Instability of three-dimensional frameworks

Khumbah, Fidelis Morfaw (1992) Instability of three-dimensional frameworks. University of Southampton, Doctoral Thesis.

Abstract

Recently, there has been an increasing use of thin-walled open-section primary and secondary members in structural frameworks. These members are often connected off-centre, offering eccentric restraints to each other. Such restraints are capable of both causing local deformation to the members meeting at the point of restraint, and influencing the mode of instability of the framework. The object of this study is to investigate the effect of such restraints on the stability of such frameworks. To do so, a methodology for analysing arbitrary frameworks connected off-centre is developed, implemented on a FORTRAN computer system, and investigated experimentally. A 14x14 non-linear element stiffness matrix composed of the twelve standard, and two warping, degrees of freedom is developed. In order to ensure compatibility of displacement at the restraint point, a procedure for transforming this matrix, together with the externally applied forces, to coincide with the point of restraint is developed. This is implemented in a FORTRAN program, accounting for the orientation of the member in space. The program is thoroughly tested by analysing existing examples of beams, columns, and 2- and 3-D frameworks connected at their centroids. The structures are subject to axial and bending loading, supported in various ways, and exhibit a wide variety of buckling characteristics. The eigenvalue eigenvector approach is used in the program, employing the Vianello-Stodola technique, to obtain the stability mode and load. Two methods of evaluating the local flexibility matrix of a section are devised. One method applies a statically zero force-stress system of loading to an ANSYS beam model made from area elements. The resulting displacements obtained from an analysis of such a model are considered as the local flexibility of the section at the point of application of the force. In the second method, the local flexibility matrix is obtained from the displacements obtained when a unit force is applied to the ANSYS model, and those obtained when the model is analysed as having a rigid cross-section. A method of combining this matrix to the 14x14 stiffness matrix is devised and implemented in the program.

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