engleski

Mathematical model for calculating eigenvalues of continuous bridge ggirder in transversal direction

The article describes mathematical model of RC continuous bridge girder in transversal direction. Chosen disposition of the bridge is continuous beam over three spans (0, 7L+L+0, 7L) with two single-column-bent, and two different cases of end supports: pinned support at the ends of the bridge and free translation supports at the end of the bridge(console in the the transversal direction). Columns are pinned to bridge girder in transversal direction and have free rotation at the top. Vibration of the structure is described with partial differential equation of IVth order (wave equation) as well as with partial differential equations of the theory of elasticity. Columns are modeled in transversal direction as springs with stiffnesess which correspondent to the console bending stiffness. Shear stiffness, as well as rotation and translation of the column foundation are neglected, but it can be easily incorporated in the calculations through reduction of the stiffness. After introduction of the boundary condition, system of partial differential equations of IV order is reduced to system of 12 linearly independent equations with 12 unknowns. The solution of the system is found in the roots of matrix. Since determinant of the system matrix is very complex, it is not possible to find direct solution. One of the iterative method must be used. Newton s method in this case.

concrete bridge; transversal direction; partial differencial equations; wave equation; frequency

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