Minor Axis Bending Research Articles

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.

INVESTIGATION OF FLEXURAL BEHAVIOUR OF STAINLESS STEEL CHANNEL SECTIONS

AbstractIn this paper, the design of austenitic stainless steel channel sections subjected to minor axis bending, specifically with tension in the web (“u” orientation) is analyzed. The values of moment resistance are predicted using Eurocode 3 criteria and the Continuous Strength Method (CSM), which are then compared with numerical models to assess effectiveness. The modeling is performed through ANSYS and calibrated with literature tests. It was found that Eurocode presents a considerable disparity in results, as well as an overly cautious response (on average, half the numerical load). The CSM reflects the performance more accurately but still with a certain level of conservatism (on average, around 35% lower).

Buckling analyses of cold-formed steel lipped channel members under minor-axis eccentric load

This paper numerically investigates the buckling behavior of cold-formed steel (CFS) lipped channel members under combined compression and minor axis bending (CaMAB). The numerical models are validated against existing tests. The influences of eccentricity on buckling behaviors are studied, and the results indicate that for the eccentricity toward the web side or lipped side, the failure modes of structural members are mainly controlled by local-global buckling interactions or distortional-global buckling interactions, respectively. The maximum ultimate load capacity may occur at the eccentricity toward the lipped side. Furthermore, a comparison of the load capacity obtained from the interaction formula of the standard EN 1993-1-3 and finite element analysis (FEA) is presented. In addition, the current direct strength method (DSM) curves are modified by considering the effect of the buckling interaction.

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.

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.

Design of Aluminum Alloy H-Sections under Minor-Axis Bending

Much research has been reported on the global response of aluminum alloy H-sections members, while studies on the local buckling behavior of H-sections under pure bending remain relatively limited. The purpose of the research is to investigate the response of aluminum alloy H-sections subjected to minor axis bending. Using a finite element model, this study analyzed the stress distribution and failure mechanism of aluminum alloy H-sections under minor-axis bending and obtained the ultimate capacities of cross-sections covering a wide range of plate slenderness. The results were compared with the strength predictions based on EN1999-1-1 and the effective width method in AS/NZS 4600. The flange slenderness was found to play the most significant role in determining the normalized capacity. The sections are shown to exhibit an elastic-plastic stress distribution in the tensile flanges. The comparisons given in this study indicate that EN1999-1-1 underestimates the predicted bending strengths. The predictions based on the effective width method are shown to be more accurate than EN1999-1-1. An alternative design method is proposed for treating aluminum H-sections in minor axis bending. This method considers plastic stress distributions in the tensile flanges after the compressed flanges have locally buckled.

Design of aluminum alloy channel sections bent about the minor axis

Aluminum alloy extruded channel sections are often used as rafters for light roofs, columns in framed buildings and chords of roof trusses. In this paper, a numerical study is carried out on the response of aluminum alloy channel sections under minor axis bending. Numerical models were developed and validated based on the experimental data of aluminum alloy channel sections under minor-axis bending. Subsequently, parametric studies covering various cross-sectional geometries were performed to expand the numerical data. The results were used to assess the applicability of Eurocode 9 slenderness limits, revealing that the Class 2 and Class 3 limits for outstand flanges under stress gradient with peak compression at tip are too conservative. Moreover, Eurocode 9 underestimates the predicted bending strengths of slender cross-sections due to the lack of consideration of the effect of stress gradient. The equivalent stress gradient factor applied in the effective thickness approach was proposed based on the buckling coefficient of BS 5950. For channel sections bent about minor-axis with the web in compression, flanges exhibit pronounced inelastic behavior even when the web locally buckles. An alternative design method based on the ultimate shape factor of a rectangular plate is proposed for semi-compact and slender channel sections in minor-axis bending (producing compression in the web), which leads to more favorable and less scattered capacity predictions.

Structural behaviour and design of press-braked S690 high strength steel channel sections under combined compression and minor-axis bending

This paper presents experimental and numerical investigations into the cross-sectional behaviour and resistances of press-braked S690 high strength steel channel sections under combined compression and minor-axis bending. An experimental programme was firstly conducted and included initial local geometric imperfection measurements and ten minor-axis eccentric compression tests. The experimental programme was accompanied by a numerical modelling programme, where finite element models were developed and validated against the test results and then employed to perform parametric studies to expand the test data pool over a wider range of cross-section dimensions and loading combinations. The obtained test and numerical data were then used to assess the relevant codified design interaction curves, as provided in the European code, North American specification and Australian/New Zealand standard. The assessment results revealed that all the codified design interaction curves led to excessively conservative and scattered resistance predictions for press-braked S690 high strength steel channel sections under combined compression and minor-axis bending, mainly owing to the conservative linear shapes and inaccurate end points. Finally, a new design interaction curve, with more accurate end points and nonlinear shape, was proposed and shown to offer more accurate and consistent resistance predictions than the codified design interaction curves.

Post-fire cross-sectional behaviour of hot-rolled austenitic stainless steel channel section stub columns under combined compression and minor-axis bending

The present paper reports experimental and numerical investigations into the post-fire cross-sectional behaviour and residual resistances of hot-rolled austenitic stainless steel channel section stub columns under combined compression and minor-axis bending. An experimental programme included heating, soaking and cooling of specimens as well as post-fire initial local geometric imperfection measurements and minor-axis eccentric compression tests on fourteen specimens. The minor-axis eccentric compression test results were used in a parallel numerical modelling programme for validation of finite element models, which were then adopted to perform a series of parametric studies to generate further numerical data. Since there are no existing design rules for stainless steel structures after exposure to elevated temperatures, the relevant codified ambient temperature design interaction curves in combination with post-fire material properties were evaluated for their applicability to eccentrically loaded hot-rolled austenitic stainless steel channel section stub columns after exposure to elevated temperatures. The evaluation results revealed that the design interaction curves given in the European code and American specification led to rather conservative and scattered resistance predictions, which were attributed to the conservative end points and inefficient shapes. To address the shortcomings, new design interaction curves anchored to more accurate end points and having more efficient shapes were developed and resulted in more accurate and consistent resistance predictions than their codified counterparts. The reliability of the new design interaction curves was also confirmed by means of statistical analyses.

Cross-sectional behaviour of press-braked S690 high strength steel slender channel section stub columns under minor-axis combined loading

This paper reports laboratory testing and numerical modelling on the cross-sectional behaviour and resistances of press-braked S690 high strength steel slender channel section stub columns under combined compression and minor-axis bending. A testing programme, including initial geometric imperfection measurements and ten minor-axis eccentric compression tests, was firstly conducted. This was accompanied by a numerical modelling programme, including a validation study, where finite element models were developed and validated against test results, and a series of parametric studies, where the validated finite element models were used to generate further numerical data. The obtained test and numerical data were then adopted to evaluate the current codified design interaction curves for press-braked S690 high strength steel slender channel section stub columns under combined compression and minor-axis bending, as provided 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 and scattered resistance predictions, mainly due to the conservative end points (i.e. the cross-section compression and bending resistances). Finally, a new design interaction curve, anchored to more accurate end points, was proposed and shown to result in a higher level of design accuracy and consistency than the codified design interaction curves.

Testing, FE modelling and design of pin-ended stainless steel equal-leg angle section columns and beam–columns

The behaviour and design of pin-ended stainless steel equal-leg angle section members under compression and compression plus minor-axis bending are investigated herein. The studied members are cylindrically pinned about the minor axis. 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 and validated against the new experimental data. A numerical parametric study is then presented considering both hot-rolled and cold-formed stainless steel angle section columns alongside beam–columns with a wide range of slenderness values. Finally, new design proposals for pin-ended stainless steel equal-leg angle section members under compression and combined compression and minor-axis bending are developed and verified against the results of existing physical experiments, as well as the newly-generated test and numerical results. 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.

Experimental and numerical study of laser-welded stainless steel slender I-section beam-columns

This paper reports on an experimental and numerical study on the structural behaviour and resistances of laser-welded stainless steel slender I-section beam-columns under combined compression and minor-axis bending. A testing programme was firstly conducted, including imperfection measurements and sixteen beam-column tests. Following the testing programme, a numerical modelling programme was conducted, where finite-element models were developed and validated. The validated finite-element models were then used to perform parametric studies to derive more numerical data. The obtained test and numerical data were employed to conduct an in-depth design analysis, where the relevant interaction curves in the European and American standards for laser-welded stainless steel slender I-section beam-columns were examined. The design analysis results indicate that the European and American interaction curves lead to significant inaccuracies and scattering of the ultimate load predictions, due to inappropriate bending end points. A new interaction curve is developed, anchored to a more accurate bending end point. The new curve is shown to offer greatly improved design accuracy and consistency over the current European and American curves.

Numerical investigation and design of cold-formed steel built-up section beam-column members under moment gradients

This paper presents the numerical investigation and design of cold-formed steel (CFS) built-up section beam-column members experiencing non-uniform minor axis bending. Detailed considerations of material nonlinearity and initial imperfections were involved in developing finite element models of the thin-walled built-up section members undergoing eccentric compression. The finite element models calibrated against the existing experimental results were then employed for a parametric study. Numerical predictions of 279 built-up section beam-columns over a broad spectrum of cross-sectional geometries and moment distributions along the member length were obtained in this investigation. For the built-up open and closed section members included in the numerical analyses, non-uniformly distributed moments resulted in the strength enhancements by average of 39% and 37%, respectively. Furthermore, based on the 279 numerical predictions obtained in this investigation and 91 data collected from the literature, the nominal strengths predicted by the design rules codified in the current standards and proposed in the previous studies were examined for the CFS built-up section beam-column members with end moment ratios ranging from −1.0 to 1.0. Underpinned by the assessment results, design recommendations and modified design rules were provided for the CFS built-up open and closed section members undergoing synchronous axial load and non-uniform minor axis moment, respectively.

Structural behaviour of press-braked austenitic stainless steel slender channel section beam-columns

The present paper reports experimental and numerical studies of the structural behaviour and resistances of press-braked austenitic stainless steel slender channel section beam-columns under combined compression and minor-axis bending. An experimental programme, including initial geometric imperfection measurements and ten beam-column tests, was firstly performed. The test procedures, setups and results were fully reported. The experimental programme was accompanied by a numerical modelling programme, including a validation study, where finite element models were developed and validated against the test results, and a series of parametric studies, where the validated finite element models were used to generate further numerical data. The obtained test and numerical data were adopted to assess the current design interaction curves for press-braked austenitic stainless steel slender channel section beam-columns, as provided in the European code, American specification and Australian/New Zealand standard. The assessment results revealed that all the three codified design interaction curves led to conservative and scattered resistance predictions, due to the conservative compression and bending end points and inappropriate shapes. To address these shortcomings, a new design interaction curve has been proposed and shown to yield a higher level of design accuracy and consistency for press-braked austenitic stainless steel slender channel section beam-columns than the codified design interaction curves.

Behavior of Stainless-Steel Hot-Rolled Channel Section Beam–Columns: Testing, Modeling, and Design

This paper presents a testing and numerical modeling program on the global stability and resistance of stainless steel hot-rolled channel section beam–columns under combined compression and minor-axis bending. The testing program comprised material tests, imperfection measurements, and 18 beam–column tests. Following the testing program, systematic numerical simulations were conducted; finite-element models were developed to simulate the test observations and conduct parametric studies to obtain more numerical data. The obtained experimental and numerical results were analyzed and used to perform a design analysis, in which the accuracy of interaction curves prescribed in the US and European design codes for stainless steel hot-rolled channel section beam–columns was assessed comprehensively. The results of the design analysis generally revealed that both the US and European interaction curves yield unduly inaccurate and scattered resistance predictions due to the use of inappropriate curve shape and inaccurate end points. A new design interaction formula is proposed using a more appropriate curve shape and more-accurate end points. The new interaction curve was shown to be capable of offering greatly improved design accuracy and consistency compared with the US and European curves.

Press-braked ferritic stainless steel slender channel section beam–columns: Tests, simulations and design

This paper reports an experimental and numerical investigation into the buckling behaviour and resistance of press-braked ferritic stainless steel slender channel section beam–columns under combined compression and minor-axis bending moment. An experimental programme was firstly performed, including material coupon tests, initial global and local geometric imperfection measurements and ten beam–column tests. The experimental programme was followed by a numerical modelling programme, where finite element models were developed and validated against the experimental results and then adopted to conduct parametric studies to generate additional numerical data. Based on the obtained test and numerical data, the existing design interaction curves, as set out in the European code, American specification and Australian/New Zealand standard, were evaluated and found to result in conservative and scattered resistance predictions. An improved design interaction curve, anchored to more accurate end points and featuring more appropriate shape, was then developed and shown to offer more accurate and consistent resistance predictions for press-braked ferritic stainless steel slender channel section beam–columns over the codified design interaction curves. Statistical analyses were also performed to confirm the reliability of the new proposal.

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.

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.

Local buckling and capacity of press-braked ferritic stainless steel channel sections under minor-axis combined loading

This paper presents experimental and numerical studies of the local buckling behaviour and cross-section resistances of press-braked ferritic stainless steel channel sections under combined compression and minor-axis bending. An experimental programme was firstly conducted and included material testing, initial local geometric imperfection measurements and ten eccentric compression tests. Following the experimental programme, a numerical modelling programme was conducted, where finite element models were developed to replicate the test observations and then used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. The obtained test and numerical data were then used to assess the relevant design interaction curves for press-braked ferritic stainless steel channel sections under minor-axis combined loading, as set out in the European code and American specification. The assessment results revealed that the codified design interaction curves result in conservative and scattered resistance predictions, mainly owing to the conservative bending end point and inefficient linear shape. Finally, new design interaction curves were developed and shown to provide a higher level of design accuracy and consistency than the codified design interaction curves.

S960 ultra-high strength steel slender welded I-section beam–columns: Testing, numerical modelling and design

This paper presents experimental and numerical investigations of the buckling behaviour and resistance of S960 ultra-high strength steel slender welded I-section beam–columns under combined compression and minor-axis bending moment. An experimental programme, including initial geometric imperfection measurements and eight beam–column tests, was firstly conducted. The test procedures, setups and results were fully reported. Following the experimental programme, a numerical modelling programme was carried out, with finite element models initially developed and validated against the test results and then employed to conduct parametric studies to generate further numerical data. On the basis of the test and numerical data, the relevant design interaction curves, as provided in the European code, Australian standard and American specification, were evaluated for their applicability to S960 ultra-high strength steel slender welded I-section beam–columns. The evaluation results revealed that all three codified design interaction curves lead to conservative resistance predictions, mainly owing to the conservative end points (i.e. column buckling strength and cross-section minor-axis bending resistance). Finally, a revised Eurocode design interaction curve, with improved compression end point determined from more accurate column buckling curve and bending end point determined from the direct strength method, was finally proposed, and shown to result in more accurate resistance predictions for S960 ultra-high strength steel slender welded I-section beam–columns than the codified design interaction curves.