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M A Bradford - One of the best experts on this subject based on the ideXlab platform.
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flexural torsional buckling of shear deformable steel circular arches under a Central Concentrated Load in a thermal environment
Engineering Structures, 2021Co-Authors: Lulu Liu, M A Bradford, Airong LiuAbstract:Abstract When subjected to a constant temperature gradient, a steel circular arch will experiences non-uniform thermal expansion in its axial direction. This expansion will produces complex internal forces in the arch, which in turn will affect its flexural–torsional buckling behavior under a Central Concentrated radial Load. Hitherto, research studies of the flexural–torsional buckling of such arches are scarce. The position of the effective centroid and shear center do not coincide with the geometric centroid of the section in a temperature gradient field, and this influences the flexural–torsional buckling response. In this paper, the flexural–torsional buckling of shear deformable circular arches with in-plane elastic rotational end restraints subjected to a Central Concentrated radial Load at a constant temperature gradient field is studied. The theoretical solutions for the buckling Load of the arch including the effect of the temperature gradient field are obtained and validated by ANSYS simulations. It is found that the buckling Load decreases with an increase of the temperature differential when the included angle is small and increases with an increase of the temperature differential in case the included angle is larger than a certain value. The buckling Loads including shear deformations are higher than those ignoring shear deformations at a bigger temperature differential. The influences of shear deformations on the buckling Load are more significant at a bigger temperature differential.
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revisiting nonlinear in plane elastic buckling and postbuckling analysis of shallow circular arches under a Central Concentrated Load
Journal of Engineering Mechanics-asce, 2016Co-Authors: M A Bradford, Yanlin GuoAbstract:AbstractThis paper revisits the nonlinear in-plane analysis of a shallow pin-ended circular arch under a Central Concentrated Load. It is found that the arch may have multiple equilibrium branches and limit points, and a modified slenderness of the arch defined in the paper plays an important role in the number of the limit points and equilibrium branches. The analytical solution for the specific modified slendernesses that switch the number of equilibrium branches and limit points is derived. The analytical solutions for the Load, axial force, and radial displacements corresponding to the specific modified slendernesses are also derived. This paper deepens the understanding for the geometric nonlinear analysis of circular arches and their geometric softening and stiffening behavior and provides useful benchmarks for the analyses of shallow arches. In addition, this paper extends the current solutions of nonlinear equilibrium of arches associated with axial compression to those associated with axial tensi...
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geometric nonlinearity and long term behavior of crown pinned cfst arches
Journal of Structural Engineering-asce, 2015Co-Authors: M A BradfordAbstract:AbstractConcrete-filled steel tubular (CFST) arches are often used in engineering structures, particularly in bridge construction. In some instances, to expedite their construction and transport, curvilinear steel tube segments are fabricated and delivered to the construction site and then joined together at the crown to create a pin, so the arch becomes a crown-pinned arch. Wet concrete is then pumped into the steel tubes to form the concrete core after curing, which experiences time-dependent shrinkage and creep. This paper investigates the effects of geometric nonlinearity on the long-term in-plane behavior of crown-pinned circular CFST arches under a sustained Central Concentrated Load, and derives analytical solutions for their nonlinear response and buckling Loads. It is found that the geometric nonlinearity influences the long-term behavior of crown-pinned CFST arches significantly. The long-term deformations predicted by the nonlinear analysis are larger than those predicted by linear analysis, an...
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multiple unstable equilibrium branches and non linear dynamic buckling of shallow arches
International Journal of Non-linear Mechanics, 2014Co-Authors: Yonglin Pi, M A BradfordAbstract:Abstract An arch under a suddenly-applied Load will oscillate about its equilibrium position. If the suddenly-applied Load is sufficiently large, the oscillation may reach a position on the unstable equilibrium branch of the arch, triggering its dynamic buckling. In many cases, arches are supported by other structural members or by elastic foundations which provide elastic types of rotational restraints to the ends of the arch. When the rotational end restraints of an arch are not equal to each other, the in-plane non-linear equilibrium path of the arch may have multiple unstable branches, which will influence the dynamic buckling of the arch significantly. This paper investigates effects of multiple unstable equilibrium branches on the non-linear in-plane dynamic buckling of a shallow circular arch under a suddenly-applied Central Concentrated Load. Two methods based on the energy approach are used to derive the dynamic buckling Loads. It is found that the number and magnitude of dynamic buckling Loads are influenced significantly by the number of unstable equilibrium branches, by the stiffness of the unequal rotational end restraints, and by the included angle and slenderness ratio of the arch.
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lateral torsional elastic buckling of rotationally restrained arches with a thin walled section under a Central Concentrated Load
Thin-walled Structures, 2013Co-Authors: M A BradfordAbstract:Abstract An arch often has elastic end restraints provided by the connected structures or elastic foundations. When the arch is subjected to an in-plane Central Concentrated Load, the Load produces combined non-uniform axial compressive and bending actions with complicated distributions along the arch length and these actions are significantly influenced by the stiffness of the end restraints. These combined axial compressive and bending actions increase with an increase of external Loads and may reach the values, at which the arch suddenly deflects laterally and twists out of the plane of Loading, and fails in a lateral–torsional buckling mode. Little research of the lateral–torsional buckling of such arches has been reported in the open literature. This paper derives the analytical solution for the elastic lateral–torsional buckling Load of pin-ended circular arches with a thin-walled section and having in-plane elastic rotational end restraints under a Central Concentrated Load, using the principle of stationary potential energy in conjunction with the Rayleigh–Ritz method. The analytical solution agrees with independent finite element results very well, which indicates that the analytical solution can provide accurate predictions for the lateral–torsional buckling Loads of arches having in-plane rotational end restraints. The effects of the stiffness of rotational end restraints on the lateral–torsional buckling Load are investigated. It is found that the change of the stiffness of rotational end restraints has significant effects on the lateral–torsional buckling resistance of arches.
F Tinloi - One of the best experts on this subject based on the ideXlab platform.
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non linear in plane buckling of rotationally restrained shallow arches under a Central Concentrated Load
International Journal of Non-linear Mechanics, 2008Co-Authors: M A Bradford, F TinloiAbstract:Abstract This paper investigates the non-linear in-plane buckling of pin-ended shallow circular arches with elastic end rotational restraints under a Central Concentrated Load. A virtual work method is used to establish both the non-linear equilibrium equations and the buckling equilibrium equations. Analytical solutions for the non-linear in-plane symmetric snap-through and antisymmetric bifurcation buckling Loads are obtained. It is found that the effects of the stiffness of the end rotational restraints on the buckling Loads, and on the buckling and postbuckling behaviour of arches, are significant. The buckling Loads increase with an increase of the stiffness of the rotational restraints. The values of the arch slenderness that delineate its snap-through and bifurcation buckling modes, and that define the conditions of buckling and of no buckling for the arch, increase with an increase of the stiffness of the rotational end restraints.
Airong Liu - One of the best experts on this subject based on the ideXlab platform.
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flexural torsional buckling of shear deformable steel circular arches under a Central Concentrated Load in a thermal environment
Engineering Structures, 2021Co-Authors: Lulu Liu, M A Bradford, Airong LiuAbstract:Abstract When subjected to a constant temperature gradient, a steel circular arch will experiences non-uniform thermal expansion in its axial direction. This expansion will produces complex internal forces in the arch, which in turn will affect its flexural–torsional buckling behavior under a Central Concentrated radial Load. Hitherto, research studies of the flexural–torsional buckling of such arches are scarce. The position of the effective centroid and shear center do not coincide with the geometric centroid of the section in a temperature gradient field, and this influences the flexural–torsional buckling response. In this paper, the flexural–torsional buckling of shear deformable circular arches with in-plane elastic rotational end restraints subjected to a Central Concentrated radial Load at a constant temperature gradient field is studied. The theoretical solutions for the buckling Load of the arch including the effect of the temperature gradient field are obtained and validated by ANSYS simulations. It is found that the buckling Load decreases with an increase of the temperature differential when the included angle is small and increases with an increase of the temperature differential in case the included angle is larger than a certain value. The buckling Loads including shear deformations are higher than those ignoring shear deformations at a bigger temperature differential. The influences of shear deformations on the buckling Load are more significant at a bigger temperature differential.
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Lateral-Torsional Buckling of Shear Deformable Monosymmetric Steel I-Section Arches with Elastic Rotational-End Restraints under a Central Concentrated Load
Journal of Structural Engineering, 2021Co-Authors: Liu Lulu, Airong Liu, Mark A. BradfordAbstract:AbstractThis paper investigates the elastic lateral-torsional buckling of shear deformable circular arches of monosymmetric steel I-section with in-plane elastic rotational end constraints under a ...
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nonlinear equilibrium and buckling of fixed shallow arches subjected to an arbitrary radial Concentrated Load
International Journal of Structural Stability and Dynamics, 2017Co-Authors: M A Adford, Airong LiuAbstract:This paper is concerned with an analytical study of the nonlinear in-plane equilibrium and buckling of fixed shallow circular arches that are subjected to an arbitrary radial Concentrated Load. The structural behavior of an arch under an arbitrary radial Concentrated Load is quite different from that of an arch under a Central Concentrated Load. It is shown that a fixed arch under an arbitrary radial Concentrated Load can buckle in a limit point instability mode, but cannot buckle in a bifurcation mode, which is different from that of a fixed arch under a Central Concentrated Load that can buckle in a bifurcation mode or in a limit point instability mode. Analytical solutions for the nonlinear equilibrium path and limit point buckling Load of shallow circular arches under an arbitrary radial Concentrated Load are derived. It is found that the Load position influences the buckling Load significantly and the influence is much related to the modified slenderness of the arch defined in the paper. It is also found that when the modified slenderness of an arch is smaller than a specific value, the arch has no typical buckling behavior. The analytical solution for the relationship of the specific modified slenderness with the Load position is also derived. Comparisons with finite element (FE) results show that the analytical solutions can accurately predict the nonlinear equilibrium and buckling Load of shallow fixed arches under an arbitrary radial Concentrated Load.
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lateral torsional buckling of fixed circular arches having a thin walled section under a Central Concentrated Load
Thin-walled Structures, 2017Co-Authors: Airong LiuAbstract:Abstract When a thin-walled section arch is subjected to an in-plane Central Concentrated Load, the Load produces combined nonuniform axial compressive and bending actions, which increase with an increase of the Central Load and may reach the values, at which the arch suddenly deflects laterally and twists out of the plane of Loading, and fails in a lateral-torsional buckling mode. The elastic lateral-torsional buckling of fixed circular arches under a Central Concentrated Load has been a difficult problem to be solved, which is investigated in this paper. Accurate prebuckling analyses for axial compressive and bending actions produced by the Central Load are carried out. The analytical solution for the elastic lateral-torsional buckling Load is derived using the principle of stationary potential energy in conjunction with the Rayleigh-Ritz method. The analytical solutions for the prebuckling axial compressive and bending actions and for the elastic lateral-torsional buckling Load are compared with independent finite element results. It is found that they agree with each other very well, which validate the analytical solutions. In addition, the effects of Load height, slenderness and in-plane boundary condition on the lateral-torsional buckling Load are investigated. It is found that changes of the slenderness ratio, Load height and in-plane boundary conditions have significant effects on the lateral-torsional buckling resistance of arches. This paper provides structural researchers and designers with a deep insight and useful analytical solutions for the lateral-torsional buckling of circular arches, and establishes a sound basis for investigations on the lateral-torsional strengths of fixed circular arches in the future.
Yonglin Pi - One of the best experts on this subject based on the ideXlab platform.
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multiple unstable equilibrium branches and non linear dynamic buckling of shallow arches
International Journal of Non-linear Mechanics, 2014Co-Authors: Yonglin Pi, M A BradfordAbstract:Abstract An arch under a suddenly-applied Load will oscillate about its equilibrium position. If the suddenly-applied Load is sufficiently large, the oscillation may reach a position on the unstable equilibrium branch of the arch, triggering its dynamic buckling. In many cases, arches are supported by other structural members or by elastic foundations which provide elastic types of rotational restraints to the ends of the arch. When the rotational end restraints of an arch are not equal to each other, the in-plane non-linear equilibrium path of the arch may have multiple unstable branches, which will influence the dynamic buckling of the arch significantly. This paper investigates effects of multiple unstable equilibrium branches on the non-linear in-plane dynamic buckling of a shallow circular arch under a suddenly-applied Central Concentrated Load. Two methods based on the energy approach are used to derive the dynamic buckling Loads. It is found that the number and magnitude of dynamic buckling Loads are influenced significantly by the number of unstable equilibrium branches, by the stiffness of the unequal rotational end restraints, and by the included angle and slenderness ratio of the arch.
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Elastic flexural-torsional buckling and postbuckling of arches subjected to a Central Concentrated Load
2001Co-Authors: Yonglin Pi, M A BradfordAbstract:This paper investigates the elastic buckling and postbuckling behaviour of arches that are subjected to a Central Concentrated Load, using a finite element model developed by authors. Comparisons with existing experimental and analytical results demonstrate that the model is effective and efficient in terms of accuracy, the number of elements needed for convergence, and the ability to perform a postbuckling analysis. It is found that under a Central Concentrated Load, the elastic buckling and postbuckling behaviour of a simply supported arch is similar to that of an arch in unform bending or in uniform axial compression. The slenderness of a simply supported arch has almost no effect on its buckling behaviour. However, the slenderness of all but very stocky pin-ended arches has significant effects on their buckling behaviour. For shallow pinended arches, the elastic flexural-torsional buckling Load is reduced significantly by the large axial compression developed in the arch prior to buckling. As the included angle increases, the buckling Load of the pin-ended arch decreases significantly until a minimum value of the buckling Load is reached, and then increases. The increase of the buckling Load stops at a certain value of the included angle, and thereafter the buckling Load steadily decreases with the increase of the included angle. For stocky pin-ended arches, the buckling Load decreases steadily with the increase of the included angle. The slenderness of deep pin-ended arches has a very small effect on their buckling behaviour. There is a substantial postbuckling response for shallow pin-ended arches, due to relaxation of the axial compression after buckling. The slenderness of fixed arches has a significant effect on their buckling behaviour. The large axial compression developed in shallow fixed arches reduces the elastic flexural-torsional buckling Loads significantly. Shallow fixed arches also have a substantial postbuckling response due to the relaxation of the axial compression and the moment redistribution in the postbuckling range. For slender fixed arches with moderate or large included angles, four inflexion points can be developed in their deformed profile, which reduces their effective length and leads to a significant increase of their flexural-torsional buckling Load. After buckling, a redistribution of bending moment takes place which increases the moments at the supports and decreases the moment at mid-span, thereby increasing the postbuckling strengths. For stocky fixed arches, however, only two inflexion points can be developed in their deformed profile prior to buckling and the buckling Load decreases slightly as the included angle increases.
G S Tong - One of the best experts on this subject based on the ideXlab platform.
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elastic lateral torsional buckling of circular arches subjected to a Central Concentrated Load
International Journal of Mechanical Sciences, 2010Co-Authors: M A Bradford, G S TongAbstract:Abstract An arch under an in-plane Central Concentrated radial Load is subjected to combined axial compressive and bending actions. When these combined axial compressive and bending actions reach a certain value, the arch may suddenly deflect laterally and twist out of its plane of Loading and fail in a lateral–torsional buckling mode. This paper derives analytical solutions for the elastic lateral–torsional buckling Load of pin-ended circular arches that are subjected to a Central Concentrated Load, using the principle of stationary potential energy in conjunction with the Rayleigh–Ritz method. Analytical solutions of the buckling Load for in-plane fixed and out-of-plane pin-ended arches and for the case of the Load acting above or below the shear centre are also derived. The analytical solutions are compared with results of a commercial finite element package ANSYS and a finite element code developed by authors elsewhere for arches with different slendernesses, included angles, and cross-sections. The agreement between the analytical solutions and the finite element results is very good.