Static and free vibration analysis of variable-depth bridges of arbitrary alignments using the isoparametric spline finite strip method

The isoparametric spline finite strips for shells are employed to solve static and free vibration problems of variable-depth bridges of arbitrary alignments. Using this approach, a continuous bridge is first split up into substructures. Each substructure is modelled as an assemblage of isoparametric spline finite strips. Compatibility between substructures is ensured by suitable transformation at the interface. The presence of support diaphragms and bearings can also be accounted for. This method retains the computational efficiency of the spline finite strip method while it is much more flexible in geometric modelling. Solutions of this method are compared with other available solutions, and good agreement is observed.     

A combined finite strip/finite element method for analysing thin-walled structures

A combined finite strip/finite element method is presented for the linear analysis of thin-walled prismatic structures containing transverse diaphragms and intermediate supports. The application of the method to three representative examples is discussed.     

Static analysis of thin-walled structures using polynomial and exact solutions. Application to thin-walled pipes

A new finite element procedure for the static analysis of beam thin-walled structures of open or closed cross-section is presented. The method is a combined or mixed one, based on the superposition of beam and shell strains and displacements. An essential part of this work is the development of new shape functions (which are either ‘exact’, or polynomial) for the interpolation of the shell displacements.The above method is applied to the thin-walled curved pipe problem and compared to the von Karman approach. Excellent results are obtained, as well as a drastic reduction of the total number of nodal variables.     

The compressive post-local bucking behaviour of thin plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-local-buckling analysis of geometrically perfect thin-walled prismatic structures under uniform end shortening is developed in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the principle of minimum potential energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyse the post-local-buckling behaviour of thin flat plates. The results are discussed in detail and compared with those available from published works, wherever possible. This has provided confidence in the validity and capability of the developed finite strip in handling the post-local-buckling problem of plate structures.     

Determination of effective breadth and effective width of stiffened plates by finite strip analyses

A finite strip (FS) method is presented for the numerical investigation of two design parameters — effective breadth and effective width — of stiffened plates. For the effective breadth, stiffened plates under bending are studied. Due to the transverse bending loads there is shear transmission through the plate from the stiffener which leads to a non-uniform longitudinal stress distribution across the plate width. This phenomenon, termed as shear lag, can be represented by the ‘effective breadth concept’, and has been extensively studied by analytical methods. A linear FS method is presented which utilizes the advantages of decoupling of Fourier terms on the one hand and, on the other hand, allows the treatment of both webs and flanges using a plate model. A definitely different situation exists for estimating the effectiveness of the plate breadth (or width) of plates in the postbuckling range. The ‘concept of effect width’ is based on the fact that plates with supported longitudinal edges and/or stiffeners can accept additional load after buckling under longitudinal compression, and enables the designer to evaluate the postbuckling strength of plate structures simply by using the design parameter ‘effective width’. Several formulae (most of them empirically derived) exist for an approximative calculation of the load dependent value of the effective width. A nonlinear FS method is developed and applied to the investigation of the postcritical strength of locally buckled structures. An incremental successive iterative procedure is introduced for an effective numerical analysis.     

Ultimate strength of girders with trapezoidally corrugated webs under patch loading

Ultimate strength of steel plate girders with trapezoidally corrugated webs under patch loading is studied using a non-linear finite element method. Effect of large deflection is taken into account and a von Mises material either without strain hardening (elastic-perfectly plastic), or with strainhardening obeying Ramberg-Osgood's equation, is assumed. The following factors that influence the ultimate strength are investigate (1) strainhardening models; (2) initial imperfections (local and global); (3) variation of yield stress and strain-hardening degree at the corrugation corners due to cold forming, ‘corner-effects’; (4) loading position; (S) load distribution length, and (6) variation of geometric parameters. Based upon the numerical results obtained, an empirical formula for the prediction of the ultimate strength is suggested.     

Ultimate strength of submarine pressure hulls with failure governed by inelastic buckling

The analysis of submarine pressure hull assumes great importance among structural engineers due to the complexity involved in the collapse mechanism of stiffened shell structures. In most of the cases, the failure of stiffened shell structures occurs due to elastic buckling. But for some combinations of shell-stiffener geometry and material characteristics, the structure can fail by inelastic buckling, for which the methods of analysis are meagre. In this paper, the analysis of submarine pressure hull structure in which the failure gets governed by inelastic buckling is demonstrated. Three different approaches have been employed to investigate the ultimate strength of the ring stiffened submarine pressure hull structure with inelastic buckling modes of failure. The methods used are ‘Johnson–Ostenfeld inelastic correction’, ‘imperfection method’ and ‘finite element approach’. A typical submarine shell structure has been analysed for the inelastic buckling failure using these three approaches and the results are discussed.     

A study on the structural analysis for structural synthesis of substructures

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed–free and free–free end elements. The flexibility and stiffness matrices of the free–free end elements are the Moore–Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of a complete structure composed of two mixed types of substructures. This study provides a general form to express equilibrium equations of the entire structure by combining the equilibrium equation of each substructure and compatibility conditions. Applications demonstrate that the proposed method is effective and simple. Copyright © 2005 John Wiley & Sons, Ltd.     

Flexibility of mechanical fastenings of very thin-walled steel structures

Normal calculations of flexibility as a deformation characteristic of fastenings disregard the plastic response of screwed fastenings of very thin-walled steel structures. Preliminary tests have, however, shown that, unlike bolted fastenings in thick-walled steel structures, in screwed fastenings of very thin-walled steel structures the occurence of considerable plastic deformations can be observed from the beginning of loading. These should not be generally neglected in establishing the design characteristics of fastenings, i.e. design strength and design flexibility. This paper deals with cases in which an approximate value of ‘elastic flexibility’ can be used with sufficient accuracy, and how the analysis may be made more accurate by taking into account ‘elasto-plastic flexibility’.Extensive experimental research into the behaviour of screwed fastenings of very thin-walled steel structures subjected to non-repeated loading, repeated fluctuating and reversed loading, and multi-level loading simulating wind loading has been carried out, and ‘elastic flexibilities’ of selected fastenings have been established. At the same time, conditions for their application taking into account the elasto-plastic behaviour of fastenings subjected to repeated loading have been determined.     

An engineering approach to crashworthiness of thin-walled beams and joints in vehicle structures

The paper summarises the main points of the long-term engineering experience at Cranfield Impact Centre Ltd in the field of crashworthiness of thin-walled beams and joints in vehicle structures. Subjects covered are: the ‘hybrid’ approach to crashworthiness design/analysis (where beams and joints are treated separately from complete structures), the deep bending collapse of beams and joints from the points of view of static and dynamic testing and analytical prediction (models of hinge mechanisms, regression analysis, finite element analysis and from experimental databases). Use of the component properties in the simplified finite element analysis of complete structures is also presented. Illustrations are shown during the oral presentation.     

GBT formulation to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections

This paper presents the derivation, validates and illustrates the application of a Generalised Beam Theory (GBT) formulation developed to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections. Following a brief overview of the conventional GBT, one addresses in great detail the modifications that must be incorporated into its cross-section analysis procedure, in order to be able to handle the ‘branching’ points — they concern mostly issues related to (i) the choice of the appropriate ‘elementary warping functions’ and (ii) the determination of the ‘initial flexural shape functions’. The derived formulation is then employed to investigate the local-plate, distortional and global buckling behaviour of (i) simply supported and fixed asymmetric E-section columns and (ii) simply supported I-section beams with unequal stiffened flanges. For validation purposes, several GBT-based results are compared with ‘exact’ values, obtained by means of finite strip or shell finite element analyses.     

Project conceptualization using pragmatic methods

An important and difficult part of project management is the conceptualization stage – particularly when dealing with multiple powerful stakeholders and ‘messy’ situations. Pragmatism provides a way forward that makes central the ‘concepts’ being used to conceptualize the project (e.g. ‘timeliness’ or ‘sustainability’). This paper argues for a sequence of two approaches suggested in the literature that combine this pragmatism and soft systems thinking to conceptualize projects. These are Alexander’s ‘Synthesis’ [1] and Checkland’s ‘CATWOE’ [2]. The first identifies concepts or worldviews, the second uses these to draft a series of ‘what needs to be done’ statements. In the way of Pragmatic Systems Inquiry, these approaches suggested from the literature are then compared to a real case study: the LC-25 project.     

Continuous accountability for acceptable building performance

Complexities in building technology when not fully understood, have resulted in a less than favorable aggregate impact on the building's environment. A surprisingly high portion of U.S. non-industrial buildings do not provide satisfactory task environments. Developments in computer technology have infused new thought processes in the way we plan, design, build and operate our buildings. This paper proposes a social and technical use of Knowledge-based-systems (KBS) for continuous accountability to assure healthy buildings. Diagnostics, as an emerging discipline in building design and operation, is also discussed. A proposed framework for such accountability and the resulting ‘chain of custody’, that draws on the medical paradigm and associated diagnostic procedures is presented. It is suggested that KBS also be used for the development and interpretation of criteria for evaluating building performance from initial conception through design, construction and operation. Thus, KBS is expected to aid in the analysis of ‘virtual’ and ‘actual’ buildings that may be ‘sick’ or ‘healthy’. It is proposed that for a building to provide satisfactory performance over its life-time, the ‘life-cycle’ concept must be modified in terms of the roles, responsibilities, and configuration of the building team, and in terms of its costing procedures.     

The geometric non-linear analysis of thin-walled structures by finite strips

The geometric non-linear analysis of prismatic thin-walled structures is presented. The theory is based on the moderately large displacement assumption, giving non-linear strain-displacement relations, but linear curvature-displacement relations. The corresponding non-linear equilibrium equations are produced by the principle of stationary potential energy using the finite strip discretisation. The equilibrium equations are solved using incremental and incremental-iterative numerical methods. Thus for the simple case of the square plate in edge compression, the self-correcting incremental method gives satisfactory results. For more complex examples of loading and structural type, a variable load incremental-iterative method is adopted. It is shown that the finite strip method used in conjunction with this method can be applied in particular to problems containing load maxima.     

An assessment of the sensitivity of lattice towers to fatigue induced by wind gusts

The dynamic properties of lattice towers are closely constrained by practical economic design. It is thus possible to generalize the prediction of dynamic response, using the stochastic wind gust model, with details as outlined in the seminar ‘Wind engineering in the eighties’ (CIRIA, London, 1980). An approximation to the combined effect of resonant and non-resonant components of the response is presented, as a factor to be applied to the effective stress range based on the dynamic response alone, computed at a single ‘reference wind speed’.

Results are presented for a range of practical structures, which indicate that good detailing can generally ensure that fatigue damage caused by wind gusts does not seriously limit design. The sensitivity of the normalized results to changes of location and of tower function and geometry is shown to be relatively small.     

Laboratory testing of pipe splitting operations

Pipeline replacement ‘on line’ has been practised for many years using pipe bursting technologies, which typically involve multiple fracture and outward displacement of fragments of the existing pipeline using either pneumatic or hydraulic means. One of the most important considerations for the design of a pipe bursting operation is the pattern of ground displacement caused, and consequently the possible damage to existing adjacent services and structures. Due to the requirement for overburst, the magnitude of the typical outward pattern of displacements caused by pipe bursting following construction is much smaller than the temporary displacements that occur while the process is being carried out. The ground movements during construction will often, therefore, provide the worst case for design. However, this pattern of behaviour is complicated by the possibility of residual ground settlements if the works are carried out in loose granular soils or in soft cohesive deposits in which positive pore water pressures are generated. The pattern and magnitude of displacements have been shown by the first two authors to be dependent on several parameters following a comprehensive programme of laboratory modelling and field trials. Parallel work by Advantica Technologies Limited (formerly research, technology and engineering arms of British Gas) has resulted in the publication of tables and charts detailing ‘safe working distances’ for pipe bursting in relation to cast iron gas mains. Prediction of the ground displacements is clearly vital for the safe operation of these replacement techniques. Pipe splitting is a more recently developed technique that has been proposed for ‘on line’ replacement of ductile iron and steel pipes. This technique has advantages associated with the continuous and pseudo-static, rather than discontinuous and generally dynamic, form of expansion employed. Prior to its adoption in routine industrial practice, however, it is important that differences in the patterns of displacement to those of pipe bursting are known. To this end, Advantica Technologies Limited is currently sponsoring a programme of full-scale laboratory model testing of pipe splitting operations at the University of Birmingham. This paper describes the testing equipment used to determine the effects on the surrounding ground of the pipe splitting operation, details the programme of tests and reports the results of tests conducted in both clays and sands. From the results it was observed that the McElroy Manufacturing Inc. ‘Bullet’ pipe splitting device produced a clean split in the ductile iron pipe whereas the U-Mole Ltd. ‘Clampburster’ produced a much more fragmented host pipe. It has also been found that the orientation of the blade of the pipe splitting device has a considerable impact on the resulting ground displacements. The ‘Bullet’ device allows the orientation of the blade to remain fixed during the operation, whereas the ‘Clampburster’ device currently allows rotation of the blade during the operation. The maximum displacements resulting from both splitting devices are very similar.     

A mixed-mode method for analysing partially prismatic curved thin-walled structures

A recently proposed combined finite strip/finite element analysis of partially prismatic structures is investigated in its application to horizontally curved bridge decks. Static and dynamic behaviour is considered and the method is illustrated with examples ranging from slabs with intermediate cross-beams to a three-span trapezoidal box.     

Some comments on the numerical analysis of plates and thin-walled structures

The paper briefly reviews the theoretical analysis of plates structures that might exhibit multiple ‘loading paths’ and highlights the need for engineers using non-linear numerical modelling to be aware of the multi-mode phenomenon and to ensure that the modelling is set up in such a manner that the various ‘loading paths’ and possible changes of path would be incorporated in the modelling response. The paper presents a simple example of numerical analysis of thin-plate buckling that involves ‘coupled buckling modes’ and provides comments on suitable methods for defining in a simple and straightforward way the numerical modelling that could ensure that results from computer analysis describe the physically correct relationship between applied loadings and deformations of thin-walled structural components.     

Digital landscape modeling and visualization: a research agenda

Digital landscape models, whether made for purposes of ‘visual inference’, or for simulating and understanding behavior or other invisible aspects of the landscape, require abstractions and simplifications. Yet for many visual purposes, ‘realistic’ depictions are desirable. The conflicts between these two demands are substantial for landscape modelers. For the basic landscape elements — terrain, vegetation, and water — some standard techniques for convincing static visual representation have been developed, but many complicating questions and obstacles remain. In addition, landscapes are essentially dynamic, and digital techniques for representation of these dynamics are still in their infancy. Surveying these techniques, complications, and possibilities leads to some generalized comments about the promises and problems of landscape modeling, and to a handful of proposed research topics to help pursue the landscape modeling agenda.