Slenderness Limits Research Articles

Testing, numerical modelling and design of S690 high strength steel welded I-section stub columns

This paper describes a comprehensive testing and numerical simulation investigation into the material properties, membrane residual stresses and compression capacities of S690 high strength steel welded I-section stub columns. The testing programme was performed on eight welded I-sections fabricated from 5 mm thick S700MC high strength steel hot-rolled plates by means of gas metal arc welding, and included material tensile coupon tests, membrane residual stress measurements, initial local geometric imperfection measurements, and sixteen concentrically loaded stub column tests. A membrane residual stress distribution model for S690 high strength steel welded I-sections was firstly proposed, based on the experimentally measured results. In conjunction with the structural testing, a numerical modelling study was carried out, in which finite element models were initially developed and validated against the experimental results, and afterwards employed to conduct parametric studies, aiming at generating further structural performance data over a broader range of cross-section sizes. The obtained experimental and numerical data were used to evaluate the accuracy of the slenderness limits (for classifications of plate elements and cross-sections) and design rules for S690 high strength steel welded I-section stub columns, as set out in the European, American and Australian standards. The results of the evaluation revealed that the codified slenderness limits are accurate for the plate element and cross-section classifications of S690 welded I-sections in compression, and the established local buckling design provisions in the considered three codes result in precise and consistent cross-section compression resistance predictions for both non-slender and slender S690 welded I-section stub columns.

Slenderness limits for fabricated S960 ultra-high-strength steel and composite columns

Ultra-high-strength steel (UHSS) has been gaining increasing attention globally due to its significant structural and economic benefits. Specifically, the use of UHSS in steel and composite column sections can reduce the dimensions and self-weight of the structural components. However, the utilisation of UHSS slender sections also renders the structural members more susceptible to local buckling. The reduced ductility as well as less strain hardening of UHSS can also affect the post-buckling load. In order to clarify the local buckling and post-buckling load of compressive members using UHSS plates, the authors herein present an extensive experimental program. A total of sixteen steel and composite specimens are tested with the slenderness limits (λey) and effective widths (be/b) being identified. Finite element models which account for the effects of residual stress and initial geometric imperfection are developed to capture the buckling behaviour of the box and I-section columns. The enhancement of local buckling and post-local buckling load of UHSS composite sections due to the presence of infilled concrete is demonstrated. In addition, the slenderness limits and effective widths of both bare steel sections and composite sections incorporating UHSS plates are further compared with existing codes of practice. Corresponding design recommendations are consequently provided.

Concrete-filled steel tubular columns: Test database, design and calibration

Concrete-filled steel tubular (CFST) columns are adopted in many structural applications, especially for tall buildings, bridges and large infrastructure due to their substantial structural and economic benefits. However, the design guidelines for CFST columns with high strength materials and slender sections are still limited. In acknowledging these limitations, a large number of tests on high strength CFST columns have been conducted. In this paper, the most recent experimental data on CFST columns with high strength materials and slender sections are collected and merged with existing databases to establish a comprehensive database with over 3100 tests. The test results are then compared with those predicted from existing design codes, including Eurocode 4, Australian/New Zealand code AS/NZS 2327 and American code AISC 360-16 to calibrate their accuracy in strength prediction of CFST columns. In general, all codes give conservative predictions for CFST columns. Eurocode 4 and AS/NZS 2327 give the best predictions, whilst AISC 360-16 gives conservative predictions. The effects of material strengths and section slenderness on the code predictions are also investigated to evaluate the applicability of the codes beyond their material strength and section slenderness limits.

Performance-based slenderness limits for deformations and crack control of reinforced concrete flexural members

The use of high strength materials allows flexural members to resist the design loads or to cover long spans with a reduced depth. However, the strict cross section dimensions and reinforcement amount required in ULS are often insufficient to satisfy the serviceability limit states. Due to the complexity associated to a rigorous computation of deflections and cracks width in cracked RC members along their service life, an effective way to ensure the satisfaction of the SLS is to limit the slenderness ratio l/d of the element. In the present study, the slenderness limit concept, previously used for deflection control, is generalized to incorporate the crack width limitations in the framework of structural performance-based design. Equations for slenderness limits incorporating the main parameters influencing the service behaviour of RC members are derived. Cracking and long-term effects are accounted for through simplified coefficients derived from structural concrete mechanics and experimental observations. The proposed slenderness limits are compared with those derived from a numerical non-linear time-dependent analysis for two case studies, and also with those obtained using the EC2 procedure for deflection calculation in terms of constant applied load and constant reinforcement strain. Very good results have been obtained in terms of low errors and scatter, showing that the proposed slenderness limits are a useful tool for performance-based design of RC structures.

Cross-sectional capacity of octagonal tubular steel stub columns under uniaxial compression

This paper presents an experimental investigation on the compression behaviour of cold-formed octagonal, circular and square tubular steel stub columns. Three octagonal hollow steel tubes were examined under axial compression while three circular steel tubes and two square steel tubes were tested for comparison. Nine existing test data on octagonal hollow steel tubes were also collated for comparison. The hollow tubes were fabricated by welding two cold-formed half-section steel plates. To examine the material characteristics, flat, curved and corner coupons were extracted and tested. Residual stress distribution in longitudinal direction was also measured by sectioning method. Fifty longitudinal strips with a nominal width of 10 mm were machined by a wire cutting machine. The test results obtained from the tensile coupon tests and residual stress measurements were examined to evaluate the effect of the fabrication process on different cross-sectional shapes. The geometric imperfections of each specimen were carefully measured. Cross-sectional capacity, load-deformation relationships and failure modes of the stub columns were presented by the stub column tests. Finite element model was developed and validated against the experimental results. The experimental cross-sectional capacities were accurately predicted by the finite element models. The test data accompanied with the FE results were assessed with reference to current design provisions on cross-section classification and a suggested cross-section slenderness limit and an alternative design approach for octagonal cross-sections were proposed.

Low-Mach-number and slenderness limit for elastic Cosserat rods and its numerical investigation

This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e., low-Mach-number–slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a Gauss–Legendre collocation in space and an α-method in time.

Local and post-local buckling of fabricated high-strength steel and composite columns

High-strength structural steel plates are being increasingly used as composite columns in tall buildings, bridges and large infrastructure. The presence of concrete infill in these composite sections enhances their local buckling strength, and thus very slender steel plates can be used in their fabrication. This paper presents the results of an experimental study and numerical investigation of the local buckling slenderness limits for high-strength steel plates. A set of sixteen tests were conducted on both hollow steel and steel-concrete composite sections to explore their local and post-local buckling behaviour under axial compression. A numerical model which accounts for the effects of residual stresses and initial geometric imperfections was developed to predict the local buckling and post-local buckling response of box and I-section columns. This model was verified against the test results. Yield slenderness limits obtained from numerical results were compared with existing codes of practice for both hollow steel and composite sections incorporating high-strength steel plates.

Material response and local stability of high-chromium stainless steel welded I-sections

The present paper describes a thorough testing and finite element modelling programme on the material characteristics and local stability of welded I-sections made of a new high-chromium grade EN 1.4420 stainless steel. Structural testing was conducted on four GMA (gas metal arc) welded I-sections, and involved material testing, residual stress measurements, initial geometric imperfection measurements, eight stub column tests and eight four-point bending tests, with four for each axis of bending. A parallel numerical modelling study was then carried out, in which numerical models were developed and validated against the obtained experimental results and afterwards utilised to perform numerical parametric studies to generate additional data to supplement the test results over a broader spectrum of cross-section geometric dimensions. The experimentally and numerically obtained data were employed to evaluate the suitability of the codified slenderness limits for cross-section classification and local buckling design provisions in both Europe and America to welded I-sections made of the new high-chromium grade EN 1.4420 stainless steel. The results of the comparisons generally indicated that the established cross-section slenderness limits are applicable to the new high-chromium stainless steel welded I-sections, while the codified local buckling design rules, based on an elastic, perfectly plastic material model without taking into account the material strain hardening effect of stainless steel and the effective width method without considering the element interaction effect within the cross-section, yield safe but unduly conservative and scattered cross-section local buckling resistance predictions. The accuracy of a recently proposed continuous strength method to the design of this new type of stainless steel welded I-sections was also evaluated, indicating a substantial improvement over the established design codes, mainly owing to the rational consideration of the favourable effects of material strain hardening and element interaction in the calculation of cross-sectional capacities.

Element interactions of cold-formed stainless steel cross-sections subjected to combined compression and bending

A comprehensive numerical investigation of cold-formed stainless steel cross-sections subjected to combined compression and bending is presented in this paper. A non-linear finite element model (FEM) including geometric and material non-linearities was developed using the finite element package ABAQUS. Upon validation of the FEM, the model was then used for an extensive parametric study to investigate the interaction effects of constituent plate elements of cold-formed stainless steel square and rectangular hollow section beam-columns.The investigation indicates that the interaction effects of constituent plate elements on cross-section response are obvious particularly for slender sections. Current design provisions on Class 3 and Class 2 slenderness limits and effective width equations specified in American Specification, EC3 code and proposed by Gardner are not suitable for square and rectangular stainless steel hollow section beam-columns since the interaction effects of constituent plate elements are ignored. The new Class 3 and Class 2 slenderness limits and the section capacity design equations based on the whole cross-section response enable more accurate prediction of local buckling, thus allowing better utilization of material and more economic design.

Experimental assessment and theoretical evaluation of axial behavior of short and slender CFFT columns reinforced with steel and CFRP bars

This paper presents the test results of an experimental program to investigate the structural performance of short and slender concrete-filled fiber-reinforced polymer (FRP)-tubes (CFFTs) columns under pure axial compression load. The test parameters include: transverse reinforcement type (steel spirals versus glass-FRP (GFRP-tube), type of longitudinal reinforcement (steel and carbon-FRP (CFRP) bars), GFRP tube thickness, and slenderness ratio.Comparisons between the experimental test results and the theoretical design equations are performed in terms of ultimate load carrying capacity. The design equation is modified to accurately predict the ultimate load capacities of CFFT columns reinforced with FRP bars. Furthermore, the experimental results showed that the axial compressive strength of CFRP-reinforced CFFT columns was reduced by 22% with increasing the slenderness ratio from 8 to 20. In general, the use of the FRP tube induces a confinement effect for concrete columns which enhances the strength and ductility of such column’s section. This enhancement resulted in a slender section which increased the possibility of buckling instability of the CFFT columns. Thus, a theoretical model was conducted to develop a simplified formula for critical slenderness limit of FRP-reinforced CFFT columns to control the buckling instability mode of failure. Results indicated that the slenderness limit of 14 was suggested as a safe value for the design purposes. A parametric study was conducted which showed the significant effect of the concrete compressive strength and hoop stiffness of FRP tube on the critical slenderness ratio of FRP-reinforced CFFT columns.

Verification of second-order effects in slender reinforced masonry walls

Previous experimental and numerical works have demonstrated the effectiveness of reinforced masonry (RM) walls in tall single-storey wide-span buildings. Nevertheless, to date, EN1996 does not have a consistent approach to checking the second-order effects due to out-of-plane loads in such structures, and requirements for RM walls are too restrictive. New fibre models have been calibrated on the basis of the above tests and used to carry out parametric pushover analyses to study the influence of wall slenderness, roof vertical load and the percentage of vertical reinforcement on the out-of-plane behaviour of tall RM walls. In this numerical study, new slenderness limits for the safe use of this construction technology are defined, above which second-order moments must be calculated or failures due to instability become predominant, overcoming the shortcomings of current standards. This work also proposes and calibrates some rational approaches for evaluating second-order effects in tall RM walls, based on model column (MC) and nominal curvature (NC) methods. The reliability of the two simplified design methods is checked against the results of the above numerical models. MC method provides the best results, without limitations on the type of failure of the section (i.e. ‘balanced’, as for NC method), with errors usually lower than 25% and always conservative.

Design of Cold-Formed High-Strength Steel Tubular Stub Columns

This paper presents the numerical investigation of the compressive behavior of cold-formed high-strength steel (HSS) tubular stub columns. The nominal 0.2% proof stresses of the high-strength steel are 700, 900, and 1,100 MPa. Experimental investigations have been conducted, and the numerical methodology has been verified against the test results in a complementary study. Parametric studies on the cold-formed HSS tubular stub columns were performed using the verified models, and additional data were generated to evaluate the structural performance of such compression members. The experimental and numerical results were then compared with the predictions from the design guidelines for square hollow sections (SHS), rectangular hollow sections (RHS), and circular hollow sections (CHS). The current codified slenderness limits and design methods were examined. Modifications to the design methods for resistances of SHS, RHS, and CHS stub columns against cross-sectional yielding or local buckling are proposed in this paper.

Development of optimum cold-formed steel sections for maximum energy dissipation in uniaxial bending

Cold-formed steel (CFS) elements are increasingly used as load-bearing members in construction, including in seismic regions. More conventional hot-rolled steel and concrete building structures are typically allowed by the design standards to exceed their elastic limits in severe earthquakes, rendering parameters indicating ductility and energy dissipation of primordial importance. However, insufficient research has yet been conducted on the energy dissipation of CFS structures. In the majority of previous optimization research on CFS sections the ultimate capacity, as typically controlled by local, distortional and/or global buckling modes, is considered to be the sole optimization criterion. This paper aims to improve the seismic performance of CFS elements by optimising their geometric and material highly non-linear post-buckling behaviour to achieve maximum energy dissipation. A novel shape optimisation framework is presented using the Particle Swarm Optimisation (PSO) algorithm, linked to GMNIA ABAQUS finite element analyses. The relative dimensions of the cross-section, the location and number of intermediate stiffeners and the inclination of the lip stiffeners are considered to be the main design variables. All plate slenderness limit values and limits on the relative dimensions of the cross-sectional components as defined by Eurocode 3, as well as a number of practical manufacturing and construction limitations, are taken into account as constraints in the optimisation problem. It is demonstrated that a substantial improvement in energy dissipation capacity and ductility can be achieved through the proposed optimization framework. Optimized cross-sectional shapes are presented which dissipate up to 60% more energy through plastic deformations than a comparable commercially available lipped channel.

Compact cross-sections of mild and high-strength steel hollow-section beams

The Eurocode 3 rules for the high-strength steel (HSS: fy > 460 MPa) limit the analysis of beams to elastic global analysis and grades up to S700. In order to fully exploit the potential to design lightweight and sustainable steel structures, plastic analysis and the use of higher steel grades with fy > 700 MPa are desirable. The main concern is the low ultimate-to-yield strength ratio requirement for HSS, fu/fy > 1·05 according to BS EN 1993-1-12. Its influence on the resistance and rotation capacity of HSS square and rectangular hollow-section beams (SHS and RHS) is investigated in this study. The available results of four-point bending experiments on hollow-section beams are validated by finite-element analysis with special attention given to imperfections. Parametric study of steel grades S355–S960 indicates that the slenderness limits given in Eurocode 3 need to be reduced both for the mild steels and HSS.

Compressive behaviour of high-strength steel cross-sections

The recent increase in the use of high-strength steels (HSSs) in modern engineering practice necessitates a deeper understanding of their structural response. Given that HSS design specifications are largely based on a limited number of test data and assumed analogies with mild steel, their applicability to HSS sections needs to be assessed. In the work reported in this paper, finite-element models were developed and validated against experimental data of hot-finished S460 and S690 grade steel stub columns. Parametric studies were conducted to generate a large volume of structural performance data over a wide range of cross-section slenderness values and aspect ratios. On the basis of the results, the suitability of the Eurocode 3 (EC3) class 3 slenderness limit and the effective width equations for HSS sections were assessed. Aiming to account for element interaction effects, which are not considered in EC3, an effective cross-section method applicable to HSS slender sections was developed. Finally, the continuous-strength method was extended to stocky S460 sections, for which overly conservative strength predictions were observed. The reliability of the proposed design methods was verified according to annex D of the Eurocode structural design basis (EN 1990).

Design of cold-formed high strength steel tubular beams

A numerical investigation on cold-formed high strength steel (HSS) tubular beams is presented in this paper. The nominal 0.2% proof stresses of the HSS sections ranged from 700MPa to 1100MPa. In the complementary study [1], experimental investigation on the beam specimens have been performed. In the present study, numerical modelling methodology for beams was first validated and parametric study on the cold-formed HSS tubular beams was conducted. A total of 423 numerical data was obtained to investigate the structural performance of HSS tubular beams. The experimental and numerical results were then compared with the codified design guidelines from ANSI/AISC 360-10 [2], EN 1993-1-1 [3], AS 4100 [4] and AISI S100 [5] in addition to the predictions from Direct Strength Method (DSM) for square hollow sections (SHS), rectangular hollow sections (RHS) and circular hollow sections (CHS). The codified slenderness limits for sections subjected to bending were examined. Improvements on the design guidelines are proposed in this paper.

Tests on high-strength steel hollow sections: a review

Advances in technologies have allowed manufacturers to produce steel plates and sections with strengths of 690 MPa and higher. The use of high-strength steel has the potential for significantly reducing the material costs and the self-weight of structures. High-strength steel hollow sections can be either welded from steel plates or cold-formed from coils. Tests on different built-up high-strength steel hollow sections have been conducted around the globe, including Australia, China, Japan and the USA. The commonly used box-sections were tested; the slenderness limits and member capacities against compression were also studied. To investigate the performance of cold-formed high-strength steel hollow sections, the authors initiated a research programme in Hong Kong, which included both experimental and numerical investigations on cold-formed high-strength steel hollow sections. The sections include square, rectangular and circular hollow sections. Based on the results, recommendations on section slenderness limits and expressions for determining member capacity are proposed in these studies. This paper summarises recent research on high-strength steel hollow sections and also addresses the design recommendations and limits in codes for both built-up and cold-formed high-strength steel hollow sections.

12.14: Ultimate response and design of stainless steel continuous beams

ABSTRACTDue to lack of available experimental data, plastic design of stainless steel (SS) indeterminate structures is currently not permitted by Eurocode 3: Part 1.4, despite the excellent material ductility and the existence of a Class 1 slenderness limit, thereby compromising design efficiency. The high initial material cost warrants the development of novel design procedures, in line with the observed structural response, which fully utilise its merits, improve cost‐effectiveness and minimise material consumption. This paper focuses on the response and design of stainless steel continuous beams. FE models of austenitic and lean duplex stainless steel SHS and RHS were developed and validated against published test data. The validated FE models were used to conduct parametric studies, in order to obtain structural performance data over a range of cross‐sectional slendernesses, cross section aspect ratios, moment gradients and loading arrangements. Based on obtained results, it was concluded that the current Eurocode 3: Part 1.4 approach significantly underestimates the strength of continuous beams. This is because the formation of successive plastic hinges and moment redistribution in indeterminate structures with adequate deformation capacity, as well as the effect of strain‐hardening at cross‐sectional level, are not accounted for. It is shown that accounting for both strain‐hardening and moment redistribution is of paramount importance for design. To this end, the application of the Continuous Strength Method (CSM), which rationally accounts for local buckling at cross‐section level, is extended to the design of stainless steel indeterminate structures. Further research is underway to quantify the effect of high shear stresses on the design procedure and to extend the method to the design of pinned based and fixed based stainless steel frames.

08.38: Experimental characterisation of the flexural behaviour of rubberized concrete‐filled steel tubular members

ABSTRACTThe main objectives of the research presented in this paper are to investigate the flexural behaviour of Concrete Filled Steel Tube (CFST) columns made with Rubberized Concrete (RuC) and to identify the behavioural differences between this type of composite members and typical (standard concrete) CFST members. The influence of the rubber aggregate replacement ratio on member strength, ductility, and energy dissipation capacity is assessed. The paper begins with a description of the preparation and development of the experimental campaign, which involves the testing of 36 composite specimens (28 RuCFST and 8 standard CFST), and a single circular hollow steel tube. The selection of the specimens took into account a number of geometrical and material parameters, namely the shape of the cross‐section (circular, square and rectangular), the cross‐section slenderness and the rubber aggregate replacement ratio. A novel testing mechanism was developed as a part of an innovative testing setup, aimed at reducing both the cost and preparation time of the specimens. The columns were tested under both monotonic and cyclic lateral loading, combined with different levels of axial compression. The monotonic results were compared with the expected flexural capacities according to Eurocode 4, and the cyclic results were used to gauge the sectional slenderness limits of Eurocode 8 for different ductility classes. The test results obtained are indicative of the reduced influence of the type of concrete infill on the monotonic and cyclic flexural behaviour of these composite members, and also allow concluding that Eurocode 4 is conservative in predicting the capacity of the tested specimens. Moreover, it was found that the cross‐section slenderness does not have a significant influence on the monotonic and cyclic behaviour of the specimens, pointing out for the possible relaxation of the cross‐section slenderness limits currently specified in Eurocode 4 and 8.

Elliptical hollow section steel cantilever beams under extremely low cycle fatigue flexural load – A finite element study

A comprehensive non-linear finite element (FE) study carried out on elliptical hollow section (EHS) steel cantilever beams of 1740mm2 cross-sectional area and 1500mm long under extremely low cycle fatigue (ELCF) uni-directional flexural load along major and minor axes separately is presented using the general FE package, Abaqus. The aspect ratio (major to minor axis diameter ratio), a/b and shell thickness, t of EHS beam models are varied between 1–2.33 and 4–6mm respectively. The effect of a/b ratio and section slenderness on cyclic rotation capacity and flexural over-strength of the EHS FE beam models is investigated in this study. It is observed that the effect of a/b on rotation capacity under major axis bending is significant. Also, the cyclic flexural over-strength is not significantly affected by a/b ratio. New slenderness limits for circular hollow sections under bending are proposed. Modified slenderness parameters for EHSs under bending based on equivalent circular hollow section approach are derived. Empirical expressions for predicting cyclic rotation capacity and flexural over-strength of EHS beams are derived based on the FE study.