In engineering mechanisms, solid bodies frequently come to a contact with a variety of geometric and kinematic situations. There has been a trend to express the interaction of the contacted bodies in the form of equivalent interface forces. The interface force represents the level of load transferred from one body to another. In a static or quasi-static contact problem, the interface forces could be sensibly evaluated by integrating the normal and the shear stresses over the common interfaces. In a dynamic contact, the interface stresses and subsequently the interface forces happen to be more complicated. They are, furthermore, affected by other parameters such as inertia forces, stress waves propagation, the material strain rate dependency and damping. This paper reports interface forces recorded in a series of experimental impact tests on axially pre-compressed steel tubes along with those from the numerical simulations of the tests. To monitor the so called impact loads, two small steel rings as load cells have been built in the striker. Based on the experimental and numerical results, the concept of equivalent interface forces in the impacted tubes has been verified. It has been highlighted that the interface forces (or the impact loads) may vary on the striker or the specimen themselves, depending on the measuring locations. Effects of axial compressions on the interface forces picked up by the striker load cells, impact loads imparted to the specimen supports and on the impact duration have been discussed. It has been reported that the initial compression applied to the tubes does not remain constant during and after the impact event. The amount of variations also depends on the initial level of the tube compression.

The behaviour of axially pre-loaded steel tubes subjected to lateral impacts was already studied experimentally by the authors. One metre long tubes were first axially compressed and then impacted at their mid-span using a dropped object moving with a velocity of about 7m/s. This paper reports details and results from a numerical attempt to simulate those impact experiments. A non-linear finite element implicit time domain dynamic approach has been used for the simulation. The numerical models employed have been found to efficiently simulate the failure sequences in the tubes which were subjected to a dynamic instability. In tubes which did not fail during the impact tests, the first impact and its subsequent rebounds have been properly simulated. Different numerical outputs such as the natural frequency of vibration in the intact and impacted tubes, failure loads and time histories of the impact load, the axial load and the tube deformations have been correlated against corresponding experimental records. In general, a good level of agreement has been noticed between the numerical and experimental results. Effects from parameters such as structural damping, variations in the pre-loading, etc. on the response of the impacted members have also been studied.

Steel tubes are widely encountered in industrial applications and are commonly exposed to accidental loads. Collision between supply ships and the legs and bracing members of offshore oil rigs, impact of heavy dropped objects on these members, mishandling during the launching and installation of marine structures, explosions and collision of moving ice sheets with offshore structures are examples of such accidents. Prior to an accident, tubular structural members will be carrying their normal operational loads. It is very important that this service load (pre-loading) is considered when the effect of impact damage is going to be estimated.This paper describes the experimental studies in which axially pre-loaded tubes were examined under lateral dynamic impact loads. The tubes were impacted by a dropped object with a velocity of about 7 m/s at their mid-span. The experimental investigation was aimed at gaining an insight and understanding of the dynamic failure and behaviour of the impacted tubes and to provide bench-marking data on the response of axially loaded steel tubes subjected to lateral impact.The main advantage of the current investigation, compared with those carried out previously and reported in the literature, is that both pre-loading and dynamic effects are included in the study. From the results of the experimental work, it can be concluded that pre-loading had a marked effect on the lateral collapse capacity of the cylinders. (C) 2002 Published by Elsevier Science Ltd.

Non‐linear static buckling of simple systems associated with typical discrete critical points is comprehensively presented using elementary Catastrophe Theory . Attention is focused on the Fold and Cusp Catastrophe, all local properties of which are assessed in detail. Hence, in dealing with stability problems of potential systems there is no need to seek any of these properties since all of these are known a priori . Then, one has only to classify, after reduction, the total potential energy of a system into one of the universal unfoldings of the above types of catastrophe. Two illustrative numerical examples show the methodology of the proposed technique. Copyright © 2002 John Wiley & Sons, Ltd.

The work described in this paper forms part of a closed analytical solution for the response of tubes subjected to lateral quasi-static or dynamic impact loads. The results can be used in the analytical study of the response where the tubes are usually modeled as a series of beams resting on a deformable foundation (of rings). An attempt has been made to evaluate the characteristics of this deformable foundation or in the other words the contribution of the rings to the tube resistance. Both analytical and numerical approaches have been used. It has been found that by assuming a rigid-perfectly plastic behaviour for the ring resistance, accurate results for long tubes (L/D>15) are obtained. For tubes of moderate length, using rigid-perfectly plastic behaviour underestimates the ring resistance. A rigid-plastic expression with quadratic strengthening has been proposed for tubes of moderate length. This expression has been found to provide results which are much closer to the ring resistance for tubes with 5⩽L/D⩽15. In very short cylinders (L/D<5), it has been found that the ring resistance is dominated by the stiffness of the beams. The validity of these conclusions has been investigated by undertaking a parametric study. In this parametric study different material and geometrical properties have been examined.

This manual presents a comprehensive overview of the fundamental principles which govern the concept, analysis, design, construction and maintenance of many types of bridge. Each chapter is written by a different contributing author and each chapter includes an extensive bibliography. The chapters and authors are as follows: (1) the history and aesthetic development of bridges (Bennett,D); (2) loads and load distribution (Ryall,MJ); (3) structural analysis (Sanmugam,NE and Naragakan,R); (4) design of reinforced concrete bridges (Jackson,P); (5) design of prestressed concrete bridges (Hewson,NR); (6) design of steel bridges (Parke,GAR and Harding,JE); (7) composite construction (Collings,D); (8) design of arch bridges (Melbourne,C); (9) seismic response and design (Elnasha,AS); (10) cable stayed bridges (Farquhar,DJ); (11) suspension bridges (Jones,V and Howells,J); (12) movable bridges; (13) modern developments (Hollaway,L and Spencer,H); (14) substructures (Lindsell,P); (15) bridge accessories (Thayre,P, Jenkins,DE, Broome, RA and Grout,DJ); (16) protection (Mulheron,M); (17) bridge management (Vassie,P); (18) inspection, monitoring and assessment (Abdunur,C); (19) repair, strengthening and replacement (Darby,J).

The behaviour of an axially pre-loaded cylindrical member of an offshore structure, hit by a supply ship, has been investigated. The effects of axial pre-loading on the dynamic properties of members, the extent of damage and propagation of dynamic instability in the tubular members have also been investigated. Numerical models have been validated using available experimental data from the literature although these are mostly static with no pre-loading. Axial pre-loading was found to change the dynamic characteristics of some cylindrical members quite dramatically while it had no significant effect on others. The study examined whether there was any change in the behaviour between local and global modes when the loading was dynamic rather than static. The effect of damping on the dynamic instability of axially pre-loaded tubes under lateral dynamic loads was also studied. It was observed that for some geometries the quasi-static response can be used to define the boundary between bounded and unbounded dynamic responses. The main contribution of this study, compared with previous investigations reported in the literature, is that both pre-loading and dynamic effects have been included.

The effect of axial pre-loading on the behaviour and instability of a cylindrical member of an offshore structure struck by a supply vessel has been investigated. Numerical models have been used to analyse a tubular member with and without axial pre-loading. It has been found that axial pre-loading has a marked effect on the lateral collapse load of the member and more dramatically on the level of energy that the member can absorb prior to its collapse. The effect of different end conditions on the behaviour of the tubular members has been examined and four distinct modes of deformation for a cylindrical member under quasi-static concentrated lateral loads have been defined. The finite element model was validated using available test results from the literature. These were mostly static tests, carried out on cylindrical members with no axial loading. Good agreement was obtained between the finite element model and the test results. Significant differences have been found between the results presented in this study and previous results by the other workers who represented the impact damage as an imperfection effect.

This paper describes the results of dynamic analyses carried out on both stiffened and unstiffened panels using both simplified and advanced analytical techniques. For unstiffened panels with in-plane restraint along their edges, the dynamic response of an imperfect panel was predicted using a large displacement elastic analysis based on Lagrange's equation, with the panel being treated as a shallow shell. For stiffened panels, the finite element (FE) technique was used to establish the validity of using the simplified technique to predict the inter-stiffener panel displacements for a simply supported panel. A parametric study has been carried out to analyse the effects of in-plane boundary conditions, local stiffener buckling and initial imperfections on the overall response. The significant effect of boundary conditions is demonstrated by including the actual boundary conditions of a test frame in the finite element modelling of a large-scale stiffened floorplate panel used in an experimental test series.

A large displacement elastic analysis based on Lagrange's equation has been developed to predict the dynamic response of an imperfect plate subjected to hydrocarbon explosions. The work extends a previous model developed by Schleyer by treating the panel as a shallow shell with simply supported edges restrained against in-plane movement. The results of the approach have been correlated with a fully non-linear transient finite element analysis package, which has been used to carry out a parametric study. The limitation of the elastic approach has been highlighted but overall the method provides excellent results of engineering accuracy for many cases. It is shown that certain imperfections can have a beneficial effect on the response, although snap through can occur in some instances, producing sudden instabilities.

The paper presents a brief historical review of some of the landmarks in understanding the behaviour of plated structures including both the static and dynamic behaviour of plates. It then illustrates aspects of the behaviour of stiffened plates by reference to the results of non-linear analysis concentrating on stiffened compression flanges and webs of the type that are found in steel bridge structures.The relatively small amount of data available on the dynamic response of plates to impulse loading such as caused by explosions serves to illustrate the major needs that still exist but modem computing power can now provide the tool for developing knowledge in this area over the next few years which is very relevant to the safety of such structures as offshore oil platform top decks.

This paper presents results on the response of a typical blast wall and a tee-stiffened panel subjected to hydrocarbon explosions with geometries typical of those used in current offshore structures. The panels have been modelled using a non-linear finite element analysis package (DYNA3D) with thin shell elements for both the plate and stiffener components accounting for the effects of plasticity, strain-rate and buckling. Correlation with previous experimental work is presented together with a parameter study highlighting the effect of an increasing peak pressure and the shape of the pressure-time curve. The effect of boundary restraints is shown to have a significant influence on both the torsional response of the stiffeners and the overall panel deformations. The results are also compared with a simple single degree of freedom (SDOF) dynamic model where good correlation is obtained in the region where only limited plastic deformations occur.

A non-linear finite element (FE) package has been used to investigate the torsional behaviour of flat-bar stiffeners in longitudinally stiffened panels subject to axial loading. The effects of plate slenderness, stiffener slenderness and boundary conditions have been studied including the modelling of the outstand both as part of a stiffened panel and in isolation. A simple analytical approach is proposed by using a theoretical mechanism model developed by Murray I combined with a simple elastic loading line to give an upper bound to the tripping failure load. The results are compared with existing design guidance.

This paper describes the results of dynamic analyses carried out on both stiffened and unstiffened panels using both simplified and advanced analytical techniques. The panels have been subjected to blast loading and are typical of those found in offshore applications.For an unstiffened panel with in-plane restraint along its edges, the dynamic response of an imperfect panel is predicted using a large displacement elastic analysis based on Lagrange's equation. The panel is treated as a shallow shell using a simplified formulation based on both a single mode sinusoidal shape function and a more complex three moded function to allow for higher order deflection modes. The results have been compared with output from an explicit non-linear finite element analysis package, which has been used to carry out a parametric study. The limitations of the simplified technique are highlighted. Overall, the technique accurately predicts the influence of the imperfections, especially for the more slender panels which are more sensitive to higher mode excitation.The finite element technique has also been used to model a typical stiffened panel geometry to establish the validity of using the simplified technique to predict the interstiffener panel displacements for a simply supported panel. A parametric study has also been carried out on this geometry to establish the effects of in-plane boundary conditions, local stiffener buckling and initial imperfections on the overall response.

This paper presents a summary of research undertaken by the authors as part of a coordinated programme on buckling of offshore members carried out in the 1980s at Imperial College in London, the University of Glasgow, University College in London and ARE in Dunfermline. This particular paper relates to experimental and analytical work on the residual strength, under axial compression, of ring-stiffened cylindrical members subjected to local dent damage of the type that would result from impact from berthing vessels. Nine experiments were conducted in which local denting was induced by the application of lateral load and the post-denting axial capacity established by subsequent testing under axial compression. Finite element analyses have been carried out to attempt to reproduce both the denting and the subsequent axial testing by use of a fully non-linear package capable of predicting peak load and post-peak behaviour. Subsequently the package has been used to carry out a limited parametric investigation to identify the sensitivity of collapse strength to dent size and the geometrical parameters.

This Paper presents results on the torsional behaviour of ring StiffenerS in cylindrical shells subjected to external pressure with geometrics typical of those found in offshore platforms. A full nonlinear finite-element package has been used to obtain load deflection curves, including peak loads, unloading curves and critical buckling loads for a wide range of stiffened shell geometries and different stiffener shapes. The effects of initial imperfection, stiffener slenderness and ring spacing have been investigated. The results presented have been compared with the limited available experimental results and existing design codes and a discussion on the factors investigated is given.