Concrete filled steel hollow structural (CFS) sections are increasingly used to support large compressive loads in buildings, with the concrete infill and the steel tube working together to yield several benefits both at ambient temperature and during a fire. These members are now widely applied in the design of highly optimized multi-storey and high rise buildings where fire resistance ratings of two or more hours may be required. Whilst the response and design of these sections at ambient temperatures is reasonably well understood, their response in fire, and thus their fire resistance design, is less well established. Structural fire resistance design guidance is available but has been developed based on tests of predominantly short, concentrically-loaded, small-diameter columns in braced frames using normal strength concrete. The current prescriptive guidance is limited and the design of CFS columns is thus often based on a detailed performance based approach, which can be time consuming and expensive and which is generally not well supported by a deep understanding of CFS columns’ behaviour in real fires. This thesis aims to understand the fundamental thermal and mechanical factors at play within these sections so as to provide guidance on how to improve their design for fire resistance when applied either as unprotected or protected sections. A meta-analysis of available furnace test data is used to demonstrate that current guidance fails to capture the relevant mechanics and thus poorly predicts fire resistance. It is also demonstrated that the predictive abilities of the available design standards vary with physical characteristics of the CFS section such as shape and size. A factor which has been observed in furnace tests on CFS sections but which is not accounted for in available guidance is the formation of an air gap between the steel tube and the concrete core due to differential expansion; this affects their structural response in fire. The insulating effect of air gap formation has not previously been addressed in literature and an experimental program is presented to systematically assess the effects of a gap on the heat transfer through the section; showing that the presence of even a 1 mm gap is important. To explicitly assess the heat transfer response within both unprotected and fire protected (i.e. insulated) CFS sections, 34 large scale standard furnace tests were performed in partnership with an industry sponsor. Fourteen tests on large scale unloaded unprotected CFS sections are presented to assess current capability to predict the thermal response and to assess the effects of different sectional and material parameters on heating. New best practice thermal modelling guidance is suggested based on comparison between the models and observed temperatures from the tests. Twenty CFS specimens of varying size and shape, protected with different types and thicknesses of intumescent paint fire insulation, were also tested unloaded in a furnace to understand the thermal evolution within protected CFS sections and to develop design guidance to support application of intumescent coatings in performance based fire resistance design of CFS sections. These tests demonstrate that the intumescent coatings were far more effective than expected when applied to CFS sections, and that current methods of designing the coatings’ thickness are overly conservative. The reason for this appears to be that the calculation of effective section factor which is used in the prescription of intumescent coating thicknesses is based on the thermal response of unprotected CFS sections which display fundamentally different heating characteristics from protected sections due to the development of a thermal gradient in the concrete core. It is also demonstrated (by calculation supported by the testing presented herein) that the steel failure temperature (i.e. limiting temperature) of an unprotected CFS column in fire is significantly higher than one which is protected; procedures to determine the limiting temperature of protected sections are suggested. Finally, the residual strength of fire-exposed CFS columns is examined through structural testing of 19 of the 34 fire tested columns along with unheated control specimens. The results provide insights into the residual response of unprotected and protected CFS section exposed to fire, and demonstrate a reasonable ability to calculate their residual structural capacity. The work presented in this thesis has shed light on the ability of available guidance to rationally predict the thermal and structural response to fire of CFS columns, has improved the understanding of the thermal evolution within protected and unprotected CFS sections in fire, has provided best-practice guidance and material input parameters for both thermal and structural modelling of CFS sections, and has improved understanding of the residual capacity of CFS sections after a fire.

This thesis examines the effects of cold forming on the material properties of steel and stainless steel structural members. Extensive research has been carried out over many years on both of these materials as they are used to manufacture structural sections to various design specifications which exist in many different countries. However, to date, no design code exists in the UK for cold formed stainless steel structural members. A significant amount of research has focused on the localised effect of cold forming on material properties such as the yield and ultimate tensile strengths, particularly of steel, and this is discussed at length in Chapter 1- Literature Review. Less attention has been placed on stainless steel, but over the last 20 years with the advent of design specifications particularly in the USA, stainless steel has gained popularity for cold forming. Chapter 1 describes the research that has been carried out on stainless steel, with particular emphasis on localised forming effects. Chapter 2 gives a general introduction to Thin-Walled Structures since cold-formed structural sections are commonly used as thin-walled members. The deformation and properties of metallic materials are described in Chapter 3 showing the particular relevance to the cold forming process. This chapter is extended into Chapter 4 where the strengthening, forming and properties of metallic materials are discussed in detail, with particular attention given to the cold forming processes. Chapter 5 describes existing analytical and design code approaches to determine the increase in strength of cold formed steel structural sections, along with an empirically derived relationship to calculate the increased yield strength of stainless steel sections. Chapter 6 describes the recommendations provided by various design specifications on evaluation of the axial compression capacity of short struts subject to varying degrees of cold forming. This chapter also describes the recommendations provided by various design specifications on evaluation of both the axial compression and the combined bending and axial compression load capacities of cold formed lipped channel section stainless steel columns of short-to-medium length. The results obtained from Chapters 5 and 6 are compared to the results obtained from an extensive experimental approach as described in Chapter 7. A finite element non-linear analysis using the ANSYS finite element software package is presented in Chapter 8 which models the behaviour of cold formed stainless steel lipped channel section columns of short-to-medium length subject to pure axial compression loading and also combined bending and axial compression loading. Chapter 9 presents the experimental findings showing the relationship between material hardness and material yield strength for cold-formed areas. The results are then compared to the theoretical results from Chapter 6 to determine their accuracy in prediction of the structural behaviour of full cold formed structural member cross-sections. The load capacity obtained for axially compressed steel and stainless steel struts from experiments are compared to those obtained from the various design code predictions described in Chapter 6. Also presented are the experimental findings, design code recommendations and finite element predictions for the load capacity of stainless steel columns. Chapter 10 concludes on the work by discussing the various issues arising from the experiments, from the design code recommendations and from finite element analysis 11 M. Macdonald

Typescript. / Digitized by Kansas Correctional Industries

The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions.

Bibliography: leaves 287-294. This thesis addresses preprocessing issues for radar target classification from high resolution radar imagery. High resolution radar imagery of real aircraft in flight and of a MIRAGE aircraft on a turntable is examined. An algorithm to coherently average high resolution range profile is proposed.

Formaldehyde (HCHO) plays a primary role in tropospheric chemistry. Its photochemical activity is an important source of radical species such as HCO, H, and subsequently HO2 as well as molecular hydrogen and carbon monoxide. As a source of hydrogen radicals (HOx = OH + HO2), HCHO plays a significant role in the oxidative capacity of the atmosphere, and an important part in the interrelated chemistries of ozone and the HOx and NOx (NO + NO2) cycles. Accurate atmospheric photolysis rates of HCHO are thus required in order to properly model tropospheric chemistry. Despite extensive studies HCHO’s spectroscopy and photochemistry remains to be well characterized. Absolute room temperature absorption cross sections for the A1A2 – X1A1 electronic transition of formaldehyde have been measured over the spectral range 30285 – 32890 cm-1 (304 – 330 nm) using ultraviolet (UV) laser absorption spectroscopy. Absorption cross sections were obtained at an instrumental resolution better than 0.09 cm-1 which is slightly broader than the Doppler width of a rotational line of HCHO at 300K (~0.07 cm-1) and so we were able to resolve all but the most closely spaced lines. Qualitative comparisons with spectral simulations show varying agreement depending on vibronic band. Refined state origins and transition dipole moments for each vibronic band have been reported. There is evidence of areas of perturbation and the need to optimize higher order spectral constants. Pressure broadening parameters have been measured and increase with the strength of intermolecular interaction between formaldehyde and the collision partner. Comparisons between the available high-resolution studies and spectral simulations indicate that the HCHO absorption cross section is still not well characterized. The relative quantum yield for the production of radical products, H+HCO, from the UV photolysis of formaldehyde (HCHO) has been measured directly using a Pulsed Laser Photolysis – Pulsed Laser Induced Fluorescence (PLP – PLIF) technique across the same spectral region. Relative yields were normalized to a value of 0.69 at 31750 cm-1 based on the current NASA-JPL recommendation. The resulting absolute radical quantum yields agree well with previous experimental studies and show more wavelength dependent behavior than the recommendation. This provides support for the complicated competition among the various HCHO dissociation pathways.

The advancement of the structural steel manufacturing industry has led to the recent emergence of steel members with Elliptical Hollow Sections (EHS) and Semi Elliptical Hollow Sections (SEHS). Although these sections are gaining popularity among architects, the lack of design guidelines specifically tailored towards these sections inhibits their efficient structural use. Within this context, this thesis provides several steps towards the development of such guidelines. A review of the manufacturing process of hot-rolled steel sections is conducted with emphasis on hollow structural sections. The main factors affecting the formation of residual stresses during cooling of the sections are discussed. Lower bound plastic interaction relations for EHS subjected to combinations of axial force, bi-axial bending moments and torsion are then derived. The formulation is based on the lower bound theorem of plasticity and the maximum distortional energy density yield criterion. Its applicability for conducting the cross-sectional interaction check in structural steel design problems is illustrated through a practical example. A simplified and conservative interaction equation is then proposed based on curve fitting of the results of the lower bound solution. Upper bound interaction relations are next developed for EHS subjected to combinations of axial force, bi-axial bending moments, torsion and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. An iterative solution technique is developed to solve the resulting highly non-linear system of interaction relations. The effects of residual stresses and initial imperfections on axial compressive resistance of hot-rolled EHS are then incorporated into the lower bound interaction relations. Towards that goal, the thermo-mechanical properties of steel were extracted from the literature. A thermo-mechanical finite element model was developed for prediction of residual stresses in rolled sections. The validity of the model was assessed by comparison against residual stress measurements available in the literature. The model is then applied to predict the residual stresses in hot-rolled EHS. A series of geometric and material nonlinear finite element analyses is conducted on columns of EHS sections. The analyses include predicted residual stresses and initial out-of-straightness imperfections in order to determine the inelastic buckling capacity of EHS members and generate column curves for EHS sections. The column curves are subsequently compared to those based on Canadian, American and European design codes. Two column curve equations are proposed in a format similar to that of the Canadian Standards for buckling about major and minor axes. The column curves were subsequently combined with the interaction relations developed to provide design rules for EHS members under combined loads. The last contribution of the thesis provides a formulation of lower bound interaction relations for SEHS subject to combinations of axial force, bi-axial bending moments and torsion. An iterative scheme for solving the parametric form of the interaction relations is developed and a grid of admissible stress resultant combinations is generated. A series of trial functions are fitted to the grid of internal force combinations and two simplified and conservative interaction equations are proposed.

The advancement of the structural steel manufacturing industry has led to the recent emergence of steel members with Elliptical Hollow Sections (EHS) and Semi Elliptical Hollow Sections (SEHS). Although these sections are gaining popularity among architects, the lack of design guidelines specifically tailored towards these sections inhibits their efficient structural use. Within this context, this thesis provides several steps towards the development of such guidelines. A review of the manufacturing process of hot-rolled steel sections is conducted with emphasis on hollow structural sections. The main factors affecting the formation of residual stresses during cooling of the sections are discussed. Lower bound plastic interaction relations for EHS subjected to combinations of axial force, bi-axial bending moments and torsion are then derived. The formulation is based on the lower bound theorem of plasticity and the maximum distortional energy density yield criterion. Its applicability for conducting the cross-sectional interaction check in structural steel design problems is illustrated through a practical example. A simplified and conservative interaction equation is then proposed based on curve fitting of the results of the lower bound solution. Upper bound interaction relations are next developed for EHS subjected to combinations of axial force, bi-axial bending moments, torsion and bimoments. The formulation is based on kinematically admissible strain fields within the context of the upper bound theorem of plasticity. The interaction relations derived successfully capture the effect of confining radial strains present at welded end sections, as well as sections that are free to deform in the radial direction away from end welded sections. An iterative solution technique is developed to solve the resulting highly non-linear system of interaction relations. The effects of residual stresses and initial imperfections on axial compressive resistance of hot-rolled EHS are then incorporated into the lower bound interaction relations. Towards that goal, the thermo-mechanical properties of steel were extracted from the literature. A thermo-mechanical finite element model was developed for prediction of residual stresses in rolled sections. The validity of the model was assessed by comparison against residual stress measurements available in the literature. The model is then applied to predict the residual stresses in hot-rolled EHS. A series of geometric and material nonlinear finite element analyses is conducted on columns of EHS sections. The analyses include predicted residual stresses and initial out-of-straightness imperfections in order to determine the inelastic buckling capacity of EHS members and generate column curves for EHS sections. The column curves are subsequently compared to those based on Canadian, American and European design codes. Two column curve equations are proposed in a format similar to that of the Canadian Standards for buckling about major and minor axes. The column curves were subsequently combined with the interaction relations developed to provide design rules for EHS members under combined loads. The last contribution of the thesis provides a formulation of lower bound interaction relations for SEHS subject to combinations of axial force, bi-axial bending moments and torsion. An iterative scheme for solving the parametric form of the interaction relations is developed and a grid of admissible stress resultant combinations is generated. A series of trial functions are fitted to the grid of internal force combinations and two simplified and conservative interaction equations are proposed.

No description available.

In recent years, light gauge cold-formed steel members have been used extensively in low and mid- rise residential building construction. In cold-formed steel design there are several applications where built-up box girders are used to resist load induced in a structure when a single section is not sufficient to carry the design load. The cold-formed steel box girders may be subjected to eccentric loading when the web of one of the sections receives the load and transfers it through the connection to another section. There may be an unequal distribution of load in built-up girder assemblies loaded from one side. In the current North American Specification for the Design of Cold-Formed Steel Structural Members (CSA-S136-01, 2001), there is no guideline or design equation to calculate the flexural capacity of this type of section. AISI cold-formed steel framing design guide (2002) has recommended that the moment of resistance and inertia of the built-up section are the simple addition of the component parts, based on deflection compatibility of the two sections. However, this design approximation has not been justified by any experimental or numerical study. Very little information was found in literature about this topic. The objective of this study is the investigation of the flexural behaviour of built-up box girders assembled from cold-formed stud and track sections when subjected to eccentric loading. Finite element analysis is conducted for this purpose, being much more economical than expensive experimental testing. Detailed parametric studies are carried out to identify the factors affecting the flexural capacity of built-up cold-formed steel sections. The parametric results are used to develop a design equation for calculating the flexural capacity of built-up cold-formed steel sections.