Elliptical Hollow Sections Research Articles

Local buckling behaviour of Q690 high strength steel press-braked elliptical hollow section stub columns: Testing, numerical modelling, and design

This paper presents comprehensive investigations on the local bucking behaviour of Q690 high strength steel (HSS) press-braked elliptical hollow section (EHS) stub columns subject to concentric compression experimentally. In comparison with conventional hot-finished EHS or cold-rolled EHS, the press-braked EHS provides high precision, great construction productivity and the fabricated geometries are not limited to production assembly instrumentation. HSS press-braked EHS fabricated through press-braking process was expected to exhibit distinct behaviour compared with their counterparts constructed from the conventional fabrication routes. Well-understanding of their performance at the levels of material, and cross-section level is essential. Material properties were obtained through tensile coupon tests. Residual stresses in both membrane and bending types were measured and recorded and their impact on structural performance was also assessed. Initial local geometric imperfection measurements were conducted for all the specimens. In conjunction with experimental studies, the finite element (FE) models of Q690 HSS press-braked EHS stub columns were developed. The accuracy of the FE model for HSS press-braked EHS stub column was asserted by comparing the numerical predictions with the tested results. An extensive parametric study was conducted to generate structural performance data with a wider range of cross-section slenderness to complement the test data bank. The cross-section classification for conventional CHS codified in existing standards and the proposed slenderness limits by various researchers were evaluated. The existing slenderness limits cannot be extended to HSS press-braked EHS investigated in this study, a new slenderness limit is proposed. Moreover, the advanced design approaches of Direct Strength Method (DSM) and Continuous Strength Method (CSM) were assessed for their applicability to the cross-section resistance predictions of the examined EHS stub columns.

Axial resistance of elliptical hollow section K-joints made of high strength steel

The present study examined the axial resistance of welded elliptical hollow section (EHS) K-joints made of high-strength steel (HSS). The axial resistance of EHS K-joints was affected by a range of factors, including the geometrical parameters, orientations, chord pre-stress levels, and the mechanical properties of the high-strength steel grades. This research aimed to investigate the performance of welded EHS K-joints made of HSS under axial loading conditions with or without chord pre-stresses. Finite element analysis was employed for numerical simulations to analyze the nonlinear behaviour of EHS K-joints with HSS. It was observed from the numerical results that the orientation types significantly affected normalised resistance ratios. In contrast, β, γ, θ, and chord pre-stress levels had minimal impact, as comparisons were based on normalised resistance ratios. However, non-dimensional geometric parameters and chord pre-stress levels notably influenced the axial joint resistance of the HSS K-joints. As for predicting the axial resistances of EHS K-joints with HSS, the numerical results indicated that the existing reduction factor might be unsafe for the equivalent RHS method to be applied in the current design guides. Therefore, a new reduction factor was proposed for EHS K-joints with HSS that yield unsafe results.

Structural behaviour of cold-formed steel elliptical hollow section stub columns after exposure to ISO-834 fire curve

The present study undertakes the post-fire stub column behaviour of cold-formed steel elliptical hollow sections (CFS-EHS) by experimental and numerical analyses. A total of 18 CFS-EHS stub column specimens made up of four cross-section series was firstly prepared, heated in a gas furnace as per the ISO-834 standard fire and then naturally cooled down to ambient temperature. Four fire exposure temperatures of 300 °C, 550 °C, 750 °C and 900 °C were adopted. Details of the experimental campaign, e.g., specimen preparation, test procedures and results, are presented. Accurate finite element (FE) model was established to mimic the experimental responses from various perspectives. Exhaustive parametric studies were subsequently conducted on 224 post-fire CFS-EHS stub columns to generate substantial data. The test and FE results were compared with the strength calculations using the equivalent diameter method and equivalent rectangular hollow section method developed for hot-finished steel elliptical hollow sections without fire exposure, the Direct Strength Method (DSM) stipulated in the American Specification AISI S100, as well as the modified DSM previously calibrated for CFS-EHS without fire exposure. By replacing the material properties obtained at ambient temperature with the post-fire material properties in the aforementioned design methods, it is shown that the equivalent section methods and the existing DSM overly underestimate the column strengths, whilst the modified DSM yields precise and reliable strength estimations. It is recommended to adopt the modified DSM for calculating the residual compressive strengths of CFS-EHS stub columns after exposure to the ISO-834 standard fire.

Cold-formed stainless steel elliptical hollow sections under combined biaxial bending and axial compression - Numerical modeling and design

This paper aims to investigate the cross-section response of cold-formed stainless steel (CFSS) elliptical hollow sections (EHS) under combined biaxial bending and axial compression. In the present study, an advanced finite element (FE) model was adopted to perform a comprehensive parametric study for CFSS EHS under combined biaxial bending and axial compression, with different stainless steel alloys, as well as a broad range of cross-section sizes, aspect ratios, loading eccentricities and angles. Numerical results obtained from the parametric study were compared with the design strengths calculated by the current design rules in European code EN 1993-1-4, American specification SEI/ASCE 8-02 and Australian/New Zealand standard AS/NZS 4673. In addition, the Continuous Strength Method (CSM) for CFSS circular hollow sections (CHS) under combined actions, was also evaluated for the design of CFSS EHS under combined actions. The comparisons revealed that the current design codes EN 1993-1-4, SEI/ASCE 8-02 and AS/NZS 4673 provided conservative and very scattered predictions for CFSS EHS under combined actions. The existing CSM can provide more accurate predictions than the current design codes (i.e., AS/NZS 4673, EN 1993-1-4 and SEI/ASCE 8-02), but a further improvement is needed. In the present study, a modified CSM is proposed for CFSS EHS under combined actions, which can achieve reliable and accurate design predictions.

Machine learning models for predicting the axial compression capacity of cold‑formed steel elliptical hollow section columns

Machine learning models for predicting the axial compression capacity of cold‑formed steel elliptical hollow section columns

Local buckling response and design of stainless steel hollow sections at elevated temperatures

AbstractThe structural behaviour and design of stainless steel hollow sections in fire, including stainless steel (i) circular hollow sections (CHS), (ii) elliptical hollow sections (EHS), (iii) square hollow sections (SHS) and (iv) rectangular hollow sections (RHS), are explored in this paper. Shell finite element models of stainless steel CHS, EHS, SHS and RHS able to replicate their structural response at elevated temperatures are created. Numerical parametric studies are performed on cold‐formed and hot‐rolled austenitic, duplex and ferritic stainless steel CHS, EHS, SHS and RHS subjected to (i) pure compression, (ii) pure bending, (iii) combined axial compression and bending and (iv) combined bending and shear in fire, covering different cross‐section slendernesses and elevated temperature levels. Calibrated against the benchmark structural performance data obtained from the numerical parametric studies, the new design proposals for predicting the ultimate resistances of stainless steel CHS, EHS, SHS and RHS in fire put forward in Quan and Kucukler [1,2] are set out. It is demonstrated that relative to the design recommendations provided in the European structural steel fire design standard EN 1993‐1‐2, the proposed cross‐section design methods provide more accurate and safe‐sided ultimate resistance predictions for stainless steel CHS, EHS, SHS and RHS at elevated temperatures.

Static strengths of cold-formed steel elliptical hollow section X-joints

The newly emerged elliptical hollow section (EHS) has a vast of structural and architectural merits and is favorable for engineers and designers. This paper presents an experimental investigation concerning the structural behavior of cold-formed steel EHS X-joints. Thirty elliptical hollow section X-joints with three different brace-chord orientations were carefully designed, fabricated by robotic gas metal arc welding and tested with the braces axially compressed. The width ratio between brace and chord (β) ranged from 0.29 to 1. The brace-to-chord thickness ratio (τ) ranged from 0.58 to 1.83 and the chord width-to-thickness ratio (2γ) ranged from 10.1 to 52.6. The static strengths, failure modes and load-deformation responses are discussed. The current codified design provisions do not cover the design of cold-formed steel elliptical hollow section X-joints investigated in this study. As the performance of EHS lies between the circular and rectangular hollow sections, the feasibility of the design provisions initially calibrated for conventional X-joints as specified in the CIDECT and Eurocode 3 with incorporation of equivalent section methods as well as the design recommendations previously proposed for hot-rolled steel elliptical joints was evaluated. In general, these design methods provide accurate strength predictions for cold-formed steel elliptical hollow section X-joints. Nevertheless, the scattering of predictions is still a concern and the design method shall be further improved.

Strength enhancement and stub-column behavior of cold-formed stainless steel elliptical hollow sections

This paper aims to investigate the strength enhancement, local geometric imperfections, and stub-column behavior of cold-formed (CF) stainless steel elliptical hollow sections (EHS) by using finite element methods. In the present study, an advanced numerical approach was used to conduct a comprehensive parametric study for CF stainless steel EHS with a wide range of cross-section dimensions and slenderness values as well as different stainless steel alloys. By analyzing the generated numerical data from the parametric study, the effects of cold-forming and material parameters on the strength enhancement were examined. Predictive models of the strength enhancement as well as the local geometric imperfections for CF stainless steel EHS are proposed. The slenderness limits for CF stainless steel circular hollow sections (CHS) and CF steel EHS in the existing design methods were assessed for CF stainless steel EHS. New slenderness limits are proposed for CF stainless steel EHS. In addition, the existing equivalent diameter method, the Continuous Strength Method (CSM) and the Direct Strength Method (DSM) were evaluated for the design of CF stainless steel EHS. Modifications on these existing design methods are proposed for CF stainless steel EHS, which can improve their accuracy.

Fire design of stainless steel columns with hollow circular and elliptical sections

One of the advantages of stainless steel is its better behaviour under elevated temperatures when compared to the conventional carbon steel, which can be important for structural applications where the fire action should be considered. The second generation of Part 1–2 of Eurocode 3 (prEN 1993-1-2:2021) proposes new calculation formulae resulting from studies on profiles with I-sections. However, it is still important to evaluate the accuracy and safety of the same formulae for columns with circular and elliptical hollow sections (CHS and EHS respectively), whose application in stainless steel structures is common. Hence, this work presents a numerical parametric study on the fire resistance of columns subjected to axial compression, with CHS and EHS, considering different stainless steel grades, cross-sections and member slendernesses, and elevated temperatures. The ultimate load capacities of the columns are obtained by geometrically and materially nonlinear analyses including imperfections, using the SAFIR finite element program and considering the constitutive law based on the two-phase Ramberg-Osgood formulation proposed in prEN 1993-1-2:2021. Based on the comparisons between the numerical results and the methodology of prEN 1993-1-2:2021, small suggestions are proposed to improve the fire design formulae for the cases of CHS and EHS profiles subjected to axial compression.

Global instability of cold-formed steel elliptical hollow section members under combined compression and biaxial bending

The present study numerically investigated the global instability of cold-formed (CF) steel elliptical hollow section (EHS) members under combined compression and biaxial bending. A finite element (FE) model for CF tubular members under combined compression and biaxial bending was first developed, in which the strength enhancement, geometric imperfection and residual stresses due to roll-forming were incorporated. The FE model was validated against the existing test results. The validated FE model was employed to carry out a parametric study for CF steel EHS members, which covers an extensive range of cross-section geometries, material grades (including both high strength and normal grade steels), member slenderness, loading eccentricities and loading angles. Based on the generated FE data, the application of the current interaction design formulae for steel members under combined loading in EN 1993–1-1, together with the codified slenderness limits for circular hollow section (CHS) under combined loading, were assessed for the design of CF steel EHS members under combined compression and biaxial bending. It can be found that the design formulae in EN 1993–1-1, together with the slenderness limits for CHS, can give very conservative predictions for CF steel EHS members under combined loading. In addition, the influences of different parameters, including the loading eccentricity, loading angle, loading level and the reduction factor for lateral-torsional buckling, on the member behavior were also examined. Finally, new design recommendations are proposed for the design of CF steel EHS members under combined compression and biaxial bending.

Cross-section resistance and design of stainless steel CHS and EHS at elevated temperatures

The structural behaviour and design of stainless steel circular hollow sections (CHS) and elliptical hollow sections (EHS) at elevated temperatures are investigated in this paper. Shell finite element models of stainless steel CHS and EHS are created and validated against experimental results from the literature, which are subsequently used to generate benchmark structural performance data. Parametric studies are performed on a large number of cold-formed and hot-rolled austenitic, duplex and ferritic stainless steel CHS and EHS subjected to (i) pure axial compression, (ii) pure bending, (iii) combined axial compression and bending and (iv) combined bending and shear at elevated temperatures; the studied cases comprise 24,495 stainless steel CHS and EHS in fire and cover a wide range of cross-section slendernesses and elevated temperature levels. Calibrated against the benchmark structural performance data obtained from the numerical parametric studies, new design proposals for predicting the cross-section resistances of stainless steel CHS and EHS in fire are put forward. The accuracy, safety and reliability of the new design proposals are assessed. It is shown that in comparison to the design provisions of the European structural steel fire design standard EN 1993-1-2, the proposed design methods provide more accurate and safe-sided cross-section resistance predictions for stainless steel CHS and EHS at elevated temperatures.

Experimental investigation on cold-formed steel elliptical hollow section T-joints

A test campaign on cold-formed steel elliptical hollow section T-joints with the chord simply supported and the brace axially compressed is described in this paper. Four different sizes of elliptical hollow sections with the section aspect ratio ranged from 1.65 to 3 were employed to fabricate the T-joint specimens. Thirty-one T-joint specimens with three different types of member orientations were considered. Robotic gas metal arc welding was adopted to fabricate the elliptical hollow section T-joint specimens. The width ratio between brace and chord (β) ranged from 0.29 to 1. The brace-to-chord thickness ratio (τ) ranged from 0.60 to 1.77 and the chord width-to-thickness ratio (2γ) ranged from 10.6 to 52.3. All the T-joint specimens were tested with the chord simply supported and the brace axially compressed. The load-carrying capacities, load-deformation responses and failure modes of the elliptical hollow section T-joints are presented and discussed. Since no codified design provision is available for elliptical hollow section T-joints investigated herein, the feasibility of the design provisions originally developed for tubular T-joints with conventional cross-sections (i.e. circular hollow section and rectangular hollow section) as specified in the CIDECT and Eurocode 3 as well as the design recommendations proposed for hot-rolled steel elliptical joints was examined. Comparison results indicate that the joint strength predictions via these design methods are quite conservative and scattered for cold-formed steel elliptical hollow section T-joints.

Cold-formed steel elliptical hollow section stub columns under combined compression and biaxial bending

The paper presents a numerical study on the cross-section behavior of cold-formed (CF) steel elliptical hollow sections (EHS) under combined compression and biaxial bending. In the present study, a finite element (FE) model for CF steel tubular stub columns under combined compression and biaxial bending was first developed, in which the local geometric imperfections, residual stresses and enhanced material behavior were predicted by a rigorous numerical simulation of roll forming. The developed FE model for CF steel tubular stub columns under combined compression and biaxial bending was validated against test results of various tubular sections (including EHS). Then, the validated FE model was employed to carry out a parametric study for CF steel EHS with a large range of steel grades (including both high strength and normal grade steels), section sizes, loading eccentricities and angles. Based on the generated FE data, the traditional design specifications for doubly symmetric cross-sections under combined loading in EN 1993-1-1: 2005 (CEN, 2005) and ANSI/AISC 360-16 (AISC, 2016), as well as the current design equations for hot-finished (HF) normal grade steel EHS suggested by Gardner et al. (2011) under combined loading were evaluated for the design of CF steel EHS under combined loading. New slenderness limits of Class 2 and Class 3 sections, as well as new design equations of cross-section resistances, for CF steel EHS stub columns under combined compression and biaxial bending are proposed.

Design of concrete-filled cold-formed steel elliptical stub columns

The present paper reports an experimental and numerical investigation on the behavior of concrete-filled cold-formed steel elliptical stub columns. The test program was performed on four elliptical hollow sections infilled with concrete of three different grades (C40, C70 and C100). Thirteen fixed-ended stub columns were tested and details of test program are described in this paper. The test program was further supplemented with numerical analyses, where finite element model was firstly developed to emulate the compressive behavior observed from the tests and then used to generate more numerical data via parametric studies. The test results together with the numerical data derived herein were compared with the predictions by the current design rules for concrete-filled steel tubular columns with conventional cross-section shapes. The current American Specifications ANSI/AISC 360 and ACI318 as well as the European Code EN1994-1-1 were evaluated. The comparison demonstrated that both American Specifications result in generally conservative and reliable compressive strength predictions for concrete-filled cold-formed steel elliptical stub columns, whilst the predictions by the European Code are accurate but not reliable. New design method considering the confinement effect was proposed herein, which could provide accurate and reliable compressive resistance predictions for concrete-filled cold-formed steel elliptical stub columns.

Experimental study on additive manufactured 304L stainless steel tubular sections: Material properties and cross-sectional behavior

This paper presents an experimental investigation on the material properties and cross-sectional behavior of 304L stainless steel tubular sections additively manufactured using selective laser melting (SLM). A total of 76 tensile coupons, 76 hardness test specimens, and 25 stub columns were fabricated from 304L stainless steel powders by the SLM technique. Tension coupon tests and hardness tests were conducted to determine the mechanical properties. Residual stresses and local geometric imperfections of the stub columns were measured. The effects of coupon specimen orientations, thicknesses, and annealing conditions on the measured material properties were explored. In addition, the failure modes, ultimate load-carrying capacities and structural responses of the stub columns with four different cross-sections under axial compression were obtained and analyzed to evaluate the cross-sectional behavior. The test results of ultimate strengths were compared with the predictions calculated from the current design methods. The test results showed that the tensile strength of the coupon perpendicular to the building direction was higher than that of the coupon parallel to the building direction. Moreover, the tensile strength of the coupon increased with the increase of the coupon thickness. Considering the cross-sectional behavior, the square hollow section (SHS) and circular hollow section (CHS) had greater cross-sectional axial capacities than the rectangular hollow section (RHS) and elliptical hollow section (EHS), respectively. The introduction of a single stiffener in SHS and CHS reduced the load-carrying capacities to a certain extent.

Stress–strain model and design strength of cold-formed steel non-slender elliptical tubular stub columns

This paper aims to propose a stress–strain model for the stub column behavior of cold-formed steel non-slender elliptical hollow sections (EHS) under axial compression by considering the post-local buckling behavior and taking into account the effects of local imperfection, material nonlinearity and residual stresses. The proposed model is applicable to the sections of both high strength and normal grade steels; and is mainly defined by four key parameters, including the 0.2% proof stress, the local buckling stress and buckling strain, as well as the post-peak residual strength of a stub column. Equations are also proposed to express these key parameters in terms of the basic input cross-section parameters and virgin material properties. In order to determine these key parameters, existing test and numerical results on the structural behavior of cold-formed steel EHS stub columns were collected and analyzed, which covered a wide range of steel grades (up to 960 MPa) and section sizes. Existing design methods, which have not yet been calibrated for cold-formed high strength steel EHS, were first evaluated by comparing their predicted stub column strengths (i.e., local buckling stresses) with the collected test and numerical data. The Continuous Strength Method (CSM) was found to provide better predictions than other examined design methods. Modified CSM base curves were then developed to further improve the accuracy of the existing CSM for both the local buckling strains and design strengths of cold-formed EHS with steel grades up to 960 MPa. In addition, a theoretical framework is proposed to develop the semi-empirical equations for both the 0.2% proof stresses and local buckling stresses of stub columns by incorporating the modified CSM base curves, whereas one curve based on the conventional equivalent diameter and one curve based on equivalent diameter of the four-arc approximation. A predictive expression of the post-peak residual strengths is also presented. Predictions from the proposed stress–strain model were in a good agreement with the collected test and numerical results, which can demonstrate its accuracy and validity.

Fire resistance of stainless steel slender elliptical hollow section beam-columns

PurposeStainless steel has different advantages when compared to conventional carbon steel. The corrosion resistance and aesthetic appearance are the most known; however, its better behaviour under elevated temperatures can also be important in buildings design. In spite of the initial cost, stainless-steel application as a structural material has been increasing. Elliptical hollow sections integrate the architectural attributes of the circular hollow sections and the structural advantages of the rectangular hollow sections (RHSs). Hence, the application of stainless-steel material combined with elliptical hollow profiles stands as an interesting design option. The purpose of the paper is to better understand the resistance of stainless-steel-beam columns in case of fireDesign/methodology/approachThe research presents a numerical study on the behaviour of stainless-steel members with slender elliptical hollow section (EHS) subjected to axial compression and bending about the strong axis at elevated temperatures. A parametric numerical study is presented here considering with and without out-of-plane buckling different stainless-steel grades, cross-section and member slenderness, bending moment diagrams and elevated temperatures.FindingsThe tested design methodologies proved to be inadequate for the EHS members being in some situations too conservative.Originality/valueThe safety and accuracy of Eurocode 3 (EC3) design methodology and of a recent design proposal developed for I-sections and cold-formed RHSs are analysed applying material and geometric non-linear analysis considering imperfections with the finite element software SAFIR.

Design of stainless steel elliptical hollow sections columns in case of fire: parametric study

AbstractThe application of stainless steel as a structural material has been increasing, due to a number of desirable qualities such as its durability, resistance to corrosion and aesthetic appearance. Since it has a higher fire resistance when compared to carbon steel, it allows in some cases the absence of thermal protection. In addition to the aesthetic nature, elliptical hollow sections integrate the architectural attributes of the circular hollow sections and the structural advantages of the rectangular hollow sections. They have a better torsional behaviour than open sections and due to their shape they have a higher bending strength when compared to circular hollow profiles. Hence, the application of the material stainless steel combined with elliptical hollow sections stands as an interesting design option. The main objective of this study is to perform a parametric study to understand the fire behaviour of stainless steel columns subjected to axial compression, with Elliptical Hollow Sections and to analyse the safety and accuracy of the Eurocode 3 design methodology for these members. From comparing the obtained ultimate load bearing capacities with Eurocode 3 prescriptions, it is concluded that this design methodology is not suitable for this type of cross‐section profiles.

Reliability assessment for the Generalized Slenderness based Resistance Method for circular and elliptical hollow sections

AbstractIn the framework of the RFCS project HOLLOSSTAB, a new design method for determining the resistance of hollow section members has been developed. This method links a generalized slenderness, calculated under the effect of the combined loading, to the resistance of the cross‐section and of the member. This so‐called “Generalized Slenderness‐based Resistance Method” (GSRM) has been shown to provide accurate predictions of experimentally and numerically determined resistances of hollow sections. Nonetheless, the real benefit of this new design method could only be evaluated after a conscientiously performed reliability analysis that is presented in this paper. First, the statistical data of the input variables (cross‐section dimensions, material law) obtained through measurements are presented and compared to the assumptions of Annex E of EN 1993‐1‐1:2020. Then, the reliability analysis is outlined. In particular, attention is given to specific problems resulting from the fact that several basic parameters of GSRM have to be determined numerically (for example the critical loads under combined loading). In addition, the sensitivity of the resulting partial factors to assumptions concerning the statistical distribution of the input variables is studied and discussed.

Cross‐sectional behaviour and design of ferritic and duplex stainless steel EHS in compression

AbstractThis paper describes an investigation into the cross‐sectional behaviour of elliptical hollow section (EHS) columns made from ferritic and duplex stainless steel. The EHS is a relatively new structural shape with a number of favourable attributes including aesthetic appeal, high strength‐to‐weight ratio, good torsional resistance and excellent flexural strength. In recent years there have been significant developments in the analysis and understanding of these shapes, although most studies have focused on carbon steel EHS. The work so far is taken a step further here by considering some of the newer grades of stainless steel that are used in structural applications. A numerical model is developed and validated against test data from the literature and is then employed to generate structural performance data. Subsequently, parametric studies are performed to investigate the influence of individual parameters such as the material properties, aspect ratio and local slenderness of cross‐sectional elements. The accuracy of existing design procedures is assessed by comparing the numerical data with the resistances obtained using Eurocode 3. It is shown that the cross‐sectional slenderness limits given in Eurocode 3 for EHS members made from carbon steel can also be safely used for sections made from ferritic and duplex stainless steel.