Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Numerical Modelling of LiteSteel Beams Subject to Shear

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It has the beneficial characteristics of torsionally rigid closed rectangular flanges combined with economical fabrication processes from a single strip of high strength steel. Although the LSB sections are commonly used as flexural members, no research has been undertaken on the shear behaviour of LSBs. Therefore experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs. In this research finite element models of LSBs were developed to investigate their nonlinear shear behaviour including their buckling characteristics and ultimate shear strength. They were validated by comparing their results with available experimental results. The models provided full details of the shear buckling and strength characteristics of LSBs, and showed the presence of considerable improvements to web shear buckling in LSBs and associated post-buckling strength. This paper presents the details of the finite element models of LSBs and the results. Both finite element analysis and experimental results showed that the current design rules in cold-formed steel codes are very conservative for the shear design of LSBs. The ultimate shear capacities from finite element analyses confirmed the accuracy of proposed shear strength equations for LSBs based on the North American specification and DSM design equations. Developed finite element models were used to investigate the reduction to shear capacity of LSBs when full height web side plates were not used or when only one web side plate was used, and these results are also presented in this paper.

New design rules for the shear strength of LiteSteel Beams

Abstract: The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section produced using dual electric resistance welding and automated continuous roll-forming technologies. The innovative LSB sections have many beneficial characteristics and are commonly used as flexural members in building construction. However, limited research has been undertaken on the shear behaviour of LSBs. Therefore a detailed investigation including both numerical and experimental studies was undertaken to investigate the shear behaviour of LSBs. Finite element models of LSBs in shear were developed to simulate the nonlinear ultimate strength behaviour of LSBs including their elastic buckling characteristics, and were validated by comparing their results with experimental test results. Validated finite element models were then used in a detailed parametric study into the shear behaviour of LSBs. The parametric study results showed that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LSBs. Significant improvements to web shear buckling occurred due to the presence of torsionally rigid rectangular hollow flanges while considerable post-buckling strength was also observed. This paper therefore proposes improved shear strength design rules for LSBs within the current cold-formed steel code guidelines. It presents the details of the parametric study and the new shear strength equations. The new equations were also developed based on the direct strength method. The proposed shear strength equations have the potential to be used with other conventional cold-formed steel sections such as lipped channel sections.

New design rules for the shear strength of LiteSteel Beams with web openings

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. The LSBs are commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. However, no research has been undertaken on the shear behaviour and strength of LSBs with web openings. Therefore experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs with web openings. In this research, finite element models of LSBs with web openings in shear were developed to simulate the shear behaviour and strength of LSBs including their buckling characteristics. They were then validated by comparing their results with available experimental test results and used in a detailed parametric study. The 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 capacity of LSBs with web openings based on both experimental and parametric study results. An alternative shear design method based on an equivalent reduced web thickness was also proposed. It was found that the same shear strength design rules developed for LSBs without web openings can be used for LSBs with web openings provided the equivalent reduced web thickness equation developed in this paper is used. This is a significant advancement as it simplifies the shear design methods of LSBs with web openings considerably.

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.

Section moment capacity tests of LiteSteel Beams

The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. In addition to this unique geometry, the LSB sections also have unique characteristics relating to their stress-strain curves, residual stresses, initial geometric imperfections and hollow flanges that are not encountered in conventional hot-rolled and cold-formed steel channel sections. An experimental study including 20 section moment capacity tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. The presence of inelastic reserve bending capacity in these beams was investigated in detail although the current design rules generally limit the section moment capacities of cold-formed steel members to their first yield moments. The ultimate moment capacities from the tests were compared with the section moment capacities predicted by the current cold-formed and hot-rolled steel design standards. It was found that compact and non-compact LSB sections have greater moment capacities than their first yield moments. The current cold-formed steel design standards were found to be conservative in predicting the section moment capacities of compact and non-compact LSB sections while the hot-rolled steel design standards were able to better predict them. This paper has shown that suitable modifications are needed to the current design rules to allow the inclusion of available inelastic bending capacities of LSBs in design.

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.

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.

Inelastic bending capacity of LiteSteel Beams

Australian manufacturers recently developed a new mono-symmetric cold-formed steel hollow flange channel section known as LiteSteel Beam. The innovative LSB sections with rectangular flanges are currently being used as floor joists and bearers in buildings. In order to assess their behaviour and section moment capacity including the presence of any inelastic reserve bending capacity, 20 section moment capacity tests were conducted in this study. Test results were compared with the section moment capacities predicted by the steel design codes. Although the current cold-formed steel design rules generally limit the section moment capacities to their first yield moments, test results showed that inelastic reserve bending capacity was present in the compact and non-compact LSB sections. The results have shown that suitable modifications to the current design rules are needed to allow the inclusion of available inelastic bending capacities of LSBs in design.

Tests of LiteSteel Beams subject to combined shear and bending actions

This paper presents the details of an experimental study of a cold-formed steel beam known as LiteSteel Beam (LSB) subject to combined shear and bending actions. The LSBs have the beneficial characteristics of torsionally rigid rectangular hollow 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 and shear strengths of LSBs. To date, however, no investigation has been conducted into the strength of LSB sections under combined shear and bending actions. Hence a detailed experimental study involving 18 tests was undertaken to investigate the behaviour and strength of LSBs under combined shear and bending actions. Test results showed that AS/NZS 4600 design rules for unstiffened webs grossly underestimated the capacity of LSBs. Therefore improved design equations were proposed for the combined shear and bending capacities of LSBs based on experimental results.

Behaviour of LiteSteel beams subject to combined shear and bending actions

This paper presents the details of a numerical study of a cold-formed steel beam known as LiteSteel Beam (LSB) subject to combined shear and bending actions. The LSB sections are produced by a patented manufacturing process involving simultaneous cold-forming and electric resistance welding. They have a unique shape of a channel beam with two rectangular hollow flanges. To date, however, no investigation has been conducted into the strength of LSB sections under combined shear and bending actions. Hence a numerical study was undertaken to investigate the behaviour and strength of LSBs subject to combined shear and bending actions. In this research, finite element models of LSBs were developed to simulate the combined shear and bending behaviour and strength of LSBs. They were then validated by comparing their results with test results and used in a parametric study. Both experimental and finite element analysis results showed that the current design equations are not suitable for combined shear and bending capacities of LSBs. Hence improved design equations are proposed for the capacities of LSBs subject to combined shear and bending actions.

Experimental studies of the shear behavior and strength of LiteSteel beams with stiffened web openings

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a patented manufacturing process. It is commonly used as flexural members in residential, industrial and commercial 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. Test results have shown that the shear capacity of LSBs can be reduced considerably by the inclusion of web openings. A cost effective method of eliminating the detrimental effects of a large web opening is to attach suitable stiffeners around the web openings of LSBs. A detailed experimental study consisting of 17 shear tests was therefore undertaken to investigate the shear behaviour and strength of LSBs with stiffened circular web openings. Both plate and stud stiffeners with varying sizes and thicknesses were attached to the web elements of LSBs using a number of screw-fastening arrangements in order to develop a suitable stiffening arrangement for LSBs. Simply supported test specimens of LSBs with an aspect ratio of 1.5 were loaded at mid-span until failure. This paper presents the details of this experimental study of LSBs with stiffened web openings, and the results of their shear capacities and associated behavioural characteristics. Suitable screw-fastened plate stiffener arrangements have been recommended in order to restore the original shear capacity of LSBs.

Suitable stiffening systems for LiteSteel beams with web openings subjected to shear

Abstract: LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel section produced using a simultaneous cold-forming and dual electric resistance welding process. It is commonly used as floor joists and bearers with web openings in residential, industrial and commercial buildings. Their shear strengths are considerably reduced when web openings are included for the purpose of locating building services. A cost effective method of eliminating the detrimental effects of a large web opening is to attach suitable stiffeners around the web openings of LSBs. Experimental and numerical studies were undertaken to investigate the shear behaviour and strength of LSBs with circular web openings reinforced using plate, stud, transverse and sleeve stiffeners with varying sizes and thicknesses. Both welding and varying screw-fastening arrangements were used to attach these stiffeners to the web of LSBs. Finite element models of LSBs with stiffened web openings in shear were developed to simulate their shear behaviour and strength of LSBs. They were then validated by comparing the results with experimental test results and used in a detailed parametric study. These studies have shown that plate stiffeners were the most suitable, however, their use based on the current American standards was found to be inadequate. Suitable screw-fastened plate stiffener arrangements with optimum thicknesses have been proposed for LSBs with web openings to restore their original shear capacity. This paper presents the details of the numerical study and the results.

Effects of cold weather on durability of CFRP strengthened circular hollow steel members

Tubular members have become progressively more popular due to excellent structural properties, aesthetic appearance, corrosion and fire protection capability. However, a large number of such structures are found structurally deficient due to reduction of strength when they expose to severe environmental conditions such as marine environment, cold and hot weather. Hence strengthening and retrofitting of structural members are in high demands. In recent times Carbon Fibre Reinforced Polymers (CFRP) composites appears to be an excellent solution to enhance the load carrying capacity and serviceability of steel structures because of its superior physical and mechanical properties. However, the durability of such strengthening system under cold environmental condition has not yet been well documented to guide the engineers. This paper presents the findings of a study conducted to enhance the bond durability of CFRP strengthened steel tubular members by treating steel surface using epoxy based adhesion promoter under cold weather subjected to bending. The experimental program consisted of six number of CFRP strengthened specimens and one bare specimen. The sand blasted surface of the three specimens to be strengthened was pre-treated with MBrace primer and other three were remained untreated and then cured under ambient temperature and cold weather (3oC) for three and six months period of time. The beams were then loaded to failure under four point bending. The structural response of each specimen was predicted in terms of failure mode, failure load and mid-span deflection. The research findings show that the cold weather immersion had an adverse effect on durability of CFRP strengthened structures. Moreover, the epoxy based adhesion promoter was found to enhance the bond durability in elastic range.

Durability performance of carbon fibre-reinforced polymer strengthened circular hollow steel members under cold weather

The use of circular hollow steel members has attracted a great deal of attention during past few years because of having excellent structural properties, aesthetic appearance, corrosion and fire protection capability. However, no one can deny the structural deficiency of such structures due to reduction of strength when they are exposed to severe environmental conditions such as marine environment, cold and hot weather. Hence strengthening and retrofitting of structural steel members is now very imperative. This paper presents the findings of a research program that was conducted to study the bond durability of carbon fibre-reinforced polymer (CFRP) strengthened steel tubular members under cold weather and tested under four-point bending. Six number of CFRP-strengthened specimens and one unstrengthened specimen were considered in this program. The three specimens having sand blasted surface to be strengthened was pre-treated with MBrace primer and other three were remained untreated and then cured under ambient temperature at least four weeks and cold weather (3 C) for three and six months period of time. Quasi-static tests were then performed on beams to failure under four-point bending. The structural response of each specimen was predicted in terms of failure load, mid-span deflection, composite beam behaviour and failure mode. The research outcomes show that the cold weather immersion had an adverse effect on durability of CFRP-strengthened steel structures. Moreover, the epoxy based adhesion promoter was found to enhance the bond durability in plastic range. The analytical models presented in this study were found to be in good agreement in terms of predicting ultimate load and deflection. Finally, design factors are proposed to address the short-terms durability performance under cold weather.