A Direct Approach to the Problem of Diffraction by a Half-Plane under Mixed Boundary Conditions

A general direct technique of solving a mixed boundary value problem in the theory of diffraction by a semi-infinite plane is presented. Taking account of the correct edge-conditions, the unique solution of the problem is derived, by means of Jones' method in the theory of Wiener-Hopf technique, in the case of incident plane wave. The solution of the half-plane problem is found out in exact form. (The far-field is derived by the method of steepest descent.) It is observed that it is not the Wiener-Hopf technique which really needs any modification but a new technique is certainly required to handle the peculiar type of coupled integral equations which the Wiener-Hopf technique leads to. Eine allgemeine direkte Technik zur Lösung eines gemischten Randwertproblems in der Theorie der Beugung an einer halbunendlichen Ebene wird vorgestellt. Unter Berücksichtigung der korrekten Eckbedingungen wird mit der Methode von Jones aus der Theorie der Wiener-Hopf-Technik die eindeutige Lösung für den Fall der einfallenden ebenen Welle hergeleitet. Die Lösung des Halbebenenproblems wird in exakter Form angegeben. (Das Fernfeld wurde mit der Methode des steilsten Abstiegs bestimmt.) Es wurde bemerkt, daß es nicht die Wiener-Hopf-Technik ist, die wirklich irgend welcher Modifikationen bedurfte. Gewiß aber wird eine neue Technik zur Behandlung des besonderen Typs gekoppelter Integralgleichungen benötigt, auf die die Wiener-Hopf-Technik führt.

Diffraction of a cylindrical pulse by a half plane under mixed boundary conditions

The general time dependent source problem has been solved by the method of transforms (Laplace, Lebedev–Kontorovich in succession) and the solution is obtained in the form of an infinite series involving Legendre functions. The solutions in the case of harmonic time dependence and the incident plane wave have been derived from the above solution and are presented in the form of an infinite series. In the case of an incident plane wave, the series has been summed and the final solution involves an improper integral which behaves like a complementary error function for large values of the argument. Finally, the far field evaluation has been shown. The results are compared with those of Sommerfeld's half-plane diffraction problem with unmixed boundary conditions.

Null Dereference Verification via Over-approximated Weakest Pre-conditions Analysis

Null dereferences are a bane of programming in languages such as Java. In this paper we propose a sound, demand-driven, inter-procedurally context-sensitive dataflow analysis technique to verify a given dereference as safe or potentially unsafe. Our analysis uses an abstract lattice of formulas to find a pre-condition at the entry of the program such that a null-dereference can occur only if the initial state of the program satisfies this pre-condition. We use a simplified domain of formulas, abstracting out integer arithmetic, as well as unbounded access paths due to recursive data structures. For the sake of precision we model aliasing relationships explicitly in our abstract lattice, enable strong updates, and use a limited notion of path sensitivity. For the sake of scalability we prune formulas continually as they get propagated, reducing to true conjuncts that are less likely to be useful in validating or invalidating the formula. We have implemented our approach, and present an evaluation of it on a set of ten real Java programs. Our results show that the set of design features we have incorporated enable the analysis to (a) explore long, inter-procedural paths to verify each dereference, with (b) reasonable accuracy, and (c) very quick response time per dereference, making it suitable for use in desktop development environments.

Microstrain Around Dental Implants Supporting Fixed Partial Prostheses Under Axial and Non-Axial Loading Conditions, In Vitro Strain Gauge Analysis

The current study used strain gauge analysis to perform an in vitro evaluation of the effect of axial and non-axial loading on implant-supported fixed partial prostheses, varying the implant placement configurations and the loading points. Three internal hexagon implants were embedded in the center of each polyurethane block with in-line and offset placements. Microunit abutments were connected to the implants using a torque of 20 N.cm, and plastic prosthetic cylinders were screwed onto the abutments, which received standard patterns cast in Co-Cr alloy (n = 10). Four strain gauges (SGs) were bonded onto the surfaces of the blocks, tangentially to the implants: SG 01 mesially to implant 1, SG 02 and SG 03 mesially and distally to implant 2, respectively, and SG 04 distally to implant 3. Each metallic structure was screwed onto the abutments using a 10-N.cm torque, and axial and non-axial loads of 30 kg were applied at 5 predetermined points. The data obtained from the strain gauge analyses were analyzed statistically through the repeated measures analysis of variance and the Tukey test, with a conventional level of significance of P < 0.05. The results showed a statistically significant difference for the loading point (P = 0.0001), with point E (nonaxial) generating the highest microstrain (327.67 mu epsilon) and point A (axial) generating the smallest microstrain (208.93 mu epsilon). No statistically significant difference was found for implant placement configuration (P = 0.856). It was concluded that the offset implant placement did not reduce the magnitude of microstrain around the implants under axial and non-axial loading conditions, although loading location did influence this magnitude.

Full scale fire tests of a new light gauge steel floor-ceiling system

Cold-formed steel members can be assembled in various combinations to provide cost-efficient and safe light gauge floor systems for buildings. Such Light gauge Steel Framing (LSF) systems are widely accepted in industrial and commercial building construction. An example application is in floor-ceiling systems. Light gauge steel floor-ceiling systems must be designed to serve as fire compartment boundaries and provide adequate fire resistance. Fire-rated floor-ceiling assemblies formed with new materials and construction methodologies have been increasingly used in buildings. However, limited research has been undertaken in the past and hence a thorough understanding of their fire resistance behaviour is not available. Recently a new composite floor-ceiling system has been developed to provide higher fire rating under standard fire conditions. But its increased fire rating could not be determined using the currently available design methods. Therefore a research project was carried out to investigate its structural and fire resistance behaviour under standard fire conditions. In this research project full scale experimental tests of the new LSF floor system based on a composite ceiling unit were undertaken using a gas furnace at the Queensland University of Technology. Both the conventional and the new steel floor-ceiling systems were tested under structural and fire loads. Full scale fire tests provided a good understanding of the fire behaviour of the LSF floor-ceiling systems and confirmed the superior performance of the new composite system. This paper presents the details of this research into the structural and fire behaviour of light gauge steel floor systems protected by the new composite panel, and the results.

Improvements to the fire performance of light gauge steel floor systems

Light gauge steel frame (LSF) structures are increasingly used in commercial and residential buildings because of their non-combustibility, dimensional stability and ease of installation. A common application is in floor-ceiling systems. The LSF floor-ceiling systems must be designed to serve as fire compartment boundaries and provide adequate fire resistance. Fire-rated floor-ceiling assemblies have been increasingly used in buildings. However, limited research has been undertaken in the past and hence a thorough understanding of their fire resistance behaviour is not available. Recently a new composite floor-ceiling system has been developed to provide higher fire rating. But its increased fire rating could not be determined using the currently available design methods. Therefore a research project was conducted to investigate its structural and fire resistance behaviour under standard fire conditions. This paper presents the results of full scale experimental investigations into the structural and fire behaviour of the new LSF floor system protected by the composite ceiling unit. Both the conventional and the new floor systems were tested under structural and fire loads. It demonstrates the improvements provided by the new composite panel system in comparison to conventional floor systems. Numerical studies were also undertaken using the finite element program ABAQUS. Measured temperature profiles of floors were used in the numerical analyses and their results were compared with fire test results. Tests and numerical studies provided a good understanding of the fire behaviour of the LSF floor-ceiling systems and confirmed the superior performance of the new composite system.

Numerical modelling of load bearing steel stud walls under fire conditions

Fire design is an essential part of the overall design procedure of structural steel members and systems. Conventionally, increased fire rating is provided simply by adding more plasterboards to Light gauge Steel Frame (LSF) stud walls, which is inefficient. However, recently Kolarkar & Mahendran (2008) developed a new composite wall panel system, where the insulation was located externally between the plasterboards on both sides of the steel wall frame. Numerical and experimental studies were undertaken to investigate the structural and fire performance of LSF walls using the new composite panels under axial compression. This paper presents the details of the numerical studies of the new LSF walls and the results. It also includes brief details of the experimental studies. Experimental and numerical results were compared for the purpose of validating the developed numerical model. The paper also describes the structural and fire performance of the new LSF wall system in comparison to traditional wall systems using cavity insulation.

Vibration characteristics of plate elements subjected in-plane loads (axial loads)

Axial deformations resulting from in-plane loads (axial forces) of plate elements impact significantly on their vibration characteristics. Although, numerous methods have been developed to quantify axial forces and hence deformations of individual plate elements with different boundary conditions based on their natural frequencies, these methods are unable to apply to the plate elements in a structural system. This is because the natural frequency is a global parameter for the entire structure. Thus, this paper proposes a comprehensive vibration based procedure to quantify axial deformations of plate elements in a structural framing system. Unique capabilities of the proposed method present through illustrative examples. Keywords- Plate Elements, Dynamic Stiffness Matrix, Finite Element Method, Vibration Characteristics, Axial Deformation

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.

Quantifying in-plane deformation of plate elements using vibration characteristics

Plate elements are used in many engineering applications. In-plane loads and deformations have significant influence on the vibration characteristics of plate elements. Numerous methods have been developed to quantify the effects of in-plane loads and deformations of individual plate elements with different boundary conditions based on their natural frequencies. However, these developments cannot be applied to the plate elements in a structural system as the natural frequency is a global parameter for the entire structure. This highlights the need for a method to quantify in-plane deformations of plate elements in structural framing systems. Motivated by this gap in knowledge, this research has developed a comprehensive vibration based procedure to quantify in-plane deformation of plate elements in a structural framing system. This procedure with its unique capabilities to capture the influence of load migration, boundary conditions and different tributary areas is presented herein and illustrated through examples.

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.

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.

Numerical and experimental studies of cold-formed steel floor systems under standard fire conditions

Light gauge cold-formed steel frame (LSF) structures are increasingly used in industrial, commercial and residential buildings because of their non-combustibility, dimensional stability, and ease of installation. A floor-ceiling system is an example of its applications. LSF floor-ceiling systems must be designed to serve as fire compartment boundaries and provide adequate fire resistance. Fire rated floor-ceiling assemblies formed with new materials and construction methodologies have been increasingly used in buildings. However, limited research has been undertaken in the past and hence a thorough understanding of their fire resistance behaviour is not available. Recently a new composite panel in which an external insulation layer is used between two plasterboards has been developed at QUT to provide a higher fire rating to LSF floors under standard fire conditions. But its increased fire rating could not be determined using the currently available design methods. Research on LSF floor systems under fire conditions is relatively recent and the behaviour of floor joists and other components in the systems is not fully understood. The present design methods thus require the use of expensive fire protection materials to protect them from excessive heat increase during a fire. This leads to uneconomical and conservative designs. Fire rating of these floor systems is provided simply by adding more plasterboard sheets to the steel joists and such an approach is totally inefficient. Hence a detailed fire research study was undertaken into the structural and thermal performance of LSF floor systems including those protected by the new composite panel system using full scale fire tests and extensive numerical studies. Experimental study included both the conventional and the new steel floor-ceiling systems under structural and fire loads 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 behavioural and deflection characteristics of LSF floor joists until failure as well as related time-temperature measurements across the section and along the length of all the specimens. Full scale fire tests have shown that the structural and thermal performance of externally insulated LSF floor system was superior than traditional LSF floors with or without cavity insulation. Therefore this research recommends the use of the new composite panel system for cold-formed LSF floor-ceiling systems. The numerical analyses of LSF floor joists were undertaken using the finite element program ABAQUS based on the measured time-temperature profiles obtained from fire tests under both steady state and transient state conditions. Mechanical properties at elevated temperatures were considered based on the equations proposed by Dolamune Kankanamge and Mahendran (2011). Finite element models were calibrated using the full scale test results and used to further provide a detailed understanding of the structural fire behaviour of the LSF floor-ceiling systems. The models also confirmed the superior performance of the new composite panel system. The validated model was then used in a detailed parametric study. Fire tests and the numerical studies showed that plasterboards provided sufficient lateral restraint to LSF floor joists until their failure. Hence only the section moment capacity of LSF floor joists subjected to local buckling effects was considered in this research. To predict the section moment capacity at elevated temperatures, the effective section modulus of joists at ambient temperature is generally considered adequate. However, this research has shown that it leads to considerable over- estimation of the local buckling capacity of joist subject to non-uniform temperature distributions under fire conditions. Therefore new simplified fire design rules were proposed for LSF floor joist to determine the section moment capacity at elevated temperature based on AS/NZS 4600 (SA, 2005), NAS (AISI, 2007) and Eurocode 3 Part 1.3 (ECS, 2006). The accuracy of the proposed fire design rules was verified with finite element analysis results. A spread sheet based design tool was also developed based on these design rules to predict the failure load ratio versus time, moment capacity versus time and temperature for various LSF floor configurations. Idealised time-temperature profiles of LSF floor joists were developed based on fire test measurements. They were used in the detailed parametric study to fully understand the structural and fire behaviour of LSF floor panels. Simple design rules were also proposed to predict both critical average joist temperatures and failure times (fire rating) of LSF floor systems with various floor configurations and structural parameters under any given load ratio. Findings from this research have led to a comprehensive understanding of the structural and fire behaviour of LSF floor systems including those protected by the new composite panel, and simple design methods. These design rules were proposed within the guidelines of the Australian/New Zealand, American and European cold- formed steel structures standard codes of practice. These may also lead to further improvements to fire resistance through suitable modifications to the current composite panel system.

Experimental studies of non-load bearing steel wall systems under fire conditions

Fire safety of buildings has been recognised as very important by the building industry and the community at large. Traditionally, increased fire rating is provided by simply adding more plasterboards to light gauge steel frame (LSF) walls, which is inefficient. Many research studies have been undertaken to investigate the thermal behaviour of traditional LSF stud wall systems under standard fire conditions. However, no research has been undertaken on the thermal behaviour of LSF stud walls using the recently proposed composite panel. Extensive fire testing of both non-load bearing and load bearing wall panels was conducted in this research based on the standard time-temperature curve in AS1530.4. Three groups of LSF wall specimens were tested with no insulation, cavity insulation and the new composite panel based on an external insulation layer between plasterboards. This paper presents the details of this experimental study into the thermal performance of non-load bearing walls lined with various configurations of plasterboard and insulation. Extensive descriptive and numerical results of the tested non-load bearing wall panels given in this paper provide a thorough understanding of their thermal behaviour, and valuable time-temperature data that can be used to validate numerical models. Test results showed that the innovative composite stud wall systems outperformed the traditional stud wall systems in terms of their thermal performance, giving a much higher fire rating.