2002 Research Reports No R812-R824

Abstract
The design of unbraced steel angle section beams against biaxial bending and torsion requires the ability to predict their lateral buckling strengths when bent about the major principal axis. Present design code formulations of lateral buckling strength are based on research on doubly symmetric I-section beams, and may be inappropriate for monosymmetric and asymmetric angle section beams.

This paper presents close approximations for the elastic lateral buckling moments of equal and unequal angle section beams loaded by uniformly distributed loads which act away from the shear centre. Small and large twist rotation elastic analyses of angle section beams with initial twist rotations are used with interaction equations for the biaxial bending section capacities to investigate present design code formulations for lateral buckling strength. It is found that these code formulations are unnecessarily conservative, especially at high slendernesses, where the moment capacities predicted by them may be less than the minor axis section capacity instead of greater. An improved formulation is proposed which is simpler and more economic than the present formulations.

The use of the elastic lateral buckling approximations in the improved design moment capacity formulation is demonstrated in a worked example.

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

Abstract
The report describes the development of numerical models for analysing stainless steel plates in compression. Material tests on coupons cut in the longitudinal, transverse and diagonal directions are included as are the results of tests on stainless steel plates. Detailed comparisons are made between the experimental and numerical ultimate loads, load-displacement curves and load-strain curves. It is shown that excellent agreement with tests can be achieved by using the compressive stress-strain curve pertaining to the longitudinal direction.

The effect of anisotropy is investigated using elastic-perfectly-plastic material models, where the anisotropic material model is based on Hill’s theory. The models indicate that the effect of anisotropy is small and that it may not be required to account for anisotropy in the modelling of stainless steel plates in compression.

Keywords
Plates, stainless steel, finite elements, plasticity, anisotropy, tests.

Abstract
A theoretical study of the behaviour of structured soil is presented. A new model, which is referred to as the Structured Cam Clay model, is formulated by introducing the influence of soil structure into Modified Cam Clay. The proposed model is hierarchical, i.e., it is identical to the Modified Cam Clay soil model if a soil has no structure or if its structure is removed by loading. Three new parameters describing the effects of soil structure are introduced and the results of a parametric study are also presented. The proposed model has been used to predict the behaviour of structured soils in both compression and shearing tests. By making comparisons of predictions with experimental data and by conducting the parametric study it is demonstrated that the new model provides satisfactory qualitative and quantitative modelling of many important features of the behaviour of structured soils.

Keywords
Calcareous soils, clays, fabric, structure, constitutive relations, plasticity.

Abstract
This report describes a series of compression tests performed on stub columns fabricated from cold-formed high strength steel plates with nominal yield stress of 550 MPa. The steel is classified as G550 to Australia Standard AS1397. The test results presented in this report are the first stage of an Australian Research Council research project entitled “Compression Stability of High Strength Steel Sections with Low Strain-Hardening”. The tests included lipped-square and hexagonal sections, including 94 box-shaped fix-ended stub columns. The purpose of these tests was to determine the influence of low strain hardening of G550 steel on the compressive section capacities of the column members.

The results of the successful stub column tests have been compared with the design procedures in the Australian/New Zealand Standard for Cold-Formed Steel Structures and recent (1999) Amendments to the American Iron and Steel Institute Specification. As expected, the greatest effect of low strain hardening was for the stockier sections where material properties play an important role. For the more slender sections where elastic local buckling and post-local buckling are more important, the effect of low strain hardening does not appear to be as significant. This is contrary to recent design proposals in the USA where it was proposed that the more slender sections would be more greatly influenced by low strain hardening. A simple proposal for improved design capacity is given in the report.

Keywords
Stub-column; High Strength Steel; Compression; Box-shaped

Abstract
This report describes a series of compression tests performed on long columns fabricated from cold-formed high strength steel plates with nominal yield stress of 550 MPa. The steel is classified as G550 to Australia Standard AS1397. The test results presented in this report are the second stage of an Australian Research Council research project entitled “Compression Stability of High Strength Steel Sections with Low Strain-Hardening”. A total of 28 long columns, which were made from two thicknesses of sheet steel (0.42 mm and 0.6 mm), were tested. A box shaped section was between pinned ends over a range of lengths.

This report shows the comparison of loads obtained experimentally with those predicted on the basis of AS/NZS4600 and the AISI specification including Supplement No.1, 1999. The finite element program, ABAQUS, was also used to simulate the column behaviour. For sections which undergo local instability at loads significantly less than the ultimate loads, the column design rules in AS/NZS 4600 and the AISI Specification are unconservative if used in their current form for G550 steel. Proposals for improved column design of high strength slender sections are proposed in this report.

Keywords
Long-column; High Strength Steel; Compression; Pin-ended; LBsection; Local buckling; Overall buckling

Abstract
The report describes a series of experimental tests on tensile coupons cut from the butt welded brace-to-chord connections (T-joints) between rectangular hollow sections of equal width. The aims of the tests are to investigate whether there are any serious difficulties in producing satisfactory butt welds in the large root gaps resulting from the rounded corners of chord sections, and to establish the welding procedures that enable such connections to be pre-qualified. Rectangular hollow sections of various thicknesses and corner radii are used, resulting in root gaps ranging from 0.8 mm to 9.4 mm. Four different types of joint preparations involving the use of backing strips, fill bars, purging gas or no preparations at all are experimented with. The connections are fabricated using the Gas Metal Arc Welding (GMAW) and the Manual Metal Arc Welding (MMAW) processes. In general the GMAW process results in better quality butt welds, whether the root gap is narrow or large. A narrow root gap may present a problem if the MMAW electrode is not small enough and the brace edge is not bevelled. It is concluded that SP (Structural Purpose) butt welded connections between equal width cold-formed rectangular hollow sections which are fabricated using the GMAW and MMAW processes may be pre-qualified provided the root gap is at least 3 mm and 4 mm respectively. The prequalification applies to the horizontal and flat positions for the following weld preparations: no specific preparation, the use of backing strip and the use of purging gas on the inside of the tube. The pre-qualification does not apply to joints welded using fill bars.

Keywords
Butt welds, welded connections, rectangular hollow sections, welding, pre-qualification

Abstract
Details of a dual-actuator rig developed for testing rectangular plates simply supported on three sides, with the remaining (longitudinal) edge free, under combined uni-axial compression and in-plane bending are presented. Particular attention is given to ensuring a constant strain eccentricity to the loaded ends, as opposed to a constant load eccentricity, in order to determine the post-buckling behavior and ultimate load and moment capacities of unstiffened thin-walled elements. Strain gradients varying from pure compression to pure bending are facilitated. The results of 80 tests on unstiffened plate specimens described herein are used to establish effective width equations for unstiffened elements under stress gradients in a companion report.

Keywords
Unstiffened plates, stress gradients, plate tests, plate buckling, post-buckling strength, effective widths

Abstract
Current American design provisions treat unstiffened elements under stress gradients as if they were uniformly compressed for effective width calculations. Australian, British and European design provisions allow accurate calculation of the elastic buckling coefficient, however the same effective width equation for compressed elements is used for elements with stress gradients. In all cases, the design provisions produce conservative bending capacities for sections containing unstiffened elements under stress gradients. This report presents a design method for calculating the effective width of these elements, based on plate test results of unstiffened elements under strain gradients varying from pure compression to pure bending. It is shown that both elastic and plastic effective widths may be derived from the test results, and effective width methods based on both principles may be used for design.

Keywords
Unstiffened elements, stress gradient, elastic effective width, plastic effective width, plate tests, design

Abstract
This report presents a general design procedure for calculating the moment capacity of sections containing unstiffened elements under stress gradients. The method uses the design equations for calculating both elastic and plastic effective widths of unstiffened elements under stress gradients, based on plate test results, presented in a companion report. Current international design provisions allow the capacity of sections that contain unstiffened elements under stress gradients to be calculated on the basis of initiation of yielding in the section. This report presents non-iterative methods for the calculation of the capacity, when both elastic and plastic effective width equations are used to establish the effective section. The methods are shown to be in good agreement with experimental data of I-sections and plain channels in minor axis bending. Particular attention is given to the effect of both the elastic buckling coefficient used in the effective width method, and the use of inelastic considerations, on the bending capacity of sections that contain unstiffened elements under stress gradients. Specific design proposals are presented in the form of amendments to the current Australian standard for cold-formed steel structures.

Keywords
Moment capacity, unstiffened elements, effective width, first yield, inelastic reserve, I-sections, channel sections

Abstract
The report presents a plate strength formulation applicable to metal in general, notably metals with nonlinear stress strain curves, such as aluminium and stainless steel alloys. The formulation is based on a generalised Winter-curve featuring two material-dependent constants. Analytic expressions are derived for these constants so that they can be determined for given material properties. The material properties are assumed to be expressed in terms of the Ramberg-Osgood parameters.

The generalised formulation allows the plate strength equation to be determined for a given alloy, requiring only the Ramberg-Osgood parameters. The strength curves obtained using the generalised formulation are shown to compare well with finite element results.

The strength equations apply to uniformly compressed plates simply supported along all four edges. The validity ranges for the material properties are 3≤n≤100 and 0.001≤e≤0.003 where e=σ0.2/E0. The plates are assumed to be free of residual stress.

Keywords
Plates, nonlinear metals, design, strength, plasticity, finite elements.

Abstract
The loads applied to angle beams usually act out of the principal planes so that they cause simultaneous biaxial bending about both principal axes. The general practice for designing unbraced beams against biaxial bending is to consider the separate failure modes of either in-plane bending or lateral buckling under bending about the major principal axis, and in-plane bending about the minor principal axis, and then to use an interaction equation to combine the two principal axis strengths. However, the interaction equations provided by many codes for designing against biaxial bending are largely derived from research on doubly symmetric I-section beams, which may be inappropriate for angle section beams, while the lateral buckling rules of these codes appear to be in error for non-uniform bending with loads acting away from the shear centre.

This paper investigates the biaxial bending of unbraced steel angle beams. The biaxial bending of compact equal angles in uniform bending is considered first, and a simple interaction equation is developed for their design which utilises recent proposals for lateral buckling design. A corresponding interaction equation is developed for the design of semicompact and slender equal angles. Suggestions are then made for extending these to the biaxial bending of unequal angles under general shear centre loading, and finally, a worked example illustrating the method is provided.

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

Abstract
Attempts to extend practical advanced analyses of the in-plane behaviour of 2-D steel frames under in-plane loading to out-of-plane behaviour have been largely unsuccessful because of difficulties in modeling the effects of yielded zones, load heights, interactions between twist and axial force and moments, and end warping restraints.

Practical advanced analyses of out-of-plane behaviour need to be able to account for the influences of moment and axial force distributions, load heights, and end restraints on elastic and inelastic lateral buckling, and to be consistent with the code formulations of beam and column out-of-plane strengths.

It is proposed in this paper that the advanced analysis of 2-D frames for which local buckling is prevented be simplified by first carrying out an in-plane analysis using one of the presently available plastic hinge methods, and then by using a practical advanced analysis of the out-of-plane behaviour which is based on an inelastic lateral buckling analysis which includes allowances for residual stresses and initial crookednesses and twists. The paper makes a number of suggestions of how to develop such a practical method of advanced out-of-plane analysis for 2-D frames for which local buckling is prevented.

Keywords
Advanced analysis, frames, design, elasticity, imperfections, lateral buckling, plasticity, steel, strength.

Abstract
This paper develops a simple advanced method of designing steel members against out-of-plane failure, in which reduced elastic moduli are used in an out-of-plane buckling analysis to model the effects of high moment, residual stresses and geometrical imperfections on yielding. The reduced moduli are derived from the basic beam and column strength curves of the Australian steel code AS4100 (SA, 1998).

The strengths predicted for simply supported beams in uniform bending are exactly the same as those of AS4100, while those for simply supported columns are extremely close. The strengths predicted for simply supported beam-columns with equal and opposite end moments are a little higher than the less conservative predictions of AS4100, and are very close to the basic beam and column strengths when these are plotted against a consistent generalized slenderness.

The strengths predicted for simply supported beams under double curvature bending are somewhat less than those of the AS4100 method of design by buckling analysis, while those for beams with central concentrated loads acting at or away from the shear centre are very close, and those for end restrained beams under uniform bending and for sway columns are generally a little higher.

While the method has been developed from and compared with the Australian code AS4100, it may be modified for any other modern code for the design of steel structures. It may be more widely applied to two-dimensional frames with in-plane loading, as part of a simple method of advanced analysis in which separate assessments are made of the in-plane and out-of plane strengths.

Keywords
Advanced analysis, beams, beam-columns, columns, design, imperfections, lateral buckling, residual stresses, steel, strength, yield.