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N. S. Trahair - One of the best experts on this subject based on the ideXlab platform.
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steel cantilever strength by inelastic Lateral Buckling
Journal of Constructional Steel Research, 2010Co-Authors: N. S. TrahairAbstract:Abstract Methods used for the design of steel beams supported at both ends are not well suited for the design of cantilevers against Lateral Buckling. The end restraints are very different for cantilevers, and the maximum displacements and twist rotations take place at the free ends, instead of near mid-span. Consequently, their Buckling modes are very different to those of supported beams. The methods of allowing for the effects of the moment distribution on the elastic and inelastic Buckling of supported beams use a mean of the moment distribution, which is weighted to allow for the maximum deformations being near mid-span. These methods are clearly inappropriate for cantilevers whose deformations are greatest at the free ends. Lateral Buckling design methods for cantilevers are modifications of the methods for supported beams, but are of doubtful accuracy, and may be over conservative. In some cases there is little or no design guidance. This paper summarizes information on the effects of the moment distribution and load height on the elastic Buckling of cantilevers which can be used in the method of design by Buckling analysis. It then extends a method of designing supported beams by inelastic Buckling analysis to allow for the effects of the moment distribution on the inelastic Buckling of cantilevers. This extended method is then used to provide improved design methods for cantilevers which are consistent with those for simply supported beams. A worked example is summarized.
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steel member strength by inelastic Lateral Buckling
Journal of Structural Engineering-asce, 2004Co-Authors: N. S. Trahair, Gregory J HancockAbstract:This paper develops a simple advanced method of designing steel members against out-of-plane failure, in which reduced elastic moduli are used in an out-of-plane Buckling analysis to model the effects of high moment, residual stresses and geometrical imperfections on yielding. The reduced moduli are derived from the basic beam and column strength curves of the Australian steel code AS4100 in 1998. The strengths predicted for simply supported beams in uniform bending are exactly the same as those of AS4100, while those for simply supported columns are extremely close. The strengths predicted for simply supported beam-columns with equal and opposite end moments are a little higher than the less conservative predictions of AS4100, and are very close to the basic beam and column strengths when these are plotted against a consistent generalized slenderness. The strengths predicted for simply supported beams under double curvature bending are somewhat less than those of the AS4100 method of design by Buckling analysis, while those for beams with central concentrated loads acting at or away from the centroid are very close, and those for end restrained beams under uniform bending and for sway columns are generally a little higher. While the method has been developed from and compared with the Australian code AS4100, it may be modified for any other modern code for the design of steel structures. It may be more widely applied to two-dimensional frames with in-plane loading, as part of a simple method of advanced analysis in which separate assessments are made of the in-plane and out-of plane strengths.
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bearing shear and torsion capacities of steel angle sections
Journal of Structural Engineering-asce, 2002Co-Authors: N. S. TrahairAbstract:Steel angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion. However, many design codes do not have any design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. In this paper, proposals are developed for the section capacities of angle sections under bearing, shear, and uniform torsion. In a companion paper, consideration is given to the first-order elastic analysis of the biaxial bending of angle section beams, including the effects of restraints, and proposals are developed for the section moment capacities of angle sections under biaxial bending. The proposals in this and the companion paper can be used to design steel angle section beams which are Laterally restrained so that Lateral Buckling and second-order effects are unimportant.
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Lateral distortional Buckling of hollow flange beams
Journal of Structural Engineering-asce, 1997Co-Authors: N. S. TrahairAbstract:While the flanges of cold-formed hollow flange beams (HFBs) are very stiff torsionally, their webs are comparatively flexible, and may allow web distortion effects to reduce their resistances to Lateral Buckling. There is no simple formulation for predicting the effects of web distortion on the Lateral Buckling of HFBs. As a result, structural designers are unable either to check or to extend the available elastic Buckling predictions; thus code writers are not able to provide explicit formulations for the effects of distortion. The conversion from elastic Buckling to strength for HFBs is also questionable, since cold-formed beams have different stress-strain curves, residual stresses, and geometrical imperfections from those of hot-formed beams. This paper deals with these problems, first by finding a simple but sufficiently accurate closed-form solution for the effects of distortion on the elastic Lateral Buckling of simply supported HFBs in uniform bending, and then by developing an advanced theoretica...
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energy equation for beam Lateral Buckling
Journal of Structural Engineering-asce, 1992Co-Authors: N. S. Trahair, Sundaramoorthy RajasekaranAbstract:This paper presents a derivation of the classical energy equation for the later Buckling of doubly symmetric thin-walled beams. This is based on the use of second-order rotation components to obtain the nonlinear relationship between the longitudinal normal strain and the member deformations. The classical energy equation is compared with an alternative energy equation, and found to be significantly different in terms used to represent the work done by centroidal loads during Buckling. The difference is attributed to the omission of some nonlinear components from the longitudinal displacements used for the alternative equation. Comparisons of finite element predictions based on the two energy equations demonstrate some substantial differences with the predictions by the alternative energy equation being higher for simply supported and continuous beams, and lower for cantilevers. Comparisons show that the available experimental evidence agrees well with the classical predictions, and they provide independent evidence that the alternative energy equation is incorrect.
Mario M. Attard - One of the best experts on this subject based on the ideXlab platform.
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in plane nonlinear localised Lateral Buckling under thermal loading of rail tracks modelled as a sandwich column
International Journal of Mechanical Sciences, 2015Co-Authors: Jianbei Zhu, Mario M. AttardAbstract:Abstract The Lateral Buckling problem for continuous welded rail tracks under thermal loading has been well researched and is known to involve a localisation Buckling phenomenon where only a limited region of the track buckles. In this paper, a sandwich column model is formulated to model the rail track-tie structure as sandwich column. The constitutive relations for the thermally induced stresses and finite strain are based on a hyperelastic constitutive model. A hyperbolic function for the nonlinearity of the axial and Lateral resistance between the tracks and ballast was used. A critical track length is proposed beyond which the localisation is unaffected. Increasing the track length or changing the boundary conditions does not influence the localised Buckling behaviour for track lengths beyond the critical length. The use of fasteners with large rotational stiffness substantially increases the Lateral stability of the track-tie structure. Nonlinear numerical solutions are compared with the results in the literature. The variation in the axial compressive force within the localisation zone in the rail is studied and discussed. Parametric studies are performed on examples to identify the influence of track imperfections on the localised Lateral Buckling and safe temperature change.
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In-plane nonlinear localised Lateral Buckling of straight pipelines
Engineering Structures, 2015Co-Authors: Jianbei Zhu, Mario M. Attard, David C. KellermannAbstract:Abstract The Lateral Buckling problem for thermally loaded pipelines is known to involve a localisation phenomenon within a limited region of the pipeline rather than an extensive global mode shape. In this paper, a strategy is presented to investigate the localised Lateral Buckling of pipelines under thermal loading and friction whereupon the constitutive relations are derived for thermal stress and finite strain based on a hyperelastic constitutive model. Using this hyperelastic formulation, we investigate the critical overall pipeline length above which localised Buckling remains unchanged. The results show that increasing the length of the pipeline or changing the end boundary conditions when the pipeline length is greater than or equal to the critical overall length does not influence the localised Buckling behaviour. The solutions to several examples are compared with the results in the literature and validated by use of the finite element package ANSYS. Parametric studies on diameter, imperfection, friction and shear deformation effects are subsequently performed on examples that identify which factors influence the localised Buckling of thermal pipelines.
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Lateral Buckling of beams with shear deformations – A hyperelastic formulation
International Journal of Solids and Structures, 2010Co-Authors: Mario M. AttardAbstract:Abstract The equilibrium and Buckling equations are derived for the Lateral Buckling of a prismatic straight beam. A consistent finite strain constitutive law is used, which is based on a hyperelastic model for an isotropic material. The kinematics of the cross-sectional deformations are based on a Timoshenko type beam displacement of the cross-sectional plane using Euler angles and two shear finite rotations coupled with warping taken normal to the displaced plane. Also derived are the second order approximations to the displacements, curvatures, twist and internal actions. The constitutive relationships for the internal actions reveal new coupling terms between the bending moments, torsion and bimoment, which are functions of the cross-sectional warping and shear deformations. New Wagner type nonlinear torsion terms are derived which are functions of the warping of the cross-sectional plane, and are coupled to the twisting and shear deformations of the cross-section. Solutions are determined for the Lateral Buckling of a prismatic monosymmetric beam under pure bending and the flexural–torsional Buckling under axial compression. For the flexural–torsional Buckling problem it is found that the Euler type column Buckling formula is consistent with Haringx’s column Buckling formula while the torsional Buckling formula is different to conventional equations. The second variation of the total potential is also derived. The effects of shear deformations are explored by examining the non-dimensional Lateral Buckling equation for a simply supported beam.
David White - One of the best experts on this subject based on the ideXlab platform.
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parametric solution of Lateral Buckling of submarine pipelines
Applied Ocean Research, 2020Co-Authors: Indranil Guha, David White, Mark RandolphAbstract:Abstract Lateral Buckling analysis of on-bottom submarine pipelines is of particular interest in the offshore industry due to the complexities involved in the analysis, and the potential design efficiencies that can be unlocked. Classical Buckling theories by previous researchers and recent joint industry projects provide a basis for estimation of the critical Buckling load of a straight, or in some cases imperfect, pipe on either a rigid or elastic seabed. However, systematic solutions for the combined effects of nonlinear soil properties and the as-laid geometry – specifically the out-of-straightness – on the buckle initiation behaviour have not been developed previously. This paper reports an investigation of the Buckling problem of an imperfect (non-straight) on-bottom pipeline subjected to axial compressive loading. The seabed was modelled with Lateral and axial nonlinear, springs to idealise the load-displacement behaviour of the soil and the pipe was modelled with pipe elements. Buckling was performed by a displacement controlled finite element method with the modified Riks algorithm that is available in the commercial software ABAQUS. This numerical tool was used to develop a parametric solution for the present problem in terms of the various pipe material and geometry parameters and the Lateral and axial pipe-soil interaction parameters. In particular, the influence of the magnitude and stiffness of the Lateral pipe-soil response was investigated, highlighting the sensitivity of the pipeline response to the geotechnical inputs. The results have been synthesised in a generic non-dimensionalised design chart to estimate the Buckling load, valid for the range of inputs covered by the parametric study.
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shear strength of soil berm during Lateral Buckling of subsea pipelines
Applied Ocean Research, 2019Co-Authors: Azadeh Rismanchian, Mark Randolph, David White, C M MartinAbstract:Abstract The soil resistance developed during temperature- and pressure-induced large Lateral movements of shallowly embedded subsea flowlines is an important input parameter for the structural design process. A major source of uncertainty in calculation of the soil resistance is the undrained shear strength of the soil berm produced as the flowline moves across the seabed, which is affected by the level of remoulding. To investigate the effect of pipeline embedment and displacement amplitude on the shear strength of the berm, a set of centrifuge model tests was conducted on kaolin clay, involving Laterally moving pipelines with constant embedments in the range 5%–35% of the pipe diameter. Back-analysis of the test results, using finite element limit analysis, showed that the shear strength of the soil berm is a function of pipe displacement amplitude, pipe embedment, and soil sensitivity. On the basis of these results, we propose that the overall berm undrained shear strength may be determined as a convolution of the shear strengths of its constituent soil elements. Finally, a formula is presented for calculating the shear strength of soil elements within the soil berm, and this is used to back-analyse the overall soil berm resistance from the model tests.
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Effect of Lateral Pipe-Soil Interaction on Controlled Lateral Buckling Using Pre-Deformed Pipeline
Volume 5: Pipelines Risers and Subsea Systems, 2018Co-Authors: Jayden Chee, Alastair Walker, David WhiteAbstract:A novel approach to eliminate the onset of global Buckling in pipelines is investigated in the paper. The method is based on pre-deforming a pipeline continuously with a specific wavelength and amplitude prior to installation on the seabed. The response of the pipeline to applied high temperature and pressure was studied in conjunction with variations in the Lateral pipe-soil interaction (PSI) – both as uniform friction along the pipe and also with locally varying friction. Pipe and seabed parameters representing a typical wet-insulated infield flow line on soft clay are used. The pre-deformed pipeline has a higher buckle initiation temperature compared to a straight pipeline due to the reduced effective axial force build-up resulting from the low axial stiffness generated by the predeformed lobes along the pipeline. The results from this paper show that the strains in the predeformed pipeline are not significantly affected by the local variability of Lateral PSI but rather by the global mean PSI. At a typical Lateral soil resistance, i.e. a friction coefficient of 0.5, Lateral Buckling occurs at a very high temperature level that is not common in the subsea operation. At a very low friction, i.e. 0.1, Lateral Buckling occurs at a lower operating temperature but the strain is insignificant. The longitudinal strain of the pipeline is not highly sensitive to the Lateral PSI, which is a quite different response to an initially straight pipeline. Therefore, this method could prove to be a valuable tool for the subsea industry as it enables the pipeline to be installed and operated safely at very high temperatures without the need for Lateral Buckling design and installation of expensive structures as buckle initiators. Even if the pre-deformed pipeline buckles at a very high temperature, during cycles of heat-up and cool-down the buckle shape ‘shakes down’ by geometric rearrangement to minimize the energy, and in doing so creates a series of ‘short pipelines’ in which the longitudinal strain is self-controlled. The system is therefore shown to be very robust in the conditions investigated and not affected by one of the biggest unknowns in seabed pipeline engineering, which is the local variability in Lateral PSI.
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controlling Lateral Buckling of subsea pipeline with sinusoidal shape pre deformation
Ocean Engineering, 2018Co-Authors: Jayden Chee, Alastair Walker, David WhiteAbstract:Abstract It is common for subsea pipelines to operate at high pressures and high temperatures (HPHT) conditions. The build-up of axial force along the pipeline due to temperature and pressure differences from as-laid conditions coupled with the influence of the seabed soil that restricts free movement of the pipeline can result in the phenomenon called ‘Lateral Buckling’. The excessive Lateral deformation from Lateral Buckling may risk safe operation of the pipeline due to local axial strains that potentially could be severe enough to cause fracture failure of welds or collapse of the pipeline. Engineered buckles may be initiated reliably during operation by using special subsea structures or lay methods which are expensive. This paper introduces and exemplifies a novel method that involves continuously deforming the pipeline prior to or during installation with prescribed radius and wavelength to control Lateral Buckling that could be a valuable modification of the practical design of offshore pipelines. Previous published work has shown that installation of a pipeline with such continuous deformations is feasible. The results from an example pipeline case described here show that the pipeline can be installed and operated safely at elevated temperatures without the need for other expensive buckle initiation methods.
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large deformation finite element analysis of pipe penetration and large amplitude Lateral displacement
Canadian Geotechnical Journal, 2010Co-Authors: Dong Wangd Wang, David White, Mark RandolphAbstract:Seabed pipelines must be designed to accommodate thermal expansion — which is commonly achieved through controlled Lateral Buckling — and to resist damage from submarine slides. In both cases, the pipe moves Laterally by a significant distance and the overall pipeline response is strongly influenced by the Lateral pipe–soil resistance. Here, the process of pipe penetration and Lateral displacement is investigated using a large-deformation finite element method, with a softening rate–dependent soil model being incorporated. The calculated soil flow mechanisms, pipe resistances, and trajectories agree well with plasticity solutions and centrifuge test data. It was found that the Lateral resistance is strongly influenced by soil heave during penetration and the berm formed ahead of the pipe during Lateral displacement. For “light” pipes, the pipe rises to the soil surface and the soil failure mechanism involves sliding at the base of the berm. In contrast, “heavy” pipes dive downwards and a deep shearing zon...
Mark Randolph - One of the best experts on this subject based on the ideXlab platform.
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parametric solution of Lateral Buckling of submarine pipelines
Applied Ocean Research, 2020Co-Authors: Indranil Guha, David White, Mark RandolphAbstract:Abstract Lateral Buckling analysis of on-bottom submarine pipelines is of particular interest in the offshore industry due to the complexities involved in the analysis, and the potential design efficiencies that can be unlocked. Classical Buckling theories by previous researchers and recent joint industry projects provide a basis for estimation of the critical Buckling load of a straight, or in some cases imperfect, pipe on either a rigid or elastic seabed. However, systematic solutions for the combined effects of nonlinear soil properties and the as-laid geometry – specifically the out-of-straightness – on the buckle initiation behaviour have not been developed previously. This paper reports an investigation of the Buckling problem of an imperfect (non-straight) on-bottom pipeline subjected to axial compressive loading. The seabed was modelled with Lateral and axial nonlinear, springs to idealise the load-displacement behaviour of the soil and the pipe was modelled with pipe elements. Buckling was performed by a displacement controlled finite element method with the modified Riks algorithm that is available in the commercial software ABAQUS. This numerical tool was used to develop a parametric solution for the present problem in terms of the various pipe material and geometry parameters and the Lateral and axial pipe-soil interaction parameters. In particular, the influence of the magnitude and stiffness of the Lateral pipe-soil response was investigated, highlighting the sensitivity of the pipeline response to the geotechnical inputs. The results have been synthesised in a generic non-dimensionalised design chart to estimate the Buckling load, valid for the range of inputs covered by the parametric study.
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shear strength of soil berm during Lateral Buckling of subsea pipelines
Applied Ocean Research, 2019Co-Authors: Azadeh Rismanchian, Mark Randolph, David White, C M MartinAbstract:Abstract The soil resistance developed during temperature- and pressure-induced large Lateral movements of shallowly embedded subsea flowlines is an important input parameter for the structural design process. A major source of uncertainty in calculation of the soil resistance is the undrained shear strength of the soil berm produced as the flowline moves across the seabed, which is affected by the level of remoulding. To investigate the effect of pipeline embedment and displacement amplitude on the shear strength of the berm, a set of centrifuge model tests was conducted on kaolin clay, involving Laterally moving pipelines with constant embedments in the range 5%–35% of the pipe diameter. Back-analysis of the test results, using finite element limit analysis, showed that the shear strength of the soil berm is a function of pipe displacement amplitude, pipe embedment, and soil sensitivity. On the basis of these results, we propose that the overall berm undrained shear strength may be determined as a convolution of the shear strengths of its constituent soil elements. Finally, a formula is presented for calculating the shear strength of soil elements within the soil berm, and this is used to back-analyse the overall soil berm resistance from the model tests.
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large deformation finite element analysis of pipe penetration and large amplitude Lateral displacement
Canadian Geotechnical Journal, 2010Co-Authors: Dong Wangd Wang, David White, Mark RandolphAbstract:Seabed pipelines must be designed to accommodate thermal expansion — which is commonly achieved through controlled Lateral Buckling — and to resist damage from submarine slides. In both cases, the pipe moves Laterally by a significant distance and the overall pipeline response is strongly influenced by the Lateral pipe–soil resistance. Here, the process of pipe penetration and Lateral displacement is investigated using a large-deformation finite element method, with a softening rate–dependent soil model being incorporated. The calculated soil flow mechanisms, pipe resistances, and trajectories agree well with plasticity solutions and centrifuge test data. It was found that the Lateral resistance is strongly influenced by soil heave during penetration and the berm formed ahead of the pipe during Lateral displacement. For “light” pipes, the pipe rises to the soil surface and the soil failure mechanism involves sliding at the base of the berm. In contrast, “heavy” pipes dive downwards and a deep shearing zon...
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large deformation finite element analysis of pipe penetration and large amplitude Lateral displacement
Canadian Geotechnical Journal, 2010Co-Authors: Dong Wangd Wang, David White, Mark RandolphAbstract:Seabed pipelines must be designed to accommodate thermal expansion — which is commonly achieved through controlled Lateral Buckling — and to resist damage from submarine slides. In both cases, the ...
Jianbei Zhu - One of the best experts on this subject based on the ideXlab platform.
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in plane nonlinear localised Lateral Buckling under thermal loading of rail tracks modelled as a sandwich column
International Journal of Mechanical Sciences, 2015Co-Authors: Jianbei Zhu, Mario M. AttardAbstract:Abstract The Lateral Buckling problem for continuous welded rail tracks under thermal loading has been well researched and is known to involve a localisation Buckling phenomenon where only a limited region of the track buckles. In this paper, a sandwich column model is formulated to model the rail track-tie structure as sandwich column. The constitutive relations for the thermally induced stresses and finite strain are based on a hyperelastic constitutive model. A hyperbolic function for the nonlinearity of the axial and Lateral resistance between the tracks and ballast was used. A critical track length is proposed beyond which the localisation is unaffected. Increasing the track length or changing the boundary conditions does not influence the localised Buckling behaviour for track lengths beyond the critical length. The use of fasteners with large rotational stiffness substantially increases the Lateral stability of the track-tie structure. Nonlinear numerical solutions are compared with the results in the literature. The variation in the axial compressive force within the localisation zone in the rail is studied and discussed. Parametric studies are performed on examples to identify the influence of track imperfections on the localised Lateral Buckling and safe temperature change.
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In-plane nonlinear localised Lateral Buckling of straight pipelines
Engineering Structures, 2015Co-Authors: Jianbei Zhu, Mario M. Attard, David C. KellermannAbstract:Abstract The Lateral Buckling problem for thermally loaded pipelines is known to involve a localisation phenomenon within a limited region of the pipeline rather than an extensive global mode shape. In this paper, a strategy is presented to investigate the localised Lateral Buckling of pipelines under thermal loading and friction whereupon the constitutive relations are derived for thermal stress and finite strain based on a hyperelastic constitutive model. Using this hyperelastic formulation, we investigate the critical overall pipeline length above which localised Buckling remains unchanged. The results show that increasing the length of the pipeline or changing the end boundary conditions when the pipeline length is greater than or equal to the critical overall length does not influence the localised Buckling behaviour. The solutions to several examples are compared with the results in the literature and validated by use of the finite element package ANSYS. Parametric studies on diameter, imperfection, friction and shear deformation effects are subsequently performed on examples that identify which factors influence the localised Buckling of thermal pipelines.
