Direct Strength Method Research Articles

Direct strength prediction of cold-formed steel fixed-ended singly-symmetric columns buckling in flexural–torsional modes

The work reported in this paper is a sequel of previous numerical investigations carried out by the authors on the post-buckling behaviour, strength and Direct Strength Method (DSM) design of cold-formed steel (CFS) fixed-ended plain and lipped channel columns (both singly-symmetric with respect to the major-axis) buckling in flexural–torsional modes and experiencing global-global interaction – a coupling phenomenon involving major-axis flexural–torsional (FMT) and minor-axis flexural (Fm) buckling that was first unveiled in those studies. In the specific context of plain and lipped channel columns, a DSM-based design approach for columns buckling in FMT modes and failing in either pure FMT or FMT-Fm interactive modes was developed and shown to provide accurate, mostly safe and reliable predictions of the experimental (only a few) and numerical failure loads available. The success of this research effort encouraged the authors to extend the scope of the investigation to fixed-ended columns with other singly-symmetric cross-section shapes, namely return-lip, web-stiffened and web/flange-stiffened lipped channels, hat-sections and rack-sections (deemed representative of any arbitrary singly-symmetric cross-section). The results attained during this investigation are presented and discussed in detail – they concern the post-buckling behaviour, strength and DSM-based design of the columns analysed, including fairly extensive failure load sets (Ansys non-linear shell finite element models are used to obtain them). The main output of this work is a DSM-based design approach for arbitrary CFS fixed-ended singly-symmetric columns exhibiting pure FMT or FMT-Fm interactive failures.

Test and direct strength method on slotted perforated cold-formed steel channels subjected to eccentric compression

This paper aims to investigate the buckling behaviors of cold-formed steel (CFS) channels with slotted web holes determined by the Steel Stud Manufacturers Association (SSMA) under eccentric compression, and propose the simplified direct strength method (DSM) formulas for engineering practicing. An experimental study on 20 specimens was conducted, including 18 slotted perforated specimens with nine eccentricities increasing from −20 mm to 20 mm and 2 unperforated specimens subjected to axial compression. Two kinds of nominal lip lengths for cross sections were selected as 15 mm and 20 mm. The experimental results indicated that the failure modes of slotted perforated specimens subjected to eccentric compression depended on the position of the eccentricity. Compared with the slotted perforated specimens subjected to pure axial compression, the ultimate loads of specimens subjected to positive eccentric compression decreased by 21.70 % on average, while they decreased by 16.38 % on average for those subjected to negative eccentric compression. Moreover, a nonlinear elasto-plastic finite element model (FEM) was developed and validated against the experimental results. Furthermore, combined with the experimental results, extensive FE parametric analyses were conducted to predict the eccentricity impact coefficient formulas. Finally, based on DSM of unperforated CFS members subjected to pure axial compression in AISI S100-16 and the eccentricity impact coefficient formulas, the suitable DSM design formulas for slotted perforated CFS channels determined by the SSMA under eccentric compression were proposed, without the need to calculate the elastic buckling critical stress for slotted perforated CFS channels.

Numerical investigation and design for the local buckling behaviour of high strength steel hexagonal hollow section stub columns under axial compression

The local buckling behaviour of high strength steel (HSS) hexagonal hollow section (HexHS) stub columns encompassing three different fabrication routes under axial compression is numerically investigated in this study. Finite-element (FE) models were developed and validated against the experimental results. The validated FE models were subsequently employed to carry out parametric studies to expand structural performance data covering a wider range of geometries and cross-section slenderness as well as two different steel grades. The obtained results from FE models in line with the experimental data were used to evaluate the applicability of the existing design codes and the design approaches in literature to HSS HexHS under pure compression. The comparison indicates that the current slenderness yield limiting values in design codes cannot be simply extended to HSS HexHS stub columns. All the design codes exhibit a high degree of conservatism due to the lack of consideration for strain hardening whereas the Continuous Strength Method (CSM) was found to provide more accurate predictions than the Direct Strength Method (DSM). Modified design approaches are proposed to improve the accuracy of the strength predictions for HSS HexHS stub columns.

Numerical simulation and specification provisions for cruciform cold-formed steel built-up columns

This paper addresses the nonlinear behavior of cruciform cold-formed steel (CFS) built-up columns formed by high-strength bolts and filler plates under axial compression. Nonlinear finite element modeling using ANSYS software is developed to simulate the behavior, including both geometric and material nonlinearities, and the numerical results are compared with the test results obtained by the authors and reported in another paper, showing good agreement. The finite element model in this paper predicts the ultimate loads and buckling modes of the specimens well. Following validation, the C89 series cross-section was selected for numerical and theoretical study using a varying slenderness ratio λ, plate thickness t and bolt spacing s. The results are compared with the nominal axial resistance calculated using the existing design standards, including the direct strength method (DSM) in the AISI Specifications and the effective width method (EWM) in the provisions of Chinese code GB50018-2002. The results show that the current AISI specifications have many overestimated resistance predictions for the cruciform CFS built-up columns, and the error decreases with the increase in the slenderness ratio, while the provisions in the Chinese code are overly conservative for predicting the resistance values of the cruciform CFS built-up columns. Therefore, a design procedure based on the effective width method is proposed for the resistance evaluation of axially compressed cruciform steel built-up columns.

Post-fire flexural behaviour and performance of unrestrained cold-formed steel built-up section beams: Experimental and numerical investigation

Cold-formed steel (CFS) sections are light gauge materials widely used to construct industrial structures. CFS construction is gaining more interest among researchers, construction industries, and structural engineers due to its lightweight and cost-effective design. Fire safety in the building is a significant factor to be considered in the design and construction practices. However, limited studies are reported on experimental and finite element modelling (FEM) of back-to-back built-up channel sections under flexure with unrestrained conditions. Nine back-to-back built-up CFS sections were considered for the experiment. CFS test specimens were exposed to elevated temperatures following the ISO 834 standard fire curve for durations of 30 min (821 ℃), 60 min (925 ℃), 90 min (986 ℃), and 120 min (1029 ℃). After the temperature exposure, air- and water-cooling methods were adopted to cool the CFS specimens. The influence of temperature exposure and cooling affects CFS sections' residual load-carrying capacity and failure behaviour. A detailed physical observation was made after cooling conditions to observe the failure behaviour of CFS specimens. Experiments were performed to evaluate the influence of elevated temperature exposure on the ultimate flexural capacity, moment-deformation behaviour, load-strain behaviour and stiffness of CFS. The moment of resistance results obtained from FEM and the Direct Strength Method (DSM) were validated with experimental results. The experimental results showed that, while increasing the temperature exposure and heating duration, the CFS's load-carrying capacity decreases drastically. In the case of cooling conditions, air-cooled specimens exhibited a higher residual strength capacity, about 10–15%, compared to the water-cooled specimens. A good correlation was noted between the experiment and FEM results in failure modes.

Accuracy of Buckling Strength Curves Using Direct Strength Method in Estimating Axial Strengths of Cold-Formed Steel Members under Compression: Critical Review

Current design specifications for cold-formed steel incorporate the Direct Strength Method (DSM) to design cold-formed steel members under compression. Although the DSM has been used for quite some time, its buckling strength curves have not been experimentally assessed thoroughly. This study attempts to fulfill this objective. First, a thorough literature review was conducted to inspect the buckling strength curves in the DSM, and the issues are summarized in this paper. Second, experimental data associated with compression tests of 453 solid and 228 perforated cold-formed steel columns were collected from the literature. Design parameters (e.g., elastic critical buckling loads) of the columns were then determined and assembled with the experimental results in a database to be used as a source to assess the buckling strength curves in the DSM. Finally, the LRFD resistance factors (ϕc) of the DSM buckling strength curves were determined in accordance with the AISI S100. This paper highlights the level of accuracy of the buckling strength curves in the DSM.

Splice Connections for Built-Up Column Assemblies in Cold-Formed Steel Construction

The development of simple connection methods is necessary for increasing cold-formed steel (CFS) construction activities. A new splice connection concept for the CFS built-up column-to-column connections is presented in this paper. This simple connection concept will use the same size and shape of the geometry as the CFS built-up column, which will enable a quick erection process. The new splice connection configurations, arrangement, and installation methods for cold-formed steel construction are demonstrated. Twenty-eight experiments, which include four actual columns, two disconnected columns, and 22 columns with splice connections, are carried out. This paper examines the influence of various parameters of splice connections such as length, thickness, and number of fastener rows. The design strength of the actual column is determined using the direct strength method (with modified global and local slenderness approaches) and is compared with the results of the splice connected columns for adequacy. The force transfer mechanism and failure modes of splice connection components are demonstrated in the form of detailed sketches. The smaller length splice connections led to localized failures, while the longer splice connections enabled the uniform force distribution between the built-up column cross-sections. Finally, it is recommended that the splice connection configuration should be a minimum of 300 mm in length, the splice thickness should be equal to the CFS built-up cross-section, and two rows of fasteners for attaining the required design strength of the built-up column members.

Evaluation of local and distortional buckling strength of purlins with paired torsion bracing using Direct Strength Method

In this paper, the authors presented a methodology to predict the local and distortional buckling strength of purlins with paired torsion bracing using the Direct Strength Method. The procedure is based on the component stiffness method that utilizes a displacement compatibility approach to calculate the anchorage forces in a purlin system. The procedure considers the partial diaphragm restraint provided by the sheathing and incorporates both first order and approximate second order torsion effects to predict the actual distribution of stresses along the cross section of the purlin. This distribution of stresses can vary substantially from the conventionally assumed constrained bending distribution and thus, correspondingly, the predicted local and distortional buckling strength can differ substantially.To validate the methodology, the procedure has been used to predict the strength of a series of 12 base tests. The test series included 8 in. (203 mm) and 10 in. (254 mm) deep lipped Z-sections with both thin (0.057 in, 1.45 mm) and thick (0.100 in, 2.54 mm) profiles. The same standing seam deck and clips were used in all the tests. The detailed investigation into the behavior of the base test revealed several slight load imbalances that, when properly accounted for, can have an impact on the predicted strength. The comparison between the tested strength and predicted strength showed good correlation and the methodology was largely able to predict test anomalies such as failures at the brace location versus the mid-span and failures of the eave purlin versus the ridge purlin. The prediction methodology ignores the additional torsional restraint provided by the sheathing and thus generally resulted in a slightly conservative approximation of the local and distortional buckling strength.

Numerical investigation on local buckling behaviour of cold-formed high strength steel irregular hexagonal hollow section stub columns

The local buckling behaviour of cold-formed high strength steel (HSS) irregular hexagonal hollow section (IHexHS) stub columns under concentric compression is studied numerically in this paper. Finite-element (FE) models were developed and validated against the experimental data. The validated FE models were employed to conduct extensive parametric studies. The obtained numerical results together with the experimental data were used to evaluate the applicability of the existing design codes and design approaches to the cold-formed HSS IHexHS under concentric compression. The evaluation shows that the current slenderness yield limit values codified in design codes cannot be applied to cold-formed HSS IHexHS stub columns. The Eurocode 3 (EC3) and the North American code AISC 360-16 provide slightly over-estimated predictions for slender sections whereas the Australian code AS 4100 yields conservative predictions. For stocky sections, all the design codes show high degree of conservatism due to the lack of consideration for strain hardening. Furthermore, design approaches of Continuous Strength Method (CSM) and Generalised Slenderness Resistance Method (GSRM) have been found to provide more accurate predictions than the Direct Strength Method (DSM). Modified design approaches are also proposed to improve the accuracy of the strength predictions.

A Novel Approach to Improve the Distortional Buckling Strength of a Stiffened Cold-Formed Steel Channel Section under Axial Compression

This study investigates the distortional buckling strength of a partially closed cold-formed steel (CFS) channel section with intermediate web stiffeners and outward lips under axial compression. Generally, a closed CFS cross section has higher torsional resistance when compared to an open cross section. However, an open cross section is more popular in the construction industry. Despite the popularity of CFS open sections, distortional buckling can reduce the load-carrying capacity of such open cross sections. To improve the distortional buckling strength of the proposed selected section, a simple spacer plate is added externally to the channel section in the transverse direction. Initially, a numerical model is developed using the finite element software ANSYS, which is then validated against the experimental results available in the literature. A detailed parametric study was also conducted to investigate the influence of thickness, depth, and spacing of spacer plates on the distortional buckling strength of stiffened CFS channel sections. From the results of the parametric study, it was found that the presence of spacer plates can increase the axial capacity of stiffened CFS channel sections by as much as 32%. Finite element results were compared with the design strengths calculated in accordance with the direct strength method (DSM).

Experimental investigation of the sectional buckling of built-up cold-formed steel columns

This paper presents an experimental program investigating the local and/or distortional (sectional) buckling of built-up cold-formed steel sections subjected to pure compression. The experiments were designed to study the influence of key parameters, including buckling mode, cross-section geometry and fastener spacing, on the ultimate sectional capacity of built-up columns. Three singly- or doubly-symmetric built-up sections were considered with two sets of component lipped channel sections, one buckling predominantly in the distortional mode and one buckling in the local mode. The component sections were connected using self-drilling screws at three different spacings. Material properties, geometric imperfections and residual stresses of the specimens were measured prior to testing. A total of 36 specimens with a length of 1 m were tested under concentric compression between fixed ends, which was achieved through a special end plate connection. The specimens failed in either distortional or the interaction of local and distortional buckling modes. Compared to the sum of the capacity of component sections, the ultimate capacity in built-up columns with distortional buckling mode increased significantly with the reduction of screw spacing, whereas the increase was minor for specimens that failed through local-distortional interaction. The ultimate strength of the specimens was predicted using the current Direct Strength Method, where either conservative or overly unconservative predictions were obtained depending on the considered composite action level in the elastic buckling analysis.

Experimental study of local – Distortional interaction of press-braked stainless steel lipped channel beams

Stainless steel lipped channel beams are prone to complex buckling modes due to the large width-thickness ratio. An in-depth experimental study of local – distortional interaction of press-braked stainless steel lipped channel beams was conducted. The chemical composition was proved to meet the requirements of European and Chinese standards. A tensile test of four coupons extracted from the press-braked lipped channel beams was carried out to investigate the material properties. A total of 10 specimens composed of 20 press-braked stainless steel lipped channel beams were investigated in the bearing capacity test. The relationship of the vertical displacement of mid-span, vertical displacement of loading points, support rotation, flange deformation and web deformation with the load was obtained, as well as the bearing capacity of each specimen. According to the measured displacement and strain, the development and failure mechanism of local – distortional interaction of stainless steel lipped channel beams were revealed. All test specimens were subjected to local buckling first, then distortional buckling, and finally interaction buckling. Each specimen had a certain post buckling strength. Near the failure load, each specimen experienced a long loading process and showed good ductility. The test results were utilized to assess the existing design methods which were all based on Direct Strength Method for the guidance of engineers. The existing design methods for local – distortional interaction underestimated the bearing capacity of press-braked stainless steel lipped channel beams. The existing design methods for local buckling or distortional buckling of stainless steel beams overestimated the bearing capacity of local – distortional interaction.

DSM Formula for Local-Global Interaction Buckling of Cold-Formed Stainless Steel I-Beams

The paper presents a set of Direct Strength Method (DSM) formulae for cold-formed stainless steel I-section beams. On basis of a carefully calibrated FE model for stainless steel open-section beams featuring local-global interaction buckling, an extensive database was first established. The existing DSM formula of the best prediction performance was commented on for its drawbacks. For improved strength prediction, a traditional-form DSM formula was proposed first, and novel two-phase DSM formulae were derived on basis of a deep insight into the varying trend of the member strengths. The two-phase DSM formulae were found to be very powerful predictors yielding more accurate strength predictions over the whole range of slenderness and avoiding undue conservatism for intermediate and short members. A considerable boost in design strength by up to 39% can be achieved with the two-phase DSM formula. The DSM curves were developed with a due reliability level to fit into the current design codes.

ANÁLISE TEÓRICA PELO MÉTODO DA RESISTÊNCIA DIRETA DE SEÇÕES DUPLAS DE PERFIS DE AÇO FORMADOS A FRIO SOB COMPRESSÃO

The need for lighter, lower-cost construction has intensified, so the presence of cold-formed profiles has become common in civil construction, offering greater efficiency in the ability to withstand the current demands. The present article aimed at the theoretical study on the stability of double U and U lipped sections, composed of cold formed steel profiles, submitted to compression. Under the justification of analyzing the effectiveness of this type of structural element, with the help of the CUFSM Software that uses the Finite Strip Method, and verify the resistance by the Direct Strength Method (DSM). The objectives of this study were: to investigate the modeling in the CUFSM software for a double section with profiles connected to each other; and apply the DSM to the theoretical analysis of double sections with Brazilian commercial profiles. It was found that the variation in the number of connections influences the analysis and can reproduce the partial connection behavior. The application of folds proved to be efficient, with little influence on local instability and considerable influence on distortion instability. The DSM showed a loss of resistance for the models that presented a local failure mode, being, therefore, the most important factor regarding the resistance.

Numerical Parametric Study and Design of Pultruded GFRP Composite Channel Columns

This article reports the finite element (FE) investigation of the axial capacities of pultruded fiber-reinforced polymer (PFRP) composite channel columns. The nonlinear finite element model (FEM) was developed by using the ABAQUS package for glass fiber-reinforced polymer (GFRP) composite channel columns, which included geometric and initial geometric imperfections. The developed FEMs were verified against an experimental result available in the literature for GFRP channel columns. The validated FEMs were used to carry out the parametric study comprising 61 FE models to investigate the effect of different geometries, plate slenderness and the length of members on the axial capacities of GFRP pultruded channel columns. The results obtained from the parametric study were used to examine the accuracy of the current Italian guidelines, American pre-standard and the Direct Strength Method (DSM) proposed in the literature for GFRP channel profiles. Based on the obtained results, the suitability of the current design guidelines is assessed and, also, a new set of design equations is proposed to estimate the axial capacity of the pultruded GFRP channel columns. The new proposed set of reliable design equations witnessed a less scattered and a high degree of accuracy in determining the axial load capacity of the pultruded GFRP composite channel columns.

Sectional capacities of cold-formed perforated steel channel columns

Holes are pre-punched in the web of cold-formed steel channel columns to accommodate the technical systems. Many research studies have considered and illustrated the impacts of web holes on the capacities of such steel channel columns. These impacts have been accounted for in the American Specification AISI S100-16 using a new design method termed as the Direct Strength Method (DSM). This method allows designers to predict the capacities of cold-formed steel members on the basis of elastic buckling analyses. These analyses can be carried out by using a new module software package CUFSM recently developed by The American Iron and Steel Institute to analyse the buckling behaviors of cold-formed steel sections with perforations. This paper is aimed to apply the DSM to investigate the sectional capacities of cold-formed steel channel columns with a variety of hole dimensions. The behaviors and strengths of these perforated steel channel sections are analysed; recommendations are subsequently provided for the optimum of capacities in terms of the same hole areas. It was found that perforated channel columns with smaller heights and longer lengths are more beneficial for sectional capacities in general. .

Elastic Global Buckling Moments of Cold-rolled Aluminium Alloy Asymmetric Section Beams

Cold-rolled aluminium sections are the new products introduced by BlueScope Permalite. These products have illustrated their cost-effectiveness in comparison with the traditional extruded aluminium alloy sections, which has attracted the attention of users and researchers. Research projects on cold-rolled aluminium alloy structures have been carried out to investigate the strengths and behaviors of such members that are the base for the development of the design guidelines for this new structural type. Cold-rolled aluminum alloy sections in the form of thin-walled sections are sensitive to instability. The design guidelines, therefore, have been proposed on the basis of the design of cold-formed steel structures with the development of the Direct Strength Method. The buckling analyses are conducted to determine the elastic buckling load, which is a compulsory step for the application of this method. The buckling analyses for symmetrical sections have been thoroughly investigated whereas these analyses for asymmetric sections are not clearly regulated in the design standards. Based on the experimental and numerical investigations on cold-rolled aluminium asymmetric section beams in a research project conducted at the University of Sydney, the paper will investigate the elastic global buckling moments of these asymmetric beams by using different methods including numerical, experimental and theoretical methods. The investigated results are subsequently discussed to figure out the procedure for the determination of elastic global buckling moments of the investigated cold-rolled aluminium alloy asymmetric section beams.

Investigations into the local buckling and post-buckling behaviour of fixed-ended hybrid I-section stub columns with slender web

It has been known that thin plate can carry loads considerably more than the buckling loads. This phenomenon is defined as the post-buckling behaviour, which is affected by material properties, geometric dimensions and boundary conditions of the plate. Hybrid I-section is a design concept where flanges are made of high strength steel and web is made of lower steel grade. In order to investigate the effect of slender web on the local buckling and post buckling of hybrid I-section under pure compression, experimental studies of twelve fixed-ended I-section stub columns with slender web were conducted. Tensile coupon tests and initial local geometric imperfection measurement were carried out before stub column tests. Experimental and theoretical methods for determining the critical local buckling load of plate elements were discussed, followed by a post-test finite element analysis to investigate the effects of stub column length and sectional steel combination on the buckling behaviour. Based on the experimental and numerical results, it was observed that for specimens which web plate failed by elastic local buckling, the ultimate test loads are affected by the web strength grade, indicating that the unbuckled portion of slender web plate still provides the post-buckling strength for I-section stub columns even after yielding. By comparing the existing design methods with the numerical ultimate loads, it was found that the Eurocode 3 gives the less scattered predictions than the North American code, Australian code and Chinese code, as well as the existing direct strength method and continuous strength method.

Enhancements to the Direct Strength Method of cold-formed steel member design

The design of thin-walled cold-formed steel members must consider various forms of buckling. The Direct Strength Method simplifies strength prediction with a common approach utilizing adaptations of the Winter plate buckling formula. Recent modifications to the Direct Strength Method were developed for flexural members not symmetric about the axis of bending, which introduced a new general form to the direct strength equation. The versatility of this form provides one strength curve for the entire range of slenderness, including inelastic reserve strength. This new form was investigated for local and distortional buckling of compression members, members with holes, beam–columns, and beam–columns with holes. The proposed formulas for members without holes gave strength predictions nearly identical to the current AISI expressions. For members with holes, the proposed strength predictions were compared to test data and showed improvement over the current AISI expressions. Shear buckling strength was also investigated using the new direct strength equation form which gave equivalent predictions. Enhancement to the global buckling strength curve for flexural members was explored for alignment with column buckling and to facilitate further consistency for global buckling of beam–columns. The proposed enhancements provide improvements with a consistent set of simpler equations, advancing a new cleaner appearance to the Direct Strength Method.

Local – distortional interaction buckling of stainless steel lipped C-section beams

Based on a bearing capacity test of 10 specimens composed of 20 stainless steel lipped C-section components, a refined finite element model was established and verified to investigate the failure mode and bearing capacity. 267 numerous parametric analyses were carried out to investigate the effects of the distribution and amplitude of initial geometric imperfections, strength improvement of corner and buckling slenderness ratio on the buckling modes and bearing capacity of stainless steel beams. The effects of both distribution and amplitude of initial geometric imperfections on the bearing capacity were significant. However, the effect of amplitude of initial geometric imperfections on the buckling modes was small. When the ratio of cross-sectional area of corner to the whole cross-sectional area was smaller than 5%, the increase of strength improvement of corner to the bearing capacity was within 5%. When the ratio was larger than 5%, the increase was more significant. The existing methods for calculating the bearing capacity of local – distortional interaction buckling of carbon steel and high-strength steel lipped C-section beams underestimate that of stainless steel lipped C-section beams. Therefore, two design methods for local – distortional interaction buckling of stainless steel lipped C-section beams based on Direct Strength Method were proposed for the first time. A reliability analysis of the proposed methods was conducted to verify the reliability for engineering application.