Vibration-mode-based story damage and global damage of reinforced concrete frames

An attempt is conducted to explore the relationship between the macroscopic global damage and the local damage of shear-type RC frames. A story damage index, which can be expressed as multi-variate functions of modal parameters, is deduced based on the tridiagonal matrix of the shear-type frame. The global damage model is also originated from structural modal parameters. Due to the connection of modal damage indexes, the relationship between the macroscopic global damage and the local story damage is reasonably established. In order to validate the derivation, a case study is carried out via an 8-story shear-type frame. The sensitivities of modal damage indexes to the location and severity of local story damages are studied. The evolution of the global damage is investigated as well. Results show that the global damage is sensitive to the degree of story damage, but it's not sensitive to its location. As the number of the damaged stories increases, more and more modes will be involved. Meanwhile, the global damage evolution curve changes from the concave shape to the S-type and then finally transforms into the convex shape. Through the proposed story damage, modal damage and global damage model, a multi-level damage assessment method is established.