Murray J. Clarke

Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements

Abstract It has been pointed out in a previous paper by the authors [1] that conservative internal moments of a spatial beam are of the so-called fourth kind, and that the rotation variables which are energy-conjugate with these moments are vectorial rotations. Vectorial rotations of a spatial Euler–Bernoulli beam have nonlinear relationships with its transverse displacement derivatives [2] . This implies that strictly speaking, the first partial derivative of the strain energy with respect to a transverse displacement derivative is not a bending moment (even if we ignore the axial deformation), and that modifications should be introduced to the conventional Hermitian shape functions employed in the Rayleigh–Ritz method of finite element analysis. On the other hand, the neglect of the rotational behaviour of nodal moments has led to an incorrect stability matrix in the literature, and it is shown through numerical examples that this incorrect stability matrix cannot detect the flexural-torsional buckling load of spatial structures in which the members are not connected collinearly. The validity of the Wagner hypothesis on the coupling of axial and torsional deformations for a spatial beam-column is illustrated through a numerical example. Finally, one issue related to the Updated Lagrangian formulation addressed in this paper is the oft-used assumption of a straight configuration at the last known state.

Advanced analysis of steel building frames

Abstract The paper describes advanced analysis as defined in the Australian limit states design specification, AS 4100-1990. Advanced analysis may be used for the second-order inealstic analysis and design of frames in which the members are compact and have full lateral restraint. Some aspects of the inclusion of residual stresses, geometrical imperfections and capacity factors in advanced analysis are discussed. An advanced analysis based on the finite element method and utilising a distributed plasticity formulation has been developed at the University of Sydney and is used to perform numerical studies of the behaviour of simple structural elements and frames, including the effects of residual stresses and geometrical imperpections. Based on the results of the analyses, some observations on the importance of including imperfections in the advanced analysis of steel building frames are made.

Finite Element Modelling of Eight-Bolt Rectangular Hollow Section Bolted Moment End Plate Connections

Publisher Summary This chapter investigates the behavior of tubular bolted moment end-plate connections. The analyses were conducted using the commercially available finite element package ABAQUS. Brick elements were chosen to form the basis of the models used, as this type of element is easily adapted to model the interfaces between the connecting surface and the end plates, and bolts. The models simulated the behavior of the eight-bolt connections well, with the mean, and standard deviation of the ratio of the experimental and numerical ultimate moments being 0.96 and 0.07. The eight-bolt connections utilizing the Square Hollow Section (SHS) were generally predicted to be stiffer than the corresponding test results. This additional stiffness may be due to the inadequate modeling of the bolts. Although, the predicted ultimate loads generally corresponded well with the experimental results, the numerical analyses did not specifically model the effects of punching shear (although the effects of shear yielding were modeled in the nonlinear material behavior). The deformation and yielding patterns developed in the models correlated well with the experimental results, and the yield line analyses developed in the corresponding theoretical models.

Simple design procedure for the cold-formed tubular top chord of stressed-arch frames

Abstract Stressed-arch frames are characterized by a posttensioning procedure which is used to erect the frames from an assembled configuration at ground level to a final erected shape. During the erection process, the cold-formed tubular top chord becomes curved and is usually stressed into the inelastic range. Consequently, the strength of the tubular top chord under the additional axial compression arising from service loading cannot be assessed rationally using conventional methods for the analysis and design of steel structures built from either hot-formed or cold-formed members. This paper proposes and validates a simple design procedure for the cold-formed tubular top chord of stressed-arch frames. The possible provisions of the American Iron and Steel Institute Load and Resistance Factor Design (AISI LRFD) Specification for the design of the top chord are described briefly, although the basis of the proposed design procedure is the advanced analysis provisions of the Australian Standard for Steel Structures, AS4100–1990. In order to accommodate the rational and economical design of unconventional cold-formed steel structures such as stressed-arch frames, for which conventional analysis/design approaches are inappropriate, it is suggested that the advanced analysis/design philosophy should be incorporated into the proposed Australian Limit States Standard for cold-formed steel structures.