This research work investigates the impact behaviour of prestressed concrete beams. A total number of forty 1000 mm long model beams with a rectangular section of 44 x 65 mm were cast. The beams were divided into four with ten beams in each series. Each beam was prestressed by four 1.6 mm diameter piano vire3 and the shear reinforcement va3 varied from series to series. The test rig available was modified so that the beam could have pin-end supports with a span of 600 mm and a static or impact load could be applied at the midspan. A total number of 40 static tests (8 static and 32 post-impact-static) and 32 impact tests were performed. The static load was applied by a screw jack via a one meter long steel pressure bar. The impact load was produced by the impact of a 350 mm steel cylinder projected at velocities of 4 to 17 m/s by compressed air onto the same pressure bar. In each impact test, the impact force-time history was recorded by the electrical resistance foil strain gauges attached on the pressure bar. The transient deflections at various positions along the span were measured by linear variable differential transducers and the reaction was measured by aluminium load cells on which electrical resistance strain gauges were fixed. A dynamic plastic model proposed by Ezra(90) was developed and applied in conjunction 'with the one-degree of freedom system to evaluate the maximum dynamic midspan deflection, reactions, energy absorption capacity and the initial impact beam velocity. A comparison was made between the predicted and the experimental results.

The three years' work undertaken in this project is a purely numerical analysis of the inelastic behaviour of steel columns in fire. This is made up of three main parts, each devoted to the development and use of a numerical technique to study the behaviour of steel columns in fire. The first two chapters report on the state of the art on plate analysis, plasticity theories, column behaviour at room temperature, finite strip method and the behaviour of columns at elevated temperature. Part 1, consisting of Chapters 3 to 5, reports on the development of the small deflection finite strip method which includes the effect of plastification of component plates using deformation theory of plasticity. The validity of the method is tested by comparing with published test data on steel columns at ambient and elevated temperature. The comparisons show that the method gives good correlation with test data. Parametric studies have been carried out to assess the effects of slenderness ratios, different stress-strain-temperature representations, residual stresses, eccentricity of loading and local budding of columns. In addition the inelastic behaviour of an H-section under uniform end couples is studied. Part 2, consisting of Chapters 6 and 7, reports on the development of a finite element method which includes the effect of thermal gradients over the member cross-section. The method is compared with test data on both uniformly and non-uniformly heated columns. This shows a good correlation between the method and experiment. Parametric studies have been carried out to assess the effects of initial out-of-straightness, different end conditions, thermal gradients and interaction of eccentricity of loading with thermal gradients on columns. In addition a simple Shanley's column theory is utilised to demonstrate the interaction effect of eccentricity of loading with thermal gradients on columns. Part 3, consisting of Chapter 8, reports on the development of a large deflection finite strip method which includes flow theory of plasticity. The method has not been used for any parametric study. Finally, general conclusions and recommendations for future works are presented in Chapter 9. It is hoped that the valuable information provided in this thesis will be useful in providing a better understanding on the real behaviour of steel columns in fire.

The fabrication and placement of conventional shear rein- forcement are time consuming and costly and its use in thin structural concrete members is often impractical. Fibre reinforcement is known to control flexural and shear cracking and can therefore be used to replace conventional shear reinforcement. This investigation consists of experimental and theoretical studies into the use of crimped steel fibres as shear reinforcement in reinforced concrete beams. Eighteen reinforced lightweight concrete beams with thin web were fabricated and tested under four point loading. The para- meters studied were the fibre content, the shear span/effective depth ratio and the amount of main steel. Subsidiary tests on concentric pull-out specimens and shear transfer specimens were carried out to study- the influence of steel fibres on the bond stress slip characteristics of a deformed bar (Tor Bar) and the stiffness and ultimate strength of the shear-transfer mechanism across a definite plane respectively. The inclusion of fibres increased the ultimate strength of the beams by 63 to 211.5%. Fibre concrete beams had more flexural and shear cracks and showed substantially greater ductility at failure than their plain concrete counterparts. The fibres in the pull-out specimens were effective in controlling the splitting cracks and transforming a sudden bond failure into a gradual one. The fibres increased the ultimate shear strength of the shear transfer specimens by 9.9 to 101.8%. The stiffness of the shear transfer mechanism was not, however, significantly affected. A simple approach based on the Standard Method of the CEB-FIP Model Code is proposed to determine the ultimate shear resistance of fibre reinforced concrete beams. It predicts adequately the ultimate shear strength of steel fibre reinforced concrete beams. A nonlinear 3-dimensional finite element model was developed to predict the entire structural response up to failure of both plain and fibre reinforced concrete beams subjected to short_. term monotonically increasing loading. The concrete is represented by 8-nodeisoparametric hexahedra and the tension steel by bar elements. The finite element model predicts satisfactorily the structural behaviour of both plain and fibre reinforced concrete beams.

A three-dimensional finite element computer program has been developed which can predict the behaviour of steel-framed buildings, including the supported floor system, in any specified fire scenario. The developed software provides a more realistic prediction of structural behaviour at elevated temperatures, than is possible with models which are limited to frame analysis, since the building structure is considered as a more complete entity. Confidence in the software is strengthened by comparison with test results to the extent that different structural and fire scenarios may in future be investigated very cheaply. This could lead to a better understanding of the behaviour of steel, framed structures during fires and to more rational approaches to specification of fire protection requirements, which are currently rather expensive in terms of material and fixing costs. The steel beam-column members are represented by one-dimensional two-noded elements which incorporate both material and geometrical non-linearities. These can model three-dimensional steel member behaviour including lateral-torsional buckling. Temperature gradients can be specified through the steel cross-section and also along its length. Spring elements, of zero length, have been introduced to represent semi-rigid joints. These degrade in stiffness and strength with rise in temperature and are represented by any specified moment-rotation-temperature relationship. Unloading from an inelastic state has been modelled for both the steel members and connections, allowing the behaviour of the frame during the cooling phase of a fire to be investigated. This will enable the repairability of the frame to be assessed after a fire has occurred. The flooring system is represented by shell finite elements, which are linear elastic and include thermal strains, although the temperature distribution through the slab's thickness must be assumed uniform. A simplified method of representing cracking in the concrete has been introduced by placing a limit on its maximum bending stress. The node position of the steel one-dimensional finite elements can be displaced to allow connection to the two-dimensional shell elements at a common point. This allows composite action between the beam and supported slab to be modelled. Comparison has been made between computer simulations and fire tests on the full-scale test frame at Cardington. It has been shown that modelling isolated members is highly unrealistic. However models which incorporate a significant amount of the structure surrounding the heated zone, including the membrane action of the flooring system, perform far better when compared to actual tests. These comparisons indicate that the future development of design methods for fire safety of structures needs to be steered away from its traditional emphasis on isolated member behaviour, and towards considering the interaction of the whole building structure with the aim of avoiding disproportionate collapse.

The aim of the present work is to develop a sophisticated analytical model for columns within three-dimensional assemblies in fire conditions. A preliminary investigation into this problem resulted in the development of a simplified approach for the analysis of isolated columns in fire. This model is based on the Perry-Robertson approach to defining critical loads of imperfect columns at ambient temperature. It takes into account uniform and gradient temperature distributions across the section of an isolated pin-ended column. It also accounts for initial out-of-straightness, load eccentricity and equal end-moments. A three-dimensional finite element model has subsequently been developed for the analysis of frames in fire conditions. This model is based on a beam finite element with a single node at each end of the element. At each node eight degrees of freedom are introduced. The finite element solution of the problem is obtained using an incremental iterative procedure based on the Newton-Raphson method, adapted to account for elevated temperature effects. The developed procedure offers a unique treatment of the thermal effects which allows solutions to be arrived at regardless of the problem's boundary conditions. The finite element formulation takes into consideration geometrical and material nonlinearities, initial out-of-straightness and residual stresses. It allows for virtually any temperature distribution across and along the structural members, and the analysis can handle any three-dimensional skeletal steel structure. The developed model allows the material mechanical properties to be expressed either as trilinear or continuous functions which vary with temperature. A computer program, 3DFIRE, has been developed based on the above-mentioned formulation and validated extensively against a wide range of previous analytical and experimental work. This program has then been used to perform parametric studies to establish the most prominent features of column behaviour in fire whether as isolated members or as part of structural assemblies. These studies have yielded a large amount of data from which generalised conclusions have been made. The analysis has been extended recently to include composite beams within the structural assembly. This development was undertaken to enable analytical studies on the test building at Cardington, in which fire tests are planned to take place in the near future.

The present work is concerned with the development of a finite element approach and its subsequent use for behavioural studies on steel frames in fire conditions. The nonlinear structural analysis is based on a tangent stiffness formulation using large deformation theory. Deterioration in material strength and stiffness at increasing temperature is represented by a set of nonlinear stress-straintemperature relationships using a Ramberg-Osgood equation in which creep effects are implicitly included. The clearly nonlinear form of steel material properties at elevated temperatures is better represented as a set of continuous stressstrain relationship than in a bilinear form although provision is made for any form of relationship to be included. Structures subject to increasing loads or temperatures are analysed using an incremental Newton-Raphson iterative procedure. The analysis permits collapse load or critical temperature to be calculated at a specified temperature or load level respectively, and provides a complete load-deformation and temperature-deformation history for two-dimensional multistorey steel frames. A nonlinear method of frame analysis, based on largedeformation theory, has been used which includes the effect of geometric nonlinearity, temperature-dependent nonlinear material behaviour and variation in temperature distribution both along and across the section. The effects of thermal strains, residual stresses and thermal bowing are also included and different values of the elastic stiffnesses of the support conditions can be considered. A beam element with two nodes and three degrees of freedom at each node is used in the analysis. Gradual penetration of yielding through the cross-section is accounted for using the transformed area approach. The validity of this method is tested by comparing with experimental and analytical data covering as wide a range of problem parameters as possible. The comparisons show good agreement with this data. The method has been used to study a number of aspects of frame behaviour in fire. The influence of slenderness ratio, stress-strain representation and material models, various forms of protection, magnitude of residual stress and thermal gradient along and across the section of a frame are investigated. An approximate curve based on statistical analysis of the derived results is suggested as a simple means of predicting the critical temperature or collapse load of a uniformly heated steel frame. Further examples are presented which illustrate the special form of moment redistribution that occurs at elevated temperatures for frames that contain partially heated elements. Finally, general conclusions and recommendations for future work are presented.

The main aim of the present research is to develop a method of analysis for structural frames exposed to fire including the effects of material and geometric non-linearities. A matrix stiffness method based on a secant stiffness approach is used providing a full temperature deformation history. The approach has previously been used for the analysis of continuous beams and is extended in the present work to include axial forces. These not only affect the longitudinal displacement, but also reduce the member stiffness and create secondary moments due to the p-delta effect. The influence of material unloading on the moment-axial force-curvature relationship is studied by examining a cross-section subjected to different combinations of bending moment and axial force at both ambient temperature and in fire. A computer program, based on the method is used to conduct a limited parametric study. This includes the influence of slenderness ratio, the magnitude of axial load and moment, the size of cross-section and grade of steel. Both uniform and non-uniform temperature profiles are considered for isolated beams, columns and simple portal frame. The importance of the p-delta effect is also investigated.

A review of the research carried out on the subject of castellated beams revealed that one subject had remained largely untouched — lateral stability. This was despite the fact that the fabrication process had increased their strength and rigidity about the , plane of loading at the expense of lateral stiffness. This emphasis on in—plane behaviour stemmed from the need to catalogue the failure modes particular to castellated beams. However because of the high number of parameters necessary to describe a castellated beam and their high degree of internal redundancy, little that can be regarded as firm design recommendations and no provisions against lateral buckling have been included in national codes of practice, particularly in the present British codes. This is why the draft of the new British code for structural steelwork 8/20 to be published as BS 5950 suggests the use of the simple Vierendeel analogy for in—plane behaviour and has adopted the conservative approach of 0..11.3.2 to the prevention of lateral buckling in which the contribution of the web and tension flange are ignored. The work undertaken herein had the aim of mainly providing the missing quantitative data on the lateral —torsional buckling strength of castellated sections currently available in the U.K. Eight full size castellated beams were tested. The results of these plus the few cases reported in the literature were used as a basis for a critical evaluation of several design approaches. Comparisons between the test results and the strength predicted by B/20 were found to be generally acceptable provided cross— sectional properties at a castellation were used in the calculations. Similar results were obtained for the two — stage procedure of BS 449 and BS 153 whereas the use of Table 3 in the former was shown to lead to rather low load factors. A preliminary test programme on small scale beams showed the negligible effect that the holes had on lateral buckling behaviour. Finally a computer program which was used to calculate a value of elastic critical load confirmed that the web post did not distort when the beams failed.

An important problem encountered by foundation engineers involves partially saturated soils which possess considerable in-situ dry strength that is largely lost when the soils become wetted. Foundation design in such soils is difficult at best. In many cases, deep foundations may be required to transmit foundation loads to suitable bearing strata below the 'collapsible' soil deposit. This research has studied the behaviour and performance of stone columns confined and not confined by geofabrics and rigid piles, as deep foundations, in collapsible soil subjected to inundation. Laboratory tests were carried out, under controlled conditions of sand density and surcharge pressure, using six different types of foundation supports (a sand column, sand columns confined by T700, T1000, T1500 or T2000 geofabrics and a rigid pile). Each type of foundation was considered in three different lengths 250 mm, 300 mm and 410 mm. This work consisted of installing and loading 'model' foundations into a stress controlled pot containing a collapsible soil and allowing a slow rise of the water level inside it. The tests were designed to investigate the efficiency of these types of foundation supports on the improvement of the carrying capacity and on the reduction of settlement of the ground. The reduction in vertical compression of the 'piles' was also studied analytically using an analytical approach adopted and developed from models applied to soft soils. The experimental results are compared with analytical predictions. The comparisons show that the reduction in vertical compression of the 'pile' is governed by its stiffness and its length. These variables are of prime importance in the general performance of the 'pile'.

The objectives of the research were threefold. Firstly, to improve .the numerical modelling capability for reinforced embankments constructed over soft compressible soils containing vertical drains. Secondly, to demonstrate the ability to model accurately such embankments. Finally, to develop simplified procedures to be used in the design of embankments over soft soils. The modifications to the finite element program, CRISP, included the incorporation of three additional elements: modelling the reinforcement, the soil/reinforcement interface and the vertical drains. The facility to vary permeability with stress level was also implemented. A technique for modelling the consolidation of soil containing vertical drains in plane strain finite element analyses was developed and validated. The modified program was validated in three ways. Firstly, each element was used to analyse simple problems so that the correct formulation was ensured. Secondly, a series of analyses was carried out of problems for which analytical solutions were available; these problems involved collapse of undrained sub soils and consolidation around a single vertical drain. Thirdly, an analysis of a case history of an embankment constructed over a normally consolidated clay, improved with vertical drains, was performed. Based on the results of the previous finite element analyses, and an additional analysis of an idealized two-stage constructed embankment, simple design procedures have been proposed. Firstly, a method for the design of single stage embankments and, secondly, a method for the calculation of subsoil strength increases in multi-stage construction, which can be used in conjucntion with limit equilibrium analyses. It is concluded that the finite element method is a useful technique for the analysis of reinforced embankments over soft soils containing vertical drains.