Beam Bridge Damage Identification Method Based On Flexibility Curvature Matrix

Structural damage identification is one of the core contents of the bridge health monitoring system,and there are many identification methods.Because the damage index of flexibility type only needs low-order modes to perform damage identification,and low-order modes can be easily ensure accuracy in engineering measurements.The engineering application value is relatively high.Therefore,the damage index of flexibility curvature has attracted the attention of a large number of scholars and many research works have been carried out.In the paper,based on the uniform load surface curvature(ULSC)theory,a general form of weighted damage index is deduced,and different indicators can be obtained according to different weighted values,it can simplify some of the previous flexibility curvature indicators.Due to the existence of positive and negative offset in the calculation of ULSC,it has a certain impact on the damage identification effect.Some flexibility-based damage indicators may affect the calculation of the damage degree due to two curvature calculation.The paper proposed a new damage index,which is marked as the absolute diagonal of mode flexibility curvature(MFCAD).The new index directly calculates the frequency and mode shape without forming a flexibility matrix,which greatly simplifies the calculation.According to the relationship between displacement and stiffness,it is assumed that the damage has little influence on the modal distribution of the beam,ie,the modal distribution of the beam before and after damage is approximately the same.Because the damage degree cannot be effectively identified when directly use the mode shape for damage identification.In the paper,the damage degree of the index is calculated by using the curvature of the weighted flexibility matrix instead of the mode shape curvature.Based on the relative changes of the index before and after damage and the relationship between the nodal damage degree and the elemental damage degree,the calculation method of structural damage degree of the index is proposed.For statically determinate structure,the bending moment does not change before and after structural damage.For the statically indeterminate structure,the internal force redistribution phenomenon occurs after the structural damage,which will cause the calculation result to be lower than the actual situation.Therefore,the damage degree of the statically indeterminate structure is revised in the paper.The basic beam structural systems:simply supported beam,cantilevered beam,hinge supported at on end and fix supported at the other end beam,fix supported beam and continuous beam were used to analyze the damage location and damage degree of the new index.The results were compared with other indicators.The new index presented in the paper has advantages in damage location and damage degree identification.The index can perform good damage location and damage degree identification for a variety of structure types.In order to further verify the applicability of the new indicator,the application of new indicator was discussed by selecting examples of continuous beam with equal height,continuous beam with variable cross-section,continuous rigid bridge with single-limbed thin-wall piers and continuous rigid bridge with double-limbed thin-wall piers.The results show that the new index presented in the paper has a good effect on damage location and damage degree identification;the index can completely identify the damage location of the bridge,and the identification effect is good.The damage degree identification of the beam damage between the double-limbed thin-wall piers is not good due to the influence of shear deformation.The damage degree identification of the remaining bridge is correct.