UBC Theses and Dissertations
Computer analysis of planar and spatial grid frameworks. Kinra, Ravindar Kumar
The application of the stiffness approach to the exact analysis of both planar and spatial grid frameworks of any complexity and high degree of statical indeterminacy is presented. Ordinarily, even the simplest planar grid is such a highly redundant structure that it cannot be analyzed rigorously by manual methods without recourse to some simplifying assumptions at the expense of accuracy. In general, most authors neglect the effect of member torsional rigidities in order to reduce the size of the problem and make use of the plate theory for the purpose of evaluating deflections. Matrix methods of analysis, however, remove the necessity for resorting to any such approximations and prove extremely convenient for computer application. The fundamentals of the stiffness approach are explained in complete detail and applied to the analysis of rectangular planar grids. For the purpose of comparison, example grids given by Ewell, Okubo ɛ Abrams and Woinowsky-Krieger have been analyzed by the stiffness method and the comparative results are tabulated. The principle of orthogonal transformation, which is an essential part of the analysis of diagrids and spatial grids is fully described and its application demonstrated by various numerical examples including a skew bridge, a cantilever diagrid and a hyperbolic paraboloid space grid. The application of stiffness analysis has been further extended to problems involving temperature changes and support settlements and, also, the procedure to reduce the size of symmetrical structures is described. A special successive elimination and matrix partitioning technique has also been introduced in order to enable the solution of extremely large numbers of simultaneous equations within the limited core memory capacity of digital computers, by taking advantage of the band form of the stiffness matrices of structures. A complete Fortran II computer program for the IBM 1620 and a 1405 disk file is given, as well as, sample inputs and outputs of the IBM 1620 and 7090. After the first attempts by Engessers in 1889 and Zschetzsche in 1893, a great variety of hand calculation methods have been developed for the analysis of planar grid frameworks. Among these, Hendry ɛ Jaeger's harmonic analysis and C. Massonet's anisotropic plate theory methods are the most convenient and easily applicable, in the opinion of the author. The basic assumptions and underlying principles of both these methods are outlined and the procedure of analysis is illustrated by means of a numerical example in each case. Furthermore, in order to obtain an idea of their accuracy several planar grids with 2 to 6 longitudinals have been analyzed by the stiffness method, harmonic analysis and anisotropic plate theory. In every case, two solutions have been performed, assuming the constituent members of the grid to possess first zero and then maximum values of torsional rigidity. The comparative values of the load distribution factors for the longitudinal and transversal bending moments have been tabulated.
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