Direct Strength Method Design Research Articles

Behavior, Failure, and Direct Strength Method Design of Steel Angle Columns: Geometrical Simplicity versus Structural Complexity

AbstractThis work provides a state-of-the-art report on the current knowledge concerning the structural behavior and design, by means of the Direct Strength Method (DSM), of steel equal-leg angle c...

Experiments on load-bearing cold-formed steel sheathed studs at elevated temperatures

This paper assesses the stability and strength of sheathed cold-formed steel studs at elevated temperatures. Short and intermediate-length studs braced with gypsum, fire-rated gypsum, and oriented strand board were subjected to compressive axial load and temperatures ranging from 20 °C to 600 °C. A total of 40 tests were conducted in the steady-state regime, where the studs were first heated, then a compressive axial load was applied until failure occurred. Results show that the load-carrying capacity of the structural members decreases with increasing temperature, as the mechanical properties of the cold-formed steel reduce, and the bracing provided by the sheathing degrades. Local and distortional cross-section buckling failures are observed in the cold-formed steel member. The stabilizing effect and increase of load-carrying capacity attributed to the sheathing at ambient temperature is eventually lost at elevated temperature and the behavior of the sheathed studs becomes similar to the behavior of unsheathed members. Direct Strength Method design equations provided in the U.S. AISI S100 design specification are used with experimentally determined elevated temperature properties to predict the load-carrying capacity of the studs, then compared to experimental results to explore the feasibility of current design methods for performance-based fire design applications.

Mode interaction in cold‐formed steel members: state‐of‐art report

AbstractExtended keynote paper of Eurosteel 2021This is Part 2 of a two‐part paper providing a state‐of‐art report of the most recent findings concerning the behaviour, strength and Direct Strength Method (DSM) design of cold‐formed steel (CFS) columns and beams affected by mode coupling phenomena not adequately covered by the current specifications for CFS members. This second paper covers interactions involving global buckling modes, namely local‐distortional‐global (L‐D‐G), distortional‐global (D‐G) and global‐global (flexural‐torsional/flexural – FT‐F) interaction – note that local‐global (L‐G) interaction, already well mastered by the technical/scientific community, is not dealt with. Like Part 1 [1], this paper also addresses experimental tests, numerical simulations and DSM‐based design approaches, intended to i) acquire in‐depth knowledge on the non‐linear behaviour (elastic and elastic‐plastic), load‐carrying capacity and failure mode nature of the members under consideration, and ii) make use of the above knowledge to develop, propose and assess the merits of efficient DSM‐based design approaches to estimate their failure loads/moments. Taking into account the fundamental concepts and DSM design curves presented in Part 1 [1], the paper addresses separately each mode coupling phenomenon dealt with, for columns, and only D‐G interaction for beams – recall that L‐D interaction (columns and beams) was covered in Part 1 [1]. For columns undergoing L‐D‐G interaction and angle columns susceptible to FT‐F interaction, the work reported includes experimental studies, numerical simulations and DSM‐based design considerations and/or guidelines. For columns and beams experiencing D‐G interaction and channel columns prone to FT‐F coupling, only numerical results are reported – they reveal surprising behavioural features that will be very useful in planning future test campaigns and achieving efficient design approaches. Finally, the two‐part paper closes with a few concluding remarks and a perspective about future developments in this field.

Mode interaction in cold‐formed steel members: state‐of‐art report

AbstractExtended keynote paper of Eurosteel 2021This two‐part paper provides a state‐of‐art report on the most recent findings concerning the behaviour, strength and Direct Strength Method (DSM) design of cold‐formed steel (CFS) columns and beams affected by mode coupling phenomena not adequately covered by the current specifications for CFS members, namely local‐distortional (L‐D), local‐distortional‐global (L‐D‐G), distortional‐global (D‐G) and global‐global (flexural‐torsional/flexural – FT‐F) interaction. The paper addresses experimental tests, numerical simulations and DSM‐based design approaches that are intended to i) acquire in‐depth knowledge on the non‐linear behaviour (elastic and elastic‐plastic), load‐carrying capacity and failure mode nature of the members under consideration, and ii) make use of that knowledge to develop, propose and assess the merit of efficient DSM‐based design approaches to estimate their failure loads/moments. Initially, illustrative column results are briefly presented to help grasp some fundamental concepts, namely the characterisation of i) the aforementioned mode coupling phenomena, ii) different sources of mode interaction that may lead to failure load/moment erosion, and iii) the most detrimental initial geometrical imperfections. The DSM design curves currently codified and two strength curves recently developed for column flexural‐torsional and beam distortional failures are presented next. The two‐part paper then addresses separately each mode coupling phenomenon dealt with, for columns, but only L‐D and D‐G interaction for beams – while L‐D interaction (in columns and beams) appears in Part 1, the remaining column and beam coupling phenomena (all involving global buckling) are dealt with in Part 2 [1]. For columns undergoing L‐D and L‐D‐G interaction, beams experiencing L‐D interaction and angle columns susceptible to FT‐F interaction, the work reported includes experimental studies, numerical simulations and DSM‐based design considerations and/or guidelines. For the remaining coupling phenomena, only numerical results are reported, but they unveil interesting (and unexpected) behavioural features that will help plan future test campaigns and achieve efficient design approaches. Finally, the two‐part paper closes with a few concluding remarks and an outlook regarding future developments in this field.

Consistent and Simplified Direct Strength Method for Design of Cold-Formed Steel Structural Members under Localized Loading

The direct strength method (DSM) is a newly developed design method for cold-formed steel members due to its reliability and consistency. It has been well developed and incorporated in the North American Specification and the Australian/New Zealand Standard for the design of cold-formed steel members under compression, bending, and recently, in shear. To date, there are no DSM rules for the design of cold-formed members under localized loading resulting in the web-crippling phenomenon. Recent literature has attempted to propose the DSM design equations for four localized loading cases including the interior one-flange (IOF), end one-flange (EOF), interior two-flange (ITF), and end two-flange (ETF) loading cases specified in the design specifications/standards. However, these proposed DSM equations were calibrated differently depending on the types of loading cases and geometric shapes of the cross-sections by varying coefficients and exponents in the DSM equations. In this paper, consistent and simplified DSM equations previously proposed by the authors are explained and calibrated for use in the design specifications/standards. They include new plastic mechanism models developed for determining the yield load and also cover the design of sections in the inelastic reserve range as observed. Detailed explanations of the yield load (Py) component and references to computing the buckling load (Pcr) component are given. A design example is also included.

Shear tests and design of cold-formed steel channels with central square holes

Abstract In the latest North American Specification S100:2016 Edition and the most up-to-date Australian/New Zealand Standard AS/NZS 4600:2018, the Direct Strength Method (DSM) shear design rules for unperforated channel sections have been adopted. To date, for perforated sections, there is no DSM design rule for shear in the current Specification/Standard while the conventional reduction factor method is still in use to calculate shear strengths for these sections. This paper summarises the test results in an experimental program aiming to determine the ultimate shear strengths of high strength cold-formed C-sections with square holes centrally cut from the webs. A total number of 24 tests were performed using lipped channel sections in which 18 tests were conducted with central square holes of variable thicknesses and sizes, and the remaining 6 were tested with no holes in the webs. Three different section thicknesses and square hole sizes were chosen for investigation in this study. In addition, Finite Element Method (FEM) analysis was initially developed to validate against test results, and the accurate results from the FEM were then employed in a parametric study for the extension of test data by varying the section thicknesses and the hole sizes. In the DSM shear design equations, two inputs namely the shear buckling load, Vcr, and the shear yielding load, Vy, are required. The numerical solutions for Vcr for whole sections with central square holes have been proposed by first author in previous research studies. For Vy in this paper, a new and simplified model is proposed based on net web areas. Recommendations for an extension to the DSM shear design rules for channel sections with square holes up to certain hole size limit are given.

Distortional strength of end-bolted CFS lipped channel columns: Experimental investigation, numerical simulations and DSM design

This paper reports the results of an experimental investigation and numerical simulations concerning the influence of bolted end support conditions on the failure loads of cold-formed steel lipped channel columns buckling and failing in distortional modes, as well as on their prediction by means of the Direct Strength Method (DSM). The end supports consist of pairs of cylindrical high-strength bolts with hexagonal heads and nuts, which are inserted in standard-sized holes located at the intersections of the cross-section flanges with the minor principal centroidal axis (parallel to the web). After selecting the column geometries (cross-section dimensions and lengths) and yield stresses, the test set-up and procedure are described in detail, and the experimental results obtained are presented and discussed. Such results consist of initial imperfection measurements, equilibrium paths relating the applied load to key column displacements, deformed configurations (including the collapse mode) and failure loads. Next, those same experimental results are used to validate a previously developed shell finite model, which is subsequently employed to obtain additional numerical failure load data concerning the end-bolted columns under scrutiny. Then, attention is turned to assessing the merits of the available DSM column distortional design curves. Because it is concluded that these design curves clearly overestimate the failure load data obtained, new/modified strength curves are preliminarily proposed and shown to considerably improve the prediction quality (safety and reliability) of the end-bolted column failure loads, thus providing motivation and encouragement to continue the search for an efficient DSM-based design approach for end-bolted columns failing in distortional modes. • Experimental and numerical investigation on end-bolted lipped channel columns failing distortionally • Procedure and results of test campaign involving 13 column specimens described and discussed. • Validated SFE model employed to perform parametric study and gather distortional failure load data. • Available DSM design curves found to grossly overestimate the experimental and numerical failure loads. • Proposal of DSM-based design approaches that improve considerably the failure load prediction quality.

Proposal to Improve the DSM Design of Cold-Formed Steel Angle Columns: Need, Background, Quality Assessment, and Illustration

AbstractThis paper presents a proposal for the codification of an efficient design approach based on the direct strength method (DSM) for cold-formed steel equal-leg angle columns with short-to-int...

On the direct strength method design of columns against global failures

This paper reports an in-depth and extensive numerical investigation aimed at assessing the accuracy of the current Direct Strength Method (DSM) design curve in predicting the failure load of cold-formed steel columns collapsing in global modes, namely flexural or flexural-torsional modes. This study concerns fixed-ended columns with a wide variety of cross-section shapes: plain channels, lipped channels, double-fold (return) lipped channels, web-stiffened lipped channels, web/flange-stiffened lipped channels, lipped zed-sections, hat-sections, rack-sections and I-sections (formed by back-to-back plain channels). The first part of the work is devoted to plain channel columns and starts with a parametric study aimed at gathering failure loads of columns with continuously varying geometries and yield stresses, so that they (i) buckle in either major-axis flexural-torsional or minor-axis flexural modes and (ii) cover a wide slenderness range. These failure loads are then used to assess the quality of their predictions yielded by the codified global DSM design and to propose modifications to improve this quality. The second part of the work employs the modified DSM-based global design curves, as well as the current one, to predict a fairly large number of numerical failure loads of columns exhibiting the remaining eight cross-section shapes. This extensive parametric study shows that the failure load predictions provided by the proposed/modified DSM global strength curves (i) have very high quality and, for the columns considered, (ii) clearly outperform those yielded by the current design curve. In addition, the advantages and disadvantages of the proposed DSM global design curves are also discussed.

Experimental validation of the Direct Strength Method for shear spans with high aspect ratios

Shear behaviour of cold-formed steel beams with an aspect ratio (shear-span/web-depth) of 1.0 has been studied thoroughly, mainly using central point load tests. However, for beams with higher aspect ratios, the effect of bending causes a reduction of shear capacity and alters the failure modes. This paper introduces a new test setup, the dual actuator test rig, which is equipped with two actuators moving independently at customizable displacement rates to control and minimize applied bending moments in the shear spans of interest. Shear strength close to pure shear capacity can be therefore reached even at an aspect ratio of 2.0. Experimental series recently performed at the University of Sydney on channel section members using the new test configuration is presented. The experimental results together with other available experimental data are combined and used to validate and re-calibrate the Direct Strength Method design formulae incorporated in the AISI S100:2016 Specification and the AS/NZS 4600:2018 Standard.

Structural performance of cold-formed steel elliptical hollow section pin-ended columns

The structural performance of cold-formed steel elliptical hollow section pin-ended columns buckled about the minor axis was studied through experimental and numerical investigation. Four cross-section series with five different column lengths were designed in the test program to include a wide range of cross-section geometries and column slenderness. Finite element model was developed to replicate the key test results and to perform extensive parametric study. The validation results show that the model can accurately predict the behavior of cold-formed steel elliptical hollow section pin-ended columns buckled about the minor axis. Subsequently, an extensive parametric study with a wide range of cross-section geometries and a spectrum of column slenderness was performed. Since currently there is no codified design rule on elliptical hollow section compression members, the results of 22 column tests and 280 finite element analyses were only compared with the predicted strengths by the equivalent diameter method and equivalent rectangular hollow section approach proposed by previous researchers, the traditional design methods with equivalent diameter incorporated as well as the Direct Strength Method. Reliability analysis was conducted to examine these design methods. Among these design methods, the comparisons show that the existing Direct Strength Method offers the most suitable design provisions, though further improvement remains possible. In this study, modification is proposed on the Direct Strength Method to further improve the accuracy of design strength predictions. It is suggested to adopt the modified Direct Strength Method design equations in the nominal strength predictions of cold-formed steel elliptical hollow section pin-ended columns buckled about the minor axis.

DSM Design of Cold-Formed Steel Columns Failing in Distortional Modes at Elevated Temperatures

This paper aims at investigating the structural behaviour, strength and Direct Strength Method (DSM) design of cold-formed steel columns failing in distortional modes at elevated temperatures. The results concern pin-ended and fixed-ended columns displaying four cross-section shapes, with various dimensions, subjected to 8 temperatures. It is shown that the current DSM distortional design is unable to handle adequately distortional failures at elevated temperatures. Then, a modified DSM design approach is proposed: it consists of incorporating a temperature-dependent reduction factor ratio, based on the EC3-1.2 model, in the existing strength curve—the modified design curves are shown to yield adequate failure load predictions for the set of columns under consideration. This finding provides motivation and encouragement to continue the ongoing search for an efficient DSM-based design approach for columns failing in distortional modes under elevated temperatures.

Experimental study of shear strength of cold-formed channels with an aspect ratio of 2.0

Shear behaviour of cold-formed steel beams with an aspect ratio (shear span/web depth) of 1.0 has been studied thoroughly, mainly using central point load tests. However, for beams with longer aspect ratios, the effect of bending causes reduction of shear capacity and alters the failure modes. This paper summarises experiments recently performed at the University of Sydney on channel section members using a new test configuration to minimize bending moments. Shear strength close to pure shear capacity can be therefore reached even at an aspect ratio of 2.0. The test results were compared with the strength predictions using the current direct strength method (DSM) of design for shear specified in the North American specification for the design of cold-formed steel structural members, AISI S100:2016 and the Australian/New Zealand Standard for cold-formed steel structures, AS/NZS 4600:2018. A good agreement between the experimental results and the predicted values has confirmed the viability of the DSM design rules for structures with aspect ratios up to 2.0. Numerical models were developed to foresee potential issues prior to the experimental work, and were subsequently calibrated against the tests to produce reliable results.

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.

Distortional Failure and DSM Design of Cold-Formed Steel S-Shaped Beams Under Uniform Bending

This work reports a numerical investigation on the distortional buckling/post-buckling behaviors, ultimate strength and Direct Strength Method (DSM) design of cold-formed steel S-beams, commonly used in industrial rack systems. The analyzed beams are single-span, under uniform bending, exhibiting two different end support conditions and 5 cross-sections dimensions. The post-buckling equilibrium paths and ultimate moments are obtained from shell finite element non-linear analysis through the software ANSYS. The reported results evidenced that current codified DSM distortional curve is unable to provide safely strength predictions for the selected beams.

Design of stainless steel continuous beams with tubular cross-sections

This paper presents a comprehensive study on the application of global plastic design methods, not currently allowed in European specification provisions, to stainless steel rectangular and square hollow section continuous beams. The analysis of experimental and numerical continuous beam strengths highlighted that ultimate capacity predictions calculated based on global elastic analysis result in a considerable conservatism due to strain hardening and bending moment redistribution effects. Alternatively, the assessment and reliability analyses of the traditional plastic design methods demonstrated that the Class 1 cross-section limit provided in the European specification can be safely applied for the partial safety factor γM0 currently provided. However, the analysis evidenced that including bending moment redistribution in capacity predictions is not enough since strain hardening effects play an important role when stocky cross-sections are analysed. Thus, the Continuous Strength Method for indeterminate structures was also assessed and it was found to provide accurate capacity predictions for all analysed stainless steel grades. Finally, an alternative Direct Strength Method design approach is proposed for stainless steel continuous beams based on the Direct Strength Method bending capacity. The proposed method, statistically validated, accounts for strain hardening effects and moment redistribution and provides the best resistance predictions among the different design methods considered.

07.03: Distortional‐global interaction in lipped channel beams: Part II: Strength, relevance and DSM design

ABSTRACTThis work aims at presenting and discussing numerical results concerning the post‐buckling behaviour, strength and design of two types of simply supported lipped channel (LC) beams under uniform major‐axis bending and undergoing distortional‐global (D‐G) interaction. The relevance of the interaction effects is assessed by determining 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 and, thus, different failure mode natures (global, distortional or interactive) are expected. For each beam type, combinations of 41 geometries and 11 yield stresses are dealt with, in order to (i) characterise the beams experiencing “true D‐G interaction” (RGD≈1.0) and “secondary global‐bifurcation D‐G interaction” (RGD &gt;1.0 + high Ry) and (ii) investigate the possible occurrence of “secondary distortional‐bifurcation D‐G interaction” (RGD &lt;1.0 + high Ry). 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 (i) the currently codified DSM (Direct Strength Method) beam global and distortional strength curves, and (ii) proposed DSM‐based design approaches, specifically developed to handle D‐G interactive failures.

07.12: On the design of cold‐formed steel beams with holes in shear using the direct strength method

ABSTRACTThe Direct Strength Method (DSM) design rules for cold‐formed steel members in shear have been incorporated recently into the North American Specification for the Design of Cold‐Formed Steel Structural Members (AISI S100‐12) and are being implemented in the Australian Cold‐formed steel structures standard (AS/NZS 4600:2005). Recent studies have shown that the DSM can be used for beams with web openings subjected to shear by modifying the shear load at buckling (Vcr) and shear load at yielding (Vy) to include the influence of openings. This paper presents a buckling study on cold‐formed steel beams with various aspect ratios and with a wide range of web opening locations and sizes using the Finite Element Method (FEM) in order to determine Vcr. An artificial neural network (ANN) is then applied to learn and establish the relationship between the relative geometrical dimensions of perforated members and the shear buckling coefficients (kv). As a result, a simple equation is derived to approximate kv, which is used as input to the modified DSM design equations.

13.11: DSM design approach for hot‐rolled steel angle columns

ABSTRACTThis work reports the latest results of an ongoing investigation on the Direct Strength Method (DSM) design of hot‐rolled steel equal‐leg angle columns with fixed and pinned (cylindrical or spherical hinges) supports and short‐to‐intermediate lengths, i.e., buckling in flexural‐torsional modes. It extends the scope of similar studies carried out by the authors for cold‐formed (higher leg width‐to‐thickness ratios) steel angles with the same characteristics. After reviewing (i) the most relevant findings unveiled in the studies concerning hot‐rolled steel angles, including the role played by residual stresses in eroding their ultimate strength, and (ii) the available experimental and numerical failure load data, comprising fixed‐ended and pin‐ended columns with several geometries (cross‐section dimensions and length) and reported by various researchers, the paper briefly addresses the mechanical reasoning behind an efficient DSM‐based design approach proposed by the authors in the context of cold‐formed steel (slender legs) short‐to‐intermediate angle columns. Then, the available failure load data is used to assess the quality of their estimates provided by this DSM design approach, including the determination of the corresponding Load and Resistance Factor Design (LRFD) resistance factors. It is shown that the proposed design approach can be also successfully applied to predict hot‐rolled steel angle column failure loads, leading to LRFD resistance factors above the value currently prescribed, for compression member design, by the North American Specification (ϕc=0.85).