2011 Research Reports No R914-R921

Abstract
An experimental program was established at the University of Sydney to determine the coefficient of friction between various types of timber pallets and a typical Dematic beam rail. In addition, another test series was also carried out to measure the shear stiffness of those timber pallets. The outcome of the study can be used as a guideline for further design enhancement of the drive-in rack system. This report summarizes the test results and their possible implementations.

Keywords
Drive-in racks, steel storage racks, steel structures, finite element analysis, friction coefficient, shear stiffness.

Abstract
This report is concerned with the behaviour of drive-in steel storage racks under horizontal impact load in the down-aisle direction. Such impact loads due to forklifts striking an upright is a major cause of structural failure for drive-in rack systems.

The report investigates investigate the dynamic behaviour of a standard drive-in rack subjected to a down-aisle impact load. The effect of damping ratio, masses carried by the rack as well as the friction between the pallet and the rail track are investigated for impulse loading.

Keywords
Drive-in racks, steel storage racks, steel structures, dynamic, finite element analysis, design.

Abstract
This paper summarises a number of research studies on the torsion and buckling behaviour of beams which derive from a theory developed by Wagner, who extended Timoshenko’s treatment of the elastic buckling of I-section beams and columns to members of general thin-walled open cross-section. These studies include applications of the first-order Wagner theory to the buckling of beams and cantilevers, and of the second-order Wagner theory to the large rotations and post-buckling behaviour of beams.

Keywords
Beams, bending, buckling, large rotations, post-buckling, steel, thin-walled sections, torsion.

Abstract
OpenSees is an object-oriented framework for finite element analysis. A key feature of OpenSees is the ability to integrate existing libraries and new components into the framework without the need to change the existing code. The non-linear beam-column element theory in OpenSees is based on the assumption that torsion is uniform through the length of the member and non-uniform warping torsion is excluded. In this report, a corotational mapping for three-dimensional analyses of doubly symmetric beam-column elements with warping effects is incorporated into OpenSees. Both a local linear strain assumption and a second order approximation of the Green-Lagrange strains are considered in the formulations of the beam elements at local level. Numerical examples are presented to demonstrate the accuracy of the proposed elements by comparisons with results from the literature and commercial softwares.

Keywords
Co-rotational formulation, Warping, OpenSees, Thin-walled structures.

Abstract
For shear, the design of sections for strength is usually governed by the web plate subjected to shear force and undergoing shear buckling, or yielding in shear or a combination of the two. For webs with relatively high depth-to-thickness ratios, the shear stress distribution in the web after buckling changes and significant postbuckling strength may occur as a result of the development of a diagonal tension which is called “Tension Field Action” (TFA). Recently, the full set of shear test results for the plain lipped C- and SupaCeeĀ® sections performed at the University of Sydney show that the post-buckling strength was attributed to TFA which was provided by the increased transverse restraints created by bolted connections attached to loading stiffeners over the full depth of the web panel at the supports and loading point. This improved the post-buckling strengths of the web in shear.

Firstly, the results of finite element nonlinear simulations are compared with tests where bolted connections not over the full depth of the web panel were used to validate the FE method. Then the range of test data described previously is extended using finite element models, by reducing the bolting at support and loading points in the test data to provide further guidance on the availability of TFA in particular. Design equations are provided for Tension Field Action.

Keywords
Cold-formed sections; High strength steel; Direct strength method; Effective width method; Shear Test; Tension field action; Finite element method.

Abstract
Thin-walled sections in compression and/or bending may undergo one of the three modes of local, distortional or overall (Euler) buckling, or combinations of these. The Semi-Analytical Finite Strip Method (SAFSM) developed by YK Cheung has been widely used in computer software (THIN-WALL, CUFSM) to develop the signature curve of the buckling stress versus buckling half-wavelength for a thin-walled section under compression or bending to allow identification of these modes. The minimum points on the signature curve are now used in the Direct Strength Method (DSM) of design of cold-formed sections in the American Specification and Australian/New Zealand Standard for cold-formed steel structures.

Plank and Wittrick (1974) included shear in the SAFSM theory for calculating the stiffness and stability matrices by using complex mathematics. The complex mathematics is needed to allow for the phase shifts in the buckling modes (eigenvectors) for sections under shear.

This paper summarises the theory then applies it to the buckling of channel sections in pure shear. Signature curves for shear are developed for channel sections and compared with classical solutions, and those produced by the Spline Finite Strip Method (SFSM) previously published by the authors. The effect of including a web stiffener on the signature curve and buckling modes is demonstrated.

Keywords
Cold-formed channel sections; Signature curve; Buckling analysis; Complex mathematics; Finite strip method; Shear buckling; Spline finite strip method.

Abstract
Methods of designing steel monosymmetric I-beams against lateral buckling are not well supported by research. For this paper, the inelastic buckling of monosymmetric steel I-beams under moment gradient was studied and compared with design recommendations.

For welded beams in uniform bending, inelastic buckling is initiated at moments which are often close to those which cause first yield in the compression flange. Once initiated, the inelastic buckling resistance remains constant as the slenderness decreases until strain-hardening occurs. For hot-rolled beams in uniform bending, the inelastic buckling resistance increases almost linearly as the slenderness decreases.

Three regimes are significant in the inelastic buckling resistances of hot-rolled monosymmetric beams under moment gradient, depending on which flange yields first and the end moment ratio.

Simple linear approximations of good accuracy were developed for designing hot-rolled monosymmetric beams in uniform bending, while less accurate but conservative approximations were developed for moment gradient. The use of these approximations was illustrated by a worked example.

Keywords
Beams, bending, buckling, design, inelastic, monosymmetry, steel, yield.

Abstract
Very different strengths are predicted by two different methods of designing steel cruciform columns. Both methods require design against local and flexural buckling, and while one method also requires design against torsional buckling, the other does not.

Investigations of the elastic local and torsional buckling and post-buckling of cruciforms columns show that these two modes are virtually identical.

The first yield and inelastic buckling approaches often used to formulate methods of designing columns against flexural buckling are extended to the torsional buckling design of cruciforms. These extensions show that it is sufficient to use local buckling design to guard against torsional buckling.

It is found that design methods which make separate checks against local and torsional buckling are unnecessarily severe, and are equivalent to making the same strength reduction twice. Instead, it is sufficient to ignore the torsional buckling of cruciforms provided design checks are made against local buckling as well as flexural buckling.

Keywords
Buckling, Columns, Cruciforms, Design, Flexure, Post-buckling, Steel, Torsion, Yield