Cross-section Slenderness Research Articles

Design model for concrete-filled steel tube columns under full and local compression loads

The structural behaviour of concrete-filled steel tubular columns subjected to full and local compression loads was investigated. Experiments were performed on 18 columns with different cross-sectional slenderness ratios. The experimental parameters were the local compression area ratio and the slenderness ratio. The strength index, stiffness and ductility index of the columns were obtained through experimental tests. The results revealed that the local compression area ratio and slenderness ratio are key parameters that considerably affect the strength capacity of columns subjected to full and local compression loads. Design models provided in various international codes and various studies were used to validate the experimental results. Furthermore, the suitability of these design models for predicting the strength capacity of columns subjected to full and local compression loads was examined. Finally, through regression analysis, a simplified design model was developed for predicting the strength capacity of columns under full and local compression loads.

Design of stainless steel cross-sections with outstand elements under stress gradients

A significant amount of research has been reported on stainless steel tubular sections, while studies on I- and C-sections remain relatively limited. This paper presents a comprehensive numerical study on the response of stainless steel I- and C-sections subjected to minor axis bending, with outstand flanges subjected to stress gradients. Numerical models are developed and validated against reported test data on austenitic stainless steel sections under minor axis bending. Subsequently, parametric studies using standardised material properties on austenitic, duplex and ferritic stainless steel grades, covering a wide variety of cross-section slendernesses, are carried out to expand the structural performance data. The results are used to assess the applicability of the Eurocode slenderness limits, revealing that the Class limit 3 for outstand flanges under stress gradient is overly conservative. Moreover, Eurocode underestimates the predicted bending strengths, whereas the level of accuracy and consistency improves for stocky sections, when the Continuous Strength Method is used. Aiming to address the lack of accuracy and consistency in the design predictions of slender sections, particular focus is placed on their performance. It is demonstrated that outstand elements under stress gradients exhibit significant inelastic behaviour after the compression flanges have locally buckled. Inelastic buckling behaviour is not considered in current design guidance, thus resulting in overly conservative and fundamentally incorrect strength predictions. An alternative design method based on the plastic effective width concept is proposed for slender stainless steel I- and C-sections in minor axis bending, which leads to more favourable and less scattered strength predictions.

Design of fixed-ended octagonal shaped steel hollow sections in compression

In recent years, octagonal steel hollow sections (OctHSs) have attracted significant interests from researchers and engineers, and OctHSs have been employed in civil engineering applications. However, designs of OctHSs are not included in structural steel design codes. This paper therefore presents comprehensive numerical analyses on the stub column behaviour of OctHSs. A database of 46 stub column tests reported in 6 sources were collected. Different fabrication routes, steel grades and cross-sectional slenderness were covered. Finite element (FE) modelling was carried out to replicate the test observations. The validated FE models were subsequently adopted to conduct an extensive parametric study to supplement the test database. Existing design methods in North American specifications, ASCE standard, Eurocode, Australian code and recently published literature were thoroughly discussed and evaluated. It was found that existing design methods are not applicable to the design of OctHSs. New cross-sectional slenderness limits and modifications to the existing design methods were then proposed. The cross-sectional resistance obtained from different design methods were compared with test and FE results. The applicability of the modified design methods was confirmed by statistical analyses. The reliability of the modified design methods was finally verified through reliability analyses. Results indicate that the modified design methods can be used to accurately predict the resistance of OctHSs with accepted safety levels.

Design of square and rectangular CFST cross-sectional capacities in compression

Eurocode EN 1994-1-1 currently covers design of concrete-filled steel tubular (CFST) columns using normal strength materials with nominal steel yield strength (fy) not more than 460 MPa and concrete characteristic cylinder strength less than 50 MPa. As high strength materials have been increasingly used in construction, this paper aims to extend current design equation for square and rectangular CFSTs in EN 1994-1-1 to incorporate high strength materials. A comprehensive experimental database consisting of 443 square and rectangular CFST stub column test results was developed. Statistical evaluations were undertaken and the results indicate that the current cross-section slenderness limit for square and rectangular CFSTs is too conservative and can be safely relaxed from 52235/fy to 68235/fy. The design equation could be extended to incorporate high strength materials). Then, a reliability analysis in accordance with EN 1990 was performed to evaluate the applicability of the proposed design method. It was found that the current partial factors are safe for the design of square and rectangular CFSTs with normal strength materials even after relaxation of the cross-section slenderness limit. However, modification should be applied to the existing design equation for the design of high strength materials to yield an acceptable safety level. Finally, an experimental investigation on 10 stub column tests was carried out to further verify the applicability of the proposed design recommendation. It was found that the proposed design recommendation yields satisfactory predictions when compared to test results.

Seismic design of non-dissipative embedded column base connections

Embedded Column Base (ECB) connections in seismically resistant steel moment frames are commonly designed to be stronger than the connected column, to protect them from inelastic actions. This relies on estimation of demands induced by the column and the strength capacity of the connections themselves. However, recent research indicates that prevalent approaches may be unconservative for both demand and capacity estimation, with the consequence of unintended damage/failure of the connection. Motivated by the above, this research (1) characterizes the seismic demands induced in ECB connections, and (2) evaluates various strength models for these connections, in support of improved design approaches. This is done through a virtual test program that uses validated continuum finite element simulations of interactive column-ECB subassemblies. The results suggest that the current design approaches for ECB connections are unconservative, i.e., they underestimate demands while also overestimating the ECB resistance, with the possibility of unintentional nonlinear behavior within the embedded portion of the ECB connection. This is undesirable, because the ECB connections are not usually detailed to provide plastic deformation capacity. A method is proposed to provide improved estimates of the anticipated flexural demands of non-dissipative ECB connections, along with recommendations regarding the strength models. To accomplish this, the method incorporates local cross-sectional slenderness, gravity-induced axial load demand in conjunction with load combinations imposed by current seismic design standards. The sensitivity to the steel column material grade, the imposed loading history, and axial load demands is studied, and limitations of the approach are outlined.

Tests of aluminum alloy perforated built-up sections subjected to bending

This paper presents the experimental investigation of aluminum alloy built-up flexural members with web perforations. The capacity of web would reduce due to losing of material. With the aim of identifying the influence of web holes on the flexural behavior and strength of aluminum alloy built-up sections, a total of 28 aluminum alloy built-up beams with different lengths and hole diameters were tested under both three-point and four-point bending. The failure modes include local buckling, shear buckling, and combined distortional and local buckling, which depends on the cross-sectional slenderness, the hole size, the location of holes and other factors. The design formulae of the current Direct Strength Method (DSM) for the flexural strength and shear strength of cold-formed steel beams were used for predicting the strengths of the aluminum alloy built-up beams tested in this study. The predicted strengths were also compared with the experimental strengths. It was found that the current DSM can be used to predict the flexural and shear strengths of aluminum alloy perforated built-up beams, and the predicted results are generally conservative.

Cross-sectional bending strength of steel Elliptical-Hollow-Sections (EHSs) based on Equivalent-Resistance-Capacity-Method (ERCM)

An expression for cross-sectional bending capacity prediction curve is proposed in this study based on the Direct-Strength-Method (DSM) approach using a comprehensive data from the literature on structural carbon steel Circular-Hollow-Sections (CHSs). Later, according to the Equivalent-Resistance-Capacity-Method (ERCM), improved empirical expressions for the equivalent CHS diameter of Elliptical-Hollow-Section (EHS) are derived using the proposed CHS bending capacity prediction curve and the data of EHSs from the literature. A unified set of cross-section slenderness limits for assessing the CHS and EHS members under bending is proposed. Also, the proposed expression for the bending resistance curve based on DSM is transformed into the generalized form of the traditional cylindrical shell buckling capacity curve as a practical solution in harmony with the newly introduced Reference-Resistance-Design (RRD) guidelines. Finally, the behaviour of EHS cantilever members under cyclic bending is assessed in terms of cyclic moment resistance and rotation capacities based on the authors' previous study.

Veneer-based timber circular hollow section beams: Behaviour, modelling and design

Various forms of timber hollow structural profiles have either been proposed in the literature or are already commercially available. Tests performed on Circular Hollow Section (CHS) beams showed failure modes not usually encountered in timber structures. For relatively thin-walled profiles, a sudden failure in the compression zone, with the opening of the cross-section, was observed. To confidently use and market CHS timber products, design rules considering all possible failure modes must be developed. This paper presents a Finite Element (FE) model of CHS timber beams which captures all experimentally observed failure modes. Cohesive zone elements were used to model the quasi-brittle failure modes of the timber material. The model was validated against ten experimental tests performed on CHS of three different cross-sectional slenderness and manufactured from juvenile hardwood Gympie messmate (Eucalyptus cloeziana) rotary peeled veneers. The model was found to accurately capture the measured structural behaviour and resulted in an average experimental-to-predicted bending capacity ratio of 1.02. The model was also used to explain the mechanisms leading to the sudden compressive failure mode. A parametric study was finally performed on 72 CHS beams of different cross-sectional slenderness. Results showed a strong correlation between the cross-sectional slenderness ratio and section capacity. Design rules are proposed and discussed.

Experimental Study of Square Concrete-Filled Welded Cold-Formed Steel Columns Under Concentric Loading

Due to the presence of composite action between steel and concrete, applications of concrete-filled tubular structures have increased rapidly in bridges, high-rise buildings and other infrastructures. In this study, a total of 15 square concrete-filled welded cold-formed steel columns were tested under concentric loading. Failure modes, ultimate strength and ductility of test specimens were analyzed on several parameters, including concrete compressive strength (f c = 27, 35 and 44 MPa), cross-sectional slenderness ratio (B/t = 25, 31 and 42) and global slenderness ratio (L/B = 3, 5 and 10). The results show that increasing the concrete compressive strength improved the ultimate strength, but decreased ductility of the test specimens. On the other hand, columns with higher slenderness ratio (B/t or L/B) showed lower ultimate strength and less ductile behavior. Failure appearances of the test columns include: outward buckling of the steel tube, crushing of in-fill concrete and welding failure at the joint. Meanwhile, no cracks were found at the corners of the test specimens due to the use of round corner cold-formed built-up steel sections. Finally, the design approaches adopted in (Eurocode-4, AISC-360-10 and Wang et al. 2017) are compared with the ultimate strength of the test columns, which shows satisfactory agreement between the predicted and experimental capacities.

Behaviour of grout-filled double-skin tubular steel stub-columns: Numerical modelling and design considerations

The use of grout-filled double-skin tubular (GFDST) sections in civil, bridge and offshore engineering applications is rapidly increasing. The design of such composite members is not directly covered by design codes, despite recent research studies investigating their performance, proposing design equations or modifying existing codified methods. Aiming to extend the available pool of structural performance data, the current study reports the results of an extensive numerical investigation on GFDST stub-columns. Finite element (FE) models, are developed and validated against published test data. A parametric investigation is conducted to evaluate the effect of key parameters, including cross-sectional slenderness, hollow ratio and the effect of concrete infill on the capacity of GFDST members. The numerically obtained load capacities along with collated test data are utilised to assess the applicability of design strength predictions based on European Code (EC4), the American Concrete Institute (ACI) and the analytical models proposed by Han et al. and Yu et al. Overall, the modified Yu et al. provided strength predictions with low scatter, whereas ACI yielded overly conservative predictions particularly for smaller hollow ratios.

Structural performance and design of hot-rolled steel SHS and RHS under combined axial compression and bending

The structural behaviour and design of hot-rolled steel square and rectangular hollow sections (SHS and RHS) under combined axial compression and bending are studied in the present paper. Finite element (FE) models were developed and validated against existing experimental results on hot-rolled normal strength and high strength steel SHS and RHS under combined loading. Upon validation against the test results, an extensive parametric study was then performed with the aim of expanding the available structural performance data over a wide range of cross-section geometries, cross-section slendernesses, steel grades and loading scenarios. Both the experimentally and numerically obtained data were utilised for an assessment of the accuracy of the current design rules in European and American standards for hot-rolled steel tubular sections under combined loading. The comparisons revealed that the codified capacity predictions are generally somewhat conservative and scattered, due mainly to the neglect of strain hardening in the case of stocky cross-sections and the rather crude treatment of the partial spread of plasticity for Class 3 (semi-compact) cross-sections. The deformation-based continuous strength method (CSM) has been successfully applied to the design of hot-rolled steel cross-sections under isolated loading conditions (i.e. compression or bending), and shown to provide more accurate and consistent ultimate resistance predictions than the existing design provisions. This paper presents the first study to extend the CSM to the design of hot-rolled steel SHS and RHS, made of both normal and high strength steels, under combined loading, underpinned by both experimentally and numerically derived data points. Advantages of the proposed approach include eliminating the discontinuity in the current codified methods, yielding more accurate and consistent resistance predictions and providing knowledge of the level of strain required to reach a given resistance. The reliability of the proposed method is statistically verified in accordance with EN 1990.

Flexural stiffness reduction for stainless steel SHS and RHS members prone to local buckling

In this paper, flexural stiffness reduction factor formulations, applicable to stainless steel members with compact cold-formed square and rectangular hollow section (SHS and RHS), are extended to account for local buckling effects and initial localized imperfection (ω). Local buckling effects and the influence of ω are accounted for by means of reducing the gross section resistance using a strength reduction factor ρ. ρ, determined by the Direct Analysis Method, depending on cross-section slenderness, is adopted. For in-plane stainless steel elements with non-compact and slender sections, results determined by the extended flexural stiffness reduction factor coupled with Geometrically Nonlinear Analysis (GNA) are verified against those determined by Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA). It is found that GNA with the extended flexural stiffness reduction factor (using beam element) generally achieves the accuracy of GMNIA (using shell element). Probabilistic studies based on 3D models with random ω are carried out to evaluate the effect of uncertainty in ω on the accuracy of GNA with the extended beam-column flexural stiffness reduction factor.

The Continuous Strength Method for the design of stainless steel hollow section columns

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.

Experimental and numerical investigation on stub column behaviour of cold-formed octagonal hollow sections

This paper presents an experimental and numerical investigation into stub column behaviour of cold-formed steel octagonal hollow sections (OctHSs). A total of 16 OctHS stub columns were tested. Tensile coupons were extracted from both flat and corner portions of hollow sections to determine corresponding material properties. Finite element (FE) models were developed using commercially available software ABAQUS to replicate the test results generated in this study. The degree to which the enhanced material properties at corners should be extended was investigated. It was found that FE models with corner material properties extended to a width of material thickness beyond the corner portions offer the best agreement with test observations. The validated FE models were then adopted to conduct parametric studies to supplement test database. Cross-sectional slenderness limits specified in current design codes, including EN 1993-1-1, ANSI/AISC 360-16, ASCE/SEI 48-11 and AISI S100-16 (DSM) were evaluated against the test results in conjunction with the FE results. It was found that current limits are not suitable for the design of OctHSs. New cross-sectional slenderness limits in accordance with EN 1993-1-1, ANSI/AISC 360-16, ASCE/SEI 48-11 and DSM were then proposed based on the test and FE results. Cross-sectional capacity predictions obtained from EN 1993-1-1, ANSI/AISC 360-16, ASCE/SEI 48-11 and DSM were also compared with test and FE results. It is shown that the capacity predictions for slender sections from ASCE/SEI 48-11 are slightly unsafe, and ANSI/AISC 360-16 produces relatively satisfactory capacity predictions.

Design of cold-rolled stainless steel rectangular hollow section columns

Considering the effects of cold-forming and strain hardening in the design of cold-formed stainless steel columns is an effective way to reduce construction costs. This approach has become a common trend in the revision of relevant design codes. A few studies were conducted in the past on two key aspects: (i) predicting the enhanced material properties in cold-formed stainless steel cross-sections and (ii) modifying the design methods to adapt to stainless steel material characteristics. However, in the existing literature, they had been separately studied, and integration of these two aspects to form a complete design method was rarely reported. In this study, a series of column tests were conducted on 19 stub and 32 long columns in rectangular hollow sections. The measured imperfections, material properties, load-displacement curves, and failure modes were reported. A new design method for columns was developed, which could clearly and accurately determine the column capacity over the space encompassed by member slenderness and cross-sectional slenderness values. The proposed design method and the method laid out in the Design Manual for Structural Stainless Steel were evaluated against the test data. It was demonstrated that the two design methods were both very conservative in predicting the column capacity when material properties in the annealed condition were used. However, their performances improved when the predicted enhanced material properties were used. Generally, the predictions of the proposed design method matched the test data better. Furthermore, a reliability analysis was conducted, and resistance factors were recommended for the corresponding design methods.

Axial Compression Testing of Bamboo-Laminated Encased Steel Tube Composite Columns

To resolve the problem of premature glue failure in square, thin-walled steel tube/bamboo-laminated composite hollow columns (SBCCs) under compression, a new type of SBCC with transverse binding bars (SBCCB) is proposed. An axial compression test was performed on nine SBCCBs to observe the compressive failure mode and analyse the influence of the net cross-sectional dimension, slenderness ratio and cross-sectional composition on the glue failure and the ultimate bearing load; the results were compared with the known limit stress of SBCCs without transverse binding bars. The experimental results indicate that the compressive damage to SBCCBs is primarily the breaking of the bamboo plywood material and glue failure between the matrix interfaces at the end and middle of the column between the binding bars. The ultimate bearing load is not only related to the dimensions of the cross section and the slenderness ratio but also impacted by the cross-sectional composition. Installing transverse binding bars can effectively reduce glue failure in the test specimens, alter the limit failure mode and significantly increase the ultimate bearing load. Compared to the limiting compressive stress on an SBCC, the limiting compressive stress on an SBCCB is 26% higher on average. A formula for calculating the axial compressive load capacity of an SBCCB was established using nonlinear regression analysis.

Numerical study of fire resistance of stainless steel circular hollow section columns

Stainless steel has countless desirable characteristics for a structural material. Although initially more expensive than conventional carbon steel, stainless steel structures can be competitive due to their smaller need for fire protection material and lower life-cycle cost, thus contributing to a more sustainable construction. The most common stainless steel groups used in structural applications are the austenitic, ferritic and austenitic–ferritic (also known as Duplex grades). This work presents a numerical study on the behaviour of stainless steel circular hollow section members under axial compression at elevated temperatures, with different cross-section slenderness. The numerically obtained ultimate load-bearing capacities are compared with simplified calculation formulae from Eurocode 3 for columns under fire situation. A parametric study, considering different stainless steel grades from the aforementioned groups, cross-sectional classes and slendernesses, is here presented for different elevated temperatures. The numerical analyses were performed with the finite element programme SAFIR, with material and geometric non-linear analysis considering imperfections. Comparisons between the numerical results and the Eurocode 3 rules demonstrated that a specific design approach must be developed for stainless steel columns under fire situation.

Behaviour and design of eccentrically loaded hot-rolled steel SHS and RHS stub columns at elevated temperatures

Abstract 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.

Cylindrical shells under uniform bending in the framework of Reference Resistance Design

The resistance of cylindrical shells and tubes under uniform bending has received significant research attention in recent times, with a number of major projects aiming to characterise their strength through both experimental and numerical studies. However, the investigated cross-section slenderness ranges have mostly addressed low radius to thickness ratios where buckling occurs after significant plasticity and the influence of geometric imperfections is relatively minor. The behaviour under uniform bending of thinner imperfection-sensitive cylinders that fail by elastic buckling was largely omitted, as was the influence of finite length effects. The value of such resistance models that are only useful for thicker cylinders is therefore somewhat limited.This paper offers the most comprehensive known characterisation of the buckling and collapse resistance of isotropic cylindrical shells and tubes under uniform bending. Expressed within the modern framework of Reference Resistance Design (RRD), it holistically incorporates the effects of material plasticity, geometric nonlinearity and sensitivity to realistic and damaging weld depression imperfections. The characterisation was made possible by the authors' recently-developed novel methodology for mass automation of nonlinear shell buckling finite element analyses. A modification of the RRD formulation is proposed which facilitates its application to systems of low slenderness, and offers a compact algebraic characterisation of all potential imperfection amplitudes for this common shell structural condition. A reliability analysis is also performed.

Experimental investigation on hollow-steel-tube columns with external confinements

Tubular steel members with slender cross-sections in compression are prone to local buckling. Different approaches, such as infilling concrete, installation of internal stiffeners and externally bonding fiber-reinforced polymer reinforcement, have been developed to retard the local buckling of steel tubular sections, and hence to improve the performance of tubular structures. In this study, a total of 35 circular hollow-steel-tube (HST) stub columns with both non-slender and slender cross-sections confined by different types of external confinements, namely steel ring, spiral and jacket confinements were tested in the experimental program. The uni-axial behavior of externally confined HST columns, including the failure mode, ultimate load-carrying capacity, stiffness and ductility, were studied and discussed. The enhancements in strength, stiffness and ductility of HST columns with different external confinements were assessed. The results indicated that the improvements on strength and stiffness of the confined HST columns were insignificant for columns with non-slender cross-sections and were considerable for columns with slender cross-sections, whilst the ductility of the HST columns was substantially enhanced by external confinements. Based on the results, equations for column ductility evaluation considering the effects of cross-section slenderness ratio, steel strength and external confinement, are proposed in this study, which are able to predict the column ductility for unconfined and externally confined HST columns.