Global optimisation of cold-formed steel sections

In this thesis, standard algorithms are used to carry out the optimisation of cold-formed steel purlins such as zed, channel and sigma sections, which are assumed to be simply supported and subjected to a gravity load. For zed, channel and sigma section, the local buckling, distortional buckling and lateral-torsional buckling are considered respectively herein. Currently, the local buckling is based on the BS 5950-5:1998 and EN 1993-1-3:2006. The distortional buckling is calculated by the direct strength method employing the elastic distortional buckling which is calculated by three available approaches such as Hancock (1995), Schafer and Pekoz (1998), Yu (2005). In the optimisation program, the lateral-torsional buckling based on BS 5950-5:1998, AISI and analytical model of Li (2004) are investigated. For the optimisation program, the programming codes are written for optimisation of channel, zed and sigma beam. The full study has been coded into a computer-based analysis program (MATLAB).

Structural behaviour of glass reinforced plastics

The aim of this research is to promote the use of G.R.P. as a structural material. In the past, the use of G.R.P. has been confined to non-load carrying applications. Such uses are still rapidly increasing but in addition significant changes have been made during the last decade in the development of semi-structural and now even fully structural applications. Glass-reinforced plastic is characterized by a high strength but a relatively low modulus of elasticity. For this reasona G.R.P. structure can expect to show large deformations as a result of which the individual structural members will fail under load due to a loss of stability rather than approaching the ultimate strength of the material. For this reason the selection of the geometrical shapes of G.R.P. structural elements is considered to be an important factor in designing G.R.P. structures. The first chapter of this thesis deals with a general review of the theoretical and experimental methods used to describe the structural properties of G.R.P. The research programme includes five stages dealing with the structural behaviour of G.R.P. The first stage (Chapter 2) begins with selecting and designing an optimum box beam cross-section which gives the maximum flexural and torsional rigidity. The second stage of investigation (Chapter 3) deals with beam to beam connections. A joint was designed and manufactured with different types of fasteners used to connect two beam units. A suitable fastener was selected and the research extended to cover the behaviour of long span beams using multiple joints. The third part of the investigation includes a study of the behaviour of box beams subjected to combined bending, shear and torsion. A special torque rig was developed to perform the tests. Creep deformation of 6 m span G.R.P. was investigated as the fourth stage under a range of loading conditions. As a result of the phenomenon of post buckling behaviour exhibited in the compression flange during testing of box beams during earlier stages of the investigation it was decided to consider this phenomenon in more detail in the final stage of the investigation. G.R.P. plates with different fibre orientation were subjected to uniaxial compression and tested up to failure. In all stages of the investigation theoretical predictions and experimental results were compared and generally good correlation between theory and experimental data was observed.

Web strength of rolled steel joists

This work is concerned with the behaviour of thin webbed rolled steel joists or universal beams when they are subjected to concentrated loads applied to the flanges. The prime concern is the effect of high direct stresses causing web failure in a small region of the beam. The review shows that although many tests have been carried out on rolled steel beams and built up girders, no series of tests has restricted the number of variables involved to enable firm conclusions to be drawn. The results of 100 tests on several different rolled steel universal beam sections having various types of loading conditions are presented. The majority of the beams are tested by loading with two opposite loads, thus eliminating the effects of bending and shear, except for a small number of beams which are tested simply supported on varying spans. The test results are first compared with the present design standard (BS 449) and it is shown that the British Standard is very conservative for most of the loading conditions included in the tests but is unsafe for others. Three possible failure modes are then considered, overall elastic buckling of the web, flexural yielding of the web due to large out of plane deflexions and local crushing of the material at the junction of the web and the root fillets. Each mode is considered theoretically and developed to establish the main variables, thus enabling a comparison to be made with the test results. It is shown that all three failure modes have a particular relevance for individual loading conditions, but that determining the failure load given the beam size and the loading conditions is very difficult in certain instances. Finally it is shown that there are some empirical relationships between the failure loads and the type of loading for various beam serial sizes.

The structural properties of glassfibre reinforced plastics

The research work described in this thesis is concerned with the development of glassfibre reinforced plastics for structural uses in Civil Engineering construction. The first stage was primarily concerned with the design of GRP lamintes with structura1 properties and method of manufacture suitable for use with relatively large structural components. A cold setting, pressure moulding technique was developed which proved to be efficient in reducing the void content in the composite and minimising the exothermic effect due to curing. The effect of fibre content and fibre arrangement on strength and stiffness of the cornposite was studied and the maximum amount of' fibre content that could be reached by the adopted type of moulding technique was determined. The second stage of the project was concerned with the introduction of steel-wire "sheets" into the GRP cornposites, to take advantage of the high modulus of steel wire to improve the GRP stiffness and to reduce deformation. The experimental observations agreed reasonably well with theoretical predictions in both first and second stages of the work. The third stage was concerned with studying the stability of GRP flat rectangular plates subjected to uniaxial compression or pure shear, to simulate compression flanges or shear webs respectively. The investigation was concentrated on the effect of fibre arrangement in the plate on buckling load. The effect of the introduction of steel-wire sheets on the plate stability in compression was also investigated. The boundary conditions were chosen to be close to those usually assumed in built-up box-sections for both compression flanges and webs. The orthotropic plate and the mid-plane symmetric were used successfully in predicting the buckling load theoretically. In determining the buckling load experimentally, two methods were used. The Southwell plot method and electrical strain gauge method. The latter proved to be more reliable in predicting the buckling load than the former, especially for plates under uniaxial compression. Sample design charts for GRP plates that yield and buckle simultaneously under compression are also presented in the thesis. The final stage of the work dealt with the design and test of GRP beams. The investigation began by finding the optimum cross-section for a GRP beam. The cross-section which was developed was a thin walled corrugated section which showed higher stiffness than other cross-sections for the same cross-sectional area (i.e. box, I, and rectangular sections). A cold setting, hand layings technique was used in manufacturing these beams wbich were of nine types depending on the type of glass reinforcement employed and the arrangement of layers in the beam. The simple bending theory was used in the beam design and proved to be satisfactory in predicting the stresses and deflections. A factor of safety of 4 was chosen for design purposes and considered to be suitable for long term use under static load. Because of its relatively low modulus, GRP beams allowable deflection was limited to 1/120th of the span which was found to be adequate for design purposes. A general discussion of the behaviour of GRP composites and their place relative to the more conventional structural material was also presented in the thesis.

Failure of steel gusset plates

This thesis examines the parameters associated with the failure of triangular steel gusset plates. Eighty two results are presented investigating the position of the applied load, the gusset plate height to length ratio, size, thickness, internal angle and the removal of the inside corner. The thickness of the loaded plate and its influence on the gusset plates failure is also investigated. Twenty two similar gusset plates were tested to investigate the welds connecting the gusset plate to the adjacent loaded and support edges. The experimental results are compared with existing methods, none of which cover all the variables tested. Some methods do not consider buckling and most of those that do are inadequate. Most of the methods do not accurately take account of the load position. An alternative method based on experimental observations is presented for design purposes. The method covers any combination of the variables tested. To test assumptions made in the theoretical work forty seven strut tests took place to investigate buckling characteristics and fifteen special gusset plates were also tested. The gusset plates were found to fail in an elastic-plastic buckling manner. A gusset plate has a specific moment of resistance capacity about it’s inside corner and the ultimate load that can be applied is dependent upon the position of the load relative to the supported edge. There is an optimum height to length ratio for strength and any increase in the internal angle from 90 degrees produces little change in moment capacity. The removal of small portions of the inside corner of a gusset plate has little effect upon its moment capacity. The loaded plate does not provide any significant moment of resistance to the applied load at failure. The main functions of the loaded and supported edge welds is to prevent the gusset plate from slipping from between the plates.

Computer simulation for tube-making by the cold roll-forming process

The conventional design of forming rolls depends heavily on the individual skill of roll designers which is based on intuition and knowledge gained from previous work. Roll design is normally a trial an error procedure, however with the progress of computer technology, CAD/CAM systems for the cold roll-forming industry have been developed. Generally, however, these CAD systems can only provide a flower pattern based on the knowledge obtained from previously successful flower patterns. In the production of ERW (Electric Resistance Welded) tube and pipe, the need for a theoretical simulation of the roll-forming process, which can not only predict the occurrence of the edge buckling but also obtain the optimum forming condition, has been recognised. A new simulation system named "CADFORM" has been devised that can carry out the consistent forming simulation for this tube-making process. The CADFORM system applied an elastic-plastic stress-strain analysis and evaluate edge buckling by using a simplified model of the forming process. The results can also be visualised graphically. The calculated longitudinal strain is obtained by considering the deformation of lateral elements and takes into account the reduction in strains due to the fin-pass roll. These calculated strains correspond quite well with the experimental results. Using the calculated strains, the stresses in the strip can be estimated. The addition of the fin-pass roll reduction significantly reduces the longitudinal compressive stress and therefore effectively suppresses edge buckling. If the calculated longitudinal stress is controlled, by altering the forming flower pattern so it does not exceed the buckling stress within the material, then the occurrence of edge buckling can be avoided. CADFORM predicts the occurrence of edge buckling of the strip in tube-making and uses this information to suggest an appropriate flower pattern and forming conditions which will suppress the occurrence of the edge buckling.

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.

Nonlinear Variational Inequalities Depending on a Parameter

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

Reply: 'Myopic foveoschisis: An ectatic retinopathy, not a schisis'

Full text: We thank Tsilimbaris et al1 for their comments on the appropriateness of the term ‘myopic foveoschisis’ to describe the condition that is characterized by the separation of neural retina layers associated with high myopia and posterior staphyloma. They have proposed the term ‘myopic ectatic retinopathy’ as a more literal and functionally more accurate descriptor of the condition to avoid the use of the word ‘schisis’, which may be misleading because it is also used to describe other conditions where there is separation of neural retina layers without the presence of staphyloma.2 Using the word ‘ectatic’ for this condition would imply that we are fairly certain about the pathogenesis and mechanistic factors that underlie its development and progression. However, this is not the case, unfortunately, as our review of the literature has shown. There are several theories ranging from vitreous traction to sclerosing changes of retinal vessels to progression of staphylomas as possible etiological factors. Therefore, it is likely to be multifactorial in nature—hence the success reported with different procedures that address either the vitreous traction factor using vitrectomy, peel plus tamponade or the scleral ectasia factor using posterior buckling techniques. In the absence of a good understanding of underlying pathogenesis, it is probably best to use purely descriptive names rather than mechanistic terms. The use of descriptive terms, even though similar, do not necessarily cause confusion as long as they are widely accepted as differentiating terminology, for example, postoperative pseudophakic cystoid macular edema (Irvine–Gass syndrome) vs cystoid macular edema associated with posterior uveitis in a phakic patient. The introduction of too many mechanistic or pathogenetic terms in the absence of clear understating of etiology can in fact cause more confusion, for example, serous chorioretinopathy vs central serous retinopathy vs serous choroidopathy. The confinement to broad descriptive terms can enhance communication and reduce confusion without committing to any presumption about etiology until it is better understood. This approach is probably best illustrated by the recent advances in the understanding of mactel21, a condition initially described and classified, using descriptive nomenclature, by Don Gass as bilateral, idiopathic acquired juxtafoveolar telangiectasis (Group2A) and as distinctly different from unilateral, congenital parafoveolar telangiectasis (Group 1A; Gass,3 pp 504–506 vs 127–128). Finally, it is worthy to note that for myopic foveoschisis associated with a staphyloma that is associated with outer layer macular detachment, Don Gass also descriptively included the additional observation (before the advent of OCT) that the retinal profile was concave rather than convex in shape, thereby differentiating it from rhegmatogenous detachments with recruitment of subretinal fluid that is associated with posteriorly located breaks and macular holes in myopic eyes. References 1.Tsilimbaris MK, Vavvas DG, Bechrakis NE. Myopic foveoschisis: an ectatic retinopathy, not aschisis. Eye 2016; 30: 328–329. 2.Powner MB, Gillies MC, Tretiach M, Scott A, Guymer RH, Hageman GS et al. Perifoveal müller cell depletion in a case of macular telangiectasia type 2. Ophthalmology 2010; 117(12): 2407–2416. 3.Gass DM. Stereoscopic Atlas of Macular Diseases: Diagnosis and Treatment, 4th edn. Mosby-Yearbook: St. Louis, 1997.

Seismic performance of hybrid fiber reinforced polymer-concrete pier columns

As part of a multi-university research program funded by NSF, a comprehensive experimental and analytical study of seismic behavior of hybrid fiber reinforced polymer (FRP)-concrete column is presented in this dissertation. Experimental investigation includes cyclic tests of six large-scale concrete-filled FRP tube (CFFT) and RC columns followed by monotonic flexural tests, a nondestructive evaluation of damage using ultrasonic pulse velocity in between the two test sets and tension tests of sixty-five FRP coupons. Two analytical models using ANSYS and OpenSees were developed and favorably verified against both cyclic and monotonic flexural tests. The results of the two methods were compared. A parametric study was also carried out to investigate the effect of three main parameters on primary seismic response measures. The responses of typical CFFT columns to three representative earthquake records were also investigated. The study shows that only specimens with carbon FRP cracked, whereas specimens with glass or hybrid FRP did not show any visible cracks throughout cyclic tests. Further monotonic flexural tests showed that carbon specimens both experienced flexural cracks in tension and crumpling in compression. Glass or hybrid specimens, on the other hand, all showed local buckling of FRP tubes. Compared with conventional RC columns, CFFT column possesses higher flexural strength and energy dissipation with an extended plastic hinge region. Among all CFFT columns, the hybrid lay-up demonstrated the highest flexural strength and initial stiffness, mainly because of its high reinforcement index and FRP/concrete stiffness ratio, respectively. Moreover, at the same drift ratio, the hybrid lay-up was also considered as the best in term of energy dissipation. Specimens with glassfiber tubes, on the other hand, exhibited the highest ductility due to better flexibility of glass FRP composites. Furthermore, ductility of CFFTs showed a strong correlation with the rupture strain of FRP. Parametric study further showed that different FRP architecture and rebar types may lead to different failure modes for CFFT columns. Transient analysis of strong ground motions showed that the column with off-axis nonlinear filament-wound glass FRP tube exhibited a superior seismic performance to all other CFFTs. Moreover, higher FRP reinforcement ratios may lead to a brittle system failure, while a well-engineered FRP reinforcement configuration may significantly enhance the seismic performance of CFFT columns.

Seismic Performance of Hybrid Fiber Reinforced Polymer-Concrete Pier Columns

As part of a multi-university research program funded by NSF, a comprehensive experimental and analytical study of seismic behavior of hybrid fiber reinforced polymer (FRP)-concrete column is presented in this dissertation. Experimental investigation includes cyclic tests of six large-scale concrete-filled FRP tube (CFFT) and RC columns followed by monotonic flexural tests, a nondestructive evaluation of damage using ultrasonic pulse velocity in between the two test sets and tension tests of sixty-five FRP coupons. Two analytical models using ANSYS and OpenSees were developed and favorably verified against both cyclic and monotonic flexural tests. The results of the two methods were compared. A parametric study was also carried out to investigate the effect of three main parameters on primary seismic response measures. The responses of typical CFFT columns to three representative earthquake records were also investigated. The study shows that only specimens with carbon FRP cracked, whereas specimens with glass or hybrid FRP did not show any visible cracks throughout cyclic tests. Further monotonic flexural tests showed that carbon specimens both experienced flexural cracks in tension and crumpling in compression. Glass or hybrid specimens, on the other hand, all showed local buckling of FRP tubes. Compared with conventional RC columns, CFFT column possesses higher flexural strength and energy dissipation with an extended plastic hinge region. Among all CFFT columns, the hybrid lay-up demonstrated the highest flexural strength and initial stiffness, mainly because of its high reinforcement index and FRP/concrete stiffness ratio, respectively. Moreover, at the same drift ratio, the hybrid lay-up was also considered as the best in term of energy dissipation. Specimens with glassfiber tubes, on the other hand, exhibited the highest ductility due to better flexibility of glass FRP composites. Furthermore, ductility of CFFTs showed a strong correlation with the rupture strain of FRP. Parametric study further showed that different FRP architecture and rebar types may lead to different failure modes for CFFT columns. Transient analysis of strong ground motions showed that the column with off-axis nonlinear filament-wound glass FRP tube exhibited a superior seismic performance to all other CFFTs. Moreover, higher FRP reinforcement ratios may lead to a brittle system failure, while a well-engineered FRP reinforcement configuration may significantly enhance the seismic performance of CFFT columns.

Structural Analysis and Form-Finding of Mycelium-Based Monolithic Domes

As sustainability becomes an integral design driver for current civil structures, new materials and forms are investigated. The aim of this study is to investigate analytically and numerically the mechanical behavior of monolithic domes composed of mycological fungi. The study focuses on hemispherical and elliptical forms, as the most typical solution for domes. The influence of different types of loading, geometrical parameters, material properties and boundary conditions is investigated in this study. For the cases covered by the classical shell theory, a comparison between the analytical and the finite element solution is given. Two case studies regarding the dome of basilica of “San Luca” (Bologna, Italy) and the dome of sanctuary of “Vicoforte” (Vicoforte, Italy) are included. After the linear analysis under loading, buckling is also investigated as a critical type of failure through a parametric study using finite elements model. Since shells rely on their shape, form-found domes are also investigated and a comparison between the behavior of the form-found domes and the hemispherical domes under the linear and buckling analysis is conducted. From the analysis it emerges that form-finding can enhance the structural response of mycelium-based domes, although buckling becomes even more critical for their design. Furthermore, an optimal height to span ratio for the buckling of form-found domes is identified. This study highlights the importance of investigating appropriate forms for the design of novel biomaterial-based structures.

Simplified PRBMs of spatial compliant multi-beam modules for planar motion

PRBMs (pseudo-rigid-body models) have been becoming important engineering technologies/methods in the field of compliant mechanisms to simplify the design and analysis through the use of the knowledge body of rigid-body mechanisms coupling with springs. This article addresses the PRBMs of spatial multi-beam modules for planar motion, which are composed of three or more symmetrical wire/slender beams parallel to each other where the planar twisting DOF (degree of freedom) is assumed to be very small for specific applications/loading conditions. Simplified PRBMs are firstly proposed through replacing each beam in spatial multi-beam module with a rigid-body link plus two identical spherical joints at its two ends. The characteristics factor, bending stiffness and twisting stiffness for the spherical joint are determined. Load-displacement equations are then derived for a class of spatial multi-beam modules and general spatial multi-beam modules using the virtual work principle and kinematic relationships. Finally, nonlinear FEA (finite element analysis) is employed with comparisons with the PRBMs. The present PRBMs have shown the ability to predict the primary nonlinear constraint characteristics such as load-stiffening effect, cross-axis coupling in the two primary translational directions and buckling load.

The Effect of Foam Core Density on the Flexural and Axial Behaviour of Sandwich Panels of Varying Slenderness with Natural Flax-FRP and Glass-FRP Composite Skins

This study investigates the effect of foam core density and skin type on the behaviour of sandwich panels as structural beams tested in four-point bending and axially compressed columns of varying slenderness and skin thickness. Bio-composite unidirectional flax fibre-reinforced polymer (FFRP) is compared to conventional glass-FRP (GFRP) as the skin material used in conjunction with three polyisocyanurate (PIR) foam cores with densities of 32, 64 and 96 kg/m3. Eighteen 1000 mm long flexural specimens were fabricated and tested to failure comparing the effects of foam core density between three-layer FFRP skinned and single-layer GFRP skinned panels. A total of 132 columns with slenderness ratios (kLe/r) ranging from 22 to 62 were fabricated with single-layer GFRP skins, and one-, three-, and five-layer FFRP skins for each of the three foam core densities. The columns were tested to failure in concentric axial compression using pinned-end conditions to compare the effects of each material type and panel height. All specimens had a foam core cross-section of 100x50 mm with 100 mm wide skins of equal thickness. In both flexural and axial loading, panels with skins comprised of three FFRP layers showed equivalent strength to those with a single GFRP layer for all slenderness ratios and core densities examined. Doubling the core density from 32 to 64 kg/m3 and tripling the density to 96 kg/m3 led to flexural strength increases of 82 and 213%, respectively. Both FFRP and GFRP columns showed a similar variety of failure modes related to slenderness. Low slenderness of 22-25 failed largely due to localized single skin buckling, while those with high slenderness of 51-61 failed primarily by global buckling followed by secondary skin buckling. Columns with intermediate slenderness experienced both localized and global failure modes. High density foam cores more commonly exhibited core shear failure. Doubling the core density of the columns resulted in peak axial load increases, across all slenderness ratios, of 73, 56, 72 and 71% for skins with one, three and five FFRP layers, and one GFRP layer, respectively. Tripling the core density resulted in respective peak load increases of 116, 130, 176 and 170%.

Carbon nanotube films for flexible electronics

Discovering scalable routes to fabricate large scale electronic devices on flexible substrates has been the goal of the newly emerging field of flexible macroelectronics. Thin film transistors (TFTs) have been fabricated on flexible substrates by using organic small-molecule and polymer-based materials, or thin layers of crystalline inorganic semiconductors. Recently, films of carbon nanotubes have been proposed as electronic materials with superior electrical performance due to exceptional electrical and mechanical properties of single-walled carbon nanotubes (SWCNTs). In this thesis, some aspects of recent research efforts on integrating arrays of carbon nanotubes into macroelectronic devices are described. Carbon nanotube films have two major uses for flexible macroelectronics. The first approach uses carbon nanotube thin films as active semiconducting materials in the channel of flexible TFTs. Even though, high-performance carbon nanotube thin film transistors have been realized, the electronic non-homogeneity of the as-grown carbon nanotubes in the film limits the device performance for some applications. In this thesis, the application of electrochemical functionalization on carbon nanotube films to improve the electronic homogeneity of the film is described. The effect of the crystal quartz substrates on the growth rate of carbon nanotubes, and whether this can be used to sort out as-grown carbon nanotubes by electronic type is also discussed. Finally, I argue that high density carbon nanotube films can also be used as highly conducting stretchable interconnects on mechanically flexible electronic circuits. The sheet resistance and the nature of the buckling of carbon nanotube films on flexible substrates are discussed.