STATIC ANALYSIS ON MODELS OF CONTINUOUS ORTHOTROPIC THIN-WALLED PRISMATIC SHELL STRUCTURES
The paper presents a linear static analysis on continuous orthotropic thin-walled shell structures simply supported at the transverse ends with a random deformable contour of the cross section. The external loads can be random as well. The class of this structures involves most of the bridges, scaffold bridges, some roof structures etc. A numerical example of steel continuous structures on five spans with an open contour of the cross-section has been solved. The examination of the structure has used the following two computation models: a prismatic structure consisting of isotropic strips, a plates and ribs, with considering their real interaction, and a smooth orthotropic plate equivalent to the structure in the first model. The displacements and forces of the structure characterizing its stressed and deformed condition have been determined. The results obtained from the two solutions have been analyzed. The study on the structure is made with the force method in combination with the analytical finite strip method (AFSM) in displacements. The basic system is obtained by separating the superstructure from the understructure at the places of intermediate supports and consists of two parts. The first part is a single span thin-walled prismatic shell structure; the second part presents supports (columns, space frames etc.). The connection between the superstructure and intermediate supports is made under random supporting conditions. The forces at the supporting points in the direction of the connections removed are assumed to be the basic unknowns of the force method. The solution of the superstructure has been accomplished by the AFSM in displacements. The structure is divided in only one (transverse) direction into a finite number of plain strips connected to each other in longitudinal linear nodes. The three displacements of the points on the node lines and the rotation around those lines have been assumed to be the basic unknown in each node. The boundary conditions of each strip of the basic system correspond to the simply support along the transverse ends and the restraint along the longitudinal ones. The particular strip of the basic system has been solved by the method of the single trigonometric series. The method is reduced to solving a discrete structure in displacements and restoring its continuity at the places of the sections made in respect to both the displacements and forces. The two parts of the basic system have been solved in sequence under the action of single values of each of the basic unknowns and with the external load. The solution of the support part is accomplished using software for analyzing structures by the FEM. The basic unknown forces have been determined from system of canonic equations, the conditions of the deformations continuity on the places of the removed connections under superstructure and intermediate supports. The final displacements and forces at a random point of a continuous superstructure have been determined using the principle of superposition. The computations have been carried by software developed with Visual Fortran version 5.0 for PC.