Influence of initial cracks on the frequency of a 60-year-old reinforced-concrete box beam

Cracking is a common form of damage in reinforced-concrete (RC) beams. Cracks affect the frequency and deflection of RC beams. Although a model for the natural frequencies of RC beams with one or two flexural cracks has been proposed, a study of the effect of numerous initial flexural cracks on RC beams is still lacking. In the present study, the frequency and deflection of a 60-year-old RC box beam with four initial flexural cracks were tested, and the natural frequency of the RC box beam was theoretically analysed using Rayleigh's method. Theoretical and test results showed that: (a) the natural frequency and stiffness of the RC box beam with four initial flexural cracks decreased by 39·0 and 62·8%, respectively; (b) the model for the natural frequency of the RC box beam with N initial flexural cracks was proposed based on the theoretical and test results; (c) the deflections of the RC box beam with four initial flexural cracks obtained from Branson's method and Eurocode 2 were both close to those from the test; and (d) Branson's method for calculating the deflection of beams with four initial flexural cracks was conservative.