Search

The application of design by finite element analysis (FEA) is becoming increasingly prevalent in applied engineering; however, codified provisions remain scarce. The vision of CEN/TC 250/SC 3 was to develop a new comprehensive document based on the existing provisions currently distributed throughout the different Eurocode 3 parts, and with extension where necessary to cover all fields of structural steel design. Within the development process, two documents are being prepared: (i) the code, prEN 1993‐1‐14 and (ii) a Technical Report. The new code aims to provide rules on the use of finite element analysis and other numerical methods for verifying ultimate limit states, serviceability limit states and fatigue. In parallel, the Technical Report will provide background information and explanations of all aspects of the code, as well as benchmark cases and design examples to support the correct application of the prEN1993‐1‐14 design rules and the necessary benchmarking required for model validation. The assumed stakeholders are mainly designers who can find direct guidance for design by finite element analysis in daily engineering practice. This current paper gives an overview of the new code and accompanying Technical Report, as well as the development process and harmonisation within the current Eurocode 3 framework. [ABSTRACT FROM AUTHOR]

In the framework of the revision of Eurocode 3, Part 1–1, several amendments have been proposed and accepted in order to improve the rules for the resistance to member buckling. For clarification, a flow chart connecting the global analysis (first or second order), the imperfections and the type of verification has been implemented for ease of use. Since the publication of the standard in 2005, many research projects have been conducted across Europe on this topic and their results have contributed to provide appropriate answers to problems identified in practice. Therefore, the revised code provides new design rules for stability. Important works of calibration have been performed in these different projects to derive appropriate values of the partial factor on the resistance side. For example, a new formulation for lateral–torsional buckling has been introduced for the calculation of the reduction factor. The consequence is a reduction of the discrepancy between the results obtained by these new methods and those from experimental or numerical tests. In order to extend the scope of Eurocode 3, Part 1–1, additional methods have been implemented in an annex to cover the stability of members with mono‐symmetric cross‐section under compression axial force, biaxial bending, with or without torsion. The format of the resistance criteria remains similar to the format of the current interaction formulae so that the designers can easily identify the evolution of the rules. This article presents in a systematic way the new implementations in the formal vote version FprEN 1993‐1‐1 of the code. [ABSTRACT FROM AUTHOR]

In this paper, the flexural‐torsional buckling response of austenitic stainless steel I‐section beam‐columns is investigated. Finite element simulations are performed with the aim of analysing the parameters affecting the behaviour of the studied members. The accuracy and safety of the existing design provisions of the European structural stainless steel design standard EN 1993‐1‐4 (2015) are assessed. A new method providing more accurate ultimate resistance predictions for austenitic stainless steel I‐section beam‐columns undergoing flexural‐torsional buckling is put forward. The higher accuracy, safety and reliability of the proposed design rules relative to EN 1993‐1‐4 (2015) are demonstrated and the new proposals have now been included in the revised Eurocode – prEN 1993‐1‐4 (2021). [ABSTRACT FROM AUTHOR]

Recent disruptive technological advances, including wire arc additive manufacturing (WAAM) and the concept of digital twins, have the potential to fundamentally transform the way in which we design, build and manage structures. WAAM is a method of metal 3D printing that is well suited to the price‐sensitive construction industry and has been used to manufacture the MX3D bridge – the world's first metal 3D printed bridge. The intricate geometry, undulating surface finish and particular material properties rendered the bridge outside the scope of any existing structural design standards; hence, physical testing and advanced numerical modelling were carried out for its safety assessment. The key features of the finite element model of the bridge, and its validation against in‐situ structural tests, are described herein. Subsequent numerical studies undertaken to verify the structural performance of the bridge under various loading scenarios are presented, while the basis for the development of the smart digital twin of the bridge is also introduced. The presented research provides insight into the use of advanced computational simulations for the verification and ongoing assessment of structures produced using new methods of manufacture. [ABSTRACT FROM AUTHOR]

Wire arc additive manufacturing (WAAM) is a method of metal three-dimensional (3D) printing that has the potential for a significant impact on the construction industry due to its ability to produce large parts with reasonable printing times and costs. However, there is currently a lack of fundamental data on the performance of structural elements produced using this method of manufacturing. Seeking to bridge this gap, the compressive behavior and resistance of WAAM square hollow sections (SHS) are investigated in this paper. In a previous study by the authors, testing reported of sheet material produced in the same manner as the studied SHS is first summarized. The production, measurement, and testing of a series of stainless steel SHS stub columns are then described. Regular cross-section profiles were chosen to isolate the influence of 3D printing and enable direct comparisons to be made against equivalent sections produced using traditional methods of manufacturing. A range of cross-section sizes and thicknesses were considered to achieve variations in the local cross-sectional slenderness of the tested specimens, allowing the influence of local buckling to be assessed. Repeat tests enabled the variability in response between specimens to be evaluated; a total of 14 SHS stub columns of seven different local slendernesses was tested, covering all cross-section classes of AISC 370 and Eurocode 3. Advanced noncontact measurement techniques were employed to determine the as-built geometric properties, while digital image correlation measurements were used to provide detailed insight into the deformation characteristics of the test specimens. Owing to the higher geometric variability of WAAM relative to conventional forming processes, the tested 3D printed stub columns were found to exhibit more variable capacities between repeat specimens than is generally displayed by stainless steel SHS. Comparisons of the stub column test results with existing structural design rules highlight the need to allow for the weakening effect of the geometric undulations that are inherent to the WAAM process in order to achieve safe-sided strength predictions. [ABSTRACT FROM AUTHOR]

Structural design rules for prestressed cold-formed steel beams, considering both the prestressing and imposed vertical loading stages, are presented herein. In the proposed approach, the cold-formed steel member is designed as a beam-column using linear interaction equations in conjunction with the Direct Strength Method (DSM), while the prestressed cable is designed by ensuring that its tensile capacity is not violated during the two loading stages. In the present paper, the design approach and the failure criteria, which define the permissible design zone for the prestressed system, are first introduced. The suitability of the design recommendations is then assessed by comparing a set of parametric finite element (FE) results for several combinations of prestress levels, beam geometries and cable sizes, with the corresponding design predictions. Finally, following reliability analysis, the implementation of the design recommendations is illustrated through a practical worked example. • Design recommendations for prestressed cold-formed steel beams developed. • Linear interaction equations in conjunction with the Direct Strength Method utilised. • Capacities of cold-formed steel beam and cable to be checked for both loading stages. • Design rules assessment through comparisons with parametric finite element results. • Implementation of design rules illustrated through a practical worked example. [ABSTRACT FROM AUTHOR]

This paper reports the second part of the study on the structural behaviour of stainless steel circular hollow sections subjected to combined axial load and bending moment. A series of numerical parametric studies is presented, using the validated finite element (FE) models from the companion paper, with the aim of generating further structural performance data over a wider range of stainless steel grades, cross-section slendernesses and combinations of loading. The considered parameters include the outer cross-section diameter, the ratio of outer cross-section diameter to thickness and the initial loading eccentricity. Both the experimentally and numerically derived section capacities were compared with the strength predictions determined from the current European code, the American specification and the Australian/New Zealand standard, allowing the applicability of each codified method to be assessed. The comparisons revealed that the current design standards generally result in unduly conservative and scattered strength predictions for stainless steel circular hollow sections under combined loading, which can be primarily attributed to the neglect of strain hardening in the determination of cross-section resistances and to the use of linear interaction formulae. To overcome these shortcomings, improved design rules are proposed through extension of the deformation-based continuous strength method (CSM) to the case of circular hollow sections subjected to combined loading. Comparisons between the proposals and the test and FE results indicate a high level of accuracy and consistency in the predictions. The reliability of the proposed approach was confirmed by means of statistical analyses according to EN 1990. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive experimental and numerical study of the global stability of stainless steel circular hollow section (CHS) structural members subjected to combined axial load and bending moment. The experimental investigation, which was carried out on two grade 1.4301 austenitic stainless steel cross-section sizes (CHS 60.5 × 2.8 and CHS 76.3 × 3), included material coupon tests, initial geometric measurements, two column tests, and ten beam–column tests. The test results were employed in a parallel numerical simulation programme for the validation of finite element (FE) models, by means of which a series of parametric studies were carried out to extend the available results over a wider range of cross-section sizes, member lengths and loading combinations. The experimentally and numerically derived data were used to assess the structural performance of CHS beam–columns and to determine the accuracy of the current design provisions given in the European code, American specification, Australian/New Zealand standard, and other recent proposed approaches. Generally, all the existing design methods were shown to yield a high degree of scatter in the prediction of beam–column strength, with both conservative and over-predicted capacities. The scatter was attributed mainly to inaccurate predictions of the column buckling and bending end points of the design beam–column interaction curves (i.e. member strengths under pure compression and pure bending, respectively) and inaccurate interaction factors. The development of improved provisions for the design of stainless steel circular hollow section beam–columns is currently underway. [ABSTRACT FROM AUTHOR]

Experimental and numerical studies of ferritic stainless steel beam-columns have been carried out and are described in this paper. Two cross-section sizes were considered in the physical testing: square hollow section (SHS) 60 × 60 × 3 and rectangular hollow section (RHS) 100 × 40 × 2, both of grade EN 1.4003 stainless steel. The experimental programme comprised material tensile coupon tests, geometric imperfection measurements, four stub column tests, two four-point bending tests, two axially-loaded column tests and ten beam-column tests. The initial eccentricities for the beam-column tests were varied to provide a wide range of bending moment-to-axial load ratios. All the test results were then employed for the validation of finite element (FE) models, by means of which a series of parametric studies was conducted to generate further structural performance data. The obtained test and FE results were utilized to evaluate the accuracy of the capacity predictions according to the current European code, American specification and Australian/New Zealand Standard, together with other recent proposals, for the design of stainless steel beam-columns. Overall, the Australian/New Zealand Standard was found to offer the most suitable design provisions, though further improvements remain possible. [ABSTRACT FROM AUTHOR]

The aims of this study are to generate experimental data and develop numerical models for aluminum alloy continuous beams, and to utilize the results to underpin the development of revised design methods for indeterminate structures. This paper presents an experimental program and finite-element (FE) analyses for two-span continuous beams (i.e., five-point bending) of square and rectangular hollow sections (SHSs and RHSs). The experimental program comprised 27 five-point bending tests with three different positioning of loads. The testing procedures and key results are reported. The test specimens were manufactured by extrusion, with 18 of grade 6061-T6 and 9 of grade 6063- T5 heat-treated aluminum alloys. The test specimens were nonslender sections, and mostly of Class 1 proportions. Generally, the specimens failed by the formation of a collapse mechanism comprising three plastic hinges. The distances between the supports and the loading points were varied in order to form the first plastic hinge in different locations, to achieve different load levels between the first hinge and collapse, and to change the rotation demands on the first hinge that formed. The FE models were developed and failure was defined as either when a plastic collapse mechanism was formed or the material fracture strain was reached on the tension flange, whichever occurred first. The numerical models were first validated against the experimentally obtained load-deflection responses, as well as the failure modes. The experimental and FE ultimate loads were both found to be beyond the theoretical loads corresponding to the formation of the first hinge as well as the calculated plastic collapse loads. A key characteristic of aluminum alloy, strain hardening, is shown to be particularly significant in both the experimental program and the numerical investigation. The validated FE models are used to generate numerical results through parametric studies in the companion paper. The development of design rules for indeterminate aluminum alloy structural systems is then described. [ABSTRACT FROM AUTHOR]

Aluminum alloys are employed in a range of structural engineering applications, supported by many international design standards, but plastic design methods are generally not permitted. In the second part of this study, an extensive numerical parametric study is conducted to assess the effect of key parameters, such as cross section slenderness, cross section aspect ratio, and moment gradient on the strength, strain hardening, and moment redistribution behavior of aluminum alloy continuous beams. The key input parameters and findings are reported herein. Based on both the experimental and parametric numerical results, the design provisions of the American, Australian/New Zealand, and European specifications as well as the traditional plastic design method, the plastic hinge method, and the continuous strength method (CSM) for indeterminate structures, the scope of which is extended in the present study, have been evaluated. The design strengths predicted by the three specifications were found to be rather conservative, while the predications of the latter three methods are more precise and consistent. The results reveal that strain hardening at the cross-sectional level and moment redistribution at the global system level have significant influence on the performance of stocky (plastic and compact sections) aluminum alloy members, which should be accounted for in design. Following reliability analysis, proposals are made for revised design provisions. [ABSTRACT FROM AUTHOR]

Abstract: General design procedures for prestressed stayed columns with a single cross-arm system are presented. The accuracy of the proposed design expressions is confirmed by comparison with the results of physical experiments and validated finite element simulations. Reliability is assessed by following the approach set out in Annex D of EN 1990. The presented resistance expressions for prestressed stayed columns are a function of the system geometry, the level of initial prestress in the cables and the global imperfection level. Worked examples are also presented to illustrate the application of the developed design approach. [Copyright &y& Elsevier]

The present generation of international structural steel design codes treats material nonlinearity through simplified elastic-plastic or rigid-plastic material models. However, the actual stress-strain response of structural steel is more complex than this and features, in particular, strain hardening. Strain hardening refers to the increase in strength beyond yield because of plastic deformation. The influence of strain hardening on the behavior and design of steel structures is examined in this study through both the experimentation and the analysis of existing data, and a method to exploit the additional capacity that arises is outlined. Both determinate and indeterminate structures are considered. The proposed design method, referred to as the continuous strength method (CSM), is a deformation-based design approach employing a continuous relationship between cross-sectional slenderness and cross-sectional deformation capacity, together with a material model that allows for strain hardening. Comparisons are made between test results generated as part of the present study and collected from existing studies, and the predictions from the CSM and Eurocode 3 (EC3). For all cases considered, the CSM, through a rational exploitation of strain hardening, offers a more accurate prediction of observed physical behavior. [ABSTRACT FROM AUTHOR]

Following the introduction of hot-finished elliptical hollow sections to the construction industry, recent research has been performed to develop supporting structural design guidance. This paper focuses on shear resistance. Twenty-four shear tests were performed on hot-finished steel elliptical hollow section members. The shear tests were arranged in a three-point bending configuration with span-to-depth ratios ranging from 1 to 8. This enabled the study of cross-section resistance in shear and the interaction between shear and bending. Measurements were taken of cross-section geometry, local initial geometric imperfections and material properties in tension. Test results, including moment--rotation histories, are presented. Additional results were generated numerically. These results have been used to verify proposed design expressions for shear resistance and resistance to combined shear and bending. Further investigations into design criteria for shear buckling are currently under way. [ABSTRACT FROM AUTHOR]

In this paper, the in-plane behaviour and design of duplex and ferritic stainless steel welded I-section beam–columns fabricated through the welding of individual hot-rolled stainless steel plates are explored. Finite element models able to replicate the structural response of stainless steel I-section members are created and validated against experimental results from the literature. Using the validated finite element models, extensive numerical parametric studies are performed, the results of which are utilised to investigate the accuracy and reliability of existing design provisions for duplex and ferritic stainless steel I-section beam–columns. Scope for improvement is revealed, prompting the development of new beam–column design rules that are compatible with those provided for carbon steel members in EN 1993-1-1. The new proposals are shown to offer improved accuracy and consistency over existing design provisions for duplex and ferritic stainless steel I-section members under combined axial compression and bending, and are recommended for inclusion in the upcoming revision to EN 1993-1-4. The reliability of the proposed design rules, with a partial safety factor γ M 1 = 1. 1 , is demonstrated. • Behaviour and design of duplex and ferritic stainless steel welded I-section beam–columns are investigated. • Finite element models able to mimic the behaviour of stainless steel beam–columns are developed. • Accuracy of existing beam–column design methods is investigated. • New design rules for duplex and ferritic stainless steel welded I-section beam–columns are proposed. • Proposed beam–column design rules lead to more accurate results relative to the existing design methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the behaviour and design of axially loaded concrete filled stainless steel circular and square hollow sections. The experimental investigation was conducted using different concrete cube strengths varied from 30 to 100 MPa. The column strengths and load-axial shortening curves were evaluated. The study is limited to cross-section capacity and has not been validated at member level. Comparisons of the tests results together with other available results from the literature have been made with existing design methods for composite carbon steel sections — Eurocode 4 and ACI. It was found that existing design guidance for carbon steel may generally be safely applied to concrete filled stainless steel tubes, though it tends to be over-conservative. A continuous strength method is proposed and it is found to provide the most accurate and consistent prediction of the axial capacity of the composite concrete filled stainless steel hollow sections due largely to the more precise assessment of the contribution of the stainless steel tube to the composite resistance. [Copyright &y& Elsevier]

Abstract: A conceptually new structural design approach has recently been proposed by the authors to predict the resistance of stainless steel members subjected to various types of loading with cross-sections formed from thin flat plates including angles, channels, lipped channels, I-sections and rectangular hollow sections (RHS). The proposed method does not follow the traditional cross-section classification approach, which primarily relies on the assumption of a bilinear, elastic–perfectly-plastic material model. Instead, deformation capacity of a cross-section is determined directly from the local buckling characteristics of the constituent plate elements. This is then used to obtain the corresponding local buckling stress utilising an appropriate material model. This basic concept is extended herein to predict compression resistance of stainless steel columns with circular hollow sections (CHS). Available test and finite element (FE) results have been used to develop the basic design equation to predict the compression resistance of cross-sections and to propose column curves to determine flexural buckling resistances. The predicted resistances have been compared to those obtained using the current Eurocode; the predictions are significantly more accurate and more consistent than those given by the existing Eurocode. [Copyright &y& Elsevier]

Stainless steel structural sections possess several features that result in a significantly different response to that of equivalent carbon steel sections. To date these features have not been fully recognized in design codes, which have largely adapted rules devised for carbon steel in a rather simplistic fashion. Recently, a new approach for dealing with local buckling and the associated loss of effectiveness that does not utilize the concepts of either cross-sectional classification or effective cross-sectional properties has been developed for stainless steel and has also been applied to other nonlinear metallic materials. The method is based directly on the deformation capacities of cross sections and covers the behavior of stainless steel members subjected to flexural buckling and combined axial load plus bending. The proposed method has been verified using test results and its performance has been compared against the existing ASCE and Eurocode design guidance for structural stainless steel. Significantly improved and more consistent predictions have been obtained using the proposed method without any extra calculation effort. [ABSTRACT FROM AUTHOR]

The influence of yield strength on the in-plane stability and design of structural steel square and rectangular hollow section (SHS and RHS) beam-columns under compression plus uniform bending is investigated in this study. Ten buckling tests were carried out on hot-finished S690 SHS 100×100×4 (in mm) specimens under combined compression plus uniaxial bending. Finite element (FE) models of SHS and RHS beam-columns were established, validated and employed to perform parametric studies, where supplementary buckling resistance data were numerically derived. Through comparisons with the test and FE data, shortcomings of the current EC3 beam-column interaction curves were revealed, particularly in the higher yield strength domain. A modified EC3 approach was developed accordingly, featuring more accurate compression end points and re-calibrated interaction factors, and was shown to significantly improve the design accuracy and consistency for both hot-finished and cold-formed SHS and RHS beam-columns over a wide spectrum of steel grades. Subsequent reliability analysis confirmed the applicability of the current EC3 partial safety factor to the proposed modified EC3 design approach. [Display omitted] • Ten hot-finished S690 square hollow section beam-columns were tested. • Finite element modelling of SHS and RHS beam-columns was carried out. • Current EC3 design rules for SHS and RHS beam-columns were assessed. • Modifications were proposed to improve the accuracy of EC3 interaction curves. • Reliability of the new design proposals was confirmed through statistical analysis. [ABSTRACT FROM AUTHOR]

Steel framed structures are affected, to greater or lesser extent, by (i) geometrical nonlinearity associated with the change in geometry of the structure under load and (ii) material nonlinearity related to the onset and spread of plasticity. In traditional design approaches, the design forces and moments within structural members are usually determined from simplified structural analyses (e.g. first or second-order elastic analysis), after which member design checks are performed to assess the strength and stability of the individual members. The extent to which the strength and deformation capacity of cross-sections is affected by local buckling is typically assessed through the concept of cross-section classification. For example, only compact (Class 1) cross-sections are considered to possess sufficient rotation capacity for plastic hinges to develop and for inelastic analysis methods to be used. This approach results in step-wise capacity predictions and is considered to be overly simplistic. Since the structural analysis of steel framed structures is typically performed using beam finite elements, which are unable to explicitly capture local buckling, a more sophisticated treatment of the available deformation capacity is required if inelastic analysis methods are to be used for all cross-section classes. A novel method of design by advanced inelastic analysis has recently been developed (Gardner et al., 2019a; Fieber et al., 2019a, 2018a, 2018b 1–4), in which strain limits are employed to represent the effects of local buckling in beam finite element models and thereby control the spread of plasticity and level of force/moment redistribution within a structure. It is thus possible to use a consistent advanced analysis framework to design structures composed of cross-sections of any class. In the present paper, application of the proposed design method to continuous beams and planar frames is illustrated and assessed. Ultimate load capacity predictions are compared against results obtained from benchmark shell finite element models that explicitly capture local buckling and to conventional steel design. It is found that the proposed method predicts safe-sided ultimate capacities that are consistently more accurate than current design methods, particularly for structures benefiting from strain hardening and for structures composed of non-compact cross-sections where inelastic redistribution is typically ignored. • Novel method for the design of steel structures using advanced analysis with strain limits is presented. • Capacity predictions compared against benchmark shell FE models for continuous beams and frames with I-section, SHS/RHS profiles. • Cross-section slenderness dependent levels of force/moment redistribution and effect of local moment gradients are captured. • The proposed design method is consistently more accurate than current EN 1993-1-1 design. [ABSTRACT FROM AUTHOR]

An experimental investigation into the cross-sectional behaviour of hot-finished high strength steel tubular sections, to support the assessment and development of structural design guidance, is presented. Two grades of quenched and tempered high strength steel – S690 and S770 and eight cross-sections – seven square hollow sections (SHS) and one rectangular hollow section (RHS), covering a wide range of local slenderness, were examined. This test programme consisted of twelve tensile coupon tests, five stub column tests and 30 short beam-column tests, with various initial loading eccentricities employed to achieve a spectrum of compression and bending combinations. Local geometric imperfection measurements were carried out on each test specimen using 3D laser-scanning, and a rational approach to analysing the local imperfection distributions using the scanned data was subsequently proposed. Following the experimental study, the current Eurocode 3 cross-section design provisions were evaluated through comparisons with the results from the present research and additional results from the literature. The experimental results and findings from the present study provide a basis for the development of numerical models and the enhancement of existing design methods in the future. • Hot-finished S690 and S770 square and rectangular hollow sections were examined. • Twelve tensile coupons, five stub columns and 30 short beam-columns were tested. • Local geometric imperfections were investigated by means of 3D laser-scanning. • Current Eurocode 3 design provisions were assessed using the experimental data. [ABSTRACT FROM AUTHOR]

• Structural behaviour and design of semi-compact (Class 3) EHS were studied; • Parametric studies were conducted to numerically expand the existing data pool; • New design methods were developed to exploit partial plastification in semi-compact EHS; • Accuracy of both the existing and proposed design methods were assessed; • Reliability of the design proposals was confirmed through statistical analyses. Current structural steel design codes typically feature a step in the cross-sectional resistance functions at the Class 2 slenderness limit due to the abrupt switch between elastic and fully plastic capacities. To address this issue, new design rules, featuring a gradual transition between elastic and plastic resistances, have been recently developed for semi-compact (Class 3) I- and box sections to account for the partial spread of plasticity. This approach is extended herein to the cross-section and member buckling design of semi-compact elliptical hollow sections (EHS). Finite element models were first established and validated against previous test results; particular attention was given to the modelling of local geometric imperfections. Parametric studies were then conducted, where over 4000 structural performance data were numerically generated covering a wide range of cross-section aspect ratios, material properties, local and global slendernesses and load combinations. Upon completion of the numerical simulation programme, structural design rules of semi-compact EHS were developed. The classification of EHS under biaxial bending and compression plus biaxial bending was initially addressed. Following this, new design expressions featuring elasto-plastic section properties were developed to exploit partial plastification at both cross-section and member buckling levels. The accuracy of the design proposals was evaluated through comparisons between the test/numerical data and the resistance predictions; the comparisons revealed that the proposed elasto-plastic cross-section and member buckling design rules lead to both improved accuracy and consistency over the existing elastic provisions. The reliability of the proposals was verified through statistical analyses in accordance with EN 1990, demonstrating their suitability for incorporation into the next revision to EN 1993-1-1. [ABSTRACT FROM AUTHOR]

• Design of steel members using advanced inelastic analysis with strain limits. • Strain limits mimic local buckling and control spread of plasticity in beam FE. • Capacity predictions were compared against 6188 benchmark shell finite element models. • Proposed design method is consistently more accurate than current EN 1993-1-1 design. Structural steel design is traditionally a two step process: first, the internal forces and moments in the structure are determined from a structural analysis. Then, a series of design checks are carried out to assess the strength and stability of individual members. The structural analysis is typically performed using beam finite elements, which are usually not able to capture local buckling explicitly. Instead, the assessment of local buckling and rotation capacity is made through the concept of cross-section classification, which places class-specific restrictions on the analysis type (i.e. plastic or elastic) and defines the cross-section resistance based on idealised stress distributions (e.g. the plastic, elastic or effective moment capacity in bending). This approach is however considered to be overly simplistic and creates artificial steps in the capacity predictions of structural members. A more consistent approach is proposed herein, whereby a second-order inelastic analysis of the structure or structural component is performed using beam finite elements, and strain limits are employed to mimic the effects of local buckling, control the spread of plasticity and ultimately define the structural resistance. The strain limits are obtained from the continuous strength method. It is shown that not only can local buckling be accurately represented in members experiencing uniform cross-sectional deformations along the length, but, by applying the strain limits to strains that are averaged over a defined characteristic length, the beneficial effects of local moment gradients can also be exploited. The proposed method is assessed against benchmark shell finite element results on isolated members subjected to bending, compression and combined loading. Compared to conventional steel design provisions and even to existing advanced design approaches utilising second-order elastic analysis, the proposed design approach provides consistently more accurate capacity predictions. [ABSTRACT FROM AUTHOR]

A comprehensive experimental and numerical study of concrete-filled double skin tubular (CFDST) stub columns is presented in this paper. A total of 23 tests was carried out on CFDST specimens with austenitic stainless steel circular hollow section (CHS) outer tubes, high strength steel CHS inner tubes, and three different grades of concrete infill (C40, C80 and C120). The ultimate load, load-deflection histories and failure modes of the stub columns are reported. The test results were employed in a parallel numerical simulation programme for the validation of the finite element (FE) model, by means of which an extensive parametric study was undertaken to extend the available results over a wide range of cross-section slendernesses, inner tube strengths and concrete grades. The experimentally and numerically derived data were then employed to assess the applicability of the existing European, Australian and North American design provisions for composite carbon steel members to the design of the studied CFDST cross-sections. Overall, the existing design rules are shown to provide generally safe-sided (less so for the higher concrete grades) but rather scattered capacity predictions. Use of an effective concrete strength is recommended for the higher concrete grades and shown to improve the consistency of the design capacity predictions. • Tests and numerical analysis were conducted on concrete-filled double skin sections. • Structural behaviour of stub columns was studied. • The applicability of the existing design provisions was assessed. • Use of an effective concrete strength is recommended for the higher concrete grades. • Modification to existing design rules shown the improvement on the design capacity predictions. [ABSTRACT FROM AUTHOR]

In current structural stainless steel design codes, local buckling is accounted for through a cross-section classification framework, which is based on an elastic, perfectly-plastic material model, providing consistency with the corresponding treatment of carbon steel cross-sections. Hence, for non-slender cross-sections, the codified design stress is limited to the 0.2% proof stress without considering the pronounced strain hardening exhibited by stainless steels, while for slender cross-sections, the effective width method is employed without considering the beneficial effect of element interaction. Previous comparisons between test results and codified predictions have generally indicated over-conservatism and scatter. This has prompted the development of more efficient design rules, which can reflect better the actual local buckling behaviour and nonlinear material response of stainless steel cross-sections. A deformation-based design approach called the continuous strength method (CSM) has been proposed for the design of stocky cross-sections, which relates the strength of a cross-section to its deformation capacity and employs a bi-linear (elastic, linear hardening) material model to account for strain hardening. In this paper, the scope of the CSM is extended to cover the design of slender stainless steel cross-sections under compression, bending and combined loading, underpinned by and validated against 794 experimental and numerical results. The proposed approach allows for the beneficial effect of element interaction within the cross-section, and is shown to yield a higher level of accuracy and consistency, as well as design efficiency, in the capacity predictions of slender stainless steel cross-sections, compared to the effective width methods employed in the current international design standards. Non-doubly symmetric sections in bending, which may be slender, but still benefit from strain hardening, are also discussed. The reliability of the CSM proposal has been confirmed by means of statistical analyses according to EN 1990, demonstrating its suitability for incorporation into future revisions of international design codes for stainless steel structures. [ABSTRACT FROM AUTHOR]

• Existing stress–strain models for conventional structural steels are reviewed. • Constitutive models are proposed to represent stress–strain curves of WAAM steels. • Over 600 experimental stress–strain curves on WAAM steels are collected and analysed. • Predictive expressions or values for the required input parameters are developed. • Accuracy of model demonstrated through comparisons with measured stress–strain curves. Interest in the use of wire arc additive manufacturing (WAAM) in construction has increased rapidly in recent years. Key to facilitating wider application is an improved understanding of the material behaviour. In particular, with structural design by finite element analysis in mind, constitutive models to describe the full range stress-strain response of WAAM steels are needed; development of such models is the focus of the present study. WAAM normal-strength steels generally exhibit a stress-strain response featuring a well-defined yield point, a yield plateau (for machined material) or slightly inclined yield plateau (for as-built material) and subsequent strain hardening, while the stress-strain response of WAAM high-strength steels is typically rounded, with no distinct yield point or plateau. This behaviour is similar to that of conventionally-produced steels, and hence can be represented analytically using existing material models, but with suitable modifications — a quad-linear or bilinear plus nonlinear hardening model and a two-stage Ramberg-Osgood model are proposed for WAAM normal- and high-strength steels, respectively. Predictive expressions or standardised values for the input parameters required in the models are developed and calibrated against a comprehensive database of WAAM steel coupon test results collected from the literature. The experimental database comprises over 600 engineering stress-strain curves and covers different feedstock wires, surface finishes (i.e. machined and as-built), material thicknesses, directions of testing and printing strategies. The proposed material models are shown to accurately predict the full stress-strain curves of WAAM steels, and are considered to be suitable for incorporation into analytical, numerical and design models for WAAM steel structures. [ABSTRACT FROM AUTHOR]

• Fourteen WAAM stainless steel tubular beams were tested in four-point bending. • 3D laser scanning and silicon casting were used to determine the specimen geometries. • Digital image correlation (DIC) was employed to monitor the deformation responses. • Test results were compared against conventional stainless steel tubular beams. • Applicability of design provisions in EN 1994–1-4, AISC 370 and CSM was assessed. Wire arc additive manufacturing (WAAM) is a promising metal 3D printing technique in the construction industry for its ability to produce large and complex-shaped elements, with reasonable printing accuracy, time and costs. There is currently, however, a lack of fundamental test data on the structural performance of WAAM elements. To address this, an experimental study into the cross-sectional behaviour of WAAM tubular beams has been conducted and is presented herein. A total of 14 stainless steel square, rectangular and irregular hollow sections, spanning over all cross-section classes of EN 1993-1-4 and AISC 370, were tested in four-point bending. 3D laser scanning, silicone casting and Archimedes' measurements were employed to collectively determine the as-built geometry and local geometric imperfections of the test specimens, while digital image correlation (DIC) was used to monitor the deformation responses of the specimens during testing. The full moment–curvature histories and key experimental results are presented and discussed. Similar cross-sectional behaviour to that of equivalent, conventionally manufactured sections was observed, with the more slender cross-sections showing increased susceptibility to local buckling. However, owing to the inherent geometric variability of WAAM, the tested 3D printed beams exhibited more variable flexural capacities between the repeat specimens than is generally displayed by conventionally produced stainless steel sections. Finally, the test results were used to assess the applicability of current cross-section design provisions in the European (EN 1993-1-4) and American (AISC 370) structural design specifications, as well as the continuous strength method (CSM), to WAAM stainless steel tubular beams. [ABSTRACT FROM AUTHOR]

Aluminium alloys are nonlinear metallic materials with rounded stress–strain curves that are not well represented by the simplified elastic-perfectly plastic material model used in most existing design specifications. Departing from current practice, the continuous strength method (CSM) is a recently developed design approach for aluminium alloy structures, which gives consideration to strain hardening for non-slender sections. The CSM is a deformation-based method and employs a base curve to define the continuous relationship between cross-section slenderness and deformation capacity. This paper explains the background and the two key components of the CSM: (1) the base curve, which is extended herein such that the method covers both non-slender and slender sections and (2) the strain hardening material model. Three international design specifications from America, Australia/New Zealand and Europe, as well as the CSM are compared with approximately 900 aluminium alloy experimental and numerical results. Reliability analyses have been carried out to assess the reliability level of different design methods according to both the American Institute of Steel Construction (AISC) and European Standard (EN 1990) approaches. Finally, worked examples of the CSM for aluminium alloy stub columns and continuous beams are illustrated in this paper. [ABSTRACT FROM AUTHOR]

Tubular profiles, such as square and rectangular hollow sections (SHS and RHS) are widely used in a range of structural engineering applications. Their thin-walled nature means that local buckling is a key design concern, which is usually addressed by adhering to specified slenderness limits. An alternative approach is to employ local plate stiffeners, which can be practically achieved in extruded aluminium alloy sections through the introduction of internal cross stiffeners. The flexural behaviour and design of aluminium alloy SHS and RHS with internal stiffeners is the subject of investigation of the present paper. The primary aims of the study are to generate experimental and numerical data for these new types of cross-section in bending, as well as to assess the applicability of different approaches to their design at cross-sectional and system levels. First, an experimental investigation was performed on aluminium alloy SHS and RHS beams with internal stiffeners subjected to three-point bending, four-point bending and five-point bending (i.e. continuous beams over three supports) of three different configurations. Finite element (FE) models were also developed and validated against the presented test data. Once validated, the models were employed to generate additional structural performance data through numerical parametric studies. Comparisons are then made between the experimental/numerical capacities and the design capacities predicted using a series of international design specifications for aluminium alloy structures, as well as the continuous strength method (CSM). The design strengths predicted by the American and Australian/New Zealand specifications were found to be conservative, while improved predictions are achieved by Eurocode 9. The most accurate and consistent predictions are obtained using the CSM, which was able to capture the significant observed strain hardening at the cross-sectional level and moment redistribution at the global system level. [ABSTRACT FROM AUTHOR]

In parallel with the experimental study described in the companion paper (Zhao et al., submitted for publication), a numerical modelling programme has been carried out to investigate further the structural behaviour of stainless steel cross-sections under combined loading. The numerical models, which were developed using the finite element (FE) package ABAQUS, were initially validated against the experiments, showing the capability of the FE models to replicate the key test results, the full experimental load–deformation histories and the observed local buckling failure modes. Upon validation of the FE models, parametric studies were conducted to generate additional structural performance data over a wide range of cross-section slenderness and combinations of loading. The experimental and numerical results were then compared with the design capacity predictions from the current European Standard EN 1993-1-4 (2006) and American Specification SEI/ASCE-8 (2002) for stainless steel structures. The comparisons revealed that the current design standards can significantly under-estimate the resistance of stainless steel cross-sections subjected to combined loading; this under-prediction of capacity can be primarily attributed to the lack of consideration of strain hardening of the material under load. The Continuous Strength Method (CSM) is a deformation-based design approach that accounts for strain hardening and has been shown to provide accurate predictions of cross-sectional resistance under compression and bending, acting in isolation. In the present paper, proposals are made to extend the scope of the CSM to the case of combined loading. Comparisons between the CSM design proposals and the test and FE results indicated a high level of accuracy and consistency in the predictions. The reliability of the proposals was confirmed by means of statistical analyses according to EN 1990 (2002). [ABSTRACT FROM AUTHOR]

Two series of simply supported bending tests on aluminium alloy square and rectangular hollow sections have been performed. The test program comprised 14 three-point bending tests and 15 four-point bending tests. The test specimens were fabricated by extrusion from grades 6061-T6 and 6063-T5 heat-treated aluminium alloys, with width-to-thickness ratios ranging from 2.8 to 20.5. Measured geometric and material properties, together with the full load–deflection histories from the test specimens, were reported. Observed failure modes included local buckling, material yielding and tensile fracture. Further experimental data were gathered from the literature. Finite element (FE) models were developed and validated against the test results, and then used to perform parametric studies, in which a total of 132 numerical results were generated. The experimental and numerical results were used to evaluate the bending resistance provisions of the American [1], Australian/New Zealand [2] and European [3] Specifications, as well as the continuous strength method (CSM). The moment capacities predicted by the three design specifications were found to be generally conservative, while the CSM provided more accurate and more consistent predictions due to the recognition and systematic exploitation of strain hardening. [ABSTRACT FROM AUTHOR]

The structural behaviour and design of cold-formed steel square and rectangular hollow section (SHS and RHS) beam–columns, made of both normal and high strength steels, are investigated in the present study through a comprehensive numerical modelling programme. Refined finite element (FE) models were first established and calibrated against a collection of existing cold-formed steel member test results from the literature. Following this, an extensive parametric study was undertaken to expand the cold-formed steel beam–column data pool, covering a wider range of steel grades, cross-section geometries, member slendernesses and loading combinations. Results from the parametric study were then used to examine the accuracy of the current codified beam–column design methods, provided in the European Standards EN 1993-1-1 (2005) and EN 1993-1-12 (2007) as well as the American Specification AISC 360-16 (2016). The comparisons revealed that the codified design rules provide varying levels of accuracy in predicting the ultimate resistances of cold-formed steel beam–columns depending on the steel grade. An improved design approach, compatible with current codified design rules in EN 1993-1-1 (2005), is proposed that features (1) recently developed column buckling curves that reflect the increasing normalised column buckling resistance with increasing steel yield strength; (2) bending moment resistances calculated using the Continuous Strength Method (CSM) and (3) new interaction curves for cold-formed steel beam–columns, which are anchored to these more accurate end points. The newly proposed design approach is shown to yield more accurate and consistent resistance predictions over current design provisions for cold-formed steel SHS and RHS beam–columns made of different steel grades, and its reliability has also been statistically verified in accordance with EN 1990. • Numerical study on cold-formed steel SHS and RHS beam–columns was conducted. • Modified EC3 column design approach was extended to columns in steel grades up to S1100. • Bending resistance predictions from CSM were adopted in beam–column design. • New beam–column design approach was developed to account for influence of steel grade. • Current EC3 partial safety factor was shown to be applicable to design proposal. [ABSTRACT FROM AUTHOR]

In current structural steel design specifications, the local buckling of cross-sections is typically treated on an element-by-element basis, with the boundary conditions along the adjoined longitudinal edges of the individual plates assumed to be simply-supported. In reality, cross-sections buckle locally as a whole and the individual plate elements interact. As a result, the boundary conditions along the adjoined longitudinal edges of the critical isolated plate (i.e. that with the lowest elastic local buckling stress) lie between lower and upper bounds of simply-supported and fixed, respectively. Based on this concept, explicit formulae to predict the elastic local buckling stress of full cross-sections of common profiles, including I-sections, have recently been developed (Gardner et al., 2019) [1]. In the present paper, the formulae for single I-sections set out in Gardner et al. (2019) [1] are extended to cover the case of three-flanged cross-sections that arise in longitudinally-stiffened plate girders and in the haunch and apex regions of portal frames. The geometry and loading of the studied cross-sections are assumed to remain constant along the member length, i.e. the influence of tapering and moment gradients on local buckling are not considered herein, but has been evaluated in parallel work (Quan et al., 2020) [2]. The proposed formulae are calibrated against results from finite strip analysis performed using CUFSM v4.05 (Li and Schafer, 2010) [3] on a range of three-flanged sections, and provide predictions of elastic local buckling stresses that are typically within 5% of the numerically obtained values. • Elastic local buckling behaviour of three-flanged cross-sections has been investigated. • Formulae for calculating the elastic local buckling stress of three-flanged cross-sections have been developed. • Accuracy of predictions using the developed formulae has been confirmed against results obtained from finite strip analysis. • The predictions using the developed formulae have also been compared with results calculated on an element-by-element basis. [ABSTRACT FROM AUTHOR]

A finite element (FE) investigation into the compressive behaviour of concrete-filled double skin tubular (CFDST) cross-sections with lean duplex and ferritic stainless steel outer tubes is presented. FE models were initially developed and validated against available test results reported in the literature. Upon successful replication of the ultimate capacities, load–deformation histories and failure modes exhibited by the tested CFDST stub columns, a parametric study was undertaken to investigate the influence of key variables, including the local slendernesses of the outer and inner tubes, the concrete strength and the adopted grade of stainless steel, on the ultimate response of the studied CFDST stub columns. Based on the generated FE data pool and the available test results, the applicability of the existing European, Australian and American design provisions for composite carbon steel members to the design of the studied CFDST cross-sections was evaluated. All the examined design rules are shown to yield unduly conservative (less so for the higher concrete grades) and rather scattered capacity predictions. Modifications to the design treatment in relation to the effective area of the outer tubes, to take due account of outward-only local buckling, and the effective compressive strength of the infilled concrete, to reflect the reduced relative effectiveness of higher concrete grades, are considered. The modified design rules are shown to improve the accuracy and consistency of the design capacity predictions. Finally, statistical analyses were carried out to demonstrate the reliability of the modified design approaches. • FE models of concrete-filled double skin sections with stainless steel outer tubes developed. • Parametric studies undertaken on over 300 CFDST specimens. • Applicability of existing design provisions assessed. • Modifications to the existing design rules shown to provide improved capacity predictions. • Reliability of the modified design rules confirmed by means of statistical analyses. [ABSTRACT FROM AUTHOR]

The structural fire response of hot-rolled steel square and rectangular hollow sections (SHS and RHS) under combined compression and bending is investigated in this study through finite element (FE) modelling. The developed FE models were firstly validated against available test results on hot-rolled steel SHS/RHS subjected to combined compression and bending at elevated temperatures. Upon validation, an extensive parametric study was then carried out to examine the resistance of hot-rolled steel SHS/RHS under combined loading at elevated temperatures, covering a wide range of cross-section slendernesses, cross-section aspect ratios, combinations of loading and temperatures up to 800 °C. The numerical data, together with the experimental results, were compared with the strength predictions according to the current structural fire design rules in the European Standard EN 1993-1-2 (2002) and American Specification AISC 360–16 (2016) for hot-rolled steel SHS/RHS under combined loading. The comparisons generally indicated significant disparities in the prediction of resistance of hot-rolled steel SHS/RHS under combined loading at elevated temperatures, owing principally to inaccurate predictions of the end points of the design interaction curves. The deformation-based continuous strength method (CSM) has been shown to provide accurate strength predictions for these end points i.e. the resistances of hot-rolled steel SHS/RHS stub columns and beams at elevated temperatures. In this study, proposals are presented to extend the scope of the CSM to the structural fire design of hot-rolled steel SHS/RHS under combined compression and bending. The CSM proposals are shown to offer improved accuracy and reliability over current design methods and are therefore recommended for incorporation into future revisions of international structural fire design codes. • Numerical models validated against fire test results for SHS/RHS under combined loading. • Validated numerical models used to perform parametric studies considering key parameters. • Current design provisions in EN 1993-1-1 and AISC 360–16 assessed using the experimental and numerical data. • The Continuous Strength Method extended to cover the fire design of SHS/RHS under combined loading. • Reliability of the CSM proposals confirmed by means of statistical analyses. [ABSTRACT FROM AUTHOR]

• Structural performance of S960 UHSS non-slender welded I-sections under combined loading is studied. • FE models are developed and validated against test results and then used to perform parametric studies. • Current design rules are assessed for their applicability to S960 UHSS welded I-sections under combined loading. • A CSM-based design approach is proposed and shown to offer improved design accuracy. The structural performance of S960 ultra-high strength steel non-slender welded I-sections subjected to combined loading is studied in the present paper. Nonlinear finite element (FE) models were first created and validated with reference to test results collected from the literature, and then used for conducting parametric studies to derive numerical data over an extensive spectrum of cross-sectional geometries, aspect ratios, as well as loading combinations. Given the lack of existing design rules for S960 ultra-high strength steel structures, the suitability of the current provisions for lower strength steels given in the European, Australian and American specifications to S960 ultra-high strength steel was assessed based on the generated numerical data. It was found that (i) the European code and Australian standard can accurately predict the strengths of Class 1 and 2 (i.e. compact) S960 ultra-high strength steel welded I-sections subjected to both strong- and weak-axis combined loading, but results generally in conservative strength predictions for Class 3 I-sections, and (ii) the American specification yields accurate strength predictions for S960 ultra-high strength steel welded I-sections subjected to strong-axis combined loading, but leads to conservative strength predictions for weak-axis combined loading. Finally, the continuous strength method (CSM) was applied to the studied S960 ultra-high strength steel non-slender welded I-sections subjected to combined loading and found to offer significantly improved design consistency and accuracy relative to the current codified provisions. The reliability of the latter design method was also confirmed by means of statistical analyses. [ABSTRACT FROM AUTHOR]

• Research studies on mechanical characteristics of aluminium alloys in and after fire are reviewed. • Structural fire behaviour of members, connections, joints and overall systems is discussed. • Passive and active fire protection measures for aluminium alloy structures are presented. • An outlook for the future research in this field is presented. Aluminium alloys are gaining increasing use in the construction industry, underpinned by extensive research and the growing availability of codified structural design rules at room temperature. More recently, considering that the material properties of aluminium alloys degrade significantly at elevated temperatures, a substantial number of studies have also been conducted to investigate the behaviour and design of aluminium alloy structures exposed to fire. This paper presents a review of recent studies on the mechanical characteristics of aluminium alloys in fire and after fire, as well as the structural behaviour of aluminium alloy structures in fire conditions, considering members, connections, joints and overall systems. In addition, possible passive and active fire protection measures for aluminium alloy structures are introduced and discussed. Lastly, recommendations for future work on the structural fire behaviour of aluminium alloy structures are set out, providing insight into aspects that require further investigations to promote the more widespread use of aluminium alloys in structural applications. [ABSTRACT FROM AUTHOR]

With the increasing use of stainless steel elements in construction, the need for comprehensive rules to enable their efficient structural design is clear. To date, the fire behaviour of stainless steel I-section beam–columns has been the subject of relatively little research. In particular, there is an absence of experimental data. To address this gap in knowledge, full-scale anisothermal fire tests on six grade 1.4301 austenitic stainless steel I-section beam–columns have been carried out; the test procedure and results are reported herein. The test specimens were subjected to eccentric axial compression with two eccentricity values so as to achieve different combinations of axial compression and uniform minor axis bending. Complementary initial local and global geometric imperfection measurements, room temperature tensile coupon tests and room temperature beam–column tests were also carried out. Based on the obtained experimental results, together with additional numerical results from a previous study, the existing design rules in the European structural steel fire design standard EN 1993-1-2 and the new design method of Kucukler et al. (2021) for stainless steel beam–columns in fire, which will be incorporated into the next version of EN 1993-1-2, are assessed. • Structural behaviour of stainless steel beam-columns in fire is investigated. • Six fire tests on stainless steel I-section beam-columns are carried out. • Complementary room temperature beam-column tests are also described. • European design method and design recommendations of Kucukler et al. are assessed. [ABSTRACT FROM AUTHOR]

The Continuous Strength Method (CSM) provides accurate resistance predictions for both stocky and slender stainless steel cross-sections; in the case of the former, allowance is made for the beneficial effects of strain hardening, while for the latter, design is simplified by the avoidance of effective width calculations. Although the CSM strain limits can be used in conjunction with advanced analysis for the stability design of members, for hand calculations, the method is currently limited to the determination of cross-sectional resistance only, i.e. member buckling resistance is not covered. To address this limitation, extension of the CSM to the design of stainless steel tubular section columns is presented herein. The proposed approach is based on the traditional Ayrton-Perry formulation, but features enhanced CSM cross-section resistances and a generalized imperfection parameter that is a function of cross-section slenderness. The value of the imperfection parameter increases as the slenderness of the cross-section reduces to compensate for the detrimental effect of plasticity on member stability that is not directly captured in the elastic/first yield Ayrton-Perry approach. The accuracy of the proposed approach is assessed against numerical results generated in the current study and existing experimental results collected from the literature. The presented comparisons show that the CSM provides consistently more accurate member buckling resistance predictions than the current EN 1993-1-4 design rules for all stainless steel grades. The reliability of the proposed approach is demonstrated through statistical analyses performed in accordance with EN 1990. Finally, the paper presents a framework through which the proposed approach can be developed for other cross-section types and materials. • A consistent CSM approach for the design of stainless steel members is presented. • The new approach allows for the influence of material nonlinearity and strain hardening. • The accuracy of the CSM for the design of columns is assessed against experimental and numerical data. • The CSM provides consistently more accurate member buckling resistance predictions than current design rules. • The reliability of the proposed approach is demonstrated through statistical analyses. [ABSTRACT FROM AUTHOR]