Distortional Global Interaction Research Articles

Axial buckling resistance of cold-formed steel built-up I-section wall panels with single- and double-layer sheathing configurations: experimental and analytical studies

ABSTRACT This paper presents experimental investigation of the axial behaviour of built-up (BU) (I-section) cold-formed steel doubly-symmetric channel with single-/double-layer sheathing on both sides configuration. Fifteen (15) monotonic concentric axial compression tests were performed on 7-BU sections with single-layer sheathing, 7-BU sections with double-layer sheathing, 1-BU section stud without sheathing. The experiments aim to enumerate ultimate axial strength, buckling interactions, failure pattern and strength enhancement due to sheathing for BU section stud members. The novelty of the study is that, for the first time an attempt is made to investigate the axial behaviour of single-/double-layer sheathed BU section panels using seven different sheathing boards. Results indicate large range of deformation behaviour, with local-global and distortional-global interaction buckling phenomena. Failure is also observed due to failing of screws in specimens with sheathing of thickness ≥ 9 mm and modulus of elasticity > 6400MPa. Also, for the first time, efficacies of four semi-analytical methods based on rational extension of direct strength method (DSM) are presented. Results suggest the insufficiency of current AISI design specifications, whereas predicted results obtained using the new modified DSM methodology are within the adequate variation range as the adopted methodology considers desired buckling interaction. The efficacy of the recommended design methodology is verified through reliability analysis.

DSM design of cold-formed steel fixed-ended lipped channel columns undergoing distortional-global interaction

This work reports a numerical investigation dealing with the post-buckling behaviour, strength, and Direct Strength Method (DSM) design of cold-formed steel fixed-ended lipped channel columns experiencing coupling between distortional and global (flexural-torsional) buckling − distortional-global (D–G) interaction. Various cross-section dimensions and lengths are considered, to ensure that the columns selected undergo different levels and types (“true”, “secondary-bifurcation distortional” or “secondary-bifurcation global”) of D–G interaction. The results presented and discussed, determined by means of Abaqus shell finite element geometrically and materially non-linear analyses, consist of elastic and elastic-plastic post-buckling equilibrium paths, failure loads and collapse modes. The steel material behaviour is deemed elastic-perfectly plastic and several yield stresses are considered, thus making it possible to cover a wide column D–G slenderness range. Particular attention is devoted to identifying the most detrimental initial geometrical imperfection shapes, in the sense that they lead to the lowest column failure loads. The numerical failure load data gathered are subsequently used to assess the merits of the available DSM-based design approaches developed to handle cold-formed steel columns undergoing D–G interaction. Since these design approaches are shown to be either inefficient and/or improvable, the above failure load data are also used to propose modifications/improvements aimed at achieving an efficient failure load prediction in the specific context of fixed-ended lipped channel columns. The success of this endeavour provides encouragement to the authors in their search for a safe, accurate and reliable DSM-based design approach capable of handling cold-formed steel columns with arbitrary cross-section shapes and/or end support conditions that fail in D–G interactive modes.

Distortional-global interaction in lipped channel and zed-section beams: Strength, relevance and DSM design

This work aims at presenting and discussing numerical results concerning the post-buckling behaviour, strength and design of cold-formed steel simply supported lipped channel and zed-section beams under uniform bending and undergoing distortional-global (D-G) interaction – two different support conditions are considered in the lipped channel beams. The relevance of the interaction effects is assessed by identifying the beams whose ultimate strength and/or failure mode are visibly affected by them. Distinct (i) global-to-distortional critical buckling moment ratios (RGD) and (ii) yield-to-non-critical buckling (distortional or global) moment ratios (Ry) are considered, which are expected to lead to different failure mode natures (global, distortional or interactive). For each beam type, combinations of 41 geometries and 11 yield stresses are considered, in order (i) to characterise the beams experiencing “true D-G interaction” (RGD ≈ 1.0) and “secondary global-bifurcation D-G interaction” (RGD > 1.0 and high Ry) and (ii) to investigate the possible occurrence of “secondary distortional-bifurcation D-G interaction” (RGD < 1.0 and high Ry). Moreover, an in-depth investigation on the elastic post-buckling behaviour is carried out, to assess how the initial geometrical imperfection shape/configuration influences the behaviour and strength of beams prone to D-G interaction. The results presented consist of (i) relevant non-linear equilibrium paths, (ii) deformed configuration evolutions along those paths and (iii) figures providing the failure mode characterisation. Then, the numerical failure moments obtained are compared with their predictions by means of (i) the currently available Direct Strength Method (DSM) beam distortional and global strength curves, and also (if necessary) (ii) proposed DSM-based design approaches, specifically developed to handle beam D-G interactive failures.

On the distortional-global interaction in cold-formed steel columns: Relevance, post-buckling behaviour, strength and DSM design

This work reports the available results of an ongoing numerical (shell finite element) investigation on the post-buckling behaviour, strength and design of fixed-ended cold-formed steel columns undergoing distortional-global (D-G) interaction. Columns with different cross-section shapes are analysed, namely plain lipped channel (LC), web-stiffened lipped channel (WSLC) and zed-section (Z) columns, in order to investigate distinct D-G interaction natures: involving either distortional and (global) flexural-torsional buckling (LC and WSLC columns) or distortional and (global) minor-axis flexural buckling (Z columns). In particular, the relevance of these D-G interaction types is discussed, by assessing when they affect visibly the column ultimate strength and/or failure mode. The results presented and discussed concern columns with various geometries and yield stresses, thus ensuring a wide variety of range combinations involving (i) global-to-distortional critical buckling load ratios (RGD) and (ii) squash-to-non critical buckling (distortional or global) load ratios (Ry) and leading to non-negligible failure load erosion. The possible occurrence and failure load impact of “secondary (distortional or global)-bifurcation D-G interaction” (RGD<1.0 or RGD>1.0 and high Ry) are investigated - it is well known that such impact may be significant in columns experiencing “true D-G interaction” (RGD≈1.0). The above results consist of (i) relevant non-linear (elastic and elastic-plastic) equilibrium paths, (ii) deformed configuration evolutions along those paths, evidencing D-G interactive effects, and (iii) figures providing the failure mode characterisation. Then, the numerical failure load data obtained are compared with their predictions by (i) the currently codified DSM (Direct Strength Method) column global and distortional strength curves, and (when necessary) (ii) proposed DSM-based design approaches, specifically developed to handle D-G interactive failures - a few design considerations are drawn from these comparisons.

GBT-based assessment of the mechanics of distortional-global interaction in thin-walled lipped channel beams

This work aims at presenting and discussing Generalised Beam Theory (GBT) numerical results concerning the elastic geometrically non-linear behaviour of simply supported lipped channel (LC) beams under uniform major-axis bending and experiencing distortional-global (D-G) interaction, making it possible to shed fresh light on the mechanics underlying this coupling phenomenon. Two LC beam geometries are considered, each exhibiting a different type of D-G interaction, namely (i) “true D-G interaction”, associated with close distortional (McrD) and global (McrG) critical buckling moments, and (ii) “secondary global-bifurcation interaction – SGI”, corresponding to McrD <<McrG. While the latter beam geometry contains a critical-mode distortional initial imperfection, the former one is analysed with initial geometrical imperfections exhibiting three critical-mode shapes (one distortional and two global, due to the lack of symmetry). Moreover, an investigation conducted to assess the possible occurrence of “secondary distortional-bifurcation D-G interaction – SDI” (McrG <<McrD) is also presented and discussed. In order to clarify the surprising behaviour of the beam undergoing a SGI, an additional beam is analysed, exhibiting a “pure” distortional post-buckling behaviour (i.e., involving no coupling phenomenon). The GBT-based results provide the evolution, along given equilibrium paths, of the beam deformed configuration (expressed in modal terms), relevant displacement profiles and modal participation diagrams. The knowledge acquired has visible impact on the development of rational design rules for CFS beams affected by D-G interaction.

On the mechanics of distortional-global interaction in fixed-ended columns

This work reports the results of a numerical investigation concerning the elastic post-buckling behaviour of fixed-ended thin-walled lipped channel and zed-section columns affected by distortional-global (D-G) interaction – “unexpected” features associated with the global buckling nature are unveiled in both cases. The columns analysed (i) exhibit cross-section dimensions and lengths ensuring the simultaneous occurrence of distortional and global critical buckling, and (ii) contain critical-mode initial geometrical imperfections (linear combinations of the critical distortional and global buckling mode shapes). For comparison and clarification purposes, the post-buckling behaviour of lipped channel columns buckling in an “isolated” distortional mode and containing “pure” distortional and global (flexural-torsional) initial geometrical imperfections are also analysed. The results presented and discussed are obtained through geometrically non-linear Generalised Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the column deformed configuration (expressed in GBT modal form), relevant displacement profiles and modal participation diagrams, making it possible to acquire in-depth insight on the mechanics underlying D-G interaction in columns. Finally, particular attention is paid to interpreting the differences exhibited by the various column post-buckling behaviours investigated.

Numerical investigation and direct strength design of cold-formed steel lipped channel columns experiencing local–distortional–global interaction

This paper reports the results of a numerical investigation concerning the relevance and Direct Strength Method (DSM) prediction of the ultimate strength erosion caused by local-distortional-global (LDG) interaction in cold-formed steel fixed-ended lipped channel columns. The geometries of the columns analysed (cross-section dimensions and lengths) were carefully selected to ensure that the three competing critical buckling loads are not more than 20% apart, thus guaranteeing a fairly high level of LDG coupling, and ordered in all the various possible sequences. In order to cover a wide slenderness range, several yield stresses are considered, falling below, in-between and above the lowest and highest critical buckling stresses. After providing a brief description of the column selection procedure, which is based on buckling analyses performed with Generalised Beam Theory (GBT), the methodology adopted to identify the most detrimental initial geometrical imperfection shape (in the sense it minimises the column strength) is addressed – it employs Koiter's asymptotic method along with a Monte Carlo simulation. Then, columns containing those initial geometrical imperfections are compressed up to failure, by means of Abaqus shell finite element analyses (SFEA), making it possible to acquire in-depth knowledge on the behaviour of lipped channel columns undergoing LDG interaction and gather considerable failure load data. Finally, the last part of the paper is devoted to the DSM prediction of those failure loads and uses the obtained “data bank” to assess whether the available design approaches are able to handle adequately the ultimate strength erosion caused by the triple interaction phenomenon under investigation – if this is not the case, new design curves must be developed.

Experimental study on cold-formed steel web stiffened lipped channel columns undergoing distortional–global interaction

This paper describes the design and testing of cold-formed steel web stiffened lipped channel sections experiencing distortional–global buckling mode interaction under axial compression. The relevant literature was reviewed, sections were selected with nearly coincident distortional and global buckling loads to have strong interaction effects. Selected sections satisfy the geometric limitations for pre qualified sections in order to apply direct strength method (DSM) in Appendix 1 of the North American Specifications (AISI-S100:2007). A total of 15 web stiffened lipped channel compression members were tested under pin with warping restrained end condition. The experimental results were compared with the current design rules in AISI-DSM and the quality of DSM based design procedures based on distortional–global mode interaction was reviewed. In addition, a reliability analysis was performed to assess the quality of current DSM and D–G interaction design procedure to predict the ultimate capacity of the sections.

Distortional–global interaction buckling of stainless steel C-beams: Part I — Experimental investigation

This paper presents experimental data for cold-formed stainless steel lipped channel beams featuring distortional–global interaction buckling. Three stainless steel alloys were employed in the tests, namely austenitic S30401, ferritic S44330 and lean duplex S32101. Coupon tests were carried out to determine the mechanical properties of the virgin sheet material as well as the work-hardened corner material of the press-braked sections. Geometric imperfections were measured for each specimen prior to testing. A total of 32 specimens were tested under four-point bending, six of which were tested with lateral bracing in order to determine the section capacity. The remaining 26 specimens, with spans ranging from 1.8m to 4.0m, were tested in a specially devised test set-up. The set-up featured a dual-actuator gravity simulator, flexible load-applying frames and idealized end support conditions, all of which contributed to minimizing uncertainties in the tests, thereby affording benchmark tests for analytical and numerical studies. Interaction buckling was observed in all tests of unbraced members.

Distortional–global interaction buckling of stainless steel C-beams: Part II — Numerical study and design

The paper presents a detailed finite element (FE) model intended for studying the distortional–global interaction buckling behaviour of thin-walled stainless steel beams. The model incorporated actual measured material properties of three stainless steel alloys (austenitic S30401, ferritic S44330 and lean duplex S32101), as well as measured initial geometric imperfections. The model was verified against the experimental data presented in the companion paper [1]. A parametric study was then carried out using the calibrated model to augment the ultimate strength database The accuracy of the Australian/New Zealand (AS/NZS 4673 [2]), American (SEI/ASCE-8 [3]) and European (Eurocode3, Part1-4 [4]) standards for stainless steel structures was evaluated using the available data. It was found that the current Australian/New Zealand and American design codes do not contain rules for checking distortional buckling strength nor do they account for distortional–global interaction buckling effects. The European standard accounts for distortional buckling effects by reducing the effective area of flange stiffeners using an effective thickness method, and covers the effect of distortional–global interaction by using the effective cross-section for overall buckling strength checks. The European code was therefore more conservative than the other two standards. Following the principles of the Australian and American design codes for cold-formed steel structures, additional provisions for checking distortional buckling strength were suggested to improve the current Australian/New Zealand and American stainless steel design codes. Variants of the proposed provisions to account for distortional–global interaction were also examined which resulted in generally better predictions than those of the European code. However, the distortional–global interaction effect was found to vary with the section slenderness, and none of the design provisions performed consistently better than others.

Influence of web members on the in-plane and out-of-plane capacities of steel storage upright frames

Global buckling behaviour, with or without interaction with distortional buckling, of storage rack members is evaluated by tests carried out according to EN 15512 (2009) [1] on compression and out-of-plane bending of upright frame modules. Based on test results for both single upright sections and frame modules, completed by numerical simulation, the present paper attempts to demonstrate that the design buckling strength of uprights can be conveniently estimated by single section tests, providing that the length of these members is calibrated for the distortional–global interaction mode.

Distortional–global interaction in lipped channel columns

This work presents and discusses numerical results concerning the post-buckling behaviour (elastic and elastic–plastic) and ultimate strength of cold-formed steel lipped channel columns experiencing distortional–global interaction. The analyses cover columns with (a) geometries selected to ensure very close global and distortional buckling loads, and (b) the support conditions usually adopted in experimental investigations: fixed-ended and pin-ended columns. A fairly large number of columns are analysed, differing in the initial geometrical imperfection shape and/or yield stress – the various initial geometrical imperfection shapes are linear combinations of the competing buckling modes with amplitudes equal to (a) 10% of the wall thickness, t (D) and (b) L/1000 (G). For clarification purposes, the column pure global elastic post-buckling behaviours are also addressed. These results are (a) elastic (mostly) and elastic–plastic non-linear equilibrium paths, (b) figures and curves providing the evolution, along the elastic paths, of column deformed configurations and, for the elastic–plastic columns, (c) figures showing the plastic strain location and growth, as well as the natures of the failure mechanisms.

Behaviour of cold-formed steel perforated sections in compression. Part 1—Experimental investigations

This paper is the first part of a study devoted to interactive buckling of steel pallet racks compression members, carried out at the CEMSIG Research Centre 〈http://cemsig.ct.upt.ro〉 from “Politehnica” University of Timisoara; this part summarizes the experimental program [1,2]. Upright members of two different cross-sections, with and without perforations, were tested according to the guidelines of European design code for pallet rack systems EN15512 [3], in order to determine the ultimate strength for specimens of length corresponding to local buckling, i.e. stub columns, and of length equal to the distance between two subsequent nodes of an upright frame, i.e. upright members. The last set of tests was devoted, mainly, to the observation of distortional buckling of upright members. However, depending on the cross-section dimensions, the length between two subsequent nodes can be often larger than distortional critical length. In such cases the test results correspond rather to the distortional–global interaction, than to pure distortion. Consequently, additional specimens having the length calibrated to correspond to distortional buckling and to interactive distortional-overall buckling range, respectively, were tested. Material tests and imperfection measurements were also performed.

Local–distortional–global interaction in lipped channel columns: Experimental results, numerical simulations and design considerations

This work aims at contributing towards understanding the structural response and predicting the ultimate strength of cold-formed steel lipped channel columns affected by local–distortional–global (LDG) interaction. Initially, the most relevant aspects concerning the buckling and elastic–plastic post-buckling behaviours of fixed-ended lipped channel columns with nearly coincident local, distortional and global (flexural–torsional) buckling loads are briefly addressed. Then, the paper (i) summarises the most important test results obtained in a recently reported experimental investigation carried out at the Federal University of Rio de Janeiro, (ii) addresses their numerical simulation by means of Abaqus shell finite element analyses (SFEA) and (iii) presents the outcome of a fairly extensive numerical parametric study performed to obtain ultimate strength data concerning fixed-ended lipped channel columns experiencing LDG interaction. Finally, the ultimate strength “data bank” gathered, consisting of 12 experimental and 134 values, are used as the starting point to assess the performance (accuracy and safety) of design approaches, based on the currently available Direct Strength Method (DSM) strength curves and intended to estimate the failure loads of cold-formed steel lipped channel columns affected by the triple mode interaction under consideration.

Ultimate limit strength of pallet racks uprights

The paper summarizes the results of experimental and numerical investigations, carried out at the CEMSIG Research Center ( http://cemsig.ct.upt.ro ) of ‘Politehnica’ University of Timisoara, on compression members of pallet racks. Members of two different cross-sections, with and without perforations, have been tested on the aim to calibrate a design approach to evaluate their ultimate strength and, on this basis, to check the buckling resistance of bar members accounting for distortional-global interaction. The lengths of upright specimens and testing procedure, for local and distortional buckling, were chosen according to European pallet rack design code provisions. Test on base materials and imperfection measurements have been also performed. In order to study the distortional-global interactive buckling, the ECBL method has been used. The paper presents the main results of these investigations.