Structural and thermal performance of cold-formed steel stud wall systems under fire conditions

Cold-formed steel stud walls are a major component of Light Steel Framing (LSF) building systems used in commercial, industrial and residential buildings. In the conventional LSF stud wall systems, thin steel studs are protected from fire by placing one or two layers of plasterboard on both sides with or without cavity insulation. However, there is very limited data about the structural and thermal performance of stud wall systems while past research showed contradicting results, for example, about the benefits of cavity insulation. This research was therefore conducted to improve the knowledge and understanding of the structural and thermal performance of cold-formed steel stud wall systems (both load bearing and non-load bearing) under fire conditions and to develop new improved stud wall systems including reliable and simple methods to predict their fire resistance rating. Full scale fire tests of cold-formed steel stud wall systems formed the basis of this research. This research proposed an innovative LSF stud wall system in which a composite panel made of two plasterboards with insulation between them was used to improve the fire rating. Hence fire tests included both conventional steel stud walls with and without the use of cavity insulation and the new composite panel system. A propane fired gas furnace was specially designed and constructed first. The furnace was designed to deliver heat in accordance with the standard time temperature curve as proposed by AS 1530.4 (SA, 2005). A compression loading frame capable of loading the individual studs of a full scale steel stud wall system was also designed and built for the load-bearing tests. Fire tests included comprehensive time-temperature measurements across the thickness and along the length of all the specimens using K type thermocouples. They also included the measurements of load-deformation characteristics of stud walls until failure. The first phase of fire tests included 15 small scale fire tests of gypsum plasterboards, and composite panels using different types of insulating material of varying thickness and density. Fire performance of single and multiple layers of gypsum plasterboards was assessed including the effect of interfaces between adjacent plasterboards on the thermal performance. Effects of insulations such as glass fibre, rock fibre and cellulose fibre were also determined while the tests provided important data relating to the temperature at which the fall off of external plasterboards occurred. In the second phase, nine small scale non-load bearing wall specimens were tested to investigate the thermal performance of conventional and innovative steel stud wall systems. Effects of single and multiple layers of plasterboards with and without vertical joints were investigated. The new composite panels were seen to offer greater thermal protection to the studs in comparison to the conventional panels. In the third phase of fire tests, nine full scale load bearing wall specimens were tested to study the thermal and structural performance of the load bearing wall assemblies. A full scale test was also conducted at ambient temperature. These tests showed that the use of cavity insulation led to inferior fire performance of walls, and provided good explanations and supporting research data to overcome the incorrect industry assumptions about cavity insulation. They demonstrated that the use of insulation externally in a composite panel enhanced the thermal and structural performance of stud walls and increased their fire resistance rating significantly. Hence this research recommends the use of the new composite panel system for cold-formed LSF walls. This research also included steady state tensile tests at ambient and elevated temperatures to address the lack of reliable mechanical properties for high grade cold-formed steels at elevated temperatures. Suitable predictive equations were developed for calculating the yield strength and elastic modulus at elevated temperatures. In summary, this research has developed comprehensive experimental thermal and structural performance data for both the conventional and the proposed non-load bearing and load bearing stud wall systems under fire conditions. Idealized hot flange temperature profiles have been developed for non-insulated, cavity insulated and externally insulated load bearing wall models along with suitable equations for predicting their failure times. A graphical method has also been proposed to predict the failure times (fire rating) of non-load bearing and load bearing walls under different load ratios. The results from this research are useful to both fire researchers and engineers working in this field. Most importantly, this research has significantly improved the knowledge and understanding of cold-formed LSF walls under fire conditions, and developed an innovative LSF wall system with increased fire rating. It has clearly demonstrated the detrimental effects of using cavity insulation, and has paved the way for Australian building industries to develop new wall panels with increased fire rating for commercial applications worldwide.

Multi-body modelling of wagon trains for crashworthiness analysis

Three-dimensional wagon train models have been developed for the crashworthiness analysis using multi-body dynamics approach. The contributions of the train size (number of wagon) to the frontal crash forces can be identified through the simulations. The effects of crash energy management (CEM) design and crash speed on train crashworthiness are examined. The CEM design can significantly improve the train crashworthiness and the consequential vehicle stability performance - reducing derailment risks.

Analysis of conical-cylinder shells fundamental characteristics for structural health diagnostics

This paper describes the formulation for the free vibration of joined conical-cylindrical shells with uniform thickness using the transfer of influence coefficient for identification of structural characteristics. These characteristics are importance for structural health monitoring to develop model. This method was developed based on successive transmission of dynamic influence coefficients, which were defined as the relationships between the displacement and the force vectors at arbitrary nodal circles of the system. The two edges of the shell having arbitrary boundary conditions are supported by several elastic springs with meridional/axial, circumferential, radial and rotational stiffness, respectively. The governing equations of vibration of a conical shell, including a cylindrical shell, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-cylindrical shells. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of previous researchers.

Three-dimensional geological modelling and multivariate statistical analysis of water chemistry data to analyse and visualise aquifer structure and groundwater composition in the Wairau Plain, Marlborough District, New Zealand

Concerns regarding groundwater contamination with nitrate and the long-term sustainability of groundwater resources have prompted the development of a multi-layered three dimensional (3D) geological model to characterise the aquifer geometry of the Wairau Plain, Marlborough District, New Zealand. The 3D geological model which consists of eight litho-stratigraphic units has been subsequently used to synthesise hydrogeological and hydrogeochemical data for different aquifers in an approach that aims to demonstrate how integration of water chemistry data within the physical framework of a 3D geological model can help to better understand and conceptualise groundwater systems in complex geological settings. Multivariate statistical techniques(e.g. Principal Component Analysis and Hierarchical Cluster Analysis) were applied to groundwater chemistry data to identify hydrochemical facies which are characteristic of distinct evolutionary pathways and a common hydrologic history of groundwaters. Principal Component Analysis on hydrochemical data demonstrated that natural water-rock interactions, redox potential and human agricultural impact are the key controls of groundwater quality in the Wairau Plain. Hierarchical Cluster Analysis revealed distinct hydrochemical water quality groups in the Wairau Plain groundwater system. Visualisation of the results of the multivariate statistical analyses and distribution of groundwater nitrate concentrations in the context of aquifer lithology highlighted the link between groundwater chemistry and the lithology of host aquifers. The methodology followed in this study can be applied in a variety of hydrogeological settings to synthesise geological, hydrogeological and hydrochemical data and present them in a format readily understood by a wide range of stakeholders. This enables a more efficient communication of the results of scientific studies to the wider community.

Modelling the interaction of keratinocytes and fibroblasts during normal and abnormal wound healing processes

The crosstalk between fibroblasts and keratinocytes is a vital component of the wound healing process, and involves the activity of a number of growth factors and cytokines. In this work, we develop a mathematical model of this crosstalk in order to elucidate the effects of these interactions on the regeneration of collagen in a wound that heals by second intention. We consider the role of four components that strongly affect this process: transforming growth factor-beta, platelet-derived growth factor, interleukin-1 and keratinocyte growth factor. The impact of this network of interactions on the degradation of an initial fibrin clot, as well as its subsequent replacement by a matrix that is mainly comprised of collagen, is described through an eight-component system of nonlinear partial differential equations. Numerical results, obtained in a two-dimensional domain, highlight key aspects of this multifarious process such as reepithelialisation. The model is shown to reproduce many of the important features of normal wound healing. In addition, we use the model to simulate the treatment of two pathological cases: chronic hypoxia, which can lead to chronic wounds; and prolonged inflammation, which has been shown to lead to hypertrophic scarring. We find that our model predictions are qualitatively in agreement with previously reported observations, and provide an alternative pathway for gaining insight into this complex biological process.

Structural behaviour and design of cold-formed steel wall systems under fire conditions

In recent times, light gauge steel framed (LSF) structures, such as cold-formed steel wall systems, are increasingly used, but without a full understanding of their fire performance. Traditionally the fire resistance rating of these load-bearing LSF wall systems is based on approximate prescriptive methods developed based on limited fire tests. Very often they are limited to standard wall configurations used by the industry. Increased fire rating is provided simply by adding more plasterboards to these walls. This is not an acceptable situation as it not only inhibits innovation and structural and cost efficiencies but also casts doubt over the fire safety of these wall systems. Hence a detailed fire research study into the performance of LSF wall systems was undertaken using full scale fire tests and extensive numerical studies. A new composite wall panel developed at QUT was also considered in this study, where the insulation was used externally between the plasterboards on both sides of the steel wall frame instead of locating it in the cavity. Three full scale fire tests of LSF wall systems built using the new composite panel system were undertaken at a higher load ratio using a gas furnace designed to deliver heat in accordance with the standard time temperature curve in AS 1530.4 (SA, 2005). Fire tests included the measurements of load-deformation characteristics of LSF walls until failure as well as associated time-temperature measurements across the thickness and along the length of all the specimens. Tests of LSF walls under axial compression load have shown the improvement to their fire performance and fire resistance rating when the new composite panel was used. Hence this research recommends the use of the new composite panel system for cold-formed LSF walls. The numerical study was undertaken using a finite element program ABAQUS. The finite element analyses were conducted under both steady state and transient state conditions using the measured hot and cold flange temperature distributions from the fire tests. The elevated temperature reduction factors for mechanical properties were based on the equations proposed by Dolamune Kankanamge and Mahendran (2011). These finite element models were first validated by comparing their results with experimental test results from this study and Kolarkar (2010). The developed finite element models were able to predict the failure times within 5 minutes. The validated model was then used in a detailed numerical study into the strength of cold-formed thin-walled steel channels used in both the conventional and the new composite panel systems to increase the understanding of their behaviour under nonuniform elevated temperature conditions and to develop fire design rules. The measured time-temperature distributions obtained from the fire tests were used. Since the fire tests showed that the plasterboards provided sufficient lateral restraint until the failure of LSF wall panels, this assumption was also used in the analyses and was further validated by comparison with experimental results. Hence in this study of LSF wall studs, only the flexural buckling about the major axis and local buckling were considered. A new fire design method was proposed using AS/NZS 4600 (SA, 2005), NAS (AISI, 2007) and Eurocode 3 Part 1.3 (ECS, 2006). The importance of considering thermal bowing, magnified thermal bowing and neutral axis shift in the fire design was also investigated. A spread sheet based design tool was developed based on the above design codes to predict the failure load ratio versus time and temperature for varying LSF wall configurations including insulations. Idealised time-temperature profiles were developed based on the measured temperature values of the studs. This was used in a detailed numerical study to fully understand the structural behaviour of LSF wall panels. Appropriate equations were proposed to find the critical temperatures for different composite panels, varying in steel thickness, steel grade and screw spacing for any load ratio. Hence useful and simple design rules were proposed based on the current cold-formed steel structures and fire design standards, and their accuracy and advantages were discussed. The results were also used to validate the fire design rules developed based on AS/NZS 4600 (SA, 2005) and Eurocode Part 1.3 (ECS, 2006). This demonstrated the significant improvements to the design method when compared to the currently used prescriptive design methods for LSF wall systems under fire conditions. In summary, this research has developed comprehensive experimental and numerical thermal and structural performance data for both the conventional and the proposed new load bearing LSF wall systems under standard fire conditions. Finite element models were developed to predict the failure times of LSF walls accurately. Idealized hot flange temperature profiles were developed for non-insulated, cavity and externally insulated load bearing wall systems. Suitable fire design rules and spread sheet based design tools were developed based on the existing standards to predict the ultimate failure load, failure times and failure temperatures of LSF wall studs. Simplified equations were proposed to find the critical temperatures for varying wall panel configurations and load ratios. The results from this research are useful to both structural and fire engineers and researchers. Most importantly, this research has significantly improved the knowledge and understanding of cold-formed LSF loadbearing walls under standard fire conditions.

Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Numerical modelling of load bearing LSF Walls under fire conditions

Abstract. Fire safety of light gauge cold-formed steel frame (LSF) stud walls is significant in the design of buildings. In this research, finite element thermal models of both the traditional LSF wall panels with cavity insulation and the new LSF composite wall panels were developed to simulate their thermal behaviour under standard and real design fire conditions. Suitable thermal properties were proposed for plasterboards and insulations based on laboratory tests and literature review. The developed models were then validated by comparing their results with available fire test results. This paper presents the details of the developed finite element models of load bearing LSF wall panels and the thermal analysis results. It shows that finite element models can be used to simulate the thermal behaviour of load bearing LSF walls with varying configurations of insulations and plasterboards. Failure times of load bearing LSF walls were also predicted based on the results from finite element thermal analyses.

Mixed-dimensional consistent coupling by multi-point constraint equations for efficient multi-scale modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multiscale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Finite element modelling of load bearing steel stud walls under real building fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. Conventionally the fire rating of load bearing wall systems made of Light gauge Steel Frames (LSF) is determined using fire tests based on the standard time-temperature curve given in ISO 834 (ISO, 1999). The standard time-temperature curve given in ISO 834 (ISO, 1999) originated from the application of wood burning furnaces in the early 1900s. However, modern commercial and residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the performance of LSF walls was undertaken using the developed real fire curves based on Eurocode parametric curves (ECS, 2002) and Barnett’s BFD curves (Barnett, 2002) using both full scale fire tests and numerical studies. It included LSF walls without any insulation, and the recently developed externally insulated composite panel system. This paper presents the details of the numerical studies and the results. It also includes brief details of the development of real building fire curves and experimental studies.

Modelling resilience in a water supply system : contrasting conditions of drought and flood

This paper presents an approach to modelling the resilience of a generic (potable) water supply system. The system is contextualized as a meta-system consisting of three subsystems to represent the natural catchment, the water treatment plant and the water distribution infrastructure for urban use. An abstract mathematical model of the meta-system is disaggregated progressively to form a cascade of equations forming a relational matrix of models. This allows the investigation of commonly implicit relationships between various operational components within the meta system, the in-depth understanding of specific system components and influential factors and the incorporation of explicit disturbances to explore system behaviour. Consequently, this will facilitate long-term decision making to achieve sustainable solutions for issues such as, meeting a growing demand or managing supply-side influences in the meta-system under diverse water availability regimes. This approach is based on the hypothesis that the means to achieve resilient supply of water may be better managed by modelling the effects of changes at specific levels that have a direct or in some cases indirect impact on higher-order outcomes. Additionally, the proposed strategy allows the definition of approaches to combine disparate data sets to synthesise previously missing or incomplete higher-order information, a scientifically robust means to define and carry out meta-analyses using knowledge from diverse yet relatable disciplines relevant to different levels of the system and for enhancing the understanding of dependencies and inter-dependencies of variable factors at various levels across the meta-system. The proposed concept introduces an approach for modelling a complex infrastructure system as a meta system which consists of a combination of bio-ecological, technical and socio-technical subsystems.

Numerical solution of stress intensity factors of multiple cracks in great number with eigen COD boundary integral equations

Based on the eigen crack opening displacement (COD) boundary integral equations, a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual boundary integral equations, the effectiveness and the efficiencies of the proposed approach are verified.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.