DSM-based Design Approaches Research Articles

Short-to-intermediate slender pin-ended cold-formed steel equal-leg angle columns: Experimental investigation, numerical simulations and DSM design

Angles exhibit a complex structural behaviour, responsible for the fact that, in the current North American Specification for Cold-Formed Steel Structures, short-to-intermediate equal-leg angle columns are (i) not yet pre-qualified for the Direct Strength Method (DSM) design and (ii) excluded from the application of the LFRD resistance factor ϕ=0.85, valid for all other cold-formed steel compression members. Recently, the specific behavioural features exhibited by the above angle columns were incorporated into the proposal of a novel DSM-based design approach, for both fixed-ended and pin-ended columns, and it was shown that this added rationality goes along with quite accurate and reliable failure load predictions. However, the investigation leading to this design proposal also unveiled that there are no available experimental failure loads of slender pin-ended columns with intermediate-to-high slenderness values, which implied that the design procedure was validated for such columns exclusively on the basis of numerical failure loads. The research work reported in this paper provides a contribution towards filling this gap, since it mainly consists of an experimental study, carried out at the Federal University of Rio de Janeiro, on the behaviour and collapse of short-to-intermediate slender pin-ended cold-formed steel equal-leg angle columns. After addressing the selection of the columns to be tested, the experimental set-up and test procedure are described in detail and the results obtained are presented and discussed. Such results involve (i) initial imperfection measurements, (ii) equilibrium paths relating the applied load to key column displacements, (iii) deformed configurations (including the collapse mode) and (iv) failure loads. Next, those same experimental results are used to validate a shell finite model previously developed by the authors, which is subsequently employed to obtain additional numerical failure load data concerning the pin-ended angle columns under scrutiny. Then, attention is turned to assessing the merits of the novel design approach. The comparison between the experimental and numerical values obtained in this work and their estimates provided by the design equations shows a very good correlation, perfectly in line with that observed in the recent studies available in the literature−this means that the validation and calibration of the above design approach may be deemed (successfully) completed. Finally, the paper closes with the presentation and assessment of small alterations to the existing design expressions, aimed at improving their accuracy and rationality, thus paving the way towards codification in the near future.

Web crippling of beams under ITF loading: A novel DSM-based design approach

A new approach to estimate the web crippling failure load of cold-formed steel beams under Internal Two Flange (ITF) loading using the Direct Strength Method (DSM) is proposed in this paper. After the description of the existing test data to calibrate the DSM-based formula, the accuracy of the analytical expressions given in Eurocode 3 [1] and the North-American Specification [2] is briefly assessed. In order to obtain additional information on the web crippling behaviour of each test specimen, several types of analyses are performed: (i) quasi-static non-linear analyses (using finite elements), (ii) elastic buckling analyses (using finite elements and the GBTWEB software), and (ii) rigid-plastic analyses (using yield-line theory). The coefficients of a DSM-based formula are determined on the basis of the set of 85 experimental results available in the literature and the corresponding buckling and plastic load values. In spite of the different cross-sections, fastening conditions and test set-ups considered in the calibration procedure, it is possible to establish a clear relationship between the web crippling slenderness and the nominal-to-plastic load ratio. Finally, it is shown that the proposed DSM-based formula for ITF loading yields reasonable predictions of web crippling loads and provides safe estimates of flange crushing loads.

Local–Distortional Interaction in Cold-formed Steel Columns: Mechanics, Testing, Numerical Simulation and Design

This paper provides an overview of the latest developments of the research activity carried out by the authors concerning the non-linear behaviour, ultimate strength and Direct Strength Method (DSM) design of cold-formed steel (plain and stiffened) columns experiencing local–distortional (L–D) interaction. Initially, numerical results obtained by means of Generalized Beam Theory (GBT) elastic post-buckling analyses are presented and their unique modal nature is used to illustrate and provide the main behavioural/mechanics features of this mode coupling phenomenon. Then, both experimental and numerical (obtained from Abaqus shell finite element analyses – SFEA) are presented and discussed, making it possible to provide clear evidence and characterize the column L-D interactive behaviour and failure. Besides reporting on two experimental test series performed by the authors, the paper also presents a critical review of other experimental results available in the literature concerning columns undergoing L–D interaction. The numerical results deal with columns exhibiting different cross-section shapes and fairly extensive parametric studies are carried out, in order to (i) assess the relevance of L–D interaction, as far as the ultimate strength erosion is concerned, and (ii) gather substantial ultimate strength data. Next, after showing the inadequacy of the currently codified DSM column design curves to predict L–D interactive failures, the paper presents and assesses the merits of DSM-based design approaches recently developed specifically to handle such failures.

On the relevance of local–distortional interaction effects in the behaviour and design of cold-formed steel columns

The paper reports the results of a numerical investigation on the relevance of web-triggered local–distortional interaction on the ultimate strength of a large number of cold-formed steel fixed-ended (plain) lipped channel, zed, hat and rack-section columns. These results concern columns with various geometries (cross-section dimensions and unrestrained length) and yield stresses, ensuring a wide variety of combined ratios between the (i) distortional and local critical buckling stresses (RDL) and (ii) yield and non-critical buckling stresses (Ry). To avoid interaction with global buckling, all columns have global critical buckling stresses much higher than their local, distortional and yield counterparts. The aim of this study is to identify combinations of these ratios for which L–D interaction is relevant, in the sense that it affects visibly the column elastic and elastic–plastic post-buckling behaviours, ultimate strength and failure mechanism – special attention is devoted to the ultimate strength erosion. The numerical ultimate strength data obtained are then compared with the predictions of (i) the currently codified DSM (Direct Strength Method) strength curves for the design of columns failing in local and distortional modes and (ii) available DSM-based design approaches specifically developed to handle local–distortional interactive failures. Then, experimental results available in the literature concerning lipped channel and rack-section columns failing in local–distortional interactive modes are used to assess the quality of the estimates provided by the DSM-based design approaches. Finally, the paper closes with some considerations on the design of cold-formed steel columns undergoing L–D interaction.

Post-buckling behaviour and DSM design of web-stiffened lipped channel columns with distortional and local mode interaction

This paper examines the design and load-carrying capacity of fixed-ended web-stiffened lipped channel columns eroded by mode interaction behaviour combined with distortional and local deformations. Initially, the paper presents the results of an experimental investigation of compressive tests on web-stiffened lipped channel columns fabricated from cold-formed mild steel with a thickness of 1.50mm, which is aimed at determining their failure load-carrying capacity; the experimental investigation also aims to provide experimental evidence of the occurrence of such coupling phenomena concerning distortional and local modes, namely, local-distortional interaction and distortional-local interactive failures. Then, the paper examines the ultimate strength data of experimental columns, both reported in this paper and collected from the literature, and concludes that the current direct strength method (DSM) provides very unsafe predictions concerning such a detrimental interaction nature. Next, two DSM-based design approaches, namely, the nominal strength against local-distortional (NLD) and distortional-local (NDL) procedures, are presented and evaluated on the basis of all available experimental ultimate strength data. Finally, proposals and design considerations based on the DSM-shape for the thin-walled cold-formed steel sections, which fail in mixed modes of distortional and local buckling, are presented.