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Abstract Often encountered in practice are, conventional types of thin rectangular plates (simply supported plate, flat slab, ...etc) that are used as floors in buildings for common purposes, rectangular ribbed plates stiffened by orthogonal ribs, and the rectangular plate having a rectangular hole with edges parallel to the plate edges that are, usually, used for large areas and heavy concentrated loads in industrial building. The previous methods that produce the exact solutions of the above mentioned cases of plates, most of them, except the finite element analysis method, is valid only for specified loading and boundary conditions at the plate edges. Herein, a mathematical modeling is prepared by using the fini te difference analysis and successive over relaxation method: it is used to analyze the behavior of the previous types of plates which are subjected to uniformly distributed loading, or concentrated loading at some points along the plate surface. The results of this model for some types of rectangular plates (solid plate, ribbed plate or having rectangular hole) with different boundary condi tions and different types of vertical loading are confirmed by comparing them wi th the results of the previous works. And it is used to make the parametric study for simply supported orthogonal ribbed plate to investigate the effect of torsional rigidity and stiffness rigidity of ribs on the resulted internal forces of plates due to transversely uniform loading, also it is used to study the distribution of the internal forces within the plate surface around the rectangular hole due to vertical loading. |