Slender Cross-sections Research Articles

The Continuous Strength Method of Cold-formed Stainless Steel Equal-leg Angle Section Stubs

Structural stainless steel requires appropriate recognition of its beneficial properties such as material nonlinearity and significant strain hardening. The recently proposed Continuous Strength Method (CSM) exploits those benefits through a strain based approach for both stocky and slender cross-sections, and is shown to yield a higher level of accuracy and consistency, as well as design efficiency, in the capacity predictions of stainless steel cross-sections. Although there have been extensive and comprehensive studies on SHS, RHS, round tubes and H-sections stubs, but research into cold-formed stainless steel equal-leg angle section stubs remains scarce. In this paper, the scope of the CSM is extended to cover the design of cold-formed stainless steel equal-leg angle section stubs. Developed FE models included material nonlinearities as well as initial geometric imperfections. A comprehensive parametric study has been carried out covering a wide range of slenderness with different cross section geometries for the considered angle stubs. Cross-section resistances obtained from the numerical study were used to assess the performance of the current Continuous Strength Method (DSM) guidelines and EC3 when applied for stainless steel equal-leg angle section stubs; obtained comparisons showed considerable conservatism. A modified design method for cold-formed stainless steel equal-leg angle section stubs is proposed herein following CSM techniques, which provides considerably more accurate predictions for the considered cold-formed stubs. Reliability of the proposed design equations is also presented showing a good agreement with both experimentally and numerically obtained results.

Structural behaviour of hardwood veneer-based circular hollow sections of different compactness

This paper presents the capacity and structural behaviour of hardwood veneer-based circular hollow sections (CHS) tested in bending, shear and compression. The sections were manufactured from early to mid-rotation (juvenile) Gympie messmate (Eucalyptus cloeziana) plantation thinned logs. In total twenty-one 167 mm Outside Diameter (OD) × 1.2 m long CHS were manufactured in seven sets of three nominally identical sections. Two different wall thicknesses were investigated to produce nine compact and twelve more slender cross-sections. The sections were also manufactured in three different structural grades. A sudden failure mode was observed in the compression zone of the slender sections tested in bending. In compression, the compact sections showed a ductile behaviour, while the slender sections showed a more brittle behaviour, with the sections bursting into longitudinal strips. While a relationship was observed between the bending and compressive capacities, and the structural grade, no such relationship was noticed for the shear capacity. Comparison to steel and concrete sections of similar outside diameter proved that the timber sections are the most efficient in terms of bending and compressive capacity to linear weight ratio. The timber sections fall behind their steel and concrete counterparts in terms of shear efficiency, however they still have enough shear capacity for representative structural applications.

The effect of non-uniform bending on the lateral stability of steel beams with slender cross-section at elevated temperatures

In this paper, the effect of non-uniform bending on the lateral torsional buckling (LTB) of steel beams with slender cross-sections subjected to elevated temperatures is numerically investigated. Local buckling is the main failure mode for slender sections whereas the lateral torsional buckling is one of the principal failure modes for beams, thus the interaction between these two failure modes greatly affects the load-bearing capacity of the beams. In the case of fire, recent studies have shown that the design procedures of Part 1–2 of Eurocode 3 are unreliable and too conservative due to the inconsistent treatment of such interaction phenomena. On the other hand, it is known that non-uniform bending has a beneficial effect on the ultimate capacity of beams but there is limited knowledge about its influence on beams with slender cross-sections. This work aims at studying the influence of non-uniform bending on the combined local-global interaction response of beams with slender open I-sections in the case of fire. The inclusion of the factor “f” in a recently proposed LTB design procedure that groups the response of the beams into different ranges of effective section factors is analysed and the accuracy of such proposal is demonstrated against around 20,000 GMNIA (Geometrically and Material Non-Linear Analyses with Imperfections) simulations. Finally, the improvements of this proposal on the current Eurocode 3 design procedure are highlighted.

End effect on determining shear modulus of timber beams in torsion tests

The end effect plays an important role in determining where the rotation measuring gauges should be located in a torsion test. A thorough review on the impact of end effect in a torsion test has been conducted, followed by an experimental validation. A close-ranged photogrammetric method using binocular stereo vision technique was employed in this study. The results have indicated that the end effect has a great impact on a region of 1.5 times the cross-sectional depth of the beam from the supports. Therefore, the distance between the gauges and the supports as specified in BS EN 408:2010+A1:2012 for the torsion test setup is not sufficient for the beams with slender cross-sections. This research has also indicated that it is more appropriate to use the depth of the beam as the referencing dimension to specify this required minimum distance.

Elastoplastic Bending Load - Carrying Capacity of Steel Members

Many members of steel structures are subjected mostly to bending. In these cases can be especially very useful to use by resources also plasticity of structural steels. Therefore, the new international and national standards for the design of steel structures allow the elastic and plastic calculation methods and procedures. The elastoplastic bending load-carrying capacity of steel members depends in a high degree on local stability of their webs and flanges. From local stability aspects the steel members can have compact or slender cross-sections. The compactness of steel cross-sections is only relative. It depends on the loading level or material utilization, and on the buckling resistance of their webs and flanges in the most loaded cross-sections and areas. The judgment of steel cross-sections compactness in this content is complicated stability problem. The new standards for the design of steel structures contain the specific classification of the cross-sections due to dimensions and slenderness of their compression and bending parts. The paper contains the results of the experimental-theoretical investigation of the elastoplastic local stability and load-carrying capacity of steel members. The proposed methodology enables the elastoplastic calculation of the cross-section bending resistance depending from the limit development of plastic strains.

Full slenderness range DSM approach for stainless steel hollow cross-section columns and beam-columns

The behaviour of austenitic, ferritic and duplex stainless steel Rectangular and Square Hollow Section members subjected to compression and combined loading is investigated in this paper. A full slenderness range Direct Strength Method (DSM) approach is proposed based on experimental results and numerical strengths obtained from FE parametric studies. The method accounts for local buckling effects and enhanced material properties are also incorporated for those members stable enough to allow partial yielding of the cross-sections. The proposed method is based on strength curves previously provided for cross-sections although additional limitations have been adopted. The DSM approach for columns is based on existing buckling curves and provides accurate resistance predictions for slender and stocky cross-sections. The proposed DSM approach for beam-columns also improves capacity predictions for stocky and slender cross-sections obtained from the traditional methods for different bending moment distributions. This is attributed to the fact that the beam-column behaviour is directly calculated with a unique strength curve, considering the member and section slendernesses based on the elastic instabilities of the section subjected to the actual stress distribution instead of calculating the compressive and flexural strengths independently and combining these through an interaction equation, as is the traditional uncoupled approach. Finally, a reliability study of the full slenderness range DSM approach is presented to determine resistance factors for the different stainless steel grades columns and beam-columns.

Numerical investigation on buckling resistance of stainless steel hollow members

Structural stainless steel requires appropriate recognition of its beneficial properties such as material nonlinearity and significant strain hardening. The Continuous Strength Method (CSM) exploits those benefits through a strain based approach for both stocky and slender cross-sections. In this paper, a new design method is proposed that combines the CSM design principles with Perry type buckling curves for stainless steel square and rectangular hollow sections (SHS and RHS) subjected to compression. Numerical models were developed to investigate effects of various parameters on column strength and to develop complete column curves for hollow members. It was observed that cross-section slenderness λp and material properties such as non-dimensional proof stress e and strain hardening exponent n significantly influence column resistances. Effects of e and n were appropriately incorporated through introduction of correction factors to modify non-dimensional member slenderness. It was observed that the shapes of column curves were mostly affected by λp, and hence imperfection parameter η, as used in Perry formulations, was expressed as a function of λp; this technique yielded separate column curves for different λp values. The proposed method includes the strain hardening benefits for stocky sections, and abolished the necessity of calculating effective cross-sectional properties for slender sections. Performance of the proposed technique is compared against those obtained by using the European guidelines.

Structural response and continuous strength method design of slender stainless steel cross-sections

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

Buckling Behaviour of Stainless Steel Square Hollow Sections

Structural stainless steel design guidelines should appropriately recognise its characteristic beneficial properties such as material nonlinearity and significant strain hardening. The Continuous Strength Method (CSM) exploits those through a strain based approach for both stocky and slender cross-sections. In this paper, a new design method is proposed that combines the CSM with Perry type buckling curves. Numerical models were developed to investigate effects of various parameters on column strength and to develop full column curves. It was observed that material nonlinearity significantly influence column strengths, and hence, different column curves were developed for a total of 20 material property combinations by calibrating imperfection factor and limiting slenderness ratio for each set. Proposed method includes the strain hardening benefits for stocky section, and abolished the necessity of calculating effective cross-sectional properties for slender sections. Performance of the proposed technique is compared against those obtained by the Eurocode EN1993-1-4.

Ultra-light gauge steel storage rack frames. Part 2 – Analysis and design considerations of second order effects

Local and distortional buckling reduces the flexural and warping rigidities of steel frames. As a result, the sway buckling load of locally unstable unbraced frames is reduced and sway deflections increase at a faster rate than corresponding locally stable unbraced frames. This leads to greater second order moments and potentially premature collapse, since commonly, unbraced steel frames are designed using elastic analyses (2nd order or 1st order with moment amplification) which assume unreduced values of the flexural and warping rigidities. This paper investigates the effects of second order moments induced by local and/or distortional buckling of the uprights of steel storage rack frames. Using results from the accompanying experimental investigation, calibrated FE models are used to predict the strength of steel storage rack frames with increasingly slender cross-sections. The FE strengths are compared to design strength predictions and conclusions are drawn about the extent to which current specifications are able to accommodate second order moments generated by local and/or distortional buckling.

Local buckling in laterally restrained steel beam-columns in case of fire

The behaviour of laterally restrained steel beam-columns with slender cross-sections (Class 4) where local buckling occurs under fire situation is numerically investigated. Although recommendations are given in Eurocode to address the local buckling for the case of fire, few studies address its influence at elevated temperatures, and more particularly its influence on the load bearing capacity of laterally restrained beam-columns, which represents an unknown safety level for the Eurocode procedures. As a primary objective of this study, the level of accuracy and safety of simplified methods of Eurocode 3 is studied based on extensive numerical investigation of several member lengths, different bending moment distributions and load ratios for various cross-sections and considering different heating temperatures. Local and global geometrical imperfections as well as residual stresses have been included in the numerical simulations. It is concluded that the Eurocode procedures lack consistency and the capacity of laterally restrained beams-columns is overestimated in many cases due to local buckling. Therefore, modifications to the current design methodology are proposed in this study leading to better estimation of the overall capacity of the laterally restrained beam-columns in case of fire, and finally, improved safety and consistency is achieved.

Behaviour and design of stainless steel slender cross-sections subjected to combined loading

The Continuous Strength Method (CSM) is a recently developed strain based design technique that produces accurate predictions for cross-section resistances for stocky sections against individual and combined actions. This paper numerically investigates the behaviour slender stainless steel cross-sections subjected to combined loading i.e. compression plus bending. Generated numerical results and available test results were used to develop CSM formulations to tackle the conservatism shown by the current international codes in predicting resistances of slender sections. Keeping the basic design philosophy in line with the current CSM design technique, interaction equations are re-calibrated herein for slender stainless steel hollow sections.

Critical temperatures of class 4 cross-sections

This paper describes an investigation on the critical temperatures of slender cross-sections according to Eurocode 3 design. Slender cross-sections are prone to local buckling, which, as the name implies, is characterized by a local failure that occurs in the presence of compressive stresses and prevents the cross-sections from developing their full plastic bending resistance or axial compression resistance, which leads to the reduction of the load bearing capacity. Eurocode 3 classifies these cross-sections as Class 4, the highest class, and suggests a default critical temperature of 350°C irrespective of the load level conditions. This study demonstrates that this temperature is too conservative especially if different degrees of utilization of the cross-section are taken into account. The establishment of a default critical temperature is invaluable from a practical standpoint and, therefore, it is the purpose of this work to recommend and validate new default critical temperatures for Class 4 cross-sections subject to compression and bending about the major axis for different reduction factors for the design load level under fire conditions, based on an extensive numerical investigation. From this study, it is observed that the critical temperatures for such cross-sections are within the range of 400°C and 600°C for the usual load levels and, based on that, new default critical temperatures are suggested.

Second-order effects in locally and/or distortionally buckled frames and design based on beam element analysis

In the design of steel portal frames, second order effects are usually accounted for by using a second order elastic analysis to calculate the deformations and internal actions of the frame. In this analysis, one-dimensional beam elements are employed irrespective of whether the cross-sections of members are slender or non-slender. However, frames composed of members with slender cross-sections may buckle in local and/or distortional modes before reaching the ultimate limit state. In this case, the flexural rigidity of the frame is reduced when local/distortional buckling occurs, and as a result it undergoes larger sway deflections than had local/distortional buckling not occurred. The additional second order moments thus caused by local/distortional bucking are not accounted for in current design provisions.In this paper, the additional second-order effects caused by the development of local/distortional buckling are studied by comparing numerically determined ultimate capacities with design capacities. The numerical ultimate strengths are based on previously calibrated geometric and material nonlinear shell finite element models, and the design capacities are determined using the Australian Standard for Cold-formed Steel Structures AS/NZS 4600. A simplified approach to account for local/distortional buckling in beam-element-based design is also proposed. The focus is on portal frames subject to in-plane sway failure.

Element interaction of cold-formed stainless steel cross-sections subjected to major axis bending

Numerical investigation of cold-formed normal and high strength stainless steel square and rectangular hollow sections subjected to major axis bending is presented in this paper. A non-linear finite element model which includes geometric and material non-linearities was developed and verified against experimental results. The material properties of the flat and corner portions of the specimen sections were carefully incorporated. It was shown that the finite element model closely predicted the failure modes, ultimate moments and deflections of the tested specimens. The model was then used for an extensive parametric study to investigate the interaction effects of constituent plate elements on Class 3 and 2 slenderness limits and cross-section moment capacities of cold-formed stainless steel square and rectangular hollow sections in bending.The numerical strengths predicted from this study together with the experimental results were compared with the theoretical elastic and plastic bending moments. It was shown that the element interaction surely influences the flexural behavior of cold-formed stainless steel square and rectangular hollow sections especially for slender cross-sections. The design provisions on Class 3 and 2 slenderness limits and effective width equations specified in ASCE Specification, EC3 Code and proposed by Gardner and Theofanous are not suitable for square and rectangular hollow sections in bending since they did not take into consideration interaction effects of constituent plate elements. Hence, the new Class 3 and Class 2 slenderness limits and the cross-section moment capacity design equations are proposed in this study based on the whole cross-section response, which carefully consider the interaction effects of constituent plate elements.

Numerical investigation of the lateral–torsional buckling of beams with slender cross sections for the case of fire

An extensive numerical study is performed to investigate the lateral–torsional buckling of steel beams with slender cross sections for the case of fire. The influence of local buckling is analysed, and the numerical results are compared to the simplified design methods of Part 1-2 of Eurocode 3 for the case of beams with Class 1 and 2 cross sections. The actual provisions of Eurocode 3 Part 1-2 are demonstrated to be unreliable. A parametric study is carried out to investigate the influence of several parameters on the resistance of laterally unrestrained steel beams with slender cross sections for the case of fire: the effective section factor, temperature, steel grade, depth-to-width ratio (h/b) and residual stresses. Based on the parametric study, a proposal for a new design curve is made for beams with slender cross sections for the case of fire, taking into account the influence of local buckling by grouping the response of beams into different ranges of effective section factors. The capacity predicted by the simplified methods using the proposed design curve leads to an improved yet safe design method compared to the results of the finite element analysis.

COMPRESSION CAPACITY OF SLENDER STAINLESS STEEL CROSS-SECTIONS

The Continuous Strength Method (CSM) is a new strain based design approach developed for nonlinear metallic materials, and has recently been successfully used for stocky stainless steel sections for which the benefit of strain hardening is more pronounced. Typically available stainless steel cross-sections are quite slender, and their failure is dominated by local plate buckling before yielding showing significant post buckling, which does not allow the definition of cross-section deformation capacity currently adopted in CSM. In this paper, a concept of equivalent elastic deformation capacity is introduced for slender sections, and the scope of CSM is extended to predict capacities for slender cross-sections under compression. Design guidelines are proposed to calculate equivalent elastic deformation capacities for various cross-section types using the current knowledge of CSM, which is used to predict the ultimate section capacity when subjected to compression. The proposed rules are verified against all available test results, and are found to in good agreement with experimental evidence.

Structural modeling of cold-formed steel portal frames

The paper describes the modeling of pitched roof cold-formed steel portal frames with slender cross-sections. Two types of finite element models are introduced: a shell finite element model and a modified beam finite element model. The shell element model involves explicit modeling of each structural member and accounts for the semi-rigid behavior of apex and eave joints by incorporating spring-like elements. The beam element model utilizes a reduced tangent rigidity method to account for cross-sectional instability. Both models are compared with results of experimentally tested portal frames, and good agreement is demonstrated.

Effective width equations accounting for element interaction for cold-formed stainless steel square and rectangular hollow sections

Rectangular hollow sections featuring high height-to-width (aspect) ratios have shown to offer improved ultimate capacity due to the effects of the interaction between the elements within the cross-section which are particularly significant for slender cross-sections (Class 4) undergoing local buckling. The European design rules dealing with stainless steel, EN 1993-1-4 [1], utilises the concept of cross-section classification and the effective width method for the design of slender cross-sections susceptible to local buckling neglecting such interaction effects, hence resulting in conservative predictions. This paper examines the benefits of element interaction effects on cold-formed ferritic stainless steel compressed sections on the basis of carefully validated finite element models. Following parametric studies, the applicability of various alternative design approaches accounting for element interaction to ferritic stainless steel is assessed and effective width curves, as well as a Class 3 limiting slenderness equation, are derived herein as an explicit function of the aspect ratio. Comparisons with the loads achieved in the FE models have shown that the proposed effective width equations allowing for the benefits of element interaction improve capacity predictions making design more cost-effective.

Lateral-torsional buckling of steel beams with slender cross-sections in case of fire

Lateral-torsional buckling of steel beams with slender cross-sections in case of fire