Damage Detection of Flexural Member by Estimated Moment Diagram

This study considers an analytical method to detect the damage location from the moment diagram calculated by the external forces and the forces required for obtaining the same deflections as the measurement deflections. The measured deflections must be a part of displacements to restrict the static behavior of the damaged beam. The constraint forces acting at measurement points are derived by minimizing the cost function of the displacement change between the undamaged and damaged beams. It is shown that the damage exists near the location that the moment ratio to be expressed by the moment values of the undamaged and damaged beams increases abruptly. However, closely neighboring damages can be found by increasing the number of finite elements and measurement points. The validity of the proposed method is illustrated in an application.