In this thesis, some nonlinear effects associated with the buckling behaviour of plated steel structures are examined using a modified finite strip method. To include the effects of plasticity over parts of the cross-section, a more general stress-strain relationship than previously included has been used. The method is also extended to account for the large deflection behaviour of perfect and imperfect plates in the elastic range. The only restriction on the method presented here is that the buckling mode varies sinusoidally in the .;, longitudinal direction, which implies either that the ends of the structure are simply supported or that the wavelength of the buckled mode is small in comparison with the overall length of the structure. The present study may be divided into three parts. In the first part the small deflection theory is used to determine the stiffness and stability matrices of ~ individual strip and these are assembled to form an overall stiffness matrix, representing a structure which may be under concentric load, eccentric load or pure bending. In some cases a structure with an overall initial imperfection is considered. The Wittrick-Williams Algorithm is used to obtain the smallest critical buckling load. The method is applicable to the analysis of various structures such as isolated plates, stiffened panels, rolled sections and stiffened box-girder bridges. To check the accuracy of the method a comparison with some published theoretical and experimental results is undertaken. Secondly, a parametric study for stiffened panels, columns, and beams is presented. For the stiffened panels, the effect of seven parameters (slenderness ratio, residual stress, dimensions and shape of the stiffener, mode of buckling, the longitudinal boundary conditions, and the yield stress) has been investigated. Approximate design curves for the optimum dimensions of panels stiffened by flat stiffeners are given. The capability of the method for the analysis of a stiffened box-girder in bending is also shown. The effect of seven parameters (dimensions and shape of the cross-section, the slenderness ratio, the material yield stress, the residual stress, the initial overall imperfection and the eccentricity of the applied load) on the inelastic buckling of columns and beams has been studied. All the results are given in nondimensional graphs or tables. Finally large deflection plate theory is applied to study the post-buckling behaviour of both perfect plates and those with initial imperfections. The work in this section is restricted to the elastic state. The longitudinal axial compression is assumed to act on the plate through two rigid bars at the ends, and various in-plane boundary conditions for the longitudinal unloaded edges have been considered. The Newton-Raphson method is used for the solution of the non-linear equations.

A number of reinforced concrete slabs have been exposed to blast and impact loading in order to access modes of slab behaviour under these extreme dynamic loadings. Two sizes of specimens were used; small scale slabs modelled the large slabs at 1: 2.5 scale. Impact loads were produced by a free falling hammer impacting coaxially onto a cylindrical bar of steel placed at rest in the centre of the slab. The steel bar was instrumented with electrical strain gauges which recorded the stress pulses produced by the impact. Blast loads were produced using explosive charges made of Plastic Explosive PE4. In most cases the charge used was hemispherical in shape and was placed centrally above the slab at close range standoffs, i.e. up to 10 times the radius of the charge. Additional blast tests were conducted in order to monitor the transient and spatial pressure distribution across the slab by using the pressure gauges placed in replica steel slab. Transient deflections of the slabs under both types of load were obtained using long stroke displacement transducers, whilst transient strains in the steel reinforcement of the slabs were obtained using electrical resistance strain gauges bonded to the steel bars at mid span point. A rotating prism high speed camera was used to film the damage on some of the small scale specimens at rates of up to 10,000 pictures per second. The Hopkinson pressure bar tests were used to obtain the dynamic characteristics of the concretes used at high rates of loading. Differeent concrete mixes were used for the 1:1 and 1:2.5 scale slabs. An analytical function of the spatial and transient blast pressure distribution based on the detonation pressure of PE4 was established. This is in close agreement to experimentally measured results. The nature of the local and overall failure are discussed, and the time sequence of the slab failure is established for the case of explosive loading. The crack pattern that occurs soon after the explosion in area of local failure has been established from the high speed films whilst the overall deflected shape was obtained from the displacement vs time records. After test scab sizes and slab perforations were used to establish a relation between the slab thickness, amount of explosive and the slab damage in respect to scabbing and perforation. The displacement records and the shape of after test damage provided the basis for comments on "gravity neglected - the ultimate strength" modelling law that was employed in this research.

The modelling of unbounded domains is an important consideration in many engineering problems, for example in fluid flow, electro-magnetics, acoustics and solid mechanics. This thesis focuses on the problem of modelling elastic solids to infinity, with the specific purpose of modelling dynamic soil-structure interaction (DSSI). However, the reader should be aware that the techniques presented may also be adapted to address those other physical phenomena. The need for techniques to model the soil domain to infinity and a qualitative introduction into the problems associated with dynamic soil-structure interaction are outlined in chapter 1. This is done to illustrate why such an abstract mathematical concept of modelling infinite domains has an important role to play within the design process of large, safety critical, civil engineering structures. A brief review of a number of alternative ways of addressing this problem is given in chapter 2. Their relative strengths and weaknesses along with the typical applicability of the techniques is discussed. A consequence of this review is the identification of a very promising rigorous approach [59] which is singled-out for further study. A detailed explanation of this (Consistent Infinitesimal Finite Element Cell Method, CIFECM) method is then given in chapter 3. Attention is restricted to the use of the technique for solving the 3-D vector wave equation in the time domain. The features of the non-linear dynamic finite element code, into which the CIFECM has been incorporated, is highlighted in chapter 4. The non-linear (microplane) material model for quasi-brittle materials is described along with the solution strategy employed. It should be mentioned that the soil is treated within this thesis as drained linear elastic medium. The method of coupling the CIFECM into the dynamic equation of force equilibrium for both directly applied and transmitted loading regimes is detailed. Application of the code follows in chapter 5; firstly by introducing the simplest test problem of one finite element coupled with one CIFECM element to model a surface foundation. Comparisons are made between the dynamic displacements resulting from the method and standard FE solutions obtained from the use of extended meshes and fixed boundary conditions, along with a study of the influence input variables. Following these examples a larger (more realistic) engineering problem is tacked involving the simulation of an aircraft impact on a reinforced concrete nuclear containment vessel. This represents the first use of the method in a 3-D nonlinear structural analysis problem. The results illustrate the practical implications of including DSSI in the analysis. III In chapter 6, a series of general observations on the method are made with an assessment of its value together with a discussion on its wider application to other engineering fields. Possible future developments to make the method more computationally efficient are finally suggested.

The thesis is concerned with investigating the role of mathematical programming in expressing the general theory of and facilitating effective computation for elasto-plastic skeletal structures subjected to deterministic sources of dynamic excitations, Static-kinematic duality, a common feature in the static analysis of structures, is extended to dynamic systems through the adoption of d'Alembert's principle. This allows the full use of graph theoretic methods for describing the fundamental structural relations in both mesh and nodal forms. For structures whose dynamic characteristics can be effectively described by a rigid-plastic constitutive law, mathematical programming formulations are presented. They are compared and contrasted with existing formulations, especially those associated with impact loading. Elasto-plastic structures are studied and their dynamic response is shown to be given by the solution of a differential linear complementarity problem. Four equivalent formulations are presented and are solved numerically through the use of direct integration methods. The effects of change of geometry may also be important in the dynamic analysis of structures. Firstly, for relatively small displacements, the method of fictitious forces is shown to lead to alternative mesh and nodal formulations. For large displacements, only the nodal method proves to be effective. An incremental differential linear complementarity problem is obtained and a suitable numerical solution procedure is proposed. Finally, a perturbation technique is established for solving the resulting differential equations and differential linear complementarity problems. It is proved that this technique is more general and flexible than the direct integration methods.

Concrete is still the most widely used construction material of modern times. In very recent years attempts have been made by using steel fibre reinforcement to improve the inherent weaknesses that concrete possesses such as its low tensile strength and the tendency to shrink on drying and to creep under stress. In this context, the use of steel fibre reinforcement together with high strength concrete corbel joints has been investigated. This study came after fibre reinforced concrete had received wide recognition for its crack and deformation control, ductility and energy absorption characteristics. In the present study, the fracture behaviour and deformation characteristics of plain conventionally reinforced concrete corbels with and without steel fibre reinforcement has been investigated. The different types of steel fibres used and other experimental materials are described in chapter 3, whereas chapter 2 gives a review of the old and current design approaches used for concrete corbel design. In chapter 4 the deformation, cracking and ultimate strength of plain high strength concrete corbels has been studied with different cube strength ranged between 25 to 90 N/mm². In chapter 5 a proposed theory to predict the ultimate strength of high and normal strength concrete corbels, conventionally reinforced, has been derived. The influence of steel fibre reinforcement on the performance of conventionally reinforced concrete corbels has been studied in chapter 6. Melt extract steel fibres were used in the majority of the corbels together with other types such as crimped, hooked and plastic fibres (polypropylene). In the same chapter 6, the theory has been extended to account for the strength gained by fibre addition. The effect of steel fibre reinforcement on the shear transfer strength has been studied in chapter 7. The theory proposed in chapter 5 has been further extended to predict the shear strength of 'push-off' type of specimens of plain and fibre reinforced concrete, with conventional steel reinforcement.

A literature survey on rock anchor design revealed that current rock anchor design methods are empirical and conservative in nature. The stability of a rock anchor depends on the assumed yield surface which has been found to be difficult to predict. A simple conical yield surface is currently adopted in practice. In this approach important rock parameters such as shear stress on the surface of the cone are usually ignored. Although both theoretical and experimental evidence are available to indicate that bond distribution along the fixed anchor length is highly non-linear at the tendon/grout/rock interfaces, current design still assumed the bond to be uniformly distributed along the whole fixed anchor length. Anchor interactions group effects, debonding at the proximal end of the anchor, the effect of tendon spacing and spacers, the effect of lateral pressure on the fixed anchor are not considered in current rock anchor design. To provide a more fundamental understanding of rock anchor behaviour a simple isoparametric finite element program has been written and thoroughly tested. The initial stress method with associated flow rules was used to simulate rock anchor behaviour. The plastic potentials used for simulating the tendon and, the grout and the rock, were respectively the Von-Mises and the octahedral shear stress yield criteria. Double nodes at interfaces provided a method of simulating a perfectly smooth interface without having to resort to special interface elements. The stress strain distribution pattern in the fixed anchor zone has been obtained for a modular ratio of 2.1, The results produced have indicated, that, in addition to physical material parameters, anchor behaviour is also dependent on the applied load, the slenderness ratio and the fixed anchor diameter. The most severe position of shearing has been found to be at the grout/rock interface. Analyses show that partial debonding is not a serious problem. Surcharge tends to reduce the shear stress at the grout/rock interface however the effect is negligible. A design curve is proposed for consideration.

Reinforced concrete deep beams have useful applications in construction. However, their design is not yet covered by the British Standard BS 8110: 1985 which explicitly states that "for the design of deep beams, reference should be made to specialist literature". A selection of literature on deep beams is considered. First, the major works that have led to design recommendations are reviewed. Then, the current major codes and manuals covering deep beams, namely the CIRIA Guide, the European CEB-FIP model code, the American ACI(318-83) (revised 1986) code and the Canadian CAN3-A22.3-MB4 code are outlined; worked examples are given in order to illustrate their practical applications and compare their different approaches to deep beam design. The purpose of this literature review was to define the deep beam problem and identify the major questions still remaining unanswered together with the limitations of the present design documents on the subject. The nature of diagonal cracking in slender deep beams has recently raised a question as to the application of the shear-strength equation in cl.3.4.2 of the CIRIA Deep Beam Guide. The effectiveness of web reinforcement on serviceability and strength of deep beams in general is also an area where strong disagreement exists. A testing programme, consisting of 15 beams of height/thickness ratios ranging from 20 to 50 and grouped in 3 different series, was performed to provide information on these two areas. The main variables were the height/thickness ratio and the quantity and arrangement of web steel. The beams were tested under concentrically applied two point-loads. Based on the test results and observations, modifications are given for the CIRIA equation and other formulae derived from stocky deep beam tests to be used in slender ones for analysis and design purposes. A new formula is also proposed for the prediction of the ultimate shear capacity. The stability of deep beams is another area which has received less attention in the past by researchers and designers who often avoided the problem by opting for stocky sections. To quote from the CIRIA Guide "as a possible criterion of failure, buckling can not be disregarded". However, information on such topic is very scarce in the literature. Currently, the only documents that provide design guidelines for buckling are the CIRIA Guide and the Portland Cement Association Design Aid, both of which are based on theoretical studies and engineering judgement. An experimental testing programme, consisting of 7 large scale beam-panels with height/thickness ratios in the range of 20 to 70 and a constant span/depth ratio of 1.0, provided buckling data against which the reliability of the two design documents was assessed. These tests confirmed that both documents offer a safe buckling design with the CIRIA Guide being too conservative. Although deep beams are frequently continuous over several spans, very little published data exist for such beams. For this purpose, 12 two-span continuous concrete deep beams with span/depth ratios less than 1.0 and having different quantities and arrangements of web reinforcement were tested under two point-loads. The specimens were heavily instrumented to obtain as much information as possible about the behaviour of the beams at each stage of loading. Applied loads and reactions were among the measurements made and enabled the actual bending moment distribution to be determined and compared to that of corresponding continuous shallow beams. Based on the test results and observations and in the light of other published work, recommendations are given for the bearing, shear and flexural design of continuous deep beams.

In recent years the use of masonry as a structural material has increased in advance of the necessary theoretical and corroborative experimental investigations. One aspect of structural masonry where particular problems have been encountered is the design of masonry panels subjected to lateral loadings. Research undertaken, principally in the United Kingdom and Australia, has led to the development of empirical methods of analysis applicable to solid rectangular panels. However, the effects of the presence of openings on the behaviour of a masonry panel has received scant attention. The aim of the research is to rectify this situation. The principal objective of the research is to put the design of this form of panel subjected to lateral load, on a more rational footing. To do this it has been necessary to investigate the behaviour of masonry panels with openings. The research can be divided in four stages. Firstly, an extensive literature survey has raised questions concerning the suitability of the current British Standard Code of Practice ,BS5628, and other design methods such as elastic plate theory, and empirical strip method, for the design of laterally load masonry panels. Secondly, a non-linear finite element analysis has been developed. The analysis is capable of analysing panels under lateral loading up to and beyond the peak load. The results obtained using the computer program were initially validated with the existing results from two previous laboratory investigations [1,2]. Initial analysis of the results from the experimental and theoretical studies highlighted areas where further investigation was required. In conjunction with the development of the computer program, the investigation involved the laboratory testing of 18 full scale panels. One of the major problems encountered was the determination of material parameters. In this work wallettes have been used to obtain flexural strength values, however the strength of the specimen is influenced by the size of specimens and the number of bed and perpend joints [3,4]. In order to clarify the position, a computer based statistics analysis similar to that reported by Lawrence [4], was employed to investigate the format of the specimens. Estimations of the single joint strengths from the wallette results were obtained from the analysis. Single joint strengths obtained from the statistics analysis were then used in the finite element analysis and comparisons with the experimental load-displacement relationships and the failure patterns made. A Monte-Carlo simulation of the finite element analysis was also carried out to investigate the effect of material variability on the failure strength of masonry panels. Good correlation has been obtained. Lastly, parameter studies using the finite element analysis and the experimental results have indicated that yield line method consistently over estimates the failure strength of masonry panels. However, the reduction of strength due to the inclusion of openings predicted by yield line is in a reasonable good agreement with the experimental results obtained. A simple formula for the design of laterally load