Numerical modelling of light gauge cold-formed steel compression members subjected to distortional buckling at elevated temperatures

Fire safety design of building structures has received greater attention in recent times due to continuing loss of properties and lives during fires. However, fire performance of light gauge cold-formed steel structures is not well understood despite its increased usage in buildings. Cold-formed steel compression members are susceptible to various buckling modes such as local and distortional buckling and their ultimate strength behaviour is governed by these buckling modes. Therefore a research project based on experimental and numerical studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. Lipped channel sections with and without additional lips were selected with three thicknesses of 0.6, 0.8, and 0.95 mm and both low and high strength steels (G250 and G550 steels). More than 150 compression tests were undertaken first at ambient and elevated temperatures. Finite element models of the tested compression members were then developed by including the degradation of mechanical properties with increasing temperatures. Comparison of finite element analysis and experimental results showed that the developed finite element models were capable of simulating the distortional buckling and strength behaviour at ambient and elevated temperatures up to 800 °C. The validated model was used to determine the effects of mechanical properties, geometric imperfections and residual stresses on the distortional buckling behaviour and strength of cold-formed steel columns. This paper presents the details of the numerical study and the results. It demonstrated the importance of using accurate mechanical properties at elevated temperatures in order to obtain reliable strength characteristics of cold-formed steel columns under fire conditions.

Improved design rules for hollow flange sections subject to lateral distortional buckling

The LiteSteel Beam (LSB) is a new hollow flange section with a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. It is subjected to lateral distortional buckling when used as flexural members, which reduces its member moment capacity. An investigation into the flexural behaviour of LSBs using experiments and numerical analyses led to the development of new design rules for LSBs subject to lateral distortional buckling. However, the comparison of moment capacity results with the new design rules showed that they were conservative for some LSB sections while slightly unconservative for others due to the effects of section geometry. It is also unknown whether these design rules are applicable to other hollow flange sections such as hollow flange beams (HFB). This paper presents the details of a study into the lateral distortional buckling behaviour of hollow flange sections such as LSBs, HFBs and their variations. A geometrical parameter defined as the ratio of flange torsional rigidity to the major axis flexural rigidity of the web (GJf/EIxweb) was found to be a critical parameter in evaluating the lateral distortional buckling behaviour and moment capacities of hollow flange sections. New design rules were therefore developed by using a member slenderness parameter modified by K, where K is a function of GJf/EIxweb. The new design rules based on the modified slenderness parameter were found to be accurate in calculating the moment capacities of not only LSBs and HFBs, but also other types of hollow flange sections.

Numerical modelling and design of LiteSteel Beams subject to lateral buckling

The LiteSteel Beam (LSB) is a new hollow flange channel section developed using a patented dual electric resistance welding and cold-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a slender web, and is commonly used as flexural members. However, the LSB flexural members are subjected to a relatively new lateral distortional buckling mode, which reduces their moment capacities. Unlike lateral torsional buckling, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and cross sectional change due to web distortion. Therefore a detailed investigation into the lateral buckling behaviour of LSB flexural members was undertaken using experiments and finite element analyses. This paper presents the details of suitable finite element models developed to simulate the behaviour and capacity of LSB flexural members subject to lateral buckling. The models included all significant effects that influence the ultimate moment capacities of such members, including material inelasticity, lateral distortional buckling deformations, web distortion, residual stresses, and geometric imperfections. Comparison of elastic buckling and ultimate moment capacity results with predictions from other numerical analyses and available buckling moment equations, and experimental results showed that the developed finite element models accurately predict the behaviour and moment capacities of LSBs. The validated model was then used in a detailed parametric study that produced accurate moment capacity data for all the LSB sections and improved design rules for LSB flexural members subject to lateral distortional buckling.

Numerical method for predicting the elastic lateral distortional buckling moment of a mono-symmetric beam with web openings

When used as floor joists, the new mono-symmetric LiteSteel beam (LSB) sections require web openings to provide access for inspections and various services. The LSBs consist of two rectangular hollow flanges connected by a slender web, and are subjected to lateral distortional buckling effects in the intermediate span range. Their member capacity design formulae developed to date are based on their elastic lateral buckling moments, and only limited research has been undertaken to predict the elastic lateral buckling moments of LSBs with web openings. This paper addresses this research gap by reporting the development of web opening modelling techniques based on an equivalent reduced web thickness concept and a numerical method for predicting the elastic buckling moments of LSBs with circular web openings. The proposed numerical method was based on a formulation of the total potential energy of LSBs with circular web openings. The accuracy of the proposed method’s use with the aforementioned modelling techniques was verified through comparison of its results with those of finite strip and finite element analyses of various LSBs.

Behaviour and design of cold-formed steel beams subject to lateral-torsional buckling

Cold-formed steel beams are increasingly used as floor joists and bearers in buildings. Their behaviour and moment capacities are influenced by lateral-torsional buckling when they are not laterally restrained adequately. Past research on lateral-torsional buckling has concentrated on hot-rolled steel beams. Hence a numerical study was undertaken to investigate the lateral-torsional buckling behaviour of simply supported cold-formed steel lipped channel beams subjected to uniform bending. For this purpose a finite element model was developed using ABAQUS and its accuracy was verified using available numerical and experimental results. It was then used in a detailed parametric study to simulate the lateral-torsional buckling behaviour and capacity of cold-formed steel beams under varying conditions. The moment capacity results were compared with the predictions from the current design rules in many cold-formed steel codes and suitable recommendations were made. European design rules were found to be conservative while Australian/New Zealand and North American design rules were unconservative. Hence the moment capacity design equations in these codes were modified in this paper based on the available finite element analysis results. This paper presents the details of the parametric study, recommendations to current design rules and the new design rules proposed in this research for lateral-torsional buckling of cold-formed steel lipped channel beams.

Elastic lateral buckling of cantilever LiteSteel beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.

Numerical study of cold-formed steel beam subject to lateral-torsional buckling

The use of cold-formed steel members as structural columns and beams in residential, industrial and commercial buildings has increased significantly in recent times. This study is focused on the use of cold-formed steel sections as flexural members subject to lateral-torsional buckling. For this purpose a finite element model of a simply supported lipped channel beam under uniform bending was developed, validated using available numerical and experimental results, and used in a detailed parametric study. The moment capacity results were then compared with the predictions from the current ambient temperature design rules in the cold-formed steel structures codes of Australia, New Zealand, North America and Europe. European design rules were found to be conservative while Australian and American design rules were unsafe. This paper presents the results of the numerical study, the comparison with the current design rules and the new proposed design rules.

Lateral torsional buckling behaviour of cold-formed steel beams at elevated temperatures

Abstract: This paper presents the details of a study into the behaviour and moment capacities of cold-formed steel lipped channel beams (LCB) subject to lateral-torsional buckling at elevated temperatures. It was based on a validated numerical model of a simply supported and laterally unrestrained LCB subjected to a uniform moment. The ultimate moment capacities from this study were compared with the predicted values using ambient and fire design methods. This study showed that the lateral torsional buckling capacity is strongly influenced by the level of non-linearity in the stress-strain curves of steel at elevated temperatures. Hence most of the current design methods based on a single buckling curve were not adequate to determine the moment capacities. This paper proposes a new design method for the cold-formed steel LCBs subject lateral-torsional buckling at elevated temperatures.

Single-subject analysis reveals varied knee mechanics during step landing in response to isokinetic fatigue of the quadriceps

Introduction: The ability to regulate joint stiffness and coordinate movement during landing when impaired by muscle fatigue has important implications for knee function. Unfortunately, the literature examining fatigue effects on landing mechanics suffers from a lack of consensus. Inconsistent results can be attributed to variable fatigue models, as well as grouping variable responses between individuals when statistically detecting differences between conditions. There remains a need to examine fatigue effects on knee function during landing with attention to these methodological limitations. Aim: The purpose of this study therefore, was to examine the effects of isokinetic fatigue on pre-impact muscle activity and post-impact knee mechanics during landing using singlesubject analysis. Methodology: Sixteen male university students (22.6+3.2 yrs; 1.78+0.07 m; 75.7+6.3 kg) performed maximal concentric and eccentric knee extensions in a reciprocal manner on an isokinetic dynamometer and step-landing trials on 2 occasions. On the first occasion each participant performed 20 step-landing trials from a knee-high platform followed by 75 maximal contractions on the isokinetic dynamometer. The isokinetic data was used to calculate the operational definition of fatigue. On the second occasion, with a minimum rest of 14 days, participants performed 2 sets of 20 step landing trials, followed by isokinetic exercise until the operational definition of fatigue was met and a final post-fatigue set of 20 step-landing trials. Results: Single-subject analyses revealed that isokinetic fatigue of the quadriceps induced variable responses in pre impact activation of knee extensors and flexors (frequency, onset timing and amplitude) and post-impact knee mechanics(stiffness and coordination). In general however, isokinetic fatigue induced sig nificant (p<0.05) reductions in quadriceps activation frequency, delayed onset and increased amplitude. In addition, knee stiffness was significantly (p<0.05) increased in some individuals, as well as impaired sagittal coordination. Conclusions: Pre impact activation and post-impact mechanics were adjusted in patterns that were unique to the individual, which could not be identified using traditional group-based statistical analysis. The results suggested that individuals optimised knee function differently to satisfy competing demands, such as minimising energy expenditure, as well as maximising joint stability and sensory information.

Single-subject analysis reveals variation in knee mechanics during step landing

Introduction: Evidence concerning the alteration of knee function during landing suffers from a lack of consensus. This uncertainty can be attributed to methodological flaws, particularly in relation to the statistical analysis of variable human movement data. Aim: The aim of this study was to compare single-subject and group analysis in quantifying alterations in the magnitude and within-participant variability of knee mechanics during a step landing task. Methods: A group of healthy men (N = 12) stepped-down from a knee-high platform for 60 consecutive trials, each trial separated by a 1-minute rest. The magnitude and within-participant variability of sagittal knee stiffness and coordination of the landing leg during the immediate postimpact period were evaluated. Coordination of the knee was quantified in the sagittal plane by calculating the mean absolute relative phase of sagittal shank and thigh motion (MARP1) and between knee rotation and knee flexion (MARP2). Changes across trials were compared between both group and single-subject statistical analyses. Results: The group analysis detected significant reductions in MARP1 magnitude. However, the single-subject analyses detected changes in all dependent variables, which included increases in variability with task repetition. Between-individual variation was also present in the timing, size and direction of alterations to task repetition. Conclusion: The results have important implications for the interpretation of existing information regarding the adaptation of knee mechanics to interventions such as fatigue, footwear or landing height. It is proposed that a familiarisation session be incorporated in future experiments on a single-subject basis prior to an intervention.

A coupled SPH-DEM model for fluid and solid mechanics of apple parenchyma cells during drying

A coupled SPH-DEM based two-dimensional (2-D) micro-scale single cell model is developed to predict basic cell-level shrinkage effects of apple parenchyma cells during air drying. In this newly developed drying model, Smoothed Particle Hydrodynamics (SPH) is used to model the low Reynolds Number fluid motions of the cell protoplasm, and a Discrete Element Method (DEM) is employed to simulate the polymer-like cell wall. Simulations results reasonably agree with published experimental drying results on cellular shrinkage properties such as cellular area, diameter and perimeter. These preliminary results indicate that the model is effective for the modelling and simulation of apple parenchyma cells during air drying.

Shear buckling characteristics of cold-formed steel channel beams

Cold-formed steel members are increasingly used as primary structural elements in the building industries around the world due to the availability of thin and high strength steels and advanced cold-forming technologies. Cold-formed lipped channel beams (LCB) are commonly used as flexural members such as floor joists and bearers. However, their shear capacities are determined based on conservative design rules. For the shear design of LCB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of LCB web panels are determined by assuming conservatively that the web panels are simply supported at the junction between their flange and web elements. Hence finite element analyses were conducted to investigate the elastic shear buckling behavior of LCBs. An improved equation for the higher elastic shear buckling coefficient of LCBs was proposed based on finite element analysis results and included in the ultimate shear capacity equations of the North American cold-formed steel codes. Finite element analyses show that relatively short span LCBs without flange restraints are subjected to a new combined shear and flange distortion action due to the unbalanced shear flow. They also show that significant post-buckling strength is available for LCBs subjected to shear. New equations were also proposed in which post-buckling strength of LCBs was included.