Major Axis Bending Research Articles

Advancements to the equivalent compression flange method

AbstractThe simplified method of the equivalent compression flange represents an illustrative and easy‐to‐use engineering model for lateral torsional buckling. The basic concept of the verification procedure has existed since its introduction in the 1950s. It is still frequently used today for preliminary design and application cases where the solution of the ‘correct lateral torsional buckling problem’ is complex and time‐consuming. To adapt the method to the current state of the art, it was further developed in the framework of the Eurocode 3 evolution. This ‘new’ method is part of the second generation of Eurocode 3, Part 1‐1 and is valid for classes 1 to 3 cross sections in major axis bending. The method must be adapted for use in other contexts and for specific applications. Applying the equivalent compression flange verification method to the structural fire design of building structures must consider the temperature‐dependent material properties of steel and their impact on the stability behaviour. Moreover, typical applications for bridge structures, runway beams, and H‐piles in combined walls require additional consideration of class 4 cross sections and various combined loadings, e. g., N–M interaction behaviour. This article presents theoretical studies on extending the simplified method of the equivalent compression flange to meet these demands. Finally, the application of the verification method is demonstrated in working examples.

Flexural behaviour and design of hybrid cold-formed steel built-up I-section beams

The current study investigates the flexural performance and design of hybrid cold-formed steel built-up I-section beams, which are increasingly popular in the construction industry. These beams combine the benefits of both an "I" section and a closed-box section in their cross-section profile. They are constructed from two identical plain channels placed back-to-back with space between them and top and bottom cover plates, fastened together by screws. A nonlinear finite element (FE) model was developed to consider initial geometric imperfections, material and geometric non-linearities. The model was validated against the test results of cold-formed steel (CFS) built-up beams from the companion paper and literature. Once validation was successful, a comprehensive parametric study using finite element modelling was conducted to generate data on hybrid cold-formed steel built-up I-section beams across a broader range of cross-sectional slenderness, hybrid ratio, aspect ratio of the cross section and thickness of the cover plates. The parametric results were used to analyse the influence of key parameters on the moment carrying capacity and buckling modes. The applicability of the current Direct Strength Method in the AISI S100–16 specifications was evaluated based on these results, revealing that it is unconservative. Additionally, modified design procedures and equations were suggested for hybrid CFS built-up I-section beams vulnerable to local buckling in major axis bending, which were then evaluated through reliability analysis.

Pin-ended stainless steel equal-leg angle section members under compression and major-axis bending: Experimentation, FE modelling and design

The behaviour and design of cylindrically-pinned stainless steel equal-leg angle section members under compression and compression combined with strong-axis bending are investigated herein. An experimental investigation, including material testing, initial geometric imperfection measurements and physical tests on hot-rolled stainless steel equal-leg angle section members is first presented. Numerical models are developed by means of shell finite element modelling formulated within ABAQUS and validated against experimental data. A numerical parametric study is then presented considering both hot-rolled and cold-formed stainless steel equal-leg angle section columns alongside beam–columns with a wide range of cross-section and member geometries. Finally, new design proposals for cylindrically-pinned stainless steel equal-leg angle section members under compression and compression plus major-axis bending are developed and verified against the results of physical experiments and numerical simulations. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the EN 1990 procedure.

An Assessment of the Eurocode 3 Simplified Formulas for Distortional Buckling of Cold-Formed Steel Lipped Channels

This paper concerns the Eurocode 3 Part 1-3 (EN 1993-1-3) methods for calculating the distortional buckling (bifurcation) load of cold-formed steel-lipped channels subjected to axial force, major and minor axis bending. More specifically, the paper presents the results of a parametric study that assesses the accuracy of the simplified method in EN 1993-1-3, which relies on direct/iterative hand calculations and an approximate mechanical model, through comparison with “exact” numerical results, obtained using semi-analytical linearized buckling analyses based on Generalized Beam Theory, which are also allowed by the code. Isoline error maps are presented for a wide range of geometric and material parameters, covering common commercial profiles and corresponding to a dataset of more than 24,000 cases. These maps make it possible to identify the parameter ranges leading to an acceptable error and, even though they strongly depend on the loading, general remarks concerning the expected error pertaining to the simplified method are drawn.

Strength Analysis of Cellular Steel Members under Combined Compression and Major-Axis Bending

Strength Analysis of Cellular Steel Members under Combined Compression and Major-Axis Bending

Global and Local Geometrical Imperfections of Pultruded GFRP Profiles Based on a Modal Approach

The ultimate capacity of pultruded glass fibre reinforced polymer (pGFRP) profiles depends significantly on geometrical imperfections (GIs), given their sensitivity to buckling phenomena arising from both thin walls and low elastic moduli. However, GIs are not yet comprehensively addressed in design guidance. This paper proposes a new approach to characterize the initial GIs of pGFRP profiles based on a modal approach. Given the lack of comprehensive knowledge in this area, this study presents a highly accurate and robust methodology to measure GIs and dimensional deviations (DDs) in pGFRP profiles using a 3D contact coordinate measurement machine (CMM). The modal approach encompasses the measurement of dimensional parameters and a point cloud transformation that enables the assessment of GIs associated with pure buckling modes of pGFRP profiles. This procedure allows the quantification of three types of global GIs associated to (i) minor-axis (weak axis), (ii) major-axis (strong axis) bending, and (iii) twist. Additionally, the procedure also includes the assessment of local GIs, considering the wall (plate-like) imperfections. The separation of GIs into these four types (shape and amplitude) is of major relevance as its paves the way to the development of analytical design formulas for the strength prediction of pGFRP members. The approach described in this paper also serves two important purposes: (i) the statistical analysis of DDs and GIs of pGFRP members, and (ii) the identification of distinct shapes and amplitudes of GIs that form the basis for reliable design considerations of pGFRP members.

Behavior of large-size and high-strength steel angle subjected to eccentric load

This paper examined the behavior of large-size and high-strength steel angle (LHS) members under eccentric load to determine their mechanical performance. The corresponding finite element models were established and validated based on the test results. Then, parametric analyses were accomplished for additional section sizes, a broad range of slenderness ratios, and varying eccentricity members. Moreover, LHS members' stability capacity formulas under eccentric load were proposed. The results show that eccentricity makes eccentric compression members have much less stability capacity and can alter their failure mode. For major axis bending members, there is a critical eccentric, and within the critical eccentric, the stability capacity of the eccentric compression member can match that of the axial compression member. The minor axis bending member's stability capacity drop under the same eccentric was larger than that of the major axis bending member. The proposed formulas have a high degree of precision and design safety margin for design, and they can display critical eccentric characteristics for major axis bending members.

Behaviour, finite element modelling and design of high strength steel homogeneous and hybrid welded I‐section beams

AbstractThe behaviour and design of homogeneous and hybrid high strength steel (HSS) beams are addressed in the present study. Six in‐plane three‐point bending tests on three different welded I‐sections were first conducted. Following the experimental investigation, a finite element (FE) modelling programme was performed, which included a validation study confirming the accuracy of the developed FE models in replicating the flexural behaviour of HSS welded I‐section beams, and a parametric study generating additional FE data on HSS welded I‐section beams over a broader range of cross‐sectional slendernesses, steel grades and loading configurations. Then, the suitability of the current Eurocode 3 cross‐section slenderness limits for HSS homogeneous and hybrid welded I‐sections in bending were evaluated. It is shown that the current Eurocode Class 2 and Class 3 slenderness limits are suitable for the classification of the outstand flange (in compression) and internal web (in bending) elements of both HSS homogeneous and hybrid welded I‐sections subjected to major axis bending, while stricter Class 1 slenderness limits are considered necessary to achieve sufficient rotation capacity for plastic design. The findings indicate that plastic design can be used for HSS structures, provided the proposed stricter Class 1 slenderness limits are employed. Further work is underway to develop advanced design approaches using second‐order inelastic analysis with strain limits for HSS welded I‐section members.

Seismic performance of partially encased concrete composite columns with corrugated web

Partially encased concrete composite (PEC) components have gained popularity recently because they are suitable for prefabricated construction. Corrugated steel plates have higher buckling strength and out-of-plane stiffness than flat plates, in this paper, an innovative corrugated web PEC column (CPEC column) was proposed, and its seismic performance was studied by cyclic loading tests. The designs and fabrications of specimens and loading system were described in detail. The seismic behavior of CPEC columns was investigated comparatively by analysis of their failure modes, hysteretic curves, ductility, energy dissipation capacity, and stiffness degradation. The test results show that the ultimate lateral load of CPEC columns under minor-axis bending is more competitive than that of ordinary PEC columns, while the ductility, energy dissipation capacity and stiffness degradation rate are close to that of ordinary PEC columns. Under major-axis bending, the “accordion effect” of corrugated web has a negative influence on the seismic behavior of CPEC columns after the concrete is crushed severely. Finally, the modified equations can be used to predict the N-M interaction curves of the CPEC columns. More experimental or numerical research should be carried out to further evaluate the seismic performance of CPEC columns quantitatively in the future.

Cross-section behaviour and design of press-braked ferritic stainless steel channel sections under combined compression and major-axis bending moment

This paper presents experimental and numerical investigations into the cross-section behaviour and resistance of press-braked ferritic stainless steel channel sections under combined compression and major-axis bending moment. An experimental programme, including initial local geometric imperfection measurements and ten major-axis eccentric compression tests, was firstly conducted, with the test setup, procedures and results reported in detail. This was followed by a numerical modelling programme, where finite element models were developed and validated against the major-axis eccentric compression test results and then adopted to conduct parametric studies to expand the test data pool over a wider range of cross-section dimensions and loading combinations. Based on the obtained test and numerical data, the design interaction curves for press-braked ferritic stainless steel channel sections under combined compression and major-axis bending moment, as given in the American specification and European code, were evaluated. The evaluation results revealed that the American specification resulted in a good level of design accuracy, while the European code led to conservative resistance predictions, due to the conservative bending end point and inefficient linear shape of the design interaction curve. New design interaction curves were also developed and shown to offer more accurate and consistent resistance predictions for press-braked ferritic stainless steel channel sections under combined compression and major-axis bending moment than the codified design interaction curves.

Lateral resistance performance evaluation of cold-formed steel zero-tolerance bolted moment-resisting frames

The experimental and analytical lateral load resisting behaviour of three cold-formed steel (CFS) moment-resisting frames with zero-tolerance bolted joints were investigated to understand the potential application of such joints in medium-span CFS portal frames. Strain gauge data were used to measure total longitudinal stresses in the column sections and were compared with analytical models. It was found that the bi-moment stress component was the second largest component after major-axis bending and can be analytically and conservatively estimated. The validity of the design approaches of monosymmetric and doubly symmetric back-to-back channel columns were also investigated. For the first time, the potential application of zero-tolerance jointed frames in medium-span CFS portal frames is demonstrated and conservative analysis and design approaches (monosymmetric) are employed.

Laboratory tests, numerical simulations and design of press-braked S690 high strength steel channel sections under major-axis combined loading

Testing and numerical modelling have been conducted to investigate the cross-sectional behaviour and resistances of press-braked S690 high strength steel channel sections under combined compression and major-axis bending. The testing programme included initial local geometric imperfection measurements and twenty major-axis eccentric compression (combined loading) tests. The numerical modelling programme included a validation study, where finite element models were developed and validated against test results, and a series of parametric studies, where the developed finite element models were adopted to generate further numerical data over a wide range of cross-section dimensions and loading combinations. The obtained test and numerical data were used to evaluate the existing design interaction curves for press-braked S690 high strength steel channel sections under combined compression and major-axis bending, as specified in the European code, North American specification, and Australian/New Zealand standard. The evaluation results revealed that the codified design interaction curves led to conservative resistance predictions, owing to the linear shapes and inaccurate end points. Improved design interaction curves featuring more efficient shapes and anchored to more accurate end points were then proposed. The proposed design interaction curves were shown to result in more accurate resistance predictions for press-braked S690 high strength steel channel sections under combined compression and major-axis bending than their codified counterparts. The reliability of the proposed design interaction curves was confirmed by means of statistical analyses.

Finite element modelling of sheathed cold-formed steel beam–columns

The structural behaviour of sheathed cold-formed steel lipped channel section columns (studs) subjected to combined compression and major axis bending is investigated herein by means of numerical modelling. Finite element (FE) models of single studs, set in tracks and connected to oriented strand board (OSB) and gypsum plasterboard sheathing under varying combinations of axial compression and horizontal loading were developed in ABAQUS and validated against experimental results reported in the literature. The developed numerical models incorporated cross-sectional and global geometric imperfections, while geometrical and material nonlinearities for both the steel and the sheathing were considered in the analyses. Particular emphasis was given to replicating the “as-built” boundary conditions at the ends of the columns, controlled by the screws connecting the column to the track and by the column–track contact interaction. The interaction between the sheathing and the column, as well as the behaviour of the fasteners connecting the two components, were also explicitly modelled. Both the shear and pull-through characteristics of the fasteners were considered and simulated based on experimental findings. Following successful validation of the finite element models, parametric studies were conducted. The results showed that substantial structural performance benefits can be achieved by the addition of sheathing to cold-formed steel members and that the spacing of the connectors has a strong influence on the member response. For a typical system, decreasing the connector spacing from 300 mm to 75 mm was found to increase stud capacity and stiffness by up to 12% and 10% respectively when in pure compression and up to 26% and 22% respectively when in pure bending; under combined loading, capacity increases of up to 29% were found.

Behaviour and design of high strength steel homogeneous and hybrid welded I-section beams

The behaviour and design of high strength steel (HSS) beams are addressed in the present study. Six in-plane three-point bending tests on three different welded I-sections − two homogeneous S690 steel welded I-sections and one hybrid welded I-section with S690 steel flanges and an S355 steel web, were first conducted. The beam tests were carried out in major axis bending and a bespoke restraint system was designed and employed in the test programme to prevent lateral-torsional buckling. Following the experimental investigation, a thorough finite element (FE) modelling programme was performed, which included a validation study confirming the accuracy of the developed FE models in replicating the flexural behaviour of HSS welded I-section beams, and a parametric study generating additional FE data on HSS welded I-section beams over a broader range of cross-sectional slendernesses, steel grades and loading configurations. The test results obtained in the present study and collected from the literature, together with the generated FE data from the parametric study, were used to evaluate the suitability of the current Eurocode 3 cross-section slenderness limits for HSS homogeneous and hybrid welded I-sections in bending. It is shown that the current Eurocode Class 2 and Class 3 slenderness limits are suitable for the classification of the outstand flange (in compression) and internal web (in bending) elements of both HSS homogeneous and hybrid welded I-sections subjected to major axis bending, while stricter Class 1 slenderness limits are considered necessary to achieve sufficient rotation capacity for plastic design. The findings from the present study indicate that plastic design can be used for HSS structures, provided the proposed stricter Class 1 slenderness limits are employed.

Local stability of laser-welded stainless steel slender I-sections under combined loading

This paper presents a comprehensive experimental and numerical investigation into the local buckling behaviour of laser-welded stainless steel slender I-sections under combined compression and bending moment. A testing programme was firstly carried out, including initial local geometric imperfection measurements and eccentric compression tests on ten laser-welded stainless steel slender I-section stub column specimens. Following the testing programme, a numerical modelling programme was conducted. Finite element models were developed and validated against the test results, and then adopted to perform parametric studies to generate additional numerical data. The obtained test and numerical data were used to evaluate the applicability of the interaction curves in the European and American codes and the continuous strength method to laser-welded stainless steel slender I-sections under combined loading. The evaluation results generally show that the three sets of considered interaction curves offer adequate design accuracy for laser-welded stainless steel slender I-sections under combined compression and major-axis bending moment, but they yield unduly conservative and scattered resistance predictions for laser-welded stainless steel slender I-sections under minor-axis combined loading, owing principally to the conservative minor-axis bending end points. Finally, an improved design interaction curve for the minor-axis combined loading case was developed and shown to yield substantially more accurate and consistent resistance predictions for laser-welded stainless steel slender I-sections under minor-axis combined loading than the three considered design methods. The reliability of the new design interaction curve was confirmed based on a reliability study.

Post-fire behaviour and residual resistance of hot-rolled stainless steel channel sections under major-axis combined loading

This paper presents experimental and numerical investigations into the post-fire local buckling behaviour and residual resistance of hot-rolled stainless steel channel sections under combined compression and major-axis bending. The experimental investigation included heating and cooling of specimens as well as post-fire material testing, initial local geometric imperfection measurements and fourteen eccentric compression tests. A subsequent numerical investigation was performed, where finite element models were developed to simulate the test results and then used to conduct parametric studies to generate additional numerical data over a wide range of cross-section dimensions and loading combinations. Due to the lack of specific design standards for stainless steel structures after exposure to elevated temperatures, the relevant ambient temperature design interaction curves, as set out in the European code and American specification, were evaluated, using post-fire material properties, for their applicability to hot-rolled stainless steel channel sections under major-axis combined loading after exposure to elevated temperatures. The evaluation results revealed that the codified design interaction curves result in conservative post-fire residual resistance predictions, due to the conservative end points and inefficient shapes. Finally, new design interaction curves, with more accurate end points and efficient shapes, were proposed and shown to provide improved design accuracy than the codified design interaction curves for hot-rolled stainless steel channel sections under major-axis combined loading after exposure to elevated temperatures.

Determination of optimal dimensions of polymer-based rectangular hollow sections based on both adequate-strength and local buckling criteria: Analytical and numerical studies

Most studies have focused on determining optimal dimensions of metal- or composite-based rectangular hollow sections (RHSs) by considering only the design requirement of strength. Different from those, an analytical procedure for the determination of optimal sectional dimensions of polymer-based RHS beams by accounting for both adequate-strength and local buckling for the first time has been presented in the context of this study. Analytical expressions which give the optimal sectional dimensions simultaneously satisfying the adequate-strength and local buckling conditions have been derived for two different loading configurations such as a pure major axis bending and a combined axial compression and major axis bending. The analytical procedure proposed in this study depends on the idea of preventing the polymer-based RHS from buckling prior to its compressive strength. This has been achieved by increasing the critical buckling stress of the RHS up to its compressive strength via optimizing its sectional dimensions. During the optimum design, different elastic and plastic material behaviors of polymers in tension and in compression have been taken into calculations. The results attained analytically have been validated against numerical predictions obtained from linear elastic eigenvalue buckling and postbuckling analyses implemented in Abaqus engineering finite element code. Thus, the analytical procedure reported in this study can be used as a benchmark in identifying the optimal dimensions of RHS members manufactured from polymers. Communicated by Davide Spinello.

Elastic local buckling formulae for thin-walled I-sections subjected to shear and direct stresses

Formulae for calculating the elastic local buckling stresses of doubly-symmetric thin-walled I-section girders subjected to combined shear and direct stresses, accounting for the interaction between the plate elements are presented. The interaction between the plate elements (i.e. the flanges and web) is bounded by a theoretical lower-bound, where there is no interaction and the critical plate is considered to be simply-supported, and a theoretical upper-bound where interaction is strongest and the critical plate is considered to have rotationally fixed edges. The interaction is accounted for by introducing an interaction coefficient ζ that quantifies the relative level of fixity between the aforementioned lower and upper bounds. Expressions to calculate ζ are calibrated using results from finite element analyses generated in Abaqus. Doubly-symmetric I-sections of varying geometric proportions loaded in shear, major axis bending, compression and a full range of combinations thereof are considered. Using the developed formulae, the elastic local buckling stresses of the studied cross-sections are accurately predicted, typically within 5% of the values obtained from FE models; this is a significant improvement over the results determined in the traditional manner in which plate element interaction effects are ignored, where the full cross-section buckling stress is shown to be underestimated by as much as 40%.

Structural Stability Verification for Steel Beam‐columns in Fire ‐ a Consistent Approach with Ambient Temperature Rules

AbstractSteel structures are characterized by a slender design, which makes stability verifications particularly important. While the design methods for steel members at ambient temperatures have been continuously developed and revised for the second generation of Eurocode 3, the method for elevated temperatures in prEN 1993‐1‐2 is still based on the corresponding rules of ENV 1993‐1‐1 of 1992. This leads to a divergence of methodology for ambient and elevated temperatures and to unnecessarily complex design methods for the engineering practice. Therefore, a harmonization of design models for ambient temperature and fire design is desirable.This paper presents a theoretical and numerical study on the stability behaviour of steel members at elevated temperatures. The structural fire behaviour of steel beams, columns and beam‐columns, i.e. flexural buckling under pure compression, lateral torsional buckling under major axis bending and spatial buckling of members under combined bending and axial compression has been investigated. Based on results available in the literature as well as an extensive numerical parametric study, reduction factors and interaction factors were determined. The new reduction and interaction factors were used to develop a design model for the member stability verification in fire that follows the format of FprEN 1993‐1‐1. Thus, engineering practice is provided with a harmonized verification method for steel members in bending and compression for ambient temperature and fire design.

Exploring Machine Learning for the Stability Analysis of Rotary‐straightened Steel Members with Multiple Stiffness Reduction Models

AbstractRotary straightened structural steel cross‐sections have a different residual stress pattern compared to those without rotary straightening, which affects structural behavior, especially in members subjected to inelastic buckling. A stiffness reduction material model for rotary‐straightened hot rolled sections was previously developed and validated for a specific set of cross‐section sizes and load conditions. Previous research has indicated that the current stiffness reduction model specified in Chapter C of AISC 360 for stability design does not accurately capture the stiffness reduction of rotary straightened W‐shapes. Particularly, the current stiffness reduction model does not always derive conservative capacity compared with the model for rotary straightened sections. This paper explores machine learning for predicting the beam‐column capacity considering different stiffness reduction models and estimating their limit load capacity. Two extreme gradient boosting models were developed for beam‐columns under major or minor axis bending. The dataset contained 1,296 finite element simulations for beam‐columns with a range of different cross‐section geometries. Excellent prediction accuracy of the developed machine learning models showed the potential of using machine learning for the stability analysis of rotary‐straightened members.