were varied to achieve a range of moment gradients; the influence of different stiffening arrangements at the loading point was also considered. Local geometric imperfections were measured by means of 3D laser-scanning prior to testing and digital image correlation (DIC) was adopted to monitor the displacement and strain fields at critical regions and to assess the local buckling half-wavelengths of the test specimens for which a consistent measurement approach was proposed. The measured local buckling half-wavelengths were compared against the elastic local buckling half-wavelengths calculated using the finite strip method. It was observed that while the measured local buckling half-wavelengths remained approximately constant up to first yield, a significant reduction in half-wavelength was observed with increasing moment due to the non-uniform spread of plasticity. The comparisons also revealed that the local buckling half-wavelengths reduced with both the presence of moment gradients and intermediate stiffeners, with a new parameter proposed to quantify the local moment gradient. It was shown from the tests that the specimens subjected to moment gradients, despite the presence of shear, exhibited higher ultimate moment capacities (up to 10.5% for stiffened specimens and 3.4% for unstiffened specimens) than those subjected to uniform moments. This is attributed to the delay in the local buckling of the critical cross-section of beams under moment gradients due to the restraint provided by the less heavily stressed adjacent cross-sections.

Numerical study on steel plate girders ‐ Intermediate transverse stiffeners axial force

AbstractTransverse stiffeners are used in steel plate girders with slender webs to provide lateral support to the web along the span and thus increase the plate girder shear resistance. Furthermore, transverse stiffeners anchor the tension field, resulting in axial compression in the stiffener. Despite this, it is widely assumed that the design axial force provided by the FprEN 1993‐1‐5 [1] for the transverse stiffeners is significantly greater than that observed in experimental testing and numerical simulations.The results of 550 nonlinear numerical simulations of plate girders loaded in shear up to failure are presented. Shear resistance and axial stiffener forces are evaluated while the effects of a wide parameter range as web aspect ratio and thickness, flange‐to‐web area ratio, and steel grade are investigated. The numerical results are compared to the European standard design values. Finally, a statistical analysis of the set of results is presented.The numerical analyses show that the axial forces installed in the intermediate transverse stiffeners are significantly lower than those specified by FprEN 1993‐1‐5 [1].

Local buckling behaviour of high strength steel tubular beams under moment gradients

AbstractThis paper presents an experimental study into the effect of moment gradients on the local buckling behaviour of hot‐rolled high strength steel square hollow section (SHS) beams. The influence of moment gradients was investigated by testing 20 beam specimens, ranging from Class 2 to Class 4 according to the cross‐section classification limits given in prEN 1993‐1‐1:2020. Both four‐ and three‐point bending loading configurations were considered with varying shear span lengths. The influence of intermediate stiffeners at the loading point was examined by employing two different loading configurations in the three‐point bending tests, achieving fully stiffened or unstiffened conditions. Local geometric imperfections were measured by means of 3D laser scanning, and the displacement and strain fields at critical regions were monitored by digital image correlation (DIC) during testing. It was shown from the tests that specimens subjected to moment gradients exhibited higher ultimate moment capacities than those subjected to uniform moments.

Machine learning‐based predictions of buckling behaviour of cold‐formed steel structural elements

AbstractDesigning thin‐walled structural members is a complex process due to the possibility of multiple instabilities. This study aimed to develop machine learning algorithms to predict the buckling behavior of thin‐walled channel elements under axial compression or bending. The algorithms were trained using feed‐forward multi‐layer Artificial Neural Networks (ANNs), with the input variables including the cross‐sectional dimensions, the thickness, the presence and location of intermediate stiffeners, and the element length. The output data included the elastic critical buckling load or moment, as well as a modal decomposition of the buckled shape into the pure buckling mode categories: local, distortional and global buckling. The Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM) were used to prepare the sample output for training. To ensure the accuracy of the developed algorithms, the ANN models were subjected to a K‐fold cross‐validation technique and featured optimized hyperparameters. The results showed that the trained algorithms had a remarkable accuracy of 98% in predicting the elastic critical buckling loads and modal decomposition of the critical buckled shapes.

Experimental behaviour of plate girders in steel – Internal forces in intermediate transverse stiffeners

Economical design of steel plate girders usually adopts slender web panels sometimes combined with large panel aspect ratio, which determines the elastic stability of the web panel. The adoption of transverse stiffeners is one efficient strategy to retard the web buckling due to shear. The primary role of intermediate transverse stiffener is clear: divide the web into panels providing lateral support to the web plate along the span – This increases the shear strength of the web. However, FprEN 1993-1-5: 2022 [1] stiffener design approach is based mainly on direct compressive forces resulting from the tension filed action in post buckling phase. According to multiple investigations, this area requirement is much higher than that found in laboratory testing and numerical simulations. The findings of experimental testing on eight plate girders with thin webs and two configurations of transverse stiffeners under ultimate load are presented. Using the web and stiffener measure strains, the internal stiffener forces are calculated past the shear failure of the plate girders. These results show that the axial compression and bending moment measured in the intermediate transverse stiffeners are considerably lower than those specified for the design by the FprEN 1993-1-5: 2022 [1].

Behavior study of the steel plate girder with a cellular honeycomb web

Based on the experimental test results of the authors, this investigation is concerned with the finite element analysis to examine and compare the load values and failure modes of the authors’ results. This research was conducted using the Abaqus software. The experimental work included the fabrication of twelve plate girders with honeycomb and flat web plate corrugation patterns, which were then tested under a single concentrated load at the midspan. According to the corrugation dimension or outer honeycomb web thickness, the honeycomb steel plate web girder is divided into three groups (60 mm, 80 mm and 100 mm). The specimens also involved plate girders with a flat web. The specimens were created with three lengths (600 mm, 1,200 mm and 1,800 mm). The Abaqus software was used in finite element models to simulate the concentrated load. The numerical results demonstrated that the 60 mm thick honeycomb web provides a greater load-bearing capacity and shear strength than other girders. The 20 mm honeycomb corrugation on the steel plate girder indicates the increased and improved shear resistance. The conclusion was that as the width of the corrugation increased, so did the steel web’s ultimate load and shear strength, resulting in a positive relationship between the critical shear buckling load of the web and the moment of inertia at the strong axis. When the dimension of the corrugation increases, the moment of inertia of the Y axis (Iy) decreases; thus, the plate girder will fail with a less critical buckling load (Pcr). Also, it can be concluded that as the steel plate thickness of the honeycomb web increases, the shear resistance increases as well. However, the spacing between the intermediate stiffener or the horizontal spacing of the web panel can enhance the shear resistance of honeycomb web girder if it was decreased due to increasing the action of tension field force that resists the diagonal tension developed at the web panel by the applied midspan concentrated force.

Study of GFRP composite stiffened panels with square opening

Fiber reinforced polymer stiffened panels are the important parts of marine structures. Square openings are necessary for functional purposes in the stiffened panels of marine structures. Finite element software ABAQUS is used to analyse of stiffened panels with and without square opening is carried out using ABAQUS. Reinforcement of square opening is necessary to obtain the original strength and stiffness of stiffened panels under axial loading and combination of axial & pressure loading. The thicknesses of intermediate stiffeners necessary to obtain the original strength and initial stiffness were determined as 8.5, 7.5 and 9 mm under axial loading, constant axial & increasing pressure loading and constant pressure and increasing axial loading respectively. The failure loadings and failure pattern of stiffened panels without opening, with unstrengthened and strengthened square opening are found. Load vs. displacement curves of stiffened panels without opening, with strengthened and unstrengthened square opening under different loading patterns are plotted and shown. The area of strengthened stiffener around opening to the area of stiffeners required to bring back the original load carrying capability of stiffened panels having square opening were determined as 1.34, 1.18 and 1.42 for axial loading, constant axial & increasing pressure loading and constant pressure & increasing axial loading respectively. Hence, the square opening in stiffened panels was observed to have critical behaviour under constant pressure and increasing axial loading.

Effects of reinforcing steel tanks with intermediate ring stiffeners on wind buckling during construction

Many tank structures may not be stable during the construction phase, and this may lead to their becoming vulnerable to buckling under environmental loading conditions such as wind. Installing intermediate ring stiffeners of the proper size at the mid-height of the cylindrical shell may be the most effective way to stabilize these structures, especially under the effects of wind action. In the study, analytical and numerical studies were conducted to identify the required strength and stiffness for the intermediate ring stiffener. First, a new cylindrical shell-to- intermediate ring stiffness ratio was derived by considering curved beam and shell membrane theories. For strength criteria, the tributary height and the effect of shell- ring interaction on the internal forces and moments were examined by making use of Linear Analysis (LA) and Geometrically Nonlinear Analysis (GNA). The stress resultants developed in the intermediate ring stiffener were identified so that they could be used as strength criteria. For stiffness criteria, by considering the changes in the buckling resistance based on the developed stiffness ratio, an expression to compute the minumum intermediate ring stiffness was determined. In addition, Geometrically Nonlinear Analysis including Imperfections (GNIA) was also performed to examine the effect of the geometric imperfections on buckling strength of the steel tank with an intermediate ring stiffener, taking different imperfection amplitudes into account. The developed design equations in simple algebraic form can be utilized for the structural stability of cylindrical steel tanks during erection.

A Novel Approach to Improve the Distortional Buckling Strength of a Stiffened Cold-Formed Steel Channel Section under Axial Compression

This study investigates the distortional buckling strength of a partially closed cold-formed steel (CFS) channel section with intermediate web stiffeners and outward lips under axial compression. Generally, a closed CFS cross section has higher torsional resistance when compared to an open cross section. However, an open cross section is more popular in the construction industry. Despite the popularity of CFS open sections, distortional buckling can reduce the load-carrying capacity of such open cross sections. To improve the distortional buckling strength of the proposed selected section, a simple spacer plate is added externally to the channel section in the transverse direction. Initially, a numerical model is developed using the finite element software ANSYS, which is then validated against the experimental results available in the literature. A detailed parametric study was also conducted to investigate the influence of thickness, depth, and spacing of spacer plates on the distortional buckling strength of stiffened CFS channel sections. From the results of the parametric study, it was found that the presence of spacer plates can increase the axial capacity of stiffened CFS channel sections by as much as 32%. Finite element results were compared with the design strengths calculated in accordance with the direct strength method (DSM).

Predicting the buckling behaviour of thin-walled structural elements using machine learning methods

The design process of thin-walled structural members is highly complex due to the possible occurrence of multiple instabilities. This research therefore aimed to develop machine learning algorithms to predict the buckling behaviour of thin-walled channel elements subjected to axial compression or bending. Feed-forward multi-layer Artificial Neural Networks (ANNs) were trained, in which the input variables comprised the cross-sectional dimensions and thickness, the presence/location of intermediate stiffeners, and the element length. The output data consisted of the elastic critical buckling load or moment, while also providing an immediate modal decomposition of the buckled shape into the traditionally defined ‘pure’ buckling mode categories (i.e. local, distortional and global buckling). The sample output for training was prepared using a combination of the Finite Strip Method (FSM) and the Equivalent Nodal Force Method (ENFM). The ANN models were subjected to a K-fold cross-validation technique and the hyperparameters were tuned using a grid search technique. The results indicated that the trained algorithms were capable of predicting the elastic critical buckling loads and carrying out the modal decomposition of the critical buckled shapes with an average accuracy (R2-value) of 98%. The influence of the various channel parameters on the output was assessed using the SHapley Additive exPlanations (SHAP) method.

Omission of intermediate stiffeners in box link beams using trapezoidal corrugated webs

In box link beams, intermediate stiffeners are often used to delay local shear bucklings, but welding operations in order to connect the intermediate stiffeners to the web of box link beams lead to increased construction costs, reduced execution speed, creating residual stresses and geometric imperfections, and weakening of materials at the junction of stiffeners to the web. The present study investigated corrugating webs of box link beams as an alternative to flat webs with intermediate stiffeners using Abaqus finite element software. First, equations were presented to determine the slenderness ratio and critical inelastic buckling stress of trapezoidal corrugated plates used as the web of box link beams. A comparison between box link beams with corrugated webs and box link beams with flat webs and intermediate stiffeners showed that box link beams with corrugated webs experienced more buckling stability, ductility, and energy dissipation due to the intrinsic geometrical characteristics of this type of web plate. The results of this study revealed that the use of trapezoidal corrugated webs in box link beams, if the geometric parameters of the corrugated webs are appropriately selected, can increase the maximum permissible compactness ratio of the web up to about 12% and 200% more compared to box link beams with flat webs and with or without intermediate stiffeners, respectively; Also, the energy dissipation of the box link specimens can be increased by about 20%.

Strength of Composite Columns Consists of Welded Double CF Sigma-Sections Filled with Concrete—An Experimental Study

In-filled tubes section is a very successful configuration for axially loaded members such as columns and struts. Steel shell tube filled with concrete has many advantages, such as eliminating the need for shuttering, reinforcement bars or ties besides increasing both flexural and axial capacities and enhancing the ductility. The main disadvantage of in-filled tubes is the need for a shell thick enough to prevent the local buckling and hence the local decomposition. Previous studies tried to solve this problem using intermediate stiffeners or shear connectors. This research presents another approach to solve this problem using double cold-formed sigma-sections (face to face) as steel shell tubes. Sixteen specimens with different lengths, cross section dimensions and shell thicknesses were tested under both concentric and eccentric compression loads. Ultimate capacities, lateral deformations and normal strains were recorded. The theoretical capacities were calculated using AISC-LRDF-94, EN-1994-04 and CSI-COL software considering full composite action, and the deviations from the experimental results were 24%, 24% and 13%, respectively.

Behaviour of Plate Girders with Intermediate Transverse Stiffeners – Experimental Investigation

AbstractTransverse stiffeners are used in slender steel plate girders along the span to give web lateral support and increase plate girder shear resistance. According to several studies, transverse stiffeners are primarily engaged in out‐of‐plane bending to laterally limit the edges of the panel as it buckles, rather than axial compression to anchor the tension field. As a result, the axial loading defined in EN 1993‐1‐5 [1] for the design of transverse stiffeners, based on tension field action, is usually deemed to be substantially larger than that observed in laboratory testing and numerical simulations. The test results of six plate girders loaded to failure, with slender webs and two transverse stiffener geometries, are presented. FE‐models that accurately replicate the tests provide a thorough view of the plate girder behaviour. The stiffeners internal forces are evaluated during plate girder loading up to failure. The transverse stiffener internal forces attained by both models are compared. It is confirmed that both the axial compression and the bending moment in the intermediate transverse stiffeners are much lower than the values prescribed by the EN 1993‐1‐5 [1].

Shape Optimisation of Cold‐Formed Steel Cross‐Sections with Longitudinal Intermediate Stiffeners

AbstractThis paper reports the development, numerical implementation and application of a novel methodology to perform a multi‐objective shape optimisation of conventional cold‐formed steel (CFS) cross‐section shapes with longitudinal intermediate stiffeners, manufactured by bending the steel sheets with roll‐forming machines. The methodology is based on a Genetic Algorithm (GA) and aims at maximising the compressive and/or flexural ultimate strength of CFS members currently used in industry with respect to local, distortional and local‐distortional interactive failures. The design approach adopted to estimate the member ultimate strengths is based on the Direct Strength Method (DSM) and Generalised Beam Theory (GBT) is used to calculate the elastic buckling loads and moments. The proposed methodology consists of adding small intermediate stiffeners, whose possible locations are pre‐defined in accordance with a map of executable fold‐line positions – the original cross‐section typology, overall dimensions and wall angles are retained. The application and potential of the developed GA‐based code is illustrated by addressing the optimisation of conventional lipped channel, lipped zed and rack cross‐section shapes for CFS members subjected to compression, bending or compression and bending.

Influence of Intermediate Stiffeners on Axial Capacity of Thin-Walled Built-Up Open and Closed Channel Section Columns

This paper investigates the post-buckling behaviour and axial capacity of thin-walled steel stiffened single-channel sections (ISSCS) and back-to-back stiffened channel sections (BISCS). BISCS were connected using fasteners at a spacing of 200 mm and with an edge distance of 100 mm. Under axial compression, 10 new ISSCS and BISCS columns with fixed-ended conditions were tested. In the experimental tests, the back-to-back channel sections failed due to a combination of local and global buckling, whereas the single-channel sections generally failed as a result of local buckling. The behaviour of both ISSCS and BISCS shows a 20% increase on an average in axial capacity through adding stiffeners at the junction of the flange and the web, in addition to stiffeners in the web. A nonlinear finite element model (FEM) with material and geometric nonlinearities was then developed. The FE model was validated against the experimental results. A comprehensive parametric study comprising 64 face-to-face intermediate stiffened channel sections (FISCS) was then conducted to study the influence of stiffener length on its axial capacity. The axial capacity obtained from the tests and FEA shows that design in accordance with the Direct Strength Method (DSM) is accurate and conservative by only 4% on average.

Stiffening optimisation of conventional cold-formed steel cross-sections based on a multi-objective Genetic Algorithm and using Generalised Beam Theory

This paper reports the development, numerical implementation and application of a novel methodology to perform a multi-objective stiffening optimisation of conventional cold-formed steel (CFS) cross-section shapes with longitudinal intermediate stiffeners, manufactured by bending the steel sheets with roll-forming machines. The methodology is based on a Genetic Algorithm (GA) and aims at maximising the compressive and/or flexural ultimate strength of CFS members currently used in industry with respect to local, distortional and local-distortional interactive failures. The design approach adopted to estimate the member ultimate strengths is based on the Direct Strength Method (DSM) and Generalised Beam Theory (GBT) is used to calculate the elastic buckling loads and moments. The proposed methodology consists of adding small intermediate stiffeners, whose possible locations are pre-defined in accordance with a map of executable fold-line positions, thus leading to an optimisation procedure whose output are alternative (stiffened) cross-sections that (i) outperform the original conventional/plain cross-section and (ii) can be fabricated with a minimal additional cost – the original cross-section typology, overall dimensions and wall angles are retained. The application and potential of the developed GA-based code is illustrated by addressing the stiffening optimisation of conventional lipped channel, lipped zed and rack cross-section shapes for CFS members subjected to compression, bending or compression and bending – the numerical results are presented in terms of cross-section families belonging to the optimal Pareto Front. For validation and assessment purposes, some optimised cross-sections obtained are compared with the “exact” solutions provided by a “brute-force search”.

Parametric study of hysteretic performance of high-strength steel framed-tube structures with web-bolted connected shear links

High-strength steel framed tube structures with web-bolted connected shear links (HSSFTS-WCSLs) combine the advantages of replaceable shear link and high-strength steel (HSS) and can effectively improve the seismic performance and recoverability of traditional steel framed-tube structures. This parametric study investigates the effects of design parameters on the hysteretic behaviors of HSSFTS-WCSL using finite element analysis. The parameters include the length ratio of the shear link, span-to-depth ratio of the spandrel beam, intermediate link web stiffener space, and design details of the web-bolted connections. According to the numerical simulation results, the recommended length ratios of the web-bolted connected shear link are between 0.84 and 1.40. The span-to-depth ratios of the spandrel beams significantly influence the strength of the structures. The web-bolted connected shear links should be placed at the middle of the spandrel beams with span-to-depth ratios lower than 4.6. The link web stiffener spaces barely influence the seismic performance of HSS-FTS-RSLs. The allowable link web stiffener spaces given in the design codes can provide reliable capacities of the structures. The details of the web-bolted connections determine the energy dissipation performance of the structure, and this effect can be optimized by effectively increasing the diameter of the bolt and thickness of the reinforcement plate. The bolts should have sufficient shear strength to avoid shear failure. Increasing the thickness of the reinforcement plates of the connections can significantly enhance the energy dissipation capacities of HSS-FTS-RSLs. The overstrength factors of the web-bolted links with length ratios between 0.84 and 1.60 range from 1.42 to 1.79.