The need for rational and reliable design methods to meet the continual demand for higher standards of performance and lower unit costs is the incentive for providing the designer with comprehensive and accurate information on the magnitude of stress concentrations associated with the geometry of a component. Theoretical stress concentration factors are used indirectly for the calculation of strength reduction factors from which the life of components suffering fluctuating loading can be predicted and are also of direct relevance in cases of failure by brittle fracture under conditions of steady loading. Fairly comprehensive and accurate information is available for the simpler loading cases such as torsion, direct load or uniform bending of many basic engineering components but, in practice, bending is generally accompanied by shear and for this condition the existing information is both scanty and unreliable. A comprehensive series of tests using two-dimensional photoelastic methods have been carried out on shouldered plate models covering a wide range of useful parameters and subjected to various loading configurations of bending with shear. By means of a consistent extrapolation procedure based on curve fitting by orthogonal polynomials and the use of other statistical methods it has been demonstrated that boundary Stresses can be described by linear expressions involving two basic factors associated, independently, with the respective effects of bending and shear. Values of the resulting basic factors are presented in the form of curves plotted against the model parameters. For design purposes, methods are examined whereby the basic information can be used, either in the form of empirical expressions from which peak stresses can be calculated for any given set of parameters, or as input data to a digital computer programmed to control an incremental plotter to give, automatically, curves of stress variation for any selected configuration of bending with shear.

This thesis presents a numerical study of crack propagation in brittle materials. The finite element method using constant strain triangular elements was used. The experimental investigation is based on Gurney and Hunt's quasi-static method of fracture testing. The applicability of the finite element method of analysis to problems of fracture mechanics is demonstrated for the simple cases where a theoretical solution is obtainable. The comparison of both solutions gives good agreement. The effect of test specimen geometry and the effect of halting the crack tip on one side of a symmetrical specimen on stability and the shape of P,u curve is investigated. Numerical P,u curves are produced and compared with those obtained experimentally. A good correlation of results may be seen. The possibility of using an O-section as a fracture toughness specimen is discussed. Determination of the crack path using dV/da energy criterion is shown and the results are verified by experiments using the brittle lacquer technique. Possible future work is discussed in the last chapter.

The problem discussed in the following thesis is that of the effect of stiffener dimension on the buckling of webplate subjected to bending. In Chapter one the problem of buckling is introduced generally and various examples of the use of horizontally stiffened webplates are mentioned. The theoretical background to the problem of the stability of plates both stiffened and unstiffened is contained in Chapter (2) together with reference to the advantages and disadvantages of various stiffener positions. Chapter (3) contains an account of a number of experimental investigations carried out on plates and girders with problems of stability relevant to the present problem. The various methods of examining these problems are also illustrated in Chapter (3). The phenomena of plate buckling is discussed in Chapter (4) together with the various methods of measuring the buckling load. The physical changes caused by buckling which are used for the purpose of measuring the buckling load are discussed and the best possible arrangement of apparatus for performing the measurements are also suggested in this chapter. In Chapter ( 5) the procedure adopted for testing is discussed and the use of sane of the methods of measurement discussed in Chapter (4) are illustrated. Here also the aims and objects of the experiments are stated. The results obtained from the experiments are discussed in Chapter (6). Discussion is first centred upon the results obtained from plates with double-sided horizontal stiffeners, starting with stiffeners at the fifth depth position and going on to stiffeners at mid-depth and those at the quarter depth. Later in this chapter the results from plates stiffened on one side only are surveyed in a general manner and this is followed by a comparison in behaviour between plates stiffened horizontally on both sides and those stiffened horizontally on one side only. The section on non-destructive tests is concluded with an examination of the effect of varying the rigidity of the double­ sided vertical stiffeners. As a preface to the section of Chapter (6) devoted to tests to failure, a study was made of the deflection contours produced in two of the girders when under load. The purpose of these contour tests was to enable the positions of the buckle-crests to be pin pointed in order to fix strain gauges in the appropriate positions. As a result of the contour plots, positions were fixed for the strain gauges for use during the failure tests and the layouts are shown at the beginning of the section of Chapter (6) on destructive tests. The results obtained from the strain gauges illustrated the development of the stresses and strains in the girder and allowed a study of the post­ buckled behaviour of the girders to be made. The results obtained gave information on the behaviour of girders initially plane and girders which were subject to sane initial imperfections. These results threw some interesting light on the comparative behaviour of the girders in these two states.

This work is concerned with the configuration and deformation of prestressed cable nets treating the nets as discrete systems. The treatment is as follows. Chapter 1 describes briefly the three main different types of cable systems used in the design of cable roofs, viz. 1) Simply suspended cables, 2) Cable girders, and 3) Cable nets. Chapter 2 deals with the initial configuration of nets for which the prestressing forces are assumed known. The main emphasis is given to closed forms of solutions because of their suitability to electronic computation. In Chapter 3 is developed a theory which will calculate the displacements and forces in any type of pinjointed link assembly, both rigid and non-rigid, subjected to any type of loading. The application of the method is based upon the minimization of the total potential by the method of steepest descent. Since the method of steepest descent was found to converge very slowly a great deal of time was spent investigating this method with a view to increasing the rate of convergence. The result of this work is given in chapter 4. Inthis chapter it is also shown that another possible way of locating the minimum total potential is by the Runge-Kutta method. The validity of the deformation theory was demonstrated by testing a flat net and a doubly curved net. The design of the model, the test results and corresponding theoretical values are given in chapter 5. In chapter 6 are given the results of an analysis of the behaviour of small saddle shaped nets carried out to investigate how the stiffness is affected by curvature and intensity of prestress. In chapter 7 it is shown how a chosen configuration can be calculated by the theory given in chapter 3. Where appropriate, conclusions on the different aspects of the work are given at the end of each chapter. A summary of these conclusions is given in chapter 8 together with suggestions for future work. Because of the very large number of tables, graphs and diagrams, these have, as far as possible, been included at the end of the thesis, as shown in the contents.

Free vibration characteristics of orthotropic plates have been examined by finite difference methods using (a) the governing differential equation of motion and (b) energy-type analysis. The first approach used in this work is called the direct substitution method in which the governing differential equation has been used for the finite difference formulation leading to the characteristic equations of vibration of an orthotropic plate.

The minimum weight design of a wide range of structures required to resist compressive loading is considered. Items which have been analysed in detail include struts of various sorts, thin plates, honeycomb core sandwich panels, wide column stiffened panels, stiffened panels with optimised support locations, and cylindrical shells stiffened by axial stiffners and rings. A further study is concerned with the effects of imperfections on a tower with corrugation stiffened walls, loaded in compression. Except for the corrugated tower, each analysis includes the effects of plasticity in a direct and realistic way by characterising stress-strain behaviour in the manner suggested by Ramberg and Osgood. Results for each type of structure are presented, together with the appropriate computer programmes.

A finite element program, applicable to the pre- and post-buckling behaviour of plates with imperfections, is developed. Suitable incremental stiffness matrices are generated for a plate element with four nodes and twenty degrees of freedom. Preliminary work, together with a prototype program, is carried out on a simple strut in order to compare various nonlinear solution techniques, both incremental and iterative. The plate program is verified by large deflection calculations for a square plate under lateral pressure, and by comparison with theoretical buckling loads for a perfect plate, closely agreeing with previous theoretical work. Experimental results in compression, both with and without an artificially introduced imperfection, are used to demonstrate real plate behaviour, and they enable a comparison to be made with computed results. Measurements of deflection are made by the Moire fringe technique, as well as by dial gauges. The program is used to investigate the effect of buckling on the compressive and shear stiffness of plates with various degrees of imperfection, including the compressive stiffness of a square plate after buckling in shear.

This dissertation presents an investigation in the energy absorbing capacity of thin-walled metal inverbucktubes loaded in axial compression. It also presents the inversion-buckling(curling-buckling) behaviour achieved in both, quasi-static and dynamic loading conditions. In addition, for the first time, the experimental results of the pressure or normal stress distribution between the inside surface of the inverbucktube and die fillet radius interface are stipulated. These were very successful, using the pressure transducer method. Furthermore, a mathematical model has been developed, based on theory of plasticity and making use of energy method. This predicts the amount of energy absorbed in the assumed seperate collapse processes. Results yielded from the theory, showed good agreement with the experimental results which had geometry factor within feasibility boundaries of inverbuckling collapse (6.5 D/2t 22.5). The successful prediction of energy absorbed, inverbuckling load and pressure distribution, not only proves the validity of the model, but also confirms the quality of the modelling approach proposed in this dissertation. Using this mathematical model, inverbucktubes could be designed, developed and applied.

The work reported here is directed towards the problem of measuring and modeling non-linear damping in steel space frame civil engineering structures. In order to gain a better understanding of the damping mechanism in such structures, tests were performed on a full scale bolted lattice structure and the results of section A show that the joint damping can be represented approximately in the form: FD = C (1 + ε |ẋ|n)ẋ where n=1. Other situations. where this form of non-linear damping occurs is in the case of fluid flow past a solid body. In offshore structures the hydro-dynamic force due to drag effects are found to be proportional to velocity squared. For non linear material damping, n, takes a value of 6. In section B, various methods of solution to the non-linear dynamical system under random excitation were studied and it was found that the Equivalent Non-Linear Differential Equation (ENL) method yields a better measure of the response of the non-linear system to white noise excitation than other approximate methods. Analytical expressions are derived for the mean-square response, probability density function and level crossing rates. With the modified ENL method (MENL) it is shown how one can extract the non-linear damping and excitation power spectral density. A good correlation is obtained between experimental and theoretical results.

Heat storage as a means to respond to the requirements for improved energy efficiency motivated this study. The objective was to evaluate the impact of thermal energy storage systems in dwellings under Mexican climatic conditions. In the first part of this work thermal behaviors of adobe traditional architecture is discussed; in the second part a latent heat storage system using phase change materials (PCMs) is proposed and assessed. The high thermal mass structural elements of adobe traditional architecture have been charactefted as heat wave modulators. Nevertheless, the moisture content in these structures also plays a significant role as a means for heat storage and potentially enhancing thermal lag. The objective of this part of the study was to assess the scope of existing coupled heat and mass transport models regarding water contained latent heat storage on porous structures. The significant contribution of latent heat storage recognized in adobe structures, led to the study of a solar-thermal storage system using (PCMs). The objective of this part of the study was twofold: 1) Enhance the existing computational models on the Stephan problem by considering the effect of regional variations (weather conditions imposed) on the boundary conditions. 2) Evaluate the impact of the solar-thermal system proposed when applied in dwellings in view of regional variations under Mexican weather conditions. Solar-thermal storage systems independent of the structure offer the possibility to be applied to existing buildings as well as new constructions. The proposal is a storage element that constitutes internal blinds in windows. The computational model of the Stephan problem was solved with the enthalpy method. Simulations were run under different sets of climatic conditions. For the first time the main factors for promoting system's optimisation, when gathered in a single comparison study, provided a more general insight on system's performance. Experimental work was also carried out regarding the charging of the heat storage unit by heat gains other than direct radiation, and the storage unit's performance as insulator. A large-scale solar simulator was constructed. Statistical analysis of experimental results showed interesting findings including: The important role that internal heat gains play on the charging of the latent heat storage unit proposed. A larger effect on the discharging ratio was found with lower air temperatures than with faster air flow rates. The faster discharging rate tests also released slightly more energy. PCM volume was found to be the most critical factor on system performance. The importance of providing the means to discharge the total quantity of heat stored was pointed out. For the cooling mode, elements to enhance discharging might be required. For system control, thermal insulation was found to be an effective measure when the discharging is required to occur over a longer period. The multiple PCM unit was found to be more efficient during the charging process (storing more energy) than units containing a single PCM. Nevertheless the single PCM unit performed better for cooling than the multiple PCM unit. The question was raised as to what extent PCM thermal conductivity actually influences system's performance. The thermal storage system proposed in this study reduced the heating system energy consumption requirements for an experimental room by 28.6%.