Use of Ritz method for damage detection of reinforced and post-tensioned concrete beams

Abstract

Damage-induced changes in modal characteristics can be detected using experimental modal analysis. In this article, based on changes in natural frequency, mode shapes, and damping ratios, a methodology for detecting damage location and severity is presented. The damage was induced by application of point load at half span location on the reinforced and post-tensioned concrete beams. The load was gradually increased to obtain different crack patterns to be used in simulation of damage scenarios. Experimental modal analysis was performed on the undamaged and damaged beams. The natural frequency and mode shapes were used to determine the location of damage. The approach is developed at an element level with a conventional finite element (FE) model by Ritz method, which is called Ritz damage detection method (RDDM). The mathematical model for both damped and undamped damaged structures have been established through the eigenvalue equations. The singular value decomposition (SVD) technique is used for determination of damage or sound index. These indexes are sensitive to the change of dynamic characteristics due to damages. This approach is applied to five simply supported post-tensioned concrete beams. The numerical results show that the exact location and severity of damage for different simulated damage scenarios could be efficiency found by the present methodology.