Damage identification of cracked reinforced concrete beams through frequency shift

The safety evaluation of reinforced concrete (RC) bridges is of the outmost importance, both for the early warning of critical states below a given safety margin and owing to plan maintenance cycles of the infrastructural network. Structural health monitoring based on dynamic testing has become widespread in the last 20 years, leading to very effective operational algorithms able to extract valuable structural features from the recorded signals. However, although in principle it is possible to identify position and severity of the damage by using a finite element model, still some identification issues are unresolved due to the non-linear nature of the oscillations of a cracked beam. In fact, the available experimental data show, for a given damage pattern, a significant underestimation of the natural frequencies given by cracked beam numerical models. This paper presents an approximate solution for the problem of a vibrating damaged RC beam with opening–closing (breathing) cracks. The solution is based on the static equivalence of the kinetic energy and allows incorporating most of the features of a beam loaded above the cracking limit and oscillating under the self-weight with breathing cracks. The comparison with a wide data set collected in the literature points out the predictive capability of the developed analytical formulas. An independent test confirms the theoretical results.