Detection of damage to bending structures using a crack index

The damage that can occur to structures by way of deformation in bending under the excitation of random forces (referred to hereafter as ‘bending structures') is considered a local state due to the harm caused by cracks. Its effects on the behaviour of the structure are discussed as discontinuity phenomena. For the simulation of such discontinuities, the bilinear stiffness reduction function, which results in asymmetrical behaviour of a damaged member when loaded in opposite directions, has been defined together with a corresponding crack index. For different damage scenarios, the effect of the non-linear behaviour of affected members has been investigated according to which damaged members can be identified by means of a crack index. The proposed damage identification method is not hampered by the existence of any kind of noise. The effectiveness and accuracy of the proposed method have been examined by applying a ‘closed-loop solution' to a six- and an eight-storey bending structure, using in each case an analytical model and different pre-defined damage scenarios. Taking into account these scenarios, several bilinear stiffness reduction functions were assumed not only for the column stiffness coefficient of one or more theoretically damaged storeys of the investigated structure, but also for the beam stiffness coefficient corresponding to one or more such storeys.