Shear behaviour and design of LiteSteel beams

OneSteel Australian Tube Mills has recently developed a new hollow flange channel cold-formed section, known as the LiteSteel Beam (LSB). The innovative LSB sections have the beneficial characteristics of torsionally rigid closed rectangular flanges combined with economical fabrication processes from a single strip of high strength steel. They combine the stability of hot-rolled steel sections with the high strength to weight ratio of conventional cold-formed steel sections. The LSB sections are commonly used as flexural members in residential, industrial and commercial buildings. In order to ensure safe and efficient designs of LSBs, many research studies have been undertaken on the flexural behaviour of LSBs. However, no research has been undertaken on the shear behaviour of LSBs. Therefore this thesis investigated the ultimate shear strength behaviour of LSBs with and without web openings including their elastic buckling and post-buckling characteristics using both experimental and finite element analyses, and developed accurate shear design rules. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the web and flange elements. Therefore finite element analyses were conducted first to investigate the elastic shear buckling behaviour of LSBs to determine the true support condition at the junction between their web and flange elements. An equation for the higher elastic shear buckling coefficient of LSBs was developed and included in the shear capacity equations in the cold-formed steel structures code, AS/NZS 4600. Predicted shear capacities from the modified equations and the available experimental results demonstrated the improvements to the shear capacities of LSBs due to the presence of higher level of fixity at the LSB flange to web juncture. A detailed study into the shear flow distribution of LSB was also undertaken prior to the elastic buckling analysis study. The experimental study of ten LSB sections included 42 shear tests of LSBs with aspect ratios of 1.0 and 1.5 that were loaded at midspan until failure. Both single and back to back LSB arrangements were used. Test specimens were chosen such that all three types of shear failure (shear yielding, inelastic and elastic shear buckling) occurred in the tests. Experimental results showed that the current cold-formed steel design rules are very conservative for the shear design of LSBs. Significant improvements to web shear buckling occurred due to the presence of rectangular hollow flanges while considerable post-buckling strength was also observed. Experimental results were presented and compared with corresponding predictions from the current design rules. Appropriate improvements have been proposed for the shear strength of LSBs based on AISI (2007) design equations and test results. Suitable design rules were also developed under the direct strength method (DSM) format. This thesis also includes the shear test results of cold-formed lipped channel beams from LaBoube and Yu (1978a), and the new design rules developed based on them using the same approach used with LSBs. Finite element models of LSBs in shear were also developed to investigate the ultimate shear strength behaviour of LSBs including their elastic and post-buckling characteristics. They were validated by comparing their results with experimental test results. Details of the finite element models of LSBs, the nonlinear analysis results and their comparisons with experimental results are presented in this thesis. Finite element analysis results showed that the current cold-formed steel design rules are very conservative for the shear design of LSBs. They also confirmed other experimental findings relating to elastic and post-buckling shear strength of LSBs. A detailed parametric study based on validated experimental finite element model was undertaken to develop an extensive shear strength data base and was then used to confirm the accuracy of the new shear strength equations proposed in this thesis. Experimental and numerical studies were also undertaken to investigate the shear behaviour of LSBs with web openings. Twenty six shear tests were first undertaken using a three point loading arrangement. It was found that AS/NZS 4600 and Shan et al.'s (1997) design equations are conservative for the shear design of LSBs with web openings while McMahon et al.'s (2008) design equation are unconservative. Experimental finite element models of LSBs with web openings were then developed and validated by comparing their results with experimental test results. The developed nonlinear finite element model was found to predict the shear capacity of LSBs with web opening with very good accuracy. Improved design equations have been proposed for the shear capacity of LSBs with web openings based on both experimental and FEA parametric study results. This thesis presents the details of experimental and numerical studies of the shear behaviour and strength of LSBs with and without web openings and the results including the developed accurate design rules.

Flexural behaviour and design of the new built-up LiteSteel beams

LiteSteel Beam (LSB) is a new cold-formed steel beam produced by OneSteel Australian Tube Mills. The new beam is effectively a channel section with two rectangular hollow flanges and a slender web, and is manufactured using a combined cold-forming and electric resistance welding process. OneSteel Australian Tube Mills is promoting the use of LSBs as flexural members in a range of applications, such as floor bearers. When LSBs are used as back to back built-up sections, they are likely to improve their moment capacity and thus extend their applications further. However, the structural behaviour of built-up beams is not well understood. Many steel design codes include guidelines for connecting two channels to form a built-up I-section including the required longitudinal spacing of connections. But these rules were found to be inadequate in some applications. Currently the safe spans of builtup beams are determined based on twice the moment capacity of a single section. Research has shown that these guidelines are conservative. Therefore large scale lateral buckling tests and advanced numerical analyses were undertaken to investigate the flexural behaviour of back to back LSBs connected by fasteners (bolts) at various longitudinal spacings under uniform moment conditions. In this research an experimental investigation was first undertaken to study the flexural behaviour of back to back LSBs including its buckling characteristics. This experimental study included tensile coupon tests, initial geometric imperfection measurements and lateral buckling tests. The initial geometric imperfection measurements taken on several back to back LSB specimens showed that the back to back bolting process is not likely to alter the imperfections, and the measured imperfections are well below the fabrication tolerance limits. Twelve large scale lateral buckling tests were conducted to investigate the behaviour of back to back built-up LSBs with various longitudinal fastener spacings under uniform moment conditions. Tests also included two single LSB specimens. Test results showed that the back to back LSBs gave higher moment capacities in comparison with single LSBs, and the fastener spacing influenced the ultimate moment capacities. As the fastener spacing was reduced the ultimate moment capacities of back to back LSBs increased. Finite element models of back to back LSBs with varying fastener spacings were then developed to conduct a detailed parametric study on the flexural behaviour of back to back built-up LSBs. Two finite element models were developed, namely experimental and ideal finite element models. The models included the complex contact behaviour between LSB web elements and intermittently fastened bolted connections along the web elements. They were validated by comparing their results with experimental results and numerical results obtained from an established buckling analysis program called THIN-WALL. These comparisons showed that the developed models could accurately predict both the elastic lateral distortional buckling moments and the non-linear ultimate moment capacities of back to back LSBs. Therefore the ideal finite element models incorporating ideal simply supported boundary conditions and uniform moment conditions were used in a detailed parametric study on the flexural behaviour of back to back LSB members. In the detailed parametric study, both elastic buckling and nonlinear analyses of back to back LSBs were conducted for 13 LSB sections with varying spans and fastener spacings. Finite element analysis results confirmed that the current design rules in AS/NZS 4600 (SA, 2005) are very conservative while the new design rules developed by Anapayan and Mahendran (2009a) for single LSB members were also found to be conservative. Thus new member capacity design rules were developed for back to back LSB members as a function of non-dimensional member slenderness. New empirical equations were also developed to aid in the calculation of elastic lateral distortional buckling moments of intermittently fastened back to back LSBs. Design guidelines were developed for the maximum fastener spacing of back to back LSBs in order to optimise the use of fasteners. A closer fastener spacing of span/6 was recommended for intermediate spans and some long spans where the influence of fastener spacing was found to be high. In the last phase of this research, a detailed investigation was conducted to investigate the potential use of different types of connections and stiffeners in improving the flexural strength of back to back LSB members. It was found that using transverse web stiffeners was the most cost-effective and simple strengthening method. It is recommended that web stiffeners are used at the supports and every third points within the span, and their thickness is in the range of 3 to 5 mm depending on the size of LSB section. The use of web stiffeners eliminated most of the lateral distortional buckling effects and hence improved the ultimate moment capacities. A suitable design equation was developed to calculate the elastic lateral buckling moments of back to back LSBs with the above recommended web stiffener configuration while the same design rules developed for unstiffened back to back LSBs were recommended to calculate the ultimate moment capacities.

Flexural behaviour and design of hollow flange steel beams

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using a patented Dual Electric Resistance Welding technique. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. It is commonly used as rafters, floor joists and bearers and roof beams in residential, industrial and commercial buildings. It is on average 40% lighter than traditional hot-rolled steel beams of equivalent performance. The LSB flexural members are subjected to a relatively new Lateral Distortional Buckling mode, which reduces the member moment capacity. Unlike the commonly observed lateral torsional buckling of steel beams, lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and web distortion. Current member moment capacity design rules for lateral distortional buckling in AS/NZS 4600 (SA, 2005) do not include the effect of section geometry of hollow flange beams although its effect is considered to be important. Therefore detailed experimental and finite element analyses (FEA) were carried out to investigate the lateral distortional buckling behaviour of LSBs including the effect of section geometry. The results showed that the current design rules in AS/NZS 4600 (SA, 2005) are over-conservative in the inelastic lateral buckling region. New improved design rules were therefore developed for LSBs based on both FEA and experimental results. A geometrical parameter (K) defined as the ratio of the flange torsional rigidity to the major axis flexural rigidity of the web (GJf/EIxweb) was identified as the critical parameter affecting the lateral distortional buckling of hollow flange beams. The effect of section geometry was then included in the new design rules using the new parameter (K). The new design rule developed by including this parameter was found to be accurate in calculating the member moment capacities of not only LSBs, but also other types of hollow flange steel beams such as Hollow Flange Beams (HFBs), Monosymmetric Hollow Flange Beams (MHFBs) and Rectangular Hollow Flange Beams (RHFBs). The inelastic reserve bending capacity of LSBs has not been investigated yet although the section moment capacity tests of LSBs in the past revealed that inelastic reserve bending capacity is present in LSBs. However, the Australian and American cold-formed steel design codes limit them to the first yield moment. Therefore both experimental and FEA were carried out to investigate the section moment capacity behaviour of LSBs. A comparison of the section moment capacity results from FEA, experiments and current cold-formed steel design codes showed that compact and non-compact LSB sections classified based on AS 4100 (SA, 1998) have some inelastic reserve capacity while slender LSBs do not have any inelastic reserve capacity beyond their first yield moment. It was found that Shifferaw and Schafer’s (2008) proposed equations and Eurocode 3 Part 1.3 (ECS, 2006) design equations can be used to include the inelastic bending capacities of compact and non-compact LSBs in design. As a simple design approach, the section moment capacity of compact LSB sections can be taken as 1.10 times their first yield moment while it is the first yield moment for non-compact sections. For slender LSB sections, current cold-formed steel codes can be used to predict their section moment capacities. It was believed that the use of transverse web stiffeners could improve the lateral distortional buckling moment capacities of LSBs. However, currently there are no design equations to predict the elastic lateral distortional buckling and member moment capacities of LSBs with web stiffeners under uniform moment conditions. Therefore, a detailed study was conducted using FEA to simulate both experimental and ideal conditions of LSB flexural members. It was shown that the use of 3 to 5 mm steel plate stiffeners welded or screwed to the inner faces of the top and bottom flanges of LSBs at third span points and supports provided an optimum web stiffener arrangement. Suitable design rules were developed to calculate the improved elastic buckling and ultimate moment capacities of LSBs with these optimum web stiffeners. A design rule using the geometrical parameter K was also developed to improve the accuracy of ultimate moment capacity predictions. This thesis presents the details and results of the experimental and numerical studies of the section and member moment capacities of LSBs conducted in this research. It includes the recommendations made regarding the accuracy of current design rules as well as the new design rules for lateral distortional buckling. The new design rules include the effects of section geometry of hollow flange steel beams. This thesis also developed a method of using web stiffeners to reduce the lateral distortional buckling effects, and associated design rules to calculate the improved moment capacities.

Stakes and motivation in tournaments : playing when there is nothing to play for but pride

Tournaments are an effective means of incentivising participants to ensure an optimal level of effort. However, situations can occur in tournaments where the final outcome of a given competitor does not depend on his/her future performance. Specifically, we study these specific situations in a data set of the group stages of European football club competitions from 1992 to 2009. We identify situations where teams are already sure to finish either first or last at the penultimate stage in the group. We show that such situations affect team performance in the last match, typically decreasing the performance of a team sure to finish first and increasing the performance of a team sure to finish last. The first finding is in line with the economic predictions yet provides interesting implications, namely that the schedule of the match order plays a significant role in the overall performance of the team. The second, counter-intuitive, finding is not well accommodated into the existing economics framework and thus we discuss two alternative explanations, one based on social pressure and the other on pride.

The relationship between parents’ self-efficacy beliefs, outcome expectations, child behaviour, and management of atopic dermatitis

Atopic dermatitis (AD) is a chronic inflammatory skin condition, characterized by intense pruritis, with a complex aetiology comprising multiple genetic and environmental factors. It is a common chronic health problem among children, and along with other allergic conditions, is increasing in prevalence within Australia and in many countries worldwide. Successful management of childhood AD poses a significant and ongoing challenge to parents of affected children. Episodic and unpredictable, AD can have profound effects on children’s physical and psychosocial wellbeing and quality of life, and that of their caregivers and families. Where concurrent child behavioural problems and parenting difficulties exist, parents may have particular difficulty achieving adequate and consistent performance of the routine management tasks that promote the child’s health and wellbeing. Despite frequent reports of behaviour problems in children with AD, past research has neglected the importance of child behaviour to parenting confidence and competence with treatment. Parents of children with AD are also at risk of experiencing depression, anxiety, parenting stress, and parenting difficulties. Although these factors have been associated with difficulty in managing other childhood chronic health conditions, the nature of these relationships in the context of child AD management has not been reported. This study therefore examined relationships between child, parent, and family variables, and parents’ management of child AD and difficult child behaviour, using social cognitive and self-efficacy theory as a guiding framework. The study was conducted in three phases. It employed a quantitative, cross-sectional study design, accessing a community sample of 120 parents of children with AD, and a sample of 64 child-parent dyads recruited from a metropolitan paediatric tertiary referral centre. In Phase One, instruments designed to measure parents’ self-reported performance of AD management tasks (Parents’ Eczema Management Scale – PEMS) and parents’ outcome expectations of task performance (Parents’ Outcome Expectations of Eczema Management Scale – POEEMS) were adapted from the Parental Self-Efficacy with Eczema Care Index (PASECI). In Phase Two, these instruments were used to examine relationships between child, parent, and family variables, and parents’ self-efficacy, outcome expectations, and self-reported performance of AD management tasks. Relationships between child, parent, and family variables, parents’ self-efficacy for managing problem behaviours, and reported parenting practices, were also examined. This latter focus was explored further in Phase Three, in which relationships between observed child and parent behaviour, and parent-reported self-efficacy for managing both child AD and problem behaviours, were explored. Phase One demonstrated the reliability of both PEMS and POEEMS, and confirmed that PASECI was reliable and valid with modification as detailed. Factor analyses revealed two-factor structures for PEMS and PASECI alike, with both scales containing factors related to performing routine management tasks, and managing the child’s symptoms and behaviour. Factor analysis was also applied to POEEMS resulting in a three-factor structure. Factors relating to independent management of AD by the parent, involving healthcare professionals in management, and involving the child in management of AD were found. Parents’ self-efficacy and outcome expectations had a significant influence on self-reported task performance. In Phase Two, relationships emerged between parents’ self-efficacy and self-reported performance of AD management tasks, and AD severity, child behaviour difficulties, parent depression and stress, conflict over parenting issues, and parents’ relationship satisfaction. Using multiple linear regressions, significant proportions of variation in parents’ self-efficacy and self-reported performance of AD management tasks were explained by child behaviour difficulties and parents’ formal education, and self-efficacy emerged as a likely mediator for the relationships between both child behaviour and parents’ education, and performance of AD management tasks. Relationships were also found between parents’ self-efficacy for managing difficult child behaviour and use of dysfunctional parenting strategies, and child behaviour difficulties, parents’ depression and stress, conflict over parenting issues, and relationship satisfaction. While significant proportions of variation in self-efficacy for managing child behaviour were explained by both child behaviour and family income, family income was the only variable to explain a significant proportion of variation in parent-reported use of dysfunctional parenting strategies. Greater use of dysfunctional parenting strategies (both lax and authoritarian parenting) was associated with more severe AD. Parents reporting lower self-efficacy for managing AD also reported lower self-efficacy for managing difficult child behaviour; likewise, less successful self-reported performance of AD management tasks was associated with greater use of dysfunctional parenting strategies. When child and parent behaviour was directly observed in Phase Three, more aversive child behaviour was associated with lower self-efficacy, less positive outcome expectations, and poorer self-reported performance of AD management tasks by parents. Importantly, there were strong positive relationships between these variables (self-efficacy, outcome expectations, and self-reported task performance) and parents’ observed competence when providing treatment to their child. Less competent performance was also associated with greater parent-reported child behaviour difficulties, parent depression and stress, parenting conflict, and relationship dissatisfaction. Overall, this study revealed the importance of child behaviour to parents’ confidence and practices in the contexts of child AD and child behaviour management. Parents of children with concurrent AD and behavioural problems are at particular risk of having low self-efficacy for managing their child’s AD and difficult behaviour. Children with more severe AD are also at higher risk of behaviour problems, and thus represent a high-risk group of children whose parents may struggle to manage the disease successfully. As one of the first studies to examine the role and correlates of parents’ self-efficacy in child AD management, this study identified a number of potentially modifiable factors that can be targeted to enhance parents’ self-efficacy, and improve parent management of child AD. In particular, interventions should focus on child behaviour and parenting issues to support parents caring for children with AD and improve child health outcomes. In future, findings from this research will assist healthcare teams to identify parents most in need of support and intervention, and inform the development and testing of targeted multidisciplinary strategies to support parents caring for children with AD.

Shear behaviour and strength of LiteSteel Beams with web openings

Abstract: The LiteSteel Beam (LSB) is a new cold-formed steel hollow flange channel beam recently developed in Australia. It is commonly used as a floor joist or bearer in buildings. Current practice in flooring systems is to include openings in the web element of floor joists or bearers so that building services can be located within them. Shear behaviour of LSBs with web openings is more complicated while their shear strengths are considerably reduced by the presence of web openings. However, no research has been undertaken on the shear behaviour and strength of LSBs with web openings. Therefore a detailed experimental study involving 26 shear tests was undertaken on simply supported LSB test specimens with web openings and an aspect ratio of 1.5. This paper presents the details of this experimental study and the results of their shear capacities and behavioural characteristics. Experimental results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs with web openings. Improved design equations have been proposed for the shear strength of LSBs with web openings based on the experimental results from this study.

Plastic bending behaviour and section moment capacities of mono-symmetric LiteSteel Beams with web openings

Recently developed cold-formed LiteSteel beam (LSB) sections have found increasing popularity in residential, industrial and commercial buildings due to their light weight and cost-effectiveness. Currently, there is significant interest in the use of LSB sections as flexural members in floor joist systems, although they can be used as flexural and compression members in a range of building systems. The plastic bending behaviour and section moment capacity of LSB sections with web holes can be assumed to differ from those without, but have yet to be investigated. Hence, no appropriate design rules for determining the section moment capacity of LSB sections with web holes are yet available. This paper presents the results of an investigation of the plastic bending behaviour and section moment capacity of LSB sections with circular web holes. LSB sections with varying circular hole diameters and degrees of spacing were considered. The paper also describes the simplified finite element (FE) modelling technique employed in this study, which incorporates all of the significant behavioural effects that influence the plastic bending behaviour and section moment capacity of these sections. The numerical and experimental test results and associated findings are also presented.

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.