No. R834, February, 2004
Rasmussen, KJR and Trahair, NS
Exact and Approximate Solutions for the Flexural Buckling of Columns with Oblique Rotational End Restraints
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Abstract
This report is concerned with the elastic flexural buckling of doubly symmetric columns with oblique restraints under concentric loading. Oblique restraints cause coupling between the principal axis deflections and rotations, and the flexural buckling mode involves simultaneous bending about both principal axes.
The report discusses the nature of oblique restraints, and presents exact and approximate solutions for the buckling loads of columns with rigid or elastic restraints against rotations at the ends. The exact solutions are obtained by solving the governing differential equations and boundary conditions, while the approximate solutions are based on energy solutions with assumed buckling displacements. The approximate solutions are sufficiently simple that they can be used in design, and are shown to be within 1% of the exact solutions.
Keywords
Buckling, columns, design, elasticity, restraints, steel.
No. R835, February, 2004
Trahair, NS and Rasmussen, KJR
Finite Element Analysis of The Flexural Buckling of Columns with Oblique Restraints
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Abstract
This paper is concerned with the elastic flexural buckling of doubly symmetric columns with oblique restraints under concentric loading. Oblique restraints cause coupling between the principal axis deflections and rotations, and the flexural buckling mode involves simultaneous bending about both principal axes.
Oblique restraints may resist deflections as well as rotations, and may be rigid or elastic. They may be concentrated at point along a column, or distributed along portions of its length.
This paper discusses the nature of oblique end restraints, summarises their finite element analysis, presents examples of their effects on the elastic buckling of columns, and demonstrates the design of columns with oblique restraints.
Keywords
Buckling, columns, design, elasticity, restraints, steel.
No. R837
Ranzi, G; Ansourian, P; Gara, F; Leoni, G and Dezi, L
Displacement-based Formulations for Composite Beams with Longitudinal Slip and vertical Uplift
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Abstract
This paper describes three novel displacement-based formulations for the analysis of composite beams with a flexible connection which is capable of deforming along the longitudinal axis of the member as well as vertically, i.e. transverse to the interface connection. For completeness, the analytical model which forms the basis of the proposed modelling technique is presented in both its weak and strong forms. The three novel finite element formulations are derived and tested using different structural systems; their nodal freedoms include the vertical and axial displacements as well as the rotations at each element end of both layers. Curvature locking problems are observed to occur for one of these elements and the origin of this behaviour is demonstrated analytically. Two applications are then proposed adopting a bi-linear constitutive relationship for the vertical interface connection to reflect the more realistic case in which, already in the linear-elastic range of the materials forming the cross-section and of the longitudinal interface connection, two vertical connection stiffnesses are required, i.e. one to model the event of separation between the layers and one when one bears against the other one.
Keywords
Composite beams, Finite Element Method, Partial interaction, Slip, Uplift
No. R838, May, 2004
Rasmussen, KJR and Hossain, MS
Design of Slender Angle Section Beam-Columns by the Direct Strength Method
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Abstract
This report is concerned with the application of the Direct Strength Method to equal angle section beam-columns with locally unstable legs. In contrast to existing design methods, which independently determine the compression and bending capacities and use an interaction equation to combine these, the Direct Strength Method determines the elastic local buckling stress for the actual stress distribution resulting from the combined action of compression and bending, and incorporates the elastic buckling stress into a direct strength equation for beam-columns.
In applying the method to equal leg angles, the torsional buckling mode is ignored when determining the overall buckling capacities, since it is accounted for through the local buckling mode, and the shift of the effective centroid is incorporated as an additional loading eccentricity. The shift in the effective centroid resulting from local buckling is determined from the actual stress distribution, as obtained using Stowell’s classical solution, in place of an effective cross-section. The predicted strengths are conservative compared to tests on slender equal angle columns, and are shown to accurately predict the variation in load with applied loading eccentricity.
Keywords
Direct Strength Method, equal angle section, beam-columns, local buckling, flexural buckling, flexural-torsional buckling, design, shift of the effective centroid.
No. R841, November, 2004
Trahair, NS and Rasmussen, KJR
Flexural-Torsional Buckling of Columns with Oblique Eccentric Restraints
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Abstract
This paper is concerned with the elastic flexural-torsional buckling of concentrically loaded columns with oblique eccentric restraints. Oblique flexural restraints may resist deflections as well as flexural rotations, while torsional restraints may resist twist rotations and warping. Flexural restraints may act at the shear centre or may be eccentric. Restraints may be concentrated at points along a column or distributed along portions of its length, and may be rigid or elastic.
Oblique flexural restraints cause coupling between the principal axis deflections and rotations, while eccentric flexural restraints cause coupling between the principal axis deflections and rotations and the twist rotations and warping displacements. The general buckling mode involves simultaneous bending about both principal axes and torsion.
This paper discusses the nature of oblique eccentric restraints, summarises their finite element analysis, presents examples of their effects on the elastic buckling of columns, and demonstrates the design of columns with oblique eccentric restraints.
Keywords
buckling, columns, design, elasticity, restraints, steel.
No. R842, November, 2004
Yang, DM and Hancock, GJ
Numerical Simulations of High Strength Steel Box-Shaped Columns
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Abstract
An experimental research project was conducted to evaluate the compression stability of high strength steel sections. To further study the structural behaviour of the columns thoroughly, finite element analyses were performed using the commercial finite element package ABAQUS.
This report presents a finite element analysis of the post-buckling behaviour of thin-walled compression members of high strength steel. A series of numerical simulations has been carried out to simulate compression tests performed on box-shaped stub columns and box-shaped long columns fabricated from coldreduced high strength steel plates with nominal yield stress of 550 MPa (AS1397). The report compares the numerical simulations with the test results.
The effect of the input parameters such as the degree of prescribed initial imperfection and the size of the element mesh on the convergence of the solution has been investigated and is discussed. The report shows the comparison of loads obtained numerically and experimentally. The accurate results of the numerical simulation shows that the finite element analysis can be used to predict the ultimate loads of thin-walled members including the postbuckling behaviour of thin-walled sections. It is demonstrated that the finite element analysis can therefore be used to design and optimize thin-walled section of high strength steel and to extrapolate beyond existing experimental data.
Keywords
High strength steel, ABAQUS, Simulation, Box-Shaped section, Sub column, Long column, Local buckling, Euler buckling
No. R843, November, 2004
Yang, DM and Hancock, GJ
Numerical Simulations of High Strength Steel Lipped-Channel Columns
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Abstract
An experimental research project was conducted to evaluate the compression stability of high strength steel sections. Three buckling modes ‘Local, Euler and Distortional buckling’ and the interaction between them were investigated. To further study the structural behaviour of the columns thoroughly, finite element analyses were performed using the commercial finite element package ABAQUS.
This report presents a finite element analysis of the post-buckling behaviour of thin-walled compression members of high strength steel. A series of numerical simulations has been carried out to simulate compression tests performed on lipped-channel section columns fabricated from cold-reduced high strength steel plates with nominal yield stress of 550 MPa (AS 1397). The report compares the numerical simulations with the test results. For the lipped-channel section columns, the stress distribution over the whole cross-section will be shown and the explanation of the failure modes will be given.
The report shows the comparison of loads obtained numerically and experimentally with those predicted on the basis of AS/NZS4600 and the North American Specification. The accurate results of the numerical simulation shows that the finite element analysis can be used to predict the ultimate loads of thinwalled members including the post-buckling behaviour of thin-walled sections.
Keywords
High strength steel; ABAQUS, Simulation, Lipped channel section, Distortional buckling