2006 Research Reports No R864-R873

Abstract
In this report, unlike the most previous investigations for wave-induced soil response, a simple analytical model for the random wave-induced soil response is established for an infinite or finite thickness. Two different wave spectra, B-M and JONSWAP spectra, are considered in the new model. The influence of random wave loading on the soil response is investigated by comparing with the corresponding representative regular wave results through a parametric study, which includes the effect of the degree of saturation, soil permeability, wave height, wave period and seabed thickness. The maximum liquefaction depth under the random waves is also examined. The difference on the soil response under the two random wave types, B-M and JONSWAP frequency spectra, is also discussed in the present work.

Keywords
Soil response, Seabed liquefaction, pore pressure, effective normal stress, shear stress, random wave, regular wave

Abstract
In this study, the dynamic response of an infinite cylindrical hole embedded in a porous medium and subjected to an axisymmetric ring load is investigated. Two scalar potentials and two vector potentials, displacements, stresses and pore pressures in the frequency-wave-number domain. Using the general solutions and a set of boundary conditions applied at the hole surface, the frequency-wave-number domain solutions for the proposed problem are determined. Numerical inversion of the Fourier transform with respect to frequency as well as the axial wave number generates the time-space domain solution. The numerical results of this paper indicate that the dynamic response of a porous medium surrounding an infinite hole is dependant upon many factors including the parameters of the porous media, the location of receivers, the boundary conditions along the surface of the hole as well as the load characteristics.

Keywords
Porous media, infinite cylindrical hole, Biot’s theory, Fourier transform

Abstract
The report derives the differential equations for the overall bifurcation of locally buckled point-symmetric columns. It is shown that flexural buckling about the minor and major principal axes are coupled in a locally buckled point-symmetric column whereas the buckling modes are uncoupled in a non-locally buckled column. The governing equations are solved for simply supported and fixed-ended columns and applied to Z-sections. Overall bifurcation curves are obtained for five Z-sections with increasingly slender flanges. It is shown that local buckling reduces the elastic torsional buckling load more so than the flexural buckling load for Z-sections, and that local buckling can cause a mode switch from the flexural to the torsional mode in Z-sections with very slender flanges.

Keywords
Z-sections, steel structures, local buckling, torsional buckling, flexural buckling, interaction buckling, finite strip analysis, bifurcation analysis.

Abstract
The bifurcation equations for locally buckled point symmetric sections are derived in a companion report [1]. In the present report, two series of experiments are reported, one on narrow flange Z-sections and one on wide flange Z-sections. The main objective of the tests was to validate the bifurcation load predictions derived in [1] against experimental values. A further objective of the tests on narrow flange sections was to investigate the change in the direction of overall buckling, as predicted bu the theory, from principal axis direction to non-principal directions. A further objective of the tests on wide flange sections was to investigate the possible change of the critical overall buckling mode from a flexural mode to a torsional mode as a result of local buckling. Agreement is generally found between analytical and experimental results.

Keywords
Z-sections, steel structures, tests, local buckling, torsional buckling, flexural buckling, interaction buckling, bifurcation analysis, finite strip analysis, finite element analysis.

Abstract
The residual mechanism of wave-induced pore water pressure accumulation in marine sediments is re-examined. Analytical approximation is derived using a linear relation fore pore pressure generation in cyclic lading, and mistakes in previous solutions (Cheng, et al., 2001. McDougal, et al., 1989) are corrected. A numerical scheme is then employed to solve the case with a non-linear relation for pore pressure generation. Both analytical and numerical solutions are verified with experimental data (Clukey, st al., 1983), and provide a better prediction of pore pressure accumulation than the previous solution (McDougal, et al., 1989). The parametric study concludes that the pore pressure accumulation and use of full non-linear relation of pore pressure become more important under the following conditions: (1) large wave amplitude, (2) longer wave period, (3) shallow water, (4) shallow soil and, (5) softer soils with a low consolidation coefficient.

Keywords
Pore pressure accumulation, shear stress, cyclic loading, liquefaction

Abstract
This report describes the experimental investigation of a series of compressive tests on a stiffened-cross shape section fabricated from cold-formed high strength steel of thickness 0.42 mm and nominal yield stress of 550 MPa. The complex shape has been chosen so that it has a local buckling mode, two distinct distortional buckling modes, and a flexural-torsional mode. The first distortional buckling mode has a shorter buckle half-wavelength and hence classified as a short half-wavelength distortional buckling mode, while the other distortional mode has a much longer buckle half-wavelength and is classified as a long half-wavelength distortional buckling mode. The compression tests were carried out in a 300kN capacity SINTEC testing machine over a range of lengths with fixed-ended conditions. The varying lengths were chosen so as to observe the buckling modes and the possibility of interaction existing design standards. The methods include the Direct Strength Method (DSM) recently incorporated in the North American Specification and the Australian Cold-Formed Steel Structures Standard AS/NZS 4600. When compared to the existing methods, the test results indicated that at intermediate and longer specimen lengths, the interaction of local distortional buckling modes has a significant effect on the strength of the sections.

This report presents the procedures taken to design the complex shape and the experiments carried out to obtain the geometric imperfections and material properties of the specimens and the test results. New design methods are proposed for the local buckling Direct Strength Method curve as well as for the distortional buckling strength curves so as to account for the effects of interaction of local and distortional buckling modes.

Keywords
Cold-formed, High strength steel, Local buckling, Distortional buckling, Interaction buckling, Intermediately-stiffened elements

Abstract
The buckling modes of cold-formed thin-walled sections with edge stiffeners are generally in the forms of the short half-wavelength local buckle, the intermediate half-wavelength distortional buckle and the long half-wavelength flexural/flexural-torsional buckle.  These buckling modes usually occur at distinct lengths.  However the possibility of the interaction of buckling modes may be present at certain lengths.  This may be due to the distortional mode interacting with the local buckling mode, both of which may be in the post-buckling range.

Local buckling has been well researched and accounted for in design standards with an effective width model developed by Von Karman et al (1932) to produce a simple model of the post-buckling reserve strength.  Distortional buckling research has made much headway in recent years at the University of Sydney by Hancock (1985), Lau and Hancock (1990), Kwon and Hancock (1992) and Yang and Hancock (2004), at Johns Hopkins University by Schafer (2002) and the Technical University of Lisbon, Portugal by Silvestre and Camotim (2004).  What has been known for some time is that the distortional mode has a post-buckling reserve strength which is generally less than that of local buckling.  However, the nature of this post-buckling reserve is not clearly understood, particularly what precipitates failure.

Some research has been done to understand the buckling mode interaction of local and distortional.  This is usually carried out by analytically separating the combined modes into its composition of individual modes.  Generalised Beam Theory (GBT) uses explicit analytical expressions to analyse the influence of local and distortional buckling modes.  Another method currently being developed is modal identification and decomposition, where a numerical method is employed to calculate the critical loads for the pure buckling modes.

The paper discusses the analysis of post-buckling in the distortional mode of a thin-walled section with edge stiffeners and the effect of interaction of buckling modes on failure loads. The analysis is based on the longitudinal stress development and redistribution using the finite element package ABAQUS.  This methodology whereby the longitudinal stress redistribution is studied is similar to the work of Von Karman et al, in predicting the post-local buckling behaviour.

Keywords
Stress distribution; local buckling; distortional buckling; interaction buckling; postbuckling behaviour; finite element analysis

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 us a major cause of structural failure for drive-in rack systems.

The report investigates the load path through the rack structure by the use of finite element analysis. A series of parametric studies is carried out to study the influence of the number of bays in the down-aside direction on the behaviour of the system. A simplified design model is also developed and compared with finite element predictions of displacements and internal forces, generally showing good agreement.

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

Abstract
The report describes tests on connections featuring self-drilling screws and gaps between the connected parts. Gap typically occur when using inserts of a smaller dimension than the overlapping section, e.g. a tube. In such connections, the screws are subjected to the combined action of shear and bending.

Tests were conducted on single and multiple screw connections loaded in shear. The gap was systematically increased from zero (pure shear) to about 1.3 times the screw diameter. Further gap-tests were conducted where the screw was inserted non-removed. These situations occur frequently in practice, particularly when access restrictions prevent perpendicular screw insertion or impede the control of the torque. Based on the tests, design equations are proposed for screw connections with gaps. A reliability analysis is included deriving an appropriate capacity factor for screw connections with gaps.

Keywords
Self-drillings screws, tubular sections, gap joints, cold-formed structures, test, design, reliability analysis

Abstract
This report describes an experimental program carried out at the University of Sydney to study the interaction of local and overall buckling in stainless steel lipped channels under compression. Three stainless steel alloys were considered: 304, 430 and 3Cr12. A number of 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.  

A total of 36 column tests were completed with the aim of studying local-overall interaction buckling. The test specimens were designed to fail in the inelastic range to incorporate the effect of the gradual loss of material stiffness into the test results. 18 specimens were tested under a nominally concentric load. The remaining specimens had the load applied with a nominal eccentricity of L_e/1500 towards the web. Since the cross-section is singly symmetric, the interaction phenomenon is further affected by the shift in effective centroid resulting from local buckling.

This report rectifies the lack of experimental data on local-overall interaction buckling in singly symmetric stainless steel columns. The results will be used in further research, specifically in the development of a reliable finite element model and in the assessment of the current design guidelines.

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