Imperial College London


Faculty of EngineeringDepartment of Civil and Environmental Engineering

Professor of Structural Engineering



+44 (0)20 7594 6058leroy.gardner




435Skempton BuildingSouth Kensington Campus





Publication Type

370 results found

Tan QH, Gardner L, Han LH, Song TYet al., 2019, Fire performance of steel reinforced concrete-filled stainless steel tubular (CFSST) columns with square cross-sections, Thin-Walled Structures, Vol: 143, ISSN: 0263-8231

Concrete-filled stainless steel tubular (CFSST) columns combine the advantages of composite action seen in concrete-filled steel tubular (CFST) columns with the durability benefits associated with stainless steel. An effective means of reducing the material usage in the outer stainless steel tube in CFSST columns is to embed an inner carbon steel profile. This enables the material costs to be reduced, while achieving similar load-bearing capacity and durability, as well as enhanced fire resistance. The behaviour of such steel reinforced composite columns, i.e. concrete-filled stainless steel tubular (CFSST) columns with outer square cross-sections and embedded carbon steel profiles, under ISO 834 standard fire conditions is investigated in this study by finite element (FE) analysis. Firstly, FE models are developed and validated against relevant published experimental data on CFSST and steel reinforced CFST columns under fire conditions. Based on the validated FE models, the working mechanisms of the studied steel reinforced CFSST columns under fire conditions are investigated by analysis of the temperature field, failure modes, axial deformation versus time response and internal force distribution. The fire performance of the studied steel reinforced CFSST columns is also evaluated in comparison with CFST and CFSST columns with the same total cross-sectional area of steel or the equivalent cross-sectional load-bearing capacity at ambient temperature. Finally, with respect to fire resistance, the optimal ratio of the cross-sectional areas of the inner carbon steel profile to the outer stainless steel tube is investigated.

Journal article

Kucukler M, Gardner L, 2019, Design of hot-finished tubular steel members using a stiffness reduction method, Journal of Constructional Steel Research, Vol: 160, Pages: 340-358, ISSN: 0143-974X

A stiffness reduction method (SRM) for the design of hot-finished tubular steel members is presented in this paper. Stiffness reduction functions that fully capture the adverse influence of imperfections and plasticity on member stability are developed. The proposed SRM is implemented by (i) reducing the flexural stiffness (EI) of the member using the developed stiffness reduction functions, (ii) performing elastic Linear Buckling Analysis (LBA) and Geometrically Nonlinear Analysis (GNA) of the member with reduced flexural stiffness and (iii) making cross-section strength checks and ensuring that the lowest buckling load amplifier from LBA is greater than or equal to 1.0. Owing to the full allowance for the spread of plasticity, residual stresses and geometrical imperfections through stiffness reduction and instability effects through LBA and GNA, the proposed approach offers an enhanced and more direct assessment of structural behaviour relative to traditional design where structural analysis is accompanied by member design equations, effective lengths and the notional load concept. The proposed method is verified against nonlinear finite element modelling for a large number of tubular steel members. Comparisons of the proposed approach against the methods recommended in the European structural steel design code EN 1993-1-1 for the design of tubular members are also provided.

Journal article

Wang F, Young B, Gardner L, 2019, Compressive testing and numerical modelling of concrete-filled double skin CHS with austenitic stainless steel outer tubes, Thin-Walled Structures, Vol: 141, Pages: 345-359, ISSN: 0263-8231

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.

Journal article

Fieber A, Gardner L, Macorini L, 2019, Formulae for determining elastic local buckling half-wavelengths of structural steel cross-sections, Journal of Constructional Steel Research, Vol: 159, Pages: 493-506, ISSN: 0143-974X

Formulae for determining elastic local buckling half-wavelengths of structural steel I-sections and box sections under compression, bending and combined loading are presented. Knowledge of local buckling half-wavelengths is useful for the direct definition of geometric imperfections in analytical and numerical models, as well as in a recently developed strain-based advanced analysis and design approach (Gardner et al., 2019a, 2019b). The underlying concept is that the cross-section local buckling response is bound by the theoretical behaviour of the isolated cross-section plates with simply-supported and fixed boundary conditions along their adjoined edges. At the isolated plate level, expressions for the half-wavelength buckling coefficient k Lb , which defines the local buckling half-wavelength of a plate as a multiple of its width b, taking into account the effects of the boundary conditions and applied loading, have been developed based on the results of finite strip analysis. At the cross-sectional level, element interaction is accounted for through an interaction coefficient ζ that ranges between 0 and 1, corresponding to the upper (simply-supported) and lower (fixed) bound half-wavelength envelopes of the isolated cross-section plates. The predicted half-wavelengths have been compared against numerical values obtained from finite strip analyses performed on a range of standard European and American hot-rolled I-sections and square/rectangular hollow sections (SHS/RHS), as well as additional welded profiles. The proposed approach is shown to predict the cross-section local buckling half-wavelengths consistently to within 10% of the numerical results.

Journal article

Kyvelou P, Gardner L, Nethercot DA, 2019, Impact statement on “Design of composite cold-formed steel flooring systems”, Structures, Vol: 20, Pages: 213-213, ISSN: 2352-0124

Journal article

Gardner L, 2019, Stability and design of stainless steel structures – Review and outlook, Thin-Walled Structures, Vol: 141, Pages: 208-216, ISSN: 0263-8231

This paper provides a review of recent developments in research and design practice surrounding the structural use of stainless steel, with an emphasis on structural stability. The nonlinear stress-strain characteristics of stainless steel, which are discussed first, give rise to a structural response that differs somewhat from that of structural carbon steel. Depending on the type and proportions of the structural element or system, the nonlinear material response can lead to either a reduced or enhanced capacity relative to an equivalent component featuring an elastic, perfectly plastic material response. In general, in strength governed scenarios, such as the in-plane bending of stocky beams, the substantial strain hardening of stainless steel gives rise to capacity benefits, while in stability governed scenarios, the early onset of stiffness degradation results in reduced capacity. This behaviour is observed at all levels of structural response including at cross-sectional level, member level and frame level, as described in the paper. Current and emerging design approaches that capture this response are also reviewed and evaluated. Lastly, with a view to the future, the application of advanced analysis to the design of stainless steel structures and the use of 3D printing for the construction of stainless steel structures are explored.

Journal article

Kyvelou P, Kyprianou C, Gardner L, Nethercot DAet al., 2019, Challenges and solutions associated with the simulation and design of cold-formed steel structural systems, Thin-Walled Structures, Vol: 141, Pages: 526-539, ISSN: 0263-8231

The treatment of cold-formed steel sections in design codes is very largely restricted to individual members under ideal conditions. More efficient design is possible if the complexities of the structural response caused by the thin plating and complex shapes, together with the actual conditions of load introduction and restraint arising from practical situations can be recognised. Traditionally this has only been possible by resorting to full-scale testing. This is, of course, time consuming and expensive; moreover, the impossibility of covering all variations of all the important problem parameters means that developing a comprehensive understanding of all aspects of the physical behaviour is unlikely. Numerical analysis offers the promise of an alternative approach. However, for this to be reliable there must be confidence that it accurately models the physical situation. For the past decade a programme of research has been underway aimed at the provision of a more complete understanding of the structural behaviour of cold-formed steel sections when employed in particular practical situations. Three such cases are addressed herein: purlins as used in the roofs of industrial buildings, beams used to support floors and columns forming part of a stud wall framing system. In each case the process has been to firstly identify all the important structural components including fastening arrangements, then to develop numerical models using ABAQUS that represent each of these physical features to a sufficient degree of accuracy, then to validate the models by comparison with all available test data, then to conduct parametric studies covering the full range of variables found in practice and, finally, to use the pool of results and the improved insights into behaviour as the basis for improved design approaches that, by more accurately capturing the key physical features, provide better predictions of performance. An important feature of this has been to ensure that the r

Journal article

Kucukler M, Gardner L, 2019, Design of web-tapered steel beams against lateral-torsional buckling through a stiffness reduction method, Engineering Structures, Vol: 190, Pages: 246-261, ISSN: 0141-0296

A stiffness reduction method for the lateral-torsional buckling (LTB) assessment of welded web-tapered steel beams is presented in this study. The method is implemented by (i) modelling a tapered steel beam using elastic beam finite elements specifically developed to represent the elastic instability response of tapered steel members, (ii) reducing the Young's modulus E and shear modulus G of each element through a stiffness reduction function considering the bending moments and cross-section properties at the middle of each element and (iii) performing an elastic Linear Buckling Analysis of the beam with reduced stiffness, referred to as LBA-SR herein. Since the adverse influence of the development of plasticity and imperfections on the ultimate member strengths are fully accounted for through stiffness reduction, the presented method does not require any further global instability assessment using member design equations; thus, the proposed method is both direct and practical. Verification of the method is shown for a wide range of web-tapered steel beams using results from nonlinear shell finite element modelling.

Journal article

dos Santos GB, Gardner L, 2019, Testing and numerical analysis of stainless steel I-sections under concentrated end-one-flange loading, Journal of Constructional Steel Research, Vol: 157, Pages: 271-281, ISSN: 0143-974X

A comprehensive investigation into the structural behaviour of austenitic stainless steel welded I-section beams under concentrated transverse end-one-flange loading is reported herein. Ten physical experiments are first described. The experimental results are then presented in terms of the full load-web shortening responses, ultimate loads, out-of-plane deformation fields and failure modes. An extensive finite element modelling study accounting for geometric, material and contact non-linearities was also performed. After successful model validation against the test results, a parametric investigation was conducted considering a range of bearing lengths, different distances of the bearing load to the member end and web slenderness values. The combined experimental and numerical data set was used to assess current European and North American design provisions for the resistance of stainless steel welded I-sections to concentrated end-one-flange loading. The results show that the current design formulae generally lead to safe-sided but rather scattered and conservative capacity predictions with considerable scope for the development of improved design formulae.

Journal article

McCann F, Gardner L, 2019, Numerical analysis and design of slender elliptical hollow sections in bending, Thin-Walled Structures, Vol: 139, Pages: 196-208, ISSN: 0263-8231

The local buckling behaviour and ultimate cross-sectional resistance of slender tubular elliptical profiles in bending are examined by means of numerical modelling. After successful validation of the numerical model against previous experimental results, a parametric study comprising 240 simulations was conducted in order to investigate the influence of cross-section aspect ratio, axis of bending, geometric imperfections and local slenderness on structural behaviour. The ultimate moments, moment–curvature relationships and failure modes obtained are discussed. It was found that, overall, postbuckling stability increases and imperfection sensitivity decreases with increasing elliptical hollow section (EHS) aspect ratio. A design method is proposed for Class 4 EHS members that reflects the reduction in resistance due to local buckling with increasing slenderness and extends the range of applicability of existing provisions. A reliability analysis was performed in accordance with EN 1990, indicating that the design methods for EHS in bending, in addition to previous design methods for EHS in compression, are suitable for use in the Eurocode framework with a recommended partial factor of unity.

Journal article

Yang L, Zhao M, Gardner L, Ning K, Wang Jet al., 2019, Member stability of stainless steel welded I-section beam-columns, Journal of Constructional Steel Research, Vol: 155, Pages: 33-45, ISSN: 0143-974X

A comprehensive experimental and numerical study is presented into the behaviour of stainless steel welded I-section beams-columns. Twenty test specimens were fabricated from grade 304 (EN 1.4301) austenitic and grade 2205 (EN 1.4406) duplex stainless steel plates – ten were tested under major axis bending plus compression and ten under minor axis bending plus compression. Material tensile coupon tests and geometric imperfection measurements were also conducted. Numerical models were developed, calibrated against the test results and subsequently employed in parametric studies considering a wider range of specimen geometries. Based on the obtained test and numerical results, the accuracy and reliability of existing design rules given in EN 1993-1-4 and AISC DG 27, as well as recent proposals, were assessed.

Journal article

Afshan S, Theofanous M, Wang J, Gkantou M, Gardner Let al., 2019, Testing, numerical simulation and design of prestressed high strength steel arched trusses, Engineering Structures, Vol: 183, Pages: 510-522, ISSN: 0141-0296

The structural behaviour of prestressed high strength steel arched trusses is studied in this paper through experimentation and numerical modelling. Four 11 m span prestressed arched trusses fabricated from S460 hot finished square hollow section members were loaded vertically to failure. Three of the tested trusses were prestressed to different levels by means of a 7-wire strand cable housed within the bottom chord, while the fourth truss contained no cable and served as a control specimen. Each truss was loaded at five points coinciding with joint locations along its span, and the recorded load-deformation responses at each loading point are presented. Inclusion and prestressing of the cable was shown to delay yielding of the bottom chord and enhance the load carrying capacity of the trusses, which ultimately failed by either in-plane or out-of-plane buckling of the top chord. For the tested trusses, around 40% increases in structural resistance were achieved through the addition of the cable, though the self-weight was increased by only approximately 3%. In parallel with the experimental programme, a finite element model was developed and validated against the test results. Upon successful replication of the experimentally observed structural response of the trusses, parametric studies were conducted to investigate the effect of key parameters such as prestress level, material grade and the top chord cross-section on the overall structural response. Based on both the experimental and numerical results, design recommendations in the form of simple design checks to be performed for such systems are provided.

Journal article

Liu F, Wang Y, Gardner L, Varma Aet al., Experimental and numerical studies of reinforced concrete columns exposed to fire, Journal of Structural Engineering, ISSN: 0733-9445

Reinforced concrete columns confined by steel tubes, also known as steel tube confined reinforced concrete (STCRC) columns, are a kind of composite column in which the outer steel tube acts predominantly as hoop reinforcement. This is achieved by the provision of breaks to the longitudinal continuity of the steel tube. The compressive behavior and seismic performance of STCRC columns have been extensively studied in the past few decades. However, knowledge of the fire behavior of STCRC columns is very limited. Hence, experimental and numerical studies to investigate the response of STCRC columns under combined thermal (fire) and structural loading are presented herein. Four full-scale STCRC columns and one concrete-filled steel tubular (CFST) column were first axially loaded and then subjected to the ISO 834 standard fire until failure. The measured furnace temperatures, specimen temperatures, axial displacement versus time curves and fire resistance of the columns are presented and discussed. A nonlinear finite element model, employing a sequentially coupled thermal-stress analysis, was then developed in ABAQUS and validated against recent fire tests on STCRC columns and concrete-filled steel tubular (CFST) columns reported in the literature. Following extensive parametric studies, a simplified method is proposed for predicting the temperatures of the steel tube, the reinforcing bars and the concrete. Design rules are then proposed for predicting the load-bearing capacity of STCRC columns exposed to the ISO 834 standard fire, which are consistent with the design method for STCRC columns at ambient temperature.

Journal article

Wang F, Young B, Gardner L, Experimental study of square and rectangular CFDST sections with stainless steel outer tubes under axial compression, Journal of Structural Engineering, ISSN: 0733-9445

A comprehensive experimental investigation into the axial compressive response of concrete-filled double skin tubular (CFDST) sections with stainless steel square and rectangular outer tubes is presented. A total of 28 tests was carried out. The experimental setup and procedures are described, and the test observations are fully reported. The test results are employed to assess the applicability of the current European and North American design provisions for composite carbon steel members to the design of the studied CFDST cross-sections. Modifications to the current design codes are also considered—a higher buckling coefficient k of 10.67 to consider the beneficial restraining effect of the concrete on the local buckling of the stainless steel outer tubes and a reduction factor η to account for the effective compressive strength of high strength concrete. Overall, the comparisons revealed that the existing design rules may generally be safely applied to the prediction of the compressive resistance of CFDST cross-sections with stainless steel outer tubes, while the modified design rules offered greater accuracy and consistency.

Journal article

Gardner L, Yun X, Fieber A, Macorini Let al., 2019, Steel design by advanced analysis: Material modeling and strain limits, Engineering, ISSN: 2095-8099

Structural analysis of steel frames is typically performed using beam elements. Since these elements are unable to explicitly capture the local buckling behavior of steel cross-sections, traditional steel design specifications use the concept of cross-section classification to determine the extent to which the strength and deformation capacity of a cross-section are affected by local buckling. The use of plastic design methods are restricted to Class 1 cross-sections, which possess sufficient rotation capacity for plastic hinges to develop and a collapse mechanism to form. Local buckling prevents the development of plastic hinges with such rotation capacity for cross-sections of higher classes and, unless computationally demanding shell elements are used, elastic analysis is required. However, this article demonstrates that local buckling can be mimicked effectively in beam elements by incorporating the continuous strength method (CSM) strain limits into the analysis. Furthermore, by performing an advanced analysis that accounts for both geometric and material nonlinearities, no additional design checks are required. The positive influence of the strain hardening observed in stocky cross-sections can also be harnessed, provided a suitably accurate stress–strain relationship is adopted; a quad-linear material model for hot-rolled steels is described for this purpose. The CSM strain limits allow cross-sections of all slenderness to be analyzed in a consistent advanced analysis framework and to benefit from the appropriate level of load redistribution. The proposed approach is applied herein to individual members, continuous beams, and frames, and is shown to bring significant benefits in terms of accuracy and consistency over current steel design specifications.

Journal article

Hadjipantelis N, Gardner L, Wadee MA, 2019, Design of prestressed cold-formed steel beams, Thin-Walled Structures, ISSN: 0263-8231

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.

Journal article

Buchanan C, Gardner L, 2019, Metal 3D printing in construction: a review of methods, research, applications, opportunities and challenges, Engineering Structures, Vol: 180, Pages: 332-348, ISSN: 0141-0296

3D printing, more formally known as additive manufacturing (AM), has the potential to revolutionise the construction industry, with foreseeable benefits including greater structural efficiency, reduction in material consumption and wastage, streamlining and expedition of the design-build process, enhanced customisation, greater architectural freedom and improved accuracy and safety on-site. Unlike traditional manufacturing methods for construction products, metal 3D printing offers ready opportunities to create non-prismatic sections, internal stiffening, openings, functionally graded elements, variable microstructures and mechanical properties through controlled heating and cooling and thermally-induced prestressing. Additive manufacturing offers many opportunities for the construction sector, but there will also be fresh challenges and demands, such as the need for more digitally savvy engineers, greater use of advanced computational analysis and a new way of thinking for the design and verification of structures, with greater emphasis on inspection and load testing. It is envisaged that AM will complement, rather than replace, conventional production processes, with clear potential for hybrid solutions and structural strengthening and repairs. These opportunities and challenges are explored in this paper as part of a wider review of different methods of metal 3D printing, research and early applications of additive manufacturing in the construction industry. Lessons learnt for metal 3D printing in construction from additive manufacturing using other materials and in other industries are also presented.

Journal article

Gardner L, Fieber A, Macorini L, 2019, Formulae for calculating elastic local buckling stresses of full structural cross-sections, Structures, Vol: 17, Pages: 2-20, ISSN: 2352-0124

Formulae for determining the full cross-section elastic local buckling stress of structural steel profiles under a comprehensive range of loading conditions, accounting for the interaction between the individual plate elements, are presented. Element interaction, characterised by the development of rotational restraint along the longitudinal edges of adjoined plates, is shown to occur in cross-sections comprising individual plates with different local buckling stresses, but also in cross-sections where the isolated plates have the same local buckling stress but different local buckling half-wavelengths. The developed expressions account for element interaction through an interaction coefficient ζ that ranges between 0 and 1 and are bound by the theoretical limits of the local buckling stress of the isolated critical plates with simply-supported and fixed boundary conditions along the adjoined edges. A range of standard European and American hot-rolled structural steel profiles, including I-sections, square and rectangular hollow sections, channel sections, tee sections and angle sections, as well as additional welded profiles, are considered. The analytical formulae are calibrated against results derived numerically using the finite strip method. For the range of analysed sections, the elastic local buckling stress is typically predicted to within 5% of the numerical value, whereas when element interaction is ignored and the plates are considered in isolation with simply-supported boundary conditions along the adjoined edges, as is customary in current structural design specifications, the local buckling stress of common structural profiles may be under-estimated by as much as 50%. The derived formulae may be adopted as a convenient alternative to numerical methods in advanced structural design calculations (e.g. using the direct strength method or continuous strength method) and although the focus of the study is on structural steel sections, the functions are

Journal article

Bu Y, Gardner L, 2019, Laser-welded stainless steel I-section beam-columns: Testing, simulation and design, Engineering Structures, Vol: 179, Pages: 23-36, ISSN: 0141-0296

The stability and design of laser-welded stainless steel I-section beam-columns are explored in this study. Owing to the high precision and low heat input of laser-welding, structural cross-sections produced using this fabrication method have smaller heat affected zones, lower thermal distortions and lower residual stresses than would typically arise from traditional welding processes. Eighteen laser-welded stainless steel beam-columns were tested to investigate the member buckling behaviour under combined compression and bending. Two I-section sizes were considered in the tests: I-50 × 50 × 4 × 4 in grade EN 1.4301 and I-102 × 68 × 5 × 5 in grade EN 1.4571 austenitic stainless steel. The two cases of minor axis bending plus compression and major axis bending plus compression with lateral restraints were investigated. The initial loading eccentricities in the beam-column tests were varied to provide a wide range of bending moment-to-axial load ratios. The test results obtained herein and from a previous experimental study were used to validate finite element (FE) models, which were subsequently employed for parametric investigations to generate further structural performance data over a wider range of cross-section sizes, member lengths and loading combinations. The obtained test and FE results were utilized to evaluate the accuracy of the beam-column capacity predictions according to the current European and North American design provisions and a recent proposal by Greiner and Kettler. Finally, an improved approach for the design of stainless steel I-section beam-columns is proposed.

Journal article

Hadjipantelis N, Gardner L, Wadee MA, 2019, Finite element modeling of prestressed cold-formed steel beams, Journal of Structural Engineering, ISSN: 0733-9445

The concept and structural benefits of prestressing cold-formed steel beams are explored inthe present paper. The prestressing is applied by means of a high-strength steel cable locatedwithin the cross-section of the beam, at an eccentric location with respect to the strong geometricaxis. The internal forces generated by the prestressing are opposite in sense to those inducedunder subsequent vertical loading. Hence, the development of detrimental compressive stresseswithin the top region of the cold-formed steel beam is delayed and thus the load-carrying capacityof the beam is enhanced. Owing to the pre-camber that is induced along the member duringthe prestressing stage, the overall deflections of the beam are also reduced significantly. In thepresent paper, following the description of the proposed concept, finite element (FE) modeling isemployed to simulate the mechanical behavior of prestressed cold-formed steel beams during theprestressing and vertical loading stages. Following the validation of the FE modeling approach, aset of parametric studies is conducted, where the influence of the key controlling parameters on thestructural benefits obtained from the prestressing process is investigated. The parametric resultsare utilized to determine how the benefits obtained from the addition of the prestressed cable canbe maximized, demonstrating the significant enhancements in the performance of the cold-formedsteel beam that can be achieved.

Journal article

Liang Y, Zhao O, Long YL, Gardner Let al., 2019, Stainless steel channel sections under combined compression and minor axis bending – Part 2: Parametric studies and design, Journal of Constructional Steel Research, Vol: 152, Pages: 162-172, ISSN: 0143-974X

Following the experimental study and finite element (FE) model validation described in the companion paper, numerical parametric studies and the evaluation of design provisions for stainless steel channel sections under combined axial compressive load and minor axis bending moment are presented herein. The parametric studies were carried out to generate additional structural performance data over a wider range of cross-section aspect ratios and slendernesses, loading combinations and bending orientations. The test data and numerical results have been carefully analysed to develop a comprehensive understanding of the structural performance of stainless steel channel sections under combined compression and minor axis bending moment, and to assess the accuracy of the existing design provisions in Europe and North America. Comparisons of ultimate loads from the tests and FE simulations with the codified resistance predictions revealed that the current design standards typically under-estimate the capacity of stainless steel channel sections under combined compression and minor axis bending moment; this is attributed primarily to the neglect of material strain hardening and the employment of conservative interaction formulae. Improved design rules featuring more efficient interaction curves, anchored to more precise end points (i.e. cross-section resistances under pure compression and bending moment), are then proposed and presented. The new design proposals are shown to yield both more accurate and more consistent resistance predictions over the existing design provisions. Finally, statistical analyses are presented to confirm the reliability of the new design proposals according to EN 1990.

Journal article

Bu Y, Gardner L, 2019, Finite element modelling and design of welded stainless steel I-section columns, Journal of Constructional Steel Research, Vol: 152, Pages: 57-67, ISSN: 0143-974X

Stainless steel is widely used in construction due to its combination of excellent mechanical properties, durability and aesthetics. Towards more sustainable infrastructure, stainless steel is expected be more commonly specified and to feature in more substantial structural applications in the future; this will require larger and typically welded cross-sections. While the structural response of cold-formed stainless steel sections has been extensively studied in the literature, welded sections have received less attention to date. The stability and design of conventionally welded and laser-welded austenitic stainless steel compression members are therefore the focus of the present research. Finite element (FE) models were developed and validated against a total of 59 experiments, covering both conventionally welded and laser-welded columns, for which different residual stress patterns were applied. A subsequent parametric study was carried out, considering a range of cross-section and member geometries. The existing experimental results, together with the numerical data generated herein, were then used to assess the buckling curves given in European, North American and Chinese design standards. Following examination of the data and reliability analysis, new buckling curves were proposed, providing, for the first time, design guidance for laser-welded stainless steel members.

Journal article

Liang Y, Zhao O, Long YL, Gardner Let al., 2019, Stainless steel channel sections under combined compression and minor axis bending – Part 1: Experimental study and numerical modelling, Journal of Constructional Steel Research, Vol: 152, Pages: 154-161, ISSN: 0143-974X

The local cross-section behaviour of stainless steel channel sections under the combined actions of axial compression and minor axis bending moment is investigated in the present paper and its companion paper, based on a comprehensive experimental and numerical study. Two channel section sizes were considered in the experimental programme, with the test specimens laser-welded at the two flange-to-web junctions from hot-rolled EN 1.4307 and EN 1.4404 austenitic stainless steel plates. The experiments involved initial local geometric imperfection measurements and 15 eccentrically loaded stub column (combined loading) tests. The loading eccentricity was varied to achieve a range of ratios of axial compression to minor axis bending moment; both orientations of bending (web in compression and web in tension) were considered. The test setup and procedures, together with the key experimental observations, including the load-carrying and deformation capacities, load-end rotation histories and failure modes, are fully reported. A finite element simulation study is then presented, in which the models were first validated against the obtained test results and then employed, in the companion paper, for parametric investigations and the assessment of design provisions.

Journal article

Zhao O, Gardner L, Young B, 2019, Finite element modelling and design of stainless steel SHS and RHS beam-columns under moment gradients, Thin-Walled Structures, Vol: 134, Pages: 220-232, ISSN: 0263-8231

Structural design formulae for beam-columns require accurate end points (i.e. accurate resistance predictions for pure compression and pure bending), should be of suitable form to capture the interaction between the different components of loading and should take due account of the influence of a moment gradient along the member length. However, existing design rules for stainless steel beam-columns do not fully capture the interaction responses observed in experiments and numerical simulations, and are often tied to inaccurate end points; the adopted equivalent uniform moment factors can also be unconservative in the case of high moment gradients. As a consequence, previous comparisons of stainless steel beam-column experimental and finite element results with codified strength predictions have often revealed a rather high degree of scatter. This prompted the present research, to develop improved design proposals for stainless steel square hollow section (SHS) and rectangular hollow section (RHS) beam-columns under moment gradients. To this end, revised design approaches are proposed firstly through the derivation of more accurate design interaction curves for stainless steel SHS and RHS beam-columns under uniform bending moment and then through the employment of more suitable equivalent uniform moment factors, underpinned by and validated against over 1500 test and numerical data points. The new design approaches are shown to lead to improved (safe-sided, accurate and consistent) resistance predictions for stainless steel SHS and RHS beam-columns under moment gradients over the current codified design rules. Finally, statistical analyses are performed to demonstrate the reliability of the proposed approaches, according to the requirements specified in EN 1990.

Journal article

Hadjipantelis N, Gardner L, Wadee M, 2018, Ninth International Conference on Advances in Steel Structures, Hong Kong, China, Ninth International Conference on Advances in Steel Structures, Publisher: Hong Kong Institute of Steel Construction Limited

Conference paper

Gardner L, Yun X, 2018, Description of stress-strain curves for cold-formed steels, Construction and Building Materials, Vol: 189, Pages: 527-538, ISSN: 0950-0618

Cold-formed steels are generally characterized by a rounded stress-strain response with no sharply defined yield point. It is shown herein that this material behaviour can be accurately described by a two-stage Ramberg-Osgood model provided that the values of the key input parameters can be established. The focus of the present paper is to develop predictive expressions for these key parameters to enable the full engineering stress-strain response of cold-formed steels to be represented. The predictive expressions are based on the analysis of a comprehensive set of material stress-strain data collected from the literature. In total, more than 700 experimentally-derived stress-strain curves on cold-formed steel material have been collected from around the world, covering a range of steel grades, thicknesses and cross-section types. The strength enhancement in the corner regions of cold-formed sections has also been analysed and the applicability of existing predictive models has been evaluated. Finally, standardized values of strain-hardening exponents used in the Ramberg-Osgood model have been recommended for both flat and corner material in cold-formed steel sections. The proposed stress-strain curves are suitable for use in advanced numerical simulations and parametric studies on cold-formed steel elements.

Journal article

dos Santos GB, Gardner L, Kucukler M, 2018, Experimental and numerical study of stainless steel I-sections under concentrated internal one-flange and internal two-flange loading, Engineering Structures, Vol: 175, Pages: 355-370, ISSN: 0141-0296

The behaviour and design of stainless steel I-section beams under concentrated transverse loading are investigated in this study. Twenty-four experiments on stainless steel I-sections, formed by the welding of hot-rolled plates, were performed. The tests were conducted under two types of concentrated transverse loading – internal one-flange (IOF) and internal two-flange (ITF) loading. The experimental set-up, procedure and results, including the full load-displacement histories, ultimate loads and failure modes, are reported. A complementary nonlinear finite element modelling study was also carried out. The models were first validated against the results of the experiments. A parametric investigation into the influence of key parameters such as the bearing length, web slenderness and level of coexistent bending moment, on the structural response was then performed. Finally, an assessment of current design provisions for the resistance of stainless steel welded I-sections to concentrated loading is presented. The results show that the current design formulae yield safe-sided, but generally rather scattered and conservative capacity predictions, with considerable scope for further development.

Journal article

Yun X, Gardner L, 2018, The continuous strength method for the design of cold-formed steel non-slender tubular cross-sections, Engineering Structures, Vol: 175, Pages: 549-564, ISSN: 0141-0296

Cold-formed steels typically exhibit a rounded stress-strain response with gradual yielding merging into strain hardening. This form of stress-strain curve is at odds with the elastic, perfectly plastic material model that underpins many of the provisions set out in current structural steel design standards. In particular, the beneficial influence of strain hardening on cross-section capacity is neglected. The continuous strength method (CSM) is a deformation-based design method that enables material strain hardening properties to be exploited, thus resulting in more accurate and consistent capacity predictions. The aim of this study is to extend the CSM to the design of cold-formed steel non-slender tubular cross-sections subjected to compression, bending and combined loading, and to verify the proposals through comparisons with existing test data from the literature and finite element results generated herein. The finite element models were first developed and validated against test results on cold-formed steel cross-sections collected from the literature. An extensive parametric study was then conducted to generate additional data over a wider range of cross-section geometries, slendernesses and loading conditions. The numerical results together with the experimental results were then compared with capacity predictions, calculated according to the current design rules in European Standard EN 1993-1-1 (2005) and American Specification AISC-360-16 (2016) as well as the CSM. The CSM is shown to provide more accurate and consistent design predictions for cold-formed steel cross-sections under different loading conditions than those obtained from existing design methods. The improvements arise from the use of the continuous deformation based design approach, as well the rational exploitation of strain hardening. Finally, the reliability levels of the different design methods were assessed by conducting reliability analyses in accordance with EN 1990 (2002).

Journal article

Yun X, Gardner L, 2018, Numerical modelling and design of hot-rolled and cold-formed steel continuous beams with tubular cross-sections, Thin-Walled Structures, Vol: 132, Pages: 574-584, ISSN: 0263-8231

The structural behaviour and design of hot-rolled and cold-formed steel continuous beams with square and rectangular hollow sections are studied in the present paper, with a focus on the beneficial effects of material strain hardening and moment redistribution. Finite element (FE) models were first developed and validated against existing test results on hot-rolled and cold-formed steel square and rectangular hollow section continuous beams. Upon validation against the experimental results, parametric studies were carried out to expand the available structural performance data over a range of cross-section geometries, cross-section slendernesses, steel grades and loading conditions. Representative material properties and residual stress patterns were incorporated into the FE models to reflect the two studied production routes – hot-rolling and cold-forming. The experimental results, together with the parametric numerical results generated herein, were then used to evaluate the accuracy of the design provisions of EN 1993-1-1 (2005) as well as the continuous strength method (CSM) for indeterminate structures, the latter of which is extended in scope in the present study. It was shown that the current provisions of EN 1993-1-1 (2005) for the design of hot-rolled and cold-formed steel continuous beams are rather conservative, while the proposed CSM yields a higher level of accuracy and consistency, due to its rational consideration of both strain hardening at the cross-sectional level and moment redistribution at the global system level. Finally, statistical analyses were carried out to assess the reliability level of the two design methods according to EN 1990 (2002).

Journal article

Zhang W, Gardner L, Wadee MA, Zhang Met al., 2018, Analytical solutions for the inelastic lateral‑torsional buckling of I‑beams under pure bending via plate‑beam theory, International Journal of Steel Structures, Vol: 18, Pages: 1440-1463, ISSN: 1598-2351

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner’s coefficient have been presented due to the limitation of Vlasov’s buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler–Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair’s formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

Journal article

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