Direct Strength Method Predictions Research Articles

Test and design of cold-formed steel closed built-up beams with double sigma sections and triple lipped channel sections

Built-up section beams fabricated from several single sections are finding increasing use in the cold-formed steel (CFS) industry due to various advantages such as higher bending capacities, innovative new shapes, and elimination of eccentricity. However, a built-up beam is connected at discrete points along the longitudinal direction, which weakens the shear and flexural rigidities of the built-up section. The structural behaviour of built-up CFS beams is therefore more complicated than that of single section beams. This paper presents an experimental investigation on the moment capacity of screw fastened built-up CFS beams. To investigate the local, distortional, and flexural-torsional buckling of built-up CFS beams, four-point bending tests of 8 braced and 24 unbraced built-up C2C (fabricated from 2 sigma sections) section beams and C3C (fabricated from 3 lipped channels) section beams are conducted. Unbraced bending test specimens are tested at three lengths covering inelastic failure at short lengths to essentially elastic failure at long lengths. The strength predictions for the tested built-up beams are calculated using the current Direct Strength Method (DSM) in the AISI-S100 Specification. The comparison between the experimental results and DSM predictions indicates that the current DSM in AISI specification is overly conservative and unreliable for the types of built-up beam sections examined in this research, due to the incorrect failure mode prediction and underestimation of the critical elastic buckling stresses which is a key input to the DSM.

An investigation on stiffened cold-formed steel unequal angle box section columns

Built-up box sections are gaining popularity as column members in cold-formed steel (CFS) construction. Applications include CFS trusses, space frames, and portal frames. Two identical CFS unequal angles are used in this article to form built-up rectangular angle box columns (BUABC). These BUABC, which can be plain or with stiffeners (longer and shorter legs), are grooved on the faces of the columns in the major and minor axis directions and connected with self-drilling screws (fasteners) through their lips. There are no reports in the literature on the advantages of stiffeners (longer and shorter legs) provided in BUABC. This paper presents 78 new results for the BUABC as plain and with stiffeners (longer and shorter legs), including 14 test results and 64 finite element (FE) results. The axial strengths of BUABC with two stiffeners in the longer leg and one stiffener in the shorter leg showed an increase of about 28% on average when compared to the axial strength of plain BUABC, according to the experimental results. The FEA-derived ultimate loads and failure modes are in good agreement with the experimental results. The verified FE model was then used in the parametric study to investigate the effect of stiffeners (longer and shorter legs) on the axial strength of BUABC. The parametric study considered two distinct geometries with two distinct lengths (300 mm and 600 mm). The axial strengths of the stub BUABC tested against the Direct Strength Method (DSM) prediction were conservative, up to 3% on average, while they were 13% conservative for the short BUABC. This shows that the DSM prediction was more conservative, with an increase in slenderness that was governed by the modified slenderness ratio. The DSM strength predictions were less conservative for the stub BUABC that failed due to local buckling, whereas the DSM strength predictions were more conservative for the short BUABC that failed due to a combination of local and flexural buckling.

Flexural strength of steel decks with square and rectangular holes: Numerical studies

Holes in steel roof decks are often provided to allow for the passage of services. Published information on structural properties and design methods of steel deck with holes is limited. To shed light on this topic, a numerical parametric study of the flexural strength of steel decks with single square and rectangular holes was performed. This paper presents results of the study. Nonlinear finite element deck models were developed in ANSYS and validated using published test results. Flexural strengths and load-deflection curves predicted by the developed models showed good agreement with the experimental data. The following parameters were varied in the study: deck type and thickness, hole width and length-to-width ratio, hole location along and across the deck span, and load type. Ultimate moment reductions due to the holes have been presented and discussed. The ultimate moments obtained numerically were compared with those predicted by the effective width and direct strength methods. Modifications of the direct strength method were proposed to allow for better predictions of the flexural strength of steel deck with holes. A method to account for the effects of hole location along and across deck span on the ultimate moment was also presented. The design methods predicted the simulation results well when the proposed design procedures were considered. It was shown that the direct strength method predictions for distortional buckling of solid decks depend on the compression-to-tension flange width ratio. The conservatism of the DSM predictions increases when the compression-to-tension flange width ratio increases.

Experimental assessment of stainless steel hot-rolled equal legs angles in compression

Although many mechanical properties of stainless steels are similar to carbon steel, their nonlinear characteristics lead to different design rules that can affect their response to local and flexural buckling. The stainless steel design standard Eurocode 3: Part 1–4 (2006) can, in principle, be used in hot-rolled, welded and cold-formed products, but its provisions are still rather conservative, with a limited application due to the lack of experimental data. One of those areas that require attention and study concerns the behaviour of columns made of hot-rolled stainless steel equal leg angles. This paper describes an experimental campaign made on hot-rolled stainless steel equal-legs angles under axial compression. The adopted cross-sections were: L64 × 64 × 4.8, L76 × 76 × 6.4 and L102 × 102 × 6.4 made of austenitic stainless steel ASTM 304 A276 (1.4301) (with corresponding leg width to thickness ratios, b/t, equal to 13.33, 11.88, 15.94). The longest specimen was 1893 mm, and the shortest one 152 mm. The collapse involved flexural-torsional and flexural buckling modes. These results were subsequently compared with Eurocode 3–1.4 provisions, and to the CSM – Continuous Strength Method and mDSM – Modified Direct Strength Method predictions. In general, the CSM and mDSM performed better than the Eurocode 3 1–4, but unsafe ultimate load predictions could also be observed in some cases.

Longitudinally stiffened web purlins under shear and bending moment

Abstract This paper aims to better understand the influence of longitudinal web stiffeners in the structural behavior of cold-formed steel purlins. A set of specimens with stiffened web and plain web cross-sections were tested on predominantly shear, combined bending and shear, and bending only. Numerical analyses carried out in CUFSM and ANSYS investigated the buckling behavior of the sections, allowing the determination of elastic critical stresses and the calculation of the resistance for the tested specimens by Direct Strength Method (DSM). Numerical results showed that the intermediate web stiffeners improve the buckling strength in loading cases of pure bending and pure shear. Experimental and numerical data were used to evaluate the interaction between bending moment and shear force, and showed that the circular interaction diagram was conservative and the results were closer to the trilinear interaction diagram. The comparison between experimental data and DSM predictions demonstrated that DSM provides accurate estimates for shear and flexural strengths of purlins with stiffened web cross-section.

Improving the Direct Strength Method prediction of column flexural-torsional failure loads

Abstract This paper reports the latest results of an ongoing investigation on the accuracy of the codified Direct Strength Method (DSM) global strength curve in predicting the ultimate strength of cold-formed steel columns failing in flexural-torsional modes. The first part of the paper is devoted exclusively to fixed-ended columns and continues recent work by the authors [1, 2] on the improvement of the flexural-torsional failure load estimation, in the moderate or high slenderness ranges − it is shown that the use of a novel set of strength curves, dependent on a cross-section normalised geometric parameter (involving the area, major and minor moments of inertia, and warping constant), leads to excellent failure load predictions, eliminating the large scatter stemming from the codified design curve and improving the DSM-based design approach proposed in [2]. The second part of the paper aims at extending the investigation to columns with other support conditions, namely three types of pinned supports, all fixed with respect to torsion and having warping prevented: end cross-sections attached to rigid plates resting on spherical or cylindrical hinges (i.e., pinned with respect to major and/or minor-axis flexure). Initially, a parametric study is performed, aimed at gathering failure loads concerning columns (i) with the cross-section shapes considered earlier (plain channels, unstiffened and stiffened lipped channels, return lipped channels, hat-sections and rack-sections), (ii) with various geometries (cross-section dimensions and lengths) and (iii) covering a wide slenderness range. These failure load data are then used to assess the quality of their estimates provided by the codified global DSM strength curve and by the strength curve set developed for fixed-ended columns. It is found that neither of them yields consistently good failure load estimates, which prompts (i) an in-depth comparative study on the elastic post-buckling strength of fixed-ended and pin-ended columns, and (ii) the proposal of modifications that lead to an efficient failure load prediction for the pin-ended columns − although the failure load set obtained in this work is necessarily limited, the fact that their predictions by the proposed DSM global design curves (i) exhibit very high quality and (ii) clearly outperform those yielded by the current design curve provides strong encouragement to search for further experimental and numerical validation.

A design criterion for identifying and designing compressive cold-formed steel members with local and distortional interactive behaviors

The objective of this paper is to develop a systematical Direct Strength Method (DSM) design formulation with a design criterion that can properly identify the occurrence of the Local and Distortional (L/D) buckling interaction for cold-formed steel compressive members and thus predict the strength. Column tests provided clear evidence of the L/D interaction and revealed the difference between the L-D and D-L interactions depending on which one buckles first. By collecting all the experimental data of cold-formed steel columns related to the L/D interaction, the current DSM predictions are first evaluated. Then, a DSM-based interaction formulation with design criterion by replacing the pure mode prediction with the interaction prediction based on the identification of the design criterion is proposed. The accuracy of the proposed method is evaluated from all the collected data experiencing the L/D interaction. Moreover, the effectiveness of the design criterion in identifying the interactive failure is also highlighted.

Tests and direct strength design on cold-formed steel channel beams with web holes

To investigate the flexural behaviors of cold-formed steel channel beams with web holes and assess the reliability of the current direct strength method (DSM) for design of cold-formed steel beams with web holes stipulated in North American Specification (NAS) (2016), ten groups of specimens with various sizes of web holes and lips were tested under four-point bending. Among them, each kind of specimens with short lips or long lips have five kinds of hole height-to-web depth ratios, 0, 0.2, 0.4, 0.6 and 0.8. It is shown that the web holes change the failure modes of beams from only distortional buckling or only local buckling to distortional-local buckling interaction controlled by distortional buckling or local-distortional buckling interaction controlled by local buckling. It is found that the moment capacities reduce slightly with a maximum reduction value of 7.0% when the ratio of hole height-to-web depth increases from 0 to 0.4, and that the moment capacities reduce dramatically with a maximum reduction value of 16.3% when the ratio of hole height-to-web depth further increases to 0.8. Moreover, ANSYS finite element (FE) program was used to simulate the beam tests, the simulation results show good agreement with the test results in terms of moment capacities and failure modes. Extensive ANSYS FE parametric analysis were carried out to verify the accurateness of critical elastic distortional buckling stress prediction method using CUFSM finite strip program and to modify the existed approximate prediction formulas of critical elastic local buckling stress applying to such beams with web holes. Furthermore, the test results and parametric analysis results were compared with the current DSM prediction results of cold-formed steel beams with web holes. It is found that the DSM in NAS (2016) provides unconservative predictions for most cold-formed steel channel beams with web holes, especially for beams failed by local-distortional buckling interaction controlled by local buckling. Therefore, the modified direct strength method formulas for cold-formed steel beams with web holes were proposed.

Buckling behaviour and design of complex-shaped aluminium mullion sections

Thin-walled aluminium mullions are the vertical framing members of the façade systems used in buildings. This article investigates the buckling behaviour of these complex-shaped aluminium mullions. For this purpose, the aluminium mullion sections were simplified into elements of varying thickness and modelled using CUFSM finite strip analysis programme. Elastic buckling analyses were performed with and without considering the availability of glass panel restraints for both negative and positive wind actions, and the results are presented in this article. The effect of providing return flanges to enable a good connectivity between the male and female mullions was also evaluated. The lateral restraints provided by glass panels were simulated using the spring stiffness option available in CUFSM, and the analyses were performed for spring stiffness values in the range of 0–1 N/mm/mm. The applicability of the buckling analysis results to the design of aluminium mullions was then evaluated using the direct strength method. For this purpose, the section moment capacities of mullions were determined from finite element analyses and compared with the direct strength method predictions using the CUFSM buckling analysis results. This comparison showed that direct strength method–based design can be adopted for the complex-shaped aluminium mullions provided their elastic buckling capacities are available. Overall, this study has provided good understanding of the buckling behaviour of mullion sections under both positive and negative wind actions and has proposed the use of direct strength method for the design of aluminium mullion sections.

Local-flexural interactive buckling of standard and optimised cold-formed steel columns

This paper aims to study the interaction of local and overall flexural buckling in cold-formed steel (CFS) channels under axial compression. Detailed nonlinear FE models were developed and validated against a total of 36 axial compression tests on CFS plain and lipped channel columns with pin-ended boundary conditions. The numerical models incorporated the non-linear stress-strain behaviour of CFS material and enhanced properties of cold-worked corner regions obtained from coupon tests. The effects of initial geometric imperfections of the specimens measured by a specially designed set-up with laser displacement transducers were also taken into account. The developed FE models produced excellent predictions of the ultimate strength of the specimens obtained from experimental tests. The validated FE models and experimental results were then used to assess the adequacy of the effective width method in Eurocode 3 (EC3) and Direct Strength Method (DSM) in estimating the design capacity of a wide range of conventional and optimised design CFS channel column sections. The results indicate that Eurocode 3 provides conservative predictions (on average 21% deviation) for the compressive capacity of plain and lipped channel sections, while in general DSM predictions are more accurate for lipped channels. A comparison between FE predictions and tested results show that geometric imperfections can change the FE predictions by up to 20% and 40%, respectively, for lipped and plain channel columns, while the strain hardening effect at the rounded corner regions of the cross-sections is negligible. The results also confirmed that the proposed numerical model is able to provide a consistent and reliable prediction on the efficiency of a previously proposed optimisation methodology.

07.01: New developments in the Direct Strength Method (DSM) for design of cold‐formed steel sections under localised loading

ABSTRACTA consistent and simplified Direct Strength Method (DSM) for design of cold‐formed (or thin‐walled) sections under localised loading, which is called web crippling, is proposed. The development of this method proposes generalised equations for design of thin‐walled sections under the four different localised load cases which are the interior one‐flange (IOF), the end one‐flange (EOF), the interior two‐flange (ITF) and the end two‐flange (ETF). The same parameters are used in the DSM equations for both the IOF and EOF load cases. However, the ITF and ETF load cases require different parameters in the DSM equations to predict the capacities of structural members. The equations contain both an inelastic reserve component and a yield load component which are different from those proposed previously in this regard.This paper briefly introduces the calculation of the buckling load and the yield load. From these two main input variables, DSM equations are used to determine the capacities of structural members under localised loading. Calibration is performed against all available experimental data to validate the accuracy of the DSM predictions.

Experimental investigation of cold-formed high strength steel tubular beams

This paper presents a test program on cold-formed high strength steel tubular beams. The nominal 0.2% proof stresses of the high strength steel were 700, 900 and 1100MPa in this study. Twenty-five four-point bending tests on circular, rectangular and square hollow structural sections were conducted. Load-deformation histories and failure modes of the beams were reported. Experimental results were compared against design values calculated from European code, Australian standard and North American specification for hot-rolled and cold-formed steel structures. In addition, the test strengths were also compared with the Direct Strength Method predictions. The compactness criteria were assessed by comparing the section slenderness to the slenderness limits in codes.

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.

Torsion of cold-formed steel lipped channels dominated by warping response

The objective of this paper is to provide benchmark test results, explanatory shell finite element models, and preliminary Direct Strength Method prediction for cold-formed steel lipped channels undergoing torsion dominated by warping response. Although the elastic theory for the torsional response of a thin-walled cold-formed steel lipped channel member is well-developed, the extent to which warping torsion dominates the response of cold-formed steel members is not widely appreciated. Further, for cold-formed steel members in torsion little exists in terms of experimental benchmarks and even less on situations beyond the classic elastic theory, including geometric nonlinearity and post-buckling, and/or material nonlinearity from partial to full plastification of the section. Here, a typical cold-formed steel lipped channel member loaded experimentally in torsion exhibits significant strength beyond first yield. Shell finite element models of the testing correlate well with the experiments and indicate the extent of plastification as the thin-walled member undergoes torsion dominated by warping response. Idealized end boundary conditions are developed for the shell finite element model that is conservative with respect to the response, and in agreement with classical expressions in the elastic regime. The shell finite element model with idealized end boundary conditions is used to develop a parametric study on ultimate torsional capacity for members dominated by warping torsion. The results indicate that torsional slenderness may be used to predict torsional capacity and indicate that Direct Strength Method predictions for torsion for members dominated by warping torsion are possible. Preliminary design expressions for warping torsion strength prediction are provided.

Assessment on Ultimate Load of Cold-formed Steel Channel (CFSC) Stub Column

Cold-formed steel is used as the non-structural and structural material in civil engineering work and building. Cold-formed steel channel is selected and cut into 100 mm, 200 mm, 300 mm, 400 mm and 500 mm. The slenderness ratio is calculated and noted as a stub or short column because below 40. The column is tested by using Universal Testing Machine to determine the ultimate load of the stub column. Besides, the CFSC is determined the material properties of CFSC for checking it’s the originality of steel based material. The experimental data are tested and compared with the Direct Strength Method (DSM). It showed that the CFSC1 with a height of 100 mm is reported to have a higher value of ultimate load when compared with other samples. When the height of the stub column increased, the ultimate load of the sample is decreased. Then, the CFSC1 also showed a higher in initial stiffness when compared with other samples. All samples are shown having a higher data in ultimate load when compared with the Direct Strength Method prediction. The ultimate load of experimental and DSM all gave a ratio below 1.03. Finally, all samples can further recommend determining the relation between the ultimate loads with variations of height of the column.

Design of high strength steel columns at elevated temperatures

The main objective of this paper is to study the behaviour and design of high strength steel columns at elevated temperatures using finite element analysis. In this study, equations predicting the yield strength and elastic modulus of high strength steel and mild steel at elevated temperatures are proposed. In addition, stress–strain curve model for high strength steel and mild steel materials at elevated temperatures is also proposed. The numerical analysis was performed on high strength steel columns over a range of column lengths for various temperatures. The nonlinear finite element model was verified against experimental results of columns at normal room and elevated temperatures. The effects of initial local and overall geometrical imperfections have been taken into consideration in the analysis. The material properties and stress–strain curves at elevated temperatures used in the finite element model were obtained from the proposed equations based on the material tests. Two series of box and I-section columns were studied using the finite element analysis to investigate the strength and behaviour of high strength steel columns at elevated temperatures. Both fixed-ended stub columns and pin-ended slender columns were considered. The column strengths predicted from the finite element analysis were compared with the design strengths predicted using the American, European and Australian specifications for hot-rolled steel columns at elevated temperatures by substituting the reduced material properties. In addition, the direct strength method, which was developed for the design of cold-formed steel columns at normal room temperature, was also used in this study to predict the high strength steel column strengths at elevated temperatures. The suitability of these design rules for high strength steel columns at elevated temperatures is assessed. Generally, it is shown that the American and European specifications as well as the direct strength method conservatively predicted the column strengths of high strength steel at elevated temperatures. The European Code predictions are slightly more conservative than the American Specification and the direct strength method predictions.