טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentHamed Ehab
SubjectDynamic Frequencies of Prestressed Bridges with
Prestressing, Cracking and Transverse
Deformations Effects
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Emeritus Yeoshua Frostig


Abstract

This study deals with the free vibration behavior of prestressed concrete bridges. Its main contribution lies in its ability to predict reliable response of the free vibration behavior of bridges. It has been done by examining the effect of three parameters that affect the natural frequencies and mode shapes of bridges: 1. Prestress forces, 2. Cracks and nonlinear behavior of concrete and steel, 3. Transverse deformations of the cross section (distortion) of the bridge. A nonlinear analytical model has been developed for the free vibration behavior of prestressed beams and bridges. It has been proved, based on the derived equations of motion, that prestressed force does not affect the natural frequency of prestressed beams as opposed to some papers in the literature. A nonlinear incremental analysis for the free vibration behavior of cracked prestressed beams with bonded cables is conducted. The model determines the natural frequencies of prestressed beams at different levels of damage. A drastic reduction in the natural frequencies is observed as the cracked region increases. Hence, it is recommended to limit the allowed loads on the damaged bridges in accordance with the level of damage observed. A general mathematical approach is developed for the free vibration analysis of girder and box bridges. The governing equations of motion and the corresponding boundary and continuity conditions are derived via the variational principle of virtual work following Hamilton’s principle. It appears that the transverse deformations significantly reduce the natural frequencies of bridges, and cause the torsional mode shapes to become the fundamental ones. Hence, it is recommended to consider the transverse deformations in the static and dynamic analysis of bridges, in order to achieve reliable designed bridges.