2007 Research Reports No R874-R887

Abstract
This paper presents a finite element investigation of the local buckling behaviour of the structural steel Elliptical Hollow Section (EHS) in compression. The theoretical elastic buckling load of an EHS is similar to that of a Circular Hollow Section (CHS) except that the diameter term, D, is replaced by D₁²/D₂, representing the major and minor diameters of the ellipse.  The overall aim is to examine whether an “equivalent CHS” can be used to model the local buckling of EHS when considering imperfections and non-linear material properties. The finite element program ABAQUS was used to examine the local buckling behaviour of EHS with a range of aspect ratios from 1:1 (CHS) to 10:1 to examine the transitional behaviour. Three types of analysis were considered. The first stage was elastic buckling with no material imperfection. The second stage considered inelastic material properties, followed by measured material properties. The final stage was to investigate how geometric imperfection affected the buckling modes. The results are benchmarked against experimental results. It was found that the use of an equivalent CHS was a reasonably good predictor of capacity of slender sections and the deformation capacity of compact sections. However, further benchmarking against experimental results is recommended.

Keywords
Elliptical Hollow Section; Local buckling; Finite element analysis; ABAQUS

Abstract
This paper presents an investigation into the strength of stub columns of hollow flange channel (LiteSteel Beam) sections manufactured by Smorgon Steel Tube Mills. Compression tests on stub columns were performed on a range of 13 groups of specimens. A reliability analysis was undertaken on the test results with respect to the calculation methods of AS/NZS 4600. It was found that the current method of applying the lower web yield stress in the entire section is conservative. Applying the separate flange and web yield stress to the individual components produces higher capacities by approximately 15%, within an acceptable level of reliability. Finite element analyses were carried out to compare the results of numerical simulation with test results and demonstrated a close prediction of the test ultimate load despite some discrepancies were observed.

Keywords
Hollow flange channel; Local buckling; Cold-formed steel; AS/NZS 4600; Design rules; Finite element analysis

Abstract
The Mindlin plate bending theory includes shear deformations in the formulation to better reproduce the behaviour of thick plates and to avoid difficulties in satisfying continuity requirements along strip boundaries. Unfortunately, in many thin plate applications over-stiff solutions are encountered due to the development of spurious stiffness contributions in the numerical solution. This phenomenon is usually referred to as “locking” and if associated with an insufficient representation of bending and shear deformations is called “shear locking”. A method for testing the performance of finite elements with regard to shear locking is described. The method is called “the monomial test” and has been introduced by Briassoulis (1988) who applied it to a series of beam and plate elements. The monomial test is applied for the first time to the isoparametric spline finite strip method. The effect of shear locking on the performance of the isoparametric spline finite strip is investigated in detail as is the ameliorating influence of selective reduced integration. The influence of the order and magnitude of the distortion of the strip, the integration scheme and the number of longitudinal sections of the isoparametric spline finite strip are analysed. Numerical examples are included to illustrate the concepts described.

Keywords
Shear locking, isoparametric spline finite strip method, thin plates, Mindlin theory, reduced integration, bending, shear.

Abstract
In a previous report [1], the isoparametric spline finite strip method was successfully applied to the in-plane stress linear elastic analysis of perforated thin-walled structures. In the present report the application of the isoparametric spline finite strip method is further extended to the bending of perforated plates.

The general theory of the isoparametric spline finite strip method is briefly introduced while the development of the Mindlin bending theory and its matrices are discussed in detail.

The reliability of the method is demonstrated by comparisons with finely meshed finite element analyses. Square plates in bending containing openings of different shapes are analysed.

Keywords
Plate bending analysis, isoparametric spline finite strip method, perforations, thin-walled elements.

Abstract
In previous reports [1, 2], the isoparametric spline finite strip method was successfully applied to the in-plane stress and bending linear elastic analyses of perforated plates. In this report the application of the isoparametric spline finite strip method is further extended to the linear elastic analysis of tri-dimensional perforated folded plate structures.

The general theory of the isoparametric spline finite strip method is briefly introduced. Kinematics assumptions and the procedure to combine in-plane (membrane) and bending characteristics are set out. Particular attention is paid to the procedure for rotating the stiffness matrix and load vector from local to global coordinates.

The reliability of the method is demonstrated by comparisons with finely meshed finite element analyses. Square stiffened plates in compression and bending containing openings of different shapes are analysed.

Keywords
Folded plate, linear elastic analysis, isoparametric spline finite strip method, perforations, thin-walled elements.

Abstract
In previous reports [1, 2], the isoparametric spline finite strip method was successfully applied to the in-plane stress and bending linear elastic analysis of perforated plates, and to the linear elastic analysis of folded plate structures [3]. In the present report the application of the isoparametric spline finite strip method is further extended to the elastic buckling analysis of perforated folded plate structures.

The general theory of the isoparametric spline finite strip method is briefly
introduced. The kinematics assumptions, strain-displacement and constitutive relations of the Mindlin plate theory are described and applied to the spline finite strip method. The corresponding matrix formulation is utilised in the equilibrium and stability equations to derive the stiffness and stability matrices. A number of numerical examples of flat and folded perforated plate structures illustrate the applicability and accuracy of the proposed method.

Keywords
Folded plate structures, elastic buckling analysis, isoparametric spline finite strip method, perforations, thin-walled elements, local buckling, distortional buckling.

Abstract
In previous reports [1, 2], the isoparametric spline finite strip method was successfully applied to the in-plane stress and bending linear elastic analysis of perforated plates. The method has been successfully applied to the elastic linear analysis and buckling analysis of folded plate structures [3, 4]. In the present report the application of the isoparametric spline finite strip method is further extended to the geometric nonlinear analysis of perforated folded plate structures.

The general theory of the isoparametric spline finite strip method is briefly
introduced. Kinematics, strain-displacements and constitutive assumptions are described and applied to the spline finite strip method. The derivation of the tangential and secant stiffness matrices is presented by applying the equilibrium condition and its incremental form. A large part of report is reserved to a review of the available nonlinear solution techniques, notably the cylindrical arc-length method. Classical nonlinear complex plate and shell problems are analysed and compared with exact solutions or with well established numerical results in order to demonstrate the reliability of the method. Furthermore, examples of the geometric nonlinear analysis of perforated flat and stiffened plates are included to highlight the effect of perforations on the behaviour of thin plate elements.

Keywords
Folded plate structures, geometric nonlinear analysis, isoparametric spline finite strip method, perforations, thin-walled elements, local buckling, distortional buckling.

Abstract
The base balance wind tunnel testing technique was used to determine the wind loading on a range of telecommunication antennas and head frames. The crosswind and torsional components of the wind loading were typically small, and the along-wind drag force dominated the response. As more antennas were added to the head frame the peak along-wind drag typically increased. The magnitude of the increase is complex due to significant shielding effects.

Keywords
Telecommunication antennas, wind loading, drag force, interference

Abstract
The Limit States Australian/New Zealand Standard AS/NZS 4600:2005 and the North American Specification for the Design of Cold-Formed Steel Structural Members 2001 (2004 Supplement) include the newly developed Direct Strength Method of Design (DSM). In both Standards, the method presented (Chapter 7 of AS/NZS 4600:2005, Appendix 1 of NAS) is limited to pure compression and pure bending. The situation of combined bending and shear as occurs in a continuous purlin system is not considered.

In order to extend the DSM to purlin systems, it is necessary to prescribe and calibrate a method for combined bending and shear. Eight different test series on purlin sheeting systems with single, double and triple spans and both uplift and downwards load cases as well as screw and concealed sheeting have been performed at the University of Sydney over a 10 year period. As many of these tests consisted of continuous lapped purlins where combined bending and shear occurred at the purlin section just outside the end of the lap, it is possible to use this test data to propose an extension to the DSM. Furthermore, calibration of the proposals using the limit states design methodology is included in the report.

This report makes two proposals for combined bending and shear, and calibrates them both for the full sets of vacuum rig test data.

Keywords
Cold-formed; High strength steel; Direct strength method; Effective width method; Vacuum test; Combined bending and shear; Reliability

Abstract
The resistances of steel I-section monorail beams to lateral buckling are difficult to assess because monorails are often not well restrained against twisting. Monorails are supported at intervals along the top flange, but are free along the bottom flange, except at supported ends where vertical stiffeners may restrain the bottom flange. The buckling resistance is increased by the loading which generally acts below the bottom flange and induces restraining torques, but it is not common to take advantage of this. The buckling resistance may also be increased by any restraints against lateral deflection and longitudinal rotation of the top flange at internal supports, but it is difficult to quantify their effects without analyzing the distortion of the monorail web. This paper analyses the influence of restraints on the elastic lateral buckling (without distortion) of monorails loaded at the bottom flange, and shows how this might be accounted for in design.

Keywords
Beams, bending, buckling, design, elasticity, member resistance,
moments, monorails, steel, torsion.

Abstract
A single angle steel beam is commonly loaded eccentrically in a plane inclined to the principal planes (Fig. 1), so that the beam undergoes primary bending and shear about both principal axes, torsion, and bearing at the supports. The strengths of such beams are affected by local buckling effects on their section resistances, and by lateral buckling effects and torsion on the interaction between the major and minor axis moments during biaxial bending.

This paper summarises the behaviour of single angle steel beams investigated in a series of recent papers. For these papers, the general case of unrestrained biaxial bending and torsion was simplified successively (Fig, 2) into restrained biaxial bending, lateral buckling, unrestrained biaxial bending, buckling and torsion, and biaxial bending and torsion.

The paper concludes that despite the apparent simplicity of single angle beams, their behaviour is often complex and their strengths difficult to predict. The papers summarised provide a design method which is rational, consistent and economical.

Keywords
Angles, beams, bending, buckling, design, elasticity, member resistance, moments, section capacity, steel, torsion.

Abstract
The elastic buckling stresses of channel sections with and without lips and subject to shear forces parallel with the web are determined where the computational modelling of the thin-walled steel sections is implemented by means of a spline finite strip analysis. Both unlipped and lipped channels are studied where the main variables are the flange width, different boundary conditions and shear flow distribution are considered in this study. The channel sections are also analysed at different lengths to investigate the effect of length/width ratio on the critical shear buckling stresses. Comparisons between cases and with classical solutions are included in this report.

Keywords
Shear buckling; Thin-walled channel sections; Lipped and unlipped channel sections; Spline finite strip method; Shear buckling capacity; Twisting and lateral buckling mode.

Abstract
Thin-walled section members can be subjected to axial force, bending and shear. In the cases of cantilever beams and continuous lapped purlins, where combined bending and shear occur at the purlin section just outside the end of the lap, thin-walled sections may buckle at a lower stress than if only one action was present without the other. The computational modelling of the thin-walled steel sections is implemented by means of a spline finite strip analysis to determine the elastic buckling stresses of channel sections subject to bending and shear alone and interaction relations under combined bending and shear. Both unlipped and lipped channels are studied where the main variables are the flange width, different boundary conditions and shear flow distribution. Comparisons between cases, and with classical solutions are included in this report.

Keywords
Shear buckling; Combined bending and Shear; Thin-walled channel sections; Lipped and unlipped channel sections; Spline finite strip method; Twisting and lateral buckling mode.

Abstract
This report describes an experimental program carried out at the University of Sydney to study the interaction of local and overall flexural buckling in stainless steel back-to-back channels under compression.

Two stainless steel alloys were considered: austenitic 304 and ferritic 404. Tests were carried out to determine the material properties. The results reveal nonlinear stress-strain behaviour with low proportionality limit, anisotropy and enhanced strength as a result of cold-working. 

24 columns were tested under an axial load, applied with a nominal eccentricity of L_e/1500. The length of the specimens varied between 500 mm and 3000 mm in 500 mm increments. Twin specimens were tested for each length. All columns were tested between pinned ends.

This report rectifies the lack of experimental data on local-overall interaction buckling in stainless steel columns with open cross-section. The results will be used in further research, specifically the development of a reliable finite element model, the assessment of the current design guidelines and the proposal of a direct strength design approach for stainless steel columns.

Keywords
Stainless steel, interaction buckling, local buckling, overall buckling, non-linear material, inelastic, anisotropy, cold-formed sections, back-to-back channels, doubly-symmetric cross-section.