2010 Research Reports No R908-R913

Abstract
The report presents a study of the capacities of steel rack frames based on linear analysis (LA), geometric nonlinear analysis (GNA) and geometric and material nonlinear analysis (GMNIA). In the case of linear and geometric nonlinear analyses, the design is carried out to the Australian cold-formed steel structures AS/NZS4600. The study includes braced, unbraced and semi-braced frames, and compact and non-compact cross-sections. The report shows axial force and bending moment paths for geometric and geometric and material nonlinear analyses, and explains the differences observed in the design capacities obtained using the different types of analysis on the basis of these paths. The report provides evidence to support the use of advanced geometric and material nonlinear analysis for the direct design of steel rack frames without the need for checking section or member capacities to a structural design standard.

Keywords
Steel Storage Racks, Australian Standard, Advanced Analysis, Design.

Abstract
The isoparametric spline finite strip method (ISFSM) is an efficient numerical method which is mostly suitable for analysing prismatic structures. It is able to simulate complex geometries such as holes and can handle arbitrary types of boundary conditions and loadings. The present report extends the application of the ISFSM to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures.

The general theory of the ISFSM is briefly introduced. The formulations of the kinematics assumptions, the geometric mapping, the strain-displacement relations, and the equilibrium conditions are presented. In particular, the plasticity theory, the constitutive relations and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted.

The arc-length method and the line search technique have been successfully integrated to work as the main nonlinear solver, and evidence has shown that the incorporation of the latter is necessary for the efficient implementation of the present analysis.

The reliability and efficiency of the method are demonstrated by a number of numerical examples, including analyses of flat plates with different material plasticity models, a classical nonlinear shell problem, perforated flat and stiffened plates, and perforated stiffened channel section storage rack uprights.

Keywords
Isoparametric spline finite strip method, Material inelasticity, Geometric nonlinear analysis, Thin-walled structures, Folded plate, Perforations, Nonlinear buckling

Abstract
This research report presents comprehensive studies of the effects of uncertainties in material properties, initial geometric imperfections and joint stiffness on the ultimate system strength of multi-storey steel support scaffold systems through a rational statistical framework and a second-order inelastic finite element (advanced) analysis. A total of 36 stick-type steel scaffold systems with Cuplok joints in various configurations (different combinations of jack extensions, number of bays, and lift heights) are considered in the studies. The report also presents a reliability analysis of support scaffold systems to determine system resistance factors that can be used for the design by advanced analysis according to the LRFD statistical framework. The proposed system resistance factors based on the system target reliability index of 3.5 vary from 0.56 to 0.70, depending on the lift height and jack extensions.

Keywords
Probabilistic study, Reliability analysis, System strength, Advanced analysis, Scaffold systems

Abstract
Methods used for the design of steel beams supported at both ends are not well suited for the design of cantilevers against lateral buckling. The end restraints are very different for cantilevers, and the maximum displacements and twist rotations take place at the free ends, instead of near mid-span. Consequently, their buckling modes are very different to those of supported beams. The methods of allowing for the effects of the moment distribution on the elastic and inelastic buckling of supported beams use a mean of the moment distribution which is weighted to allow for the maximum deformations being near mid-span. These methods are clearly inappropriate for cantilevers whose deformations are greatest at the free ends.

Lateral buckling design methods for cantilevers are modifications of the methods for supported beams, but are of doubtful accuracy, and may be over conservative. In some cases there is little or no design guidance.

This paper summarizes information on the effects of the moment distribution and load height on the elastic buckling of cantilevers which can be used in the method of design by buckling analysis. It then extends a method of designing supported beams by inelastic buckling analysis to allow for the effects of the moment distribution on the inelastic buckling of cantilevers. This extended method is then used to provide improved design methods for cantilevers which are consistent with those for simply supported beams. A worked example is summarized.

Keywords
Analysis, cantilevers, design, inelasticity, lateral buckling, steel.

Abstract
The report describes numerical non-linear simulation, based on the finite element method (FEM) using the software package ABAQUS/Standard, of high strength cold-formed SupaCee sections in shear, combined bending and shear, and bending only. These high strength (450 MPa) C-profile steel sections called SupaCee contain additional return lips and web stiffeners which enhance the bending and shear capacity of the sections (Lysaght, 2003). They are used widely in Australia as purlins in roof and wall systems.

The results of nonlinear analyses by using the finite element method (FEM) depend heavily on the imperfection assumption for the analysis of the thin-walled members. Geometric imperfections are often taken as a scaled multiple of the eigenvalue modes. Different buckling modes (Mode 1 Anti-Symmetric and Mode 2 Symmetric) are assumed with different magnitude levels of imperfection as proposed by Camotim in Portugal and Schafer in the USA. Studies of the effects of boundary condition, element types as well as mesh size are also included.

This report summarises the results of the finite element nonlinear simulations of the tests on SupaCee sections performed at the University of Sydney on a variety of section sizes and thicknesses. The test series include predominantly shear (V), combined bending and shear (MV), and bending only (M) test series. The FEM results are compared with the tests to calibrate the imperfection magnitudes and modes against the tests.

Conclusions regarding the size and type of imperfection are made in the report. It is demonstrated that the finite element analysis can therefore be used to design and optimize thin-walled sections of high strength steel.

Keywords
Cold-formed; High strength steel; Direct strength method; Effective width method; Finite element method; Combined bending and shear; shear test.