1993 Research Reports No R669-R683

Abstract
An investigation of geometric imperfections and buckling displacements in thin-walled steel decking panels is presented. Measurements were carried out along the full length of several brake-pressed specimens subject to local and distortional buckling in the compression flanges. the measurements were performed using optical levelling and close range photogrammetric techniques. Both methods provided data on the magnitudes of displacements normal to the plane of each plate. However, only photogrammetry yielded coordinates within a three dimensional reference system. the sets of displacements were analysed using spectral analysis techniques to determine imperfection and buckling characteristics.

Both optical levelling and close range photogrammetry were evaluated as methods for the detection of imperfections and the measurement of buckling displacements. the measuring precision of each technique was determined and a statistical assessment was made of the reliability of spectra obtained from each method. Optical levelling was found to be more precise for the measurement of out-of-plane displacements and yielded more useful spectra. Close range photogrammetry was found to be suitable for the determination of buckling displacements.

Abstract
This paper presents a nonlinear inelastic analysis of the biaxial bending and torsion of thin-walled steel beam-columns which is based on the principle of virtual work. the effect of geometric nonlinearity is developed using position vector analysis. Approximations are not made in the early stage of the development, and thus some significant terms for buckling and postbuckling analysis are retained. the von Mises yield criterion, the associated flow rule and the hardening rule are employed in formulating the elastic-plastic constitutive matrix for the material inelasticity. Inelastic uniform and non-uniform torsion are incorporated in the formulation as well as the linear and nonlinear geometric effects of the loads.

A corresponding finite element model for the nonlinear incremental analysis of biaxial bending and torsion of thin-walled beam-columns is presented by using the principle of virtual work. Numerical results in a companion paper (Pi and Trahair, 1993) indicate that the model presented is capable of making accurate nonlinear analyses including post-buckling analyses.

Abstract
In a companion paper, a nonlinear inelastic analysis of the biaxial bending and torsion of thin-walled beam-columns was presented. Approximations were not made in the early stage of the development, and thus some significant terms were retained. the von Mises yield criterion, the associated flow rule and the isotropic hardening rule were employed in formulating the elastic-plastic constitutive matrix for the material inelasticity. Inelastic uniform and non-uniform torsion as well as the linear and nonlinear geometric effects of the loads were incorporated in the formulation.

This paper uses the finite element procedure developed in the companion paper to investigate numerically the in-plane and out-of-plane elastic and inelastic behaviour of I-beams under different loadings. the problems studied include the large deflection in-plane elastic and inelastic behaviour of columns and beam-columns, torsion of beams and beam-columns, eccentric and inclined loading of beams, the effects of initial crookedness and twist on the lateral buckling strength of beams, and the post-buckling flexural-torsional behaviour of beams. the strength of steel I-beams is also studied.

The numerical results obtained indicate that the procedure developed is capable of carrying out an accurate nonlinear analysis including post-buckling analysis. It is demonstrated that ignoring some significant terms may lead to an overestimation of buckling loads, poor predictions of the post-buckling behaviour, and failure to find the correct maximum load capacity.

Abstract
This paper presents a theoretical study of the torsional buckling strengths of cruciform columns. the influences of both initial geometric imperfections and residual stresses are investigated. A non-linear elastic torsion theory based on simple beam-column theory is presented and used for the predictions of the torsional behaviour up to first yield. For the behaviour beyond the first yield, a non-linear finite element model is developed which is able to make a complete inelastic load-twist analysis. It is found that both initial twists and residual stresses can significantly reduce the ultimate torsional buckling strengths of cruciform columns.

Abstract
Joints can occur in tubular structures where the main member is subjected to a bending moment rather than an axial force, particularly for rigid jointed frames. A model of the strength of T-joints in Rectangular Hollow Sections (RHS) with b < 1.0 subject to combined bending and concentrated force is developed based on experimental observations of joint tests performed by the authors. the action in the chord (moment) rather than the chord normal stress is used in the development of the interaction curves. the reduction of the plastic moment capacity of inclined yield lines under axial force is considered in the study. This reduction is based on a new model for inclined yield lines under axial force recently developed by the authors.

The predicted interaction curve for the case where b =0.5 is compared with test results of the authors. A design formula is derived based on the plastic mechanism analysis for T-joints with b < 1.0 under combined bending and concentrated force.

Abstract
A series of laboratory tests on a commercial thin-walled roll-formed steel deck exhibiting two modes of elastic buckling as well as flange curling is described. A test rig was developed for the programme in order to approximate the boundary conditions implicit in a comparative numerical model and prevent premature failure due to localised stressing at the specimen ends. the decking was loaded in pure bending and its performance studied to the point of ultimate failure. the test specimens were taken from a normal production run of panels from a cold roll-forming mill.

The test series described in this report is the third in a programme carried out to determine the effectiveness of intermediate stiffeners in controlling buckling modes. Other factors affecting the structural performance of the decking, such as residual stress, material properties and flange curling, were also investigated and are described.

The experimentally determined buckling stresses are found to be comparable with studies performed using a computer analysis based on the finite strip method in which local and distortional buckling modes are prdicted. Estimates of flange curling deflections based on the Eurocode 3/Annexe A design code are found to be comparable to measured values of deflections. Test results are compared with code-based predictions of the ultimate moment capacity of each panel.

Abstract
A series of laboratory tests on commercial thin-walled roll-formed steel decking panels exhibiting serveral modes of elastic buckling as well as flange curling has been performed. the product was loaded in pure bending and its performance studied to the point of ultimate failure. the specimens were taken from a normal production run of panels from a cold roll-forming mill.

The test series described in this report is the fourth in a programme carried out to determine the effectiveness of intermediate stiffeners in controlling buckling modes. Other factors affecting the structural performance of the decks, such as residual stress, material properties and flange curling, were also investigated.

The experimentally determined buckling stresses were found to be comparable and studies performed using a computer analysis based on the finite strip method in which local and distortional buckling modes were predicted. A test rig was developed for the programme in order to approximate the boundary conditions implicit in the numerical model and prevent premature failure due to localised stressing at the specimen ends. Test results are compared with Australian design standard AS1538-1988.

Abstract
Thin-walled cold-formed profiled steel decking panels with intermediate stiffeners may exhibit distortional buckling involving membrane straining within the stiffener. Local buckling in the flat plate elements within the flanges and webs may also occur. Varying degrees of post-buckled strength reserve may be encountered in sections undergoing local and/or distortional buckling. the extent of post-buckled strength reserve, as well as the ultimate moment capacity of the panel, are of interest to designers in their efforts to produce more efficient sections.

Ultimate moment results for 27 profiled decking specimens tested in bending are compared in this report with estimates derived using a number of design standards. the standards used were the AISI Cold-formed Steel Structures Specification 1991, Eurocode 3/Annexe A (1992 draft) and Australian Standard AS1538-1988. Several additional methods for predicting the ultimate moment capacity have been proposed recently and these are also compared with the test results. the experimental results summarised and compared in this report present an opportunity to validate a variety of design methods, particularly their application to panels composed of high strength thin-gauged steels.

Abstract
A number of methods of pile group settlement prediction are reviewed and compared for idealised soil profiles. the influence on group behaviour of lateral non-homogeneity of the soil and non-linear pile-soil response are examined and found to have compensating effects.

A distinction is made between the values of Young’s modulus along, between, and below the pile group, and some correlations with the results on in-situ penetration test results are summarised.

Two methods of group settlement calculation, the interaction factor method and the equivalent raft method, are applied to three published case histories. It is found that the interaction factor method can give very satisfactory predictions of group settlement and load distribution for a small pile group, but that the equivalent raft method is more reliable for groups containing a large number of piles.

Abstract
In this paper a coupled finite and boundary element formulation is developed for the analysis of excavation in jointed rock. the presence of joints in the rock mass has been included implicitly by treating it as an appropriate anisotropic elastic continuum. the boundary element formulation for an anisotropic medium is briefly discussed. Good agreement has been found between numerical and analytical solutions for several example problems demonstrating the accuracy of the present formulation. Numerical solutions are also presented for the problems of a deep circular tunnel and a basement excavated in a variety of jointed rock masses.

Abstract
A non-linear inelastic analysis of the non-uniform torsion of I-section beams is presented in this paper. Large twist rotations are included in the geometry non-linearity. the non-linear equilibrium equations of beams in non-uniform torsion have been derived and a finite element procedure has been developed based on the analysis.

The elastic-plastic behaviour of beams in non-uniform torsion is studied using the finite element procedure and the results are compared with tests. It is found that I-section beams have much larger torsional capacities than can be predicted by linear plastic collapse analysis, and that torsional failure occurs not by the formation of a mechanism but by the tensile rupture of the flanges. A method is proposed for calculating the full plastic non-uniform torque for practical design purposes.

Abstract
The problem of fully coupled consolidation and heat flow around a rigid cylindrical heat source buried in clay has been studied. the governing equations of the problem are summarised in the paper and a finite element time-marching scheme to obtain an approximate solution to the governing equations is described. the stress-strain behaviour of the skeleton of the saturated soil has been represented by both a linear elastic model and the Modified Cam clay soil model. the results of a limited parametric study are presented with the aim of understanding the major mechanisms of soil behaviour close to buried canisters of hot radioactive waste. A range of soil properties has been included in the study, and the effects of soil disturbance during canister emplacement have also been considered.

Abstract
The report describes welded connection tests which were performed on C350L0 Rectangular Hollow Sections. the thickness of the RHS sections varied from 1.6 mm to 3.0 mm. Both butt welds and transverse fillet welds were tested, where the tension load was perpendicular to the direction of the weld. the test results lare compared with existing Australian, American, Canadian and European design formulae. Proposed design formulae are given. the reliability analysis method is used to calibrate the existing and proposed design formulae.

Abstract
The report describes welded connection tests which were performed on C350L0 Square and Rectangular Hollow Sections (SHS and RHS) with a thickness ranging from 1.6 mm to 3.0 mm. Longitudinal fillet welds were tested. the test results are compared with existing Australian, American, Canadian and European design formulae. the effect of the direction of loading, the weld length, the end return welds and the orientation of an RHS section on the weld strength are studied. Proposed design formulae are given. the reliability analysis method is used to calibrate the existing and proposed design formulae.

Abstract
The inelastic combined bending and torsion of I-section beams is investigated in this paper using the finite element method. the elastic-plastic load-deformation relationships of beams under combined bending and torsion are determined by taking into account the effects of large deformations, material inelasticity, and initial conditions of residual stresses and geometric imperfections. the interactions between in-plane bending, lateral buckling, and torsion are studied.

The effects of secondary bending actions about the minor axis caused by torsional rotations are important for the interaction between bending (with flexural-torsional buckling) and destabilising torsion. Interaction equations for the design of I-section beams against combined bending and free torsion, and against combined flexural-torsional buckling and destabilising torsion are proposed. It is found that a commonly quoted circular interaction equation for combined bending and torsion does not always provide a true lower bound for I-section beams.