Local-distortional Interaction Research Articles

Experimental and numerical investigation on cold-formed steel zed section beams with complex edge stiffeners

This paper describes the experimental and numerical investigation on the flexural performance of cold-formed steel (CFS) zed section members bent about the neutral axis parallel to the flanges. In the test program, twelve pairs of zed section specimens fabricated from steel sheets of grades G450, G500 and G550 were loaded under four-point bending. Three series of sectional shapes, namely the zed sections with plain flanges as well as complex edge stiffeners consisting of double-fold inward and outward return lips, were devised for the test specimens. In the numerical investigation, the finite element model of four-point bending members, which was developed using ABAQUS and calibrated against the experimental results, was adopted to predict the behaviour of CFS unstiffened and edge-stiffened zed section beams over wide ranges of flange-to-web width ratio, lip-to-flange width ratio, return lip-to-lip width ratio and cross-sectional compactness. Furthermore, underpinned by the bending capacities acquired from the 12 experiments and 222 FE analyses in this study as well as 22 tests available in the literature, it was demonstrated that the current direct strength method (DSM) codified in the AISI S100 generally provided conservative flexural strength predictions for the unstiffened zed section members, while led to overall slightly unconservative design for the edge-stiffened zed section beams. In addition, based upon the DSM-based approaches that were addressed in the previous studies to account for the effect of local-distortional interaction, the nominal flexural strengths of the CFS zed section members with simple and complex edge stiffeners were found to be underestimated by 17% to 21% on average. Accordingly, the modified DSM formulae were recommended in this study for the CFS unstiffened and edge-stiffened zed section beams bent about the neutral axis parallel to the flanges.

Numerical simulation of local-distortional buckling behavior of lipped C-section stainless steel columns

The stainless steel components with lipped C-section are prone to Local-Distortional Interaction Buckling (LDIB) failure when subjected to compressive load, whereas the design formula of LDIB capacity has not been well-established so far. As a follow-up work of previous experimental study, this paper aims to conduct a parametric study on the LDIB behavior of lipped C-section stainless steel columns through numerical simulation and propose the relevant calculation formulas of LDIB bearing capacity. The factors governing the buckling behavior include the initial geometric imperfection mode, the local-distortion buckling slenderness ratio, the corner region material strength improvement, and the nominal yield strength of the stainless steel materials. Based on the validated Finite Element (FE) model, the LDIB capacity of 169 lipped C-section stainless steel columns with strong-axis rotation and 201 lipped C-section stainless steel columns with weak-axis rotation were numerically computed, and the calculation formulas of LDIB capacity were then proposed using the direct strength method. Based on the comparative study, the proposed formulas deliver enhanced accuracy and robustness than the existing formulas and hence could be employed reliably for the design of lipped C-section stainless steel columns.

Flexural Behavior of Stainless Steel V-Stiffened Lipped Channel Beams

Six groups of austenitic 022Cr19Ni10 stainless steel bending specimens with three types of cross-sectional forms were used to study the impact of V-stiffeners on the failure mode and flexural behavior of stainless steel lipped channel beams. These cross-sectional forms included V-stiffeners in the web compression zone at 1/3 height near the compressed flange and no V-stiffeners on the flange, V-stiffeners in the web compression zone at 1/3 height near the compressed flange and V-stiffeners in the middle of the compressed flange, and V-stiffeners on the web at 1/2 height and V-stiffeners in the middle of the compressed and tensioned flange. The findings show that the specimens without a V-stiffener on the flange and with a V-stiffener in the web compression zone at 1/3 height near the compressed flange have a lower ultimate bearing capacity as a result of local–distortional interaction buckling. The test specimen’s flexural bearing capacity will rise with an increase in web height under the same stiffening form and other fixed cross-sectional parameters. Furthermore, the additional V-stiffeners in the middle of the flange effectively lower the width-to-thickness ratio of the stainless steel specimen with a flange that has been V-stiffened, thus increasing the specimen’s bending bearing capacity by 13% and emphasizing the distortional buckling issue. Buckling first manifests in the compression flange and is caused by the stress evolution on the web of the bending specimen, which is constrained by the V-stiffeners. The specimen’s capacity to withstand bending loads can be improved more successfully through the use of V-stiffeners in the web compression zone at 1/3 height close to the compressed flange and V-stiffeners in the middle of the compressed flange. For the test data, a finite element simulation was established, and the results are generally consistent with the test results.

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.

Research on the local-distortional interaction buckling capacity of stainless steel lipped C-section columns

The plates of the specimens subjected to a large section width to thickness ratio are prone to multiple instances of mode interaction buckling failure under compression. Hence, to investigate the local-distortional interaction buckling capacity of stainless steel lipped C-section columns, the material properties test of 4 stainless steel plate specimens and the capacity tests of 19 stainless steel lipped C-section column specimens under axial compression were carried out. The development process and failure mode of the local-distortional interaction buckling of stainless steel columns were revealed, and the local-distortional interaction buckling capacities, load-axial shortening curves, load-lateral displacement curves and load–strain curves of the stainless steel columns were obtained. The numerical analysis model of the stainless steel lipped C-section column under compression was established based on ABAQUS finite element software. The finite element results were in agreement with the test results, which verified the accuracy of the finite element model. A parametric analysis was carried out on two key factors, the initial geometric imperfection amplitude and boundary conditions, which affect the local-distortional interaction buckling capacity of stainless steel lipped C-section columns. The results show that the initial geometric imperfection amplitude of specimen has a significant influence on the local-distortional interaction buckling capacity of stainless steel lipped C-section column, while the influence of boundary conditions is small.

Local buckling in cold-formed steel built-up I-section columns: Experiments, numerical validations and design considerations

A series of axial compression tests were conducted on cold-formed steel built-up I-section columns consisting of two identical lipped channel sections connected by self-drilling screws at the web. At first, the buckling behavior, failure mode, and ultimate bearing capacity of columns with lipped channels and built-up sections were investigated. A nonlinear finite element model that can predict the built-up I-section column was established, and the model’s accuracy was validated against experimental results. Then, a method for estimating local buckling bearing capacity for built-up I-section columns under axial compression was proposed based on the local buckling critical stress calculation formula (Eq. (3)) in this paper, as well as the local buckling bearing capacity curve (Eq. (2)) of the current direct strength method. In order to simplify the calculation, based on revealing the mechanism of instability, two sets of simplified calculation formulas for local buckling critical stress suitable for different ranges of geometric parameters were given, namely Eqs. (23) and (24). Finally, the predicted capacity obtained using the proposed bearing capacity estimation method was compared with the experimental and supplementary finite element results. The comparison results show that the predicted bearing capacity of the built-up I-section column affected by the pure local buckling mode is in good agreement with the experimental or finite element results. However, this method leads to unsafe design predictions for columns with local-distortional interaction buckling.

Local-distortional interaction behaviour and design of cold-formed steel built-up columns

This research highlights the possibility of LD interaction in the built-up columns and provides a detailed design procedure to account for the strength erosion due to LD interaction. For this, a comprehensive numerical study using finite element (FE) method is performed where the FE models are validated using the test results in the literature. In this study, three types of built-up sections, i) back-to-back I section made of two lipped channels, ii) nested section made of two lipped channels, and iii) nested section made of one lipped and one unlipped channel, are selected. The effects of LD interaction, fastener spacing, and end fastener group (EFG) on the ultimate strength of built-up columns are investigated. The study reveals that the LD interaction behaviour of the built-up back-to-back I section in terms of failure mode and normalized ultimate strength result (Pu/Py) is similar to that of a lipped channel. For the built-up nested section, improved strength is observed when the lipped channel fails in distortional buckling. No improvement is observed in the LD strength of built-up sections with reduced fastener spacing or by using EFG. The study shows that the traditional direct strength method (DSM) based design procedure for LD interaction is conservative for built-up sections. Hence, a reliable design procedure is proposed based on the modified DSM equations obtained from the literature. The strength and failure mode predictions of the proposed method match well with those of experimental studies in the literature and the numerical study of this paper.

Experiments on local–distortional interaction buckling of cold-formed steel three-limbed built-up open-section columns

Cold-formed steel built-up open-section members, which are widely used in doorways, window frames, and corners, exhibit low torsion stiffness and high susceptibility to the deformation of the cross-section. Extensive research has been conducted on the pure buckling behaviour of cold-formed built-up members. However, few studies have investigated the local–distortional buckling interaction behaviour of complex built-up sections. This study aims to obtain a thorough understanding of the mechanics of three-limbed built-up open-section columns undergoing local–distortional interaction buckling through experiments and numerical simulations. Six lipped channels and 18 built-up columns were axially compressed under fixed boundary conditions. Finite element models were established and verified. Detailed parametric studies were conducted on the validated finite element models by varying the web height–thickness ratio, screw spacing, and slenderness ratio. The experimental results indicate that the studied built-up section had an evident assembly effect, and the bearing capacity of the built-up open-section column was sensitive to the web height–thickness ratio. Additionally, the numerical results show that, under local–distortional interaction buckling, the screw spacing had a minor influence on the ultimate bearing capacity of the three-limbed built-up open-section columns. The columns buckled in local–distortional interactions, with slenderness ratios ranging from 12.73 to 36.30. Finally, the validity and accuracy of the local–distortional​ interaction buckling calculation methods considering three-limbed built-up open-section columns were evaluated. With the current calculation methods, the prediction of the local–distortional buckling capacity of three-limbed open-section built-up columns is conservative.

Local‐distortional interaction in cold‐formed steel lipped channel beams: Experimental investigation

AbstractNominee Professor Eduardo de Arantes e Oliveira Award 2021This paper reports an experimental investigation on the behaviour and strength of cold‐formed high‐strength steel (G450–G500) lipped channel beams susceptible to local–distortional interaction. The experimental campaign comprised 36 tests involving simply supported beams bent about the major axis, exhibiting various ratios between their distortional and local critical buckling moments (from 1.09 to 1.46) and acted by either uniform (20 tests) or non‐uniform (trapezoidal: 16 tests) bending diagrams. The results presented and discussed consist of equilibrium paths, photos providing the evolution of the beam deformed configurations and failure moments. The paper also includes a few remarks on the design, using the Direct Strength Method, of the beams under consideration.

Design approach against column local–distortional interactive failures based on the Direct Strength Method

This paper deals with the development and merit assessment of an efficient and rational design approach intended to handle local–distortional (L–D) interactive failures in cold-formed steel columns (CFS) and based on the Direct Strength Method (DSM). Initially, a brief overview of the mechanical aspects underlying local–distortional interaction is provided, for the benefit of readers not familiar with this coupling phenomenon, and its relevance in CFS column design is addressed. Then, the available experimental failure load data, obtained for columns exhibiting various cross-section shapes (plain, web-stiffened and web-flange-stiffened lipped channels, hats and racks) are collected and used as the basis for the development, calibration and validation of this DSM-based design approach, which relies also on the current DSM local and distortional strength curves and existing numerical failure loads. It covers local–distortional​ interactive failures occurring in columns with several ratios between the distortional and local buckling loads, which are grouped in three families, denoted as “true L–D interaction”, “secondary-distortional bifurcation L–D interaction” and “secondary-local bifurcation L–D interaction”. The failure load prediction quality (accuracy and safety) and reliability of the proposed DSM-based design approach are assessed and compared with those exhibited by the existing methodologies to design CFS columns against L–D interactive failures. The reliability assessments follow the procedure prescribed by the current North American Specification for the Design of Cold-Formed Steel Structural Members and indicate that the design approach proposed in this work should be ready for codification in the near future.

Optimization design of high-strength cold-formed steel stiffened lipped channel columns under axial compression

In China's current market, there are many cold-formed thin-walled members used to construct low-rise light steel buildings. The members are mainly manufactured by 550 MPa yield strength aluminized zinc-coated steel sheets with a width of 180 mm. Since the load-carrying capacity of different section shapes significantly varies within a constant sectional area, finding the section shape with the highest load-carrying efficiency is one of the key problems. In this paper, the optimal section under axial compression is investigated. Initially, a program was written to select several candidate sections with high efficiency based on the theoretical load-carrying capacity calculation. Then, finite element analyses and loading tests were carried out on the selected sections, and the section with the highest load-carrying capacity was determined as the optimal section. The results indicate that the variation trends of the load-carrying capacity of the members with different section sizes obtained by theoretical calculation, finite element simulation, and loading test were consistent. When the ratio of web height to the sum of flange and lip width is between 1 and 2, the axial load-carrying capacity of the member is relatively high. The distortional buckling capacity is relatively higher when the lip width is larger. The short columns with optimal sections undergo local-distortional interaction buckling, whereas the long columns with optimal sections undergo the interaction among local, distortional, and overall buckling. The optimal section size, i.e., web height of 81 mm, flange width of 37.5 mm, and lip width of 12 mm, is proposed for engineering design reference.

Interaction of Stiffened and Unstiffened Element Buckling Modes in CFS Plain Channel Compression Members

Plain channel compression members are composed of stiffened (web) and unstiffened (flanges) plate elements. Effective width method (EWM) for the design of cold-formed steel (CFS) compression members accounts for unstiffened and stiffened plate elements through plate buckling coefficient, k of 0.425 and 4.0, respectively in the elastic local buckling stress (fcrl) calculation. The more recent direct strength method (DSM) recommends the local buckling strength equations for the design of plain channel compression members. A lipped stub channel compression member undergoes interaction of local buckling initiated by the stiffened elements and distortional buckling initiated by the partially stiffened flange-lip assembly. Based on finite element analysis (FEA) results, it is demonstrated that such an interaction between buckling modes initiated by the stiffened web and unstiffened flanges is possible in plain channel compression members also. The behavior of plain channels can be represented as an interaction of buckling of the unstiffened flange and stiffened web elements, which is equivalent to local-distortional interaction in lip stiffened channels. The deformation plots are also provided to understand these mode interactions. The present study focuses on stub columns and does not consider the interaction of global buckling mode.

Built-up nested cold-formed steel compression members subject to local or distortional buckling

The current cold-formed steel (CFS) design standards have not yet provided adequate design methods for built-up nested CFS channel compression members, which may fail by either local or distortional buckling, despite several research studies in recent times. These research studies have proposed improved DSM based design methods that led to capacity predictions with varying accuracy. Besides, there were some contradicting observations regarding the effects of screw connections on their compression behaviour and capacities. Hence, this research study investigated the behaviour and capacity of nested CFS channel compression members. It included experimental tests of short single channel and nested channel compression members failing by local-distortional interaction and local buckling, respectively, development and validation of suitable finite element models of nested channel compression members and finally a parametric study to (1) show that distortional buckling is not the critical failure mode of nested channel members, and (2) examine the effects of screw characteristics and spacing on their behaviour and capacities. Importantly, the accuracy of currently available design equations in the CFS design standards and recently published research papers was investigated and a simple DSM based design method is recommended. This paper presents the details of this research study, its results and findings.

Experimental investigation on cold-formed steel lipped channel beams affected by local-distortional interaction under non-uniform bending

This paper reports an experimental investigation, carried out at The University of Hong Kong, on the behaviour of cold-formed steel lipped channel beams affected by local-distortional (L-D) interaction under non-uniform bending – to the authors’ best knowledge, these are the first tests specifically devoted to this topic. This investigation consists of 16 non-conventional four-point simply supported bending tests involving twin lipped channel beams arranged in a “back-to-back” configuration and laterally restrained at the loading points. The 32 lipped channel specimens were brake-pressed from high-strength zinc-coated G450 grade structural steel sheets. Tensile coupon tests were performed to obtain the specimen material properties and initial geometrical imperfections were measured prior to testing. The beam geometries were carefully selected to enable testing beams that are prone to “true L-D interaction” (close critical distortional-to-local buckling moments) when acted by trapezoidal bending moment diagrams with four distinct gradients – all the tested specimens exhibited the sought L-D interactive nature. The output of the experimental investigation consists of (i) applied moment vs. displacement equilibrium paths, (ii) photos showing beam deformed configurations along those paths (including the failure modes) and (iii) the failure moment data. Lastly, the experimental failure moments obtained are compared with their predictions provided by the (i) current local and distortional Direct Strength Method (DSM) strength curves and (ii) available DSM-based approaches against L-D interactive failures, which were developed and calibrated exclusively in the context of beams subjected to uniform bending.

Built-up back-to-back cold-formed steel compression members failing by local and distortional buckling

The current design methods for built-up back-to-back cold-formed steel (CFS) channel compression members are considered inadequate despite several research studies in recent times. These research studies have proposed improved DSM based design equations, however, they have in general led to predictions of varying accuracy. Further, there were some contradicting observations regarding the effects of screw connections on their compression behaviour and capacities. Therefore, this research focused on the compression behaviour and capacity of built-up back-to-back CFS channel sections subject to local and/or distortional buckling. It included compression tests of short single and back-to-back channel members failing by local-distortional interaction buckling, development and validation of finite element models and finally a parametric study to examine the effects of screw fastener characteristics and arrangements on the compression behaviour and capacities of back-to-back channel members failing in local and/or distortional buckling. Using the results, the accuracy of currently available design equations in the CFS design standards and recently published research papers was investigated and a simple DSM based design method is recommended. This paper presents the details of this research and the results including its findings.

Local and Distortional Interaction Buckling of Cold-formed Thin-Walled High Strength Lipped Channel Columns

In this paper, a series of axial compression tests were conducted on lipped channel columns constructed from cold-formed high strength Grade G550 steel sheet of thickness of 1 mm in order to investigate the local and distortional interaction buckling performance. The failure modes, ultimate loads and load–displacement curves of the specimens were reported and analyzed. The experiment revealed the deformation mechanism of specimens failing in local-distortional interaction or distortional mode. Besides, a finite element model was developed to predict the buckling performance of the specimens. The effect of different imperfection shapes and material models on numerical results was investigated so that the reasonable finite element analysis can be carried out. It was found that the local buckling mode with an odd number of waves as the initial imperfection can produce practical deformation process. Meanwhile, the material model of Ramberg–Osgood can be applied for the nonlinear finite element analysis of the specimens. The parametric analysis was also performed to study the relationship between the sensitivity of specimens to local and distortional imperfections as well as the variation of bearing capacity with the geometric size. It was found that the lip width has great influence on the bearing capacity of specimens because of the significant restriction of lip on distortional deformation.

Uniformly bent CFS lipped channel beams experiencing local-distortional interaction: Experimental investigation

This paper describes a test campaign concerning the behaviour and strength of cold-formed steel (CFS) lipped channel (LC) beams experiencing local-distortional (L-D) interaction made of G450-G500 high-strength steel grades. This investigation involves the performance of 20 tests on simply supported beams arranged in a “back-to-back” configuration, subjected to four-point major-axis bending and laterally restrained at the loading points. All tested specimens failed in the expected L-D interactive modes and exhibited critical distortional-to-local buckling moment ratios ranging between 1.09 and 1.46 (i.e., prone to “true L-D interaction”). The experimental results obtained and reported consist of beam (i) moment-displacement equilibrium paths, (ii) photos evidencing the evolution of the beam deformed configurations along those equilibrium paths (including the failure modes) and (iii) failure moments - it is found that these results are in good agreement with recently performed numerical simulations. Finally, the experimental failure moments obtained are compared with their estimates provided by the (i) currently codified Direct Strength Method (DSM) strength curves associated with local and distortional failures, and (ii) other available DSM-based design approaches developed to handle L-D interactive failures. This comparison provides solid evidence that the CFS specifications must include a DSM-based design approach able to handle beam L-D interactive failures - the current L and D design curves clearly overestimate all the experimental failure moments.

Imperfection sensitivity analysis and DSM design of web-stiffened lipped channel columns experiencing local-distortional interaction

Cold-formed thin-walled steel members are commonly subjected to initial imperfection, which will greatly affect their load-carrying capacity. In this study, the load-carrying capacity and imperfection sensitivity of fixed-ended cold-formed steel web-stiffened lipped channel columns subjected to local-distortional (L-D) interactive failure (including secondary local bifurcation interaction (SLI), true L-D interaction (TI) and secondary distortional bifurcation interaction (SDI)) are investigated. A new imperfection simulation method combining finite element analysis (FEA) with the constrained finite strip method (cFSM) was firstly proposed, and then validated using experimental data from literatures. Next, 224 geometries of columns experiencing L-D interactive failure were chosen by the cFSM and their load-carrying capacity under normal state P num (with unavoidable minor initial imperfection) and those under imperfect state P imperfect (with various imperfections) were respectively obtained using FEA. The most unfavorable imperfection patterns for L-D interactive failure were summarized by comparing the P imperfect and P num of the members. Furthermore, the quality of the DSM-based design approaches for L-D interactive failure were evaluated by comparing P num with the failure load predictions of the selected columns provided by these design approaches. • An imperfection simulation method that combined FEM and constrained FSM was proposed. • The effects of imperfections on the thin-walled columns affected by L-D interaction were studied. • The accuracy and applicability of design approaches based on DSM were evaluated.

Experimental investigation on cold-formed steel stiffened lipped channel columns undergoing local-distortional interaction

Abstract The objective of this work is to report a careful experimental investigation, planned at the University of Lisbon and carried out at The University of Hong Kong, concerning the behaviour and ultimate strength of cold-formed steel web-flange-stiffened (WFSLC) and web-stiffened (WSLC) lipped channel columns undergoing local-distortional (L-D) interaction. It involves 31 specimens (16 WFSLC+ 15 WSLC), brake-pressed from high-strength zinc-coated grades G450, G500 and G550 structural steel sheets, exhibiting critical distortional-to-local buckling load ratios ranging between 0.75 and 1.88. The column geometries were carefully selected to enable testing fixed-ended columns undergoing true L-D interaction and secondary distortional-bifurcation L-D interaction (ensuring evidence of the latter required selecting rather slender columns) − all tested specimens exhibited the expected L-D interactive failures. The specimen material properties were obtained from tensile coupon tests and their initial geometrical imperfections were measured prior to testing. The experimental results presented and discussed consist of column (i) load-displacement equilibrium paths, (ii) photos evidencing the evolution of the column deformed configurations along those paths (including the failure mode) and (iii) failure loads. Finally, the experimental failure load data obtained are compared with their estimates provided by the currently codified DSM design approaches for columns failing in L and D modes, showing their inadequacy to handle L-D interactive failures − the fresh light shed by this comparison will contribute to the timely codification, in the near future, of a DSM design procedure for columns affected by L-D interaction.

Post-buckling behaviour of thin-walled regular polygonal tubular columns undergoing local-distortional interaction

This work presents and discusses numerical results of an ongoing investigation concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular columns affected by local-distortional (L-D) interaction. This investigation is conducted by means of geometrically non-linear Generalized Beam Theory (GBT) analyses, extending the knowledge on the “pure” local and distortional post-buckling behaviours of RCPS tubes recently reported by Martins et al. [1]. Due to their inherent modal nature, the GBT analyses make it possible to acquire in-depth knowledge on the structural behaviour of RCPS tubes and also to include, in a straightforward fashion, arbitrary member initial geometrical imperfections. Columns with distortional-to-local critical buckling load ratios (i) close to 1 (“true L-D interaction” – the most trivial L-D interaction type) and (ii) significantly above 1 (“secondary-distortional bifurcation L-D interaction” – the most relevant L-D interaction type) are investigated. Local/distortional critical-mode initial geometrical imperfections and (linear) combinations of both are considered in the former columns, while only local initial imperfections are dealt with in the latter ones – several amplitudes are dealt with to assess the imperfection sensitivity. For comparison and validation purposes, ABAQUS shell finite element analysis results are also reported.