A damage identification methodology considering shear deformation was presented in this paper to identify damage to semi-rigid frames with slender beams. On the basis of the successful identification of structural joint damage, the combined joint and member damage of the structure was identified. The objective function was formulated to minimize the discrepancies between the analytical and measured nodal displacements. Damage identification was performed on semi-rigid frame structures with different cross-sectional shapes, and the results were compared with those of ignoring shear deformation. Several frame structures were employed to verify the advantages and efficiency of the proposed method. The results demonstrate that the present method could significantly improve the accuracy of damage identification for semi-rigid frames compared with the method ignoring shear deformation.

Identifying the parameters of multispan rigid frames is challenging because of their complex structures and large computational workloads. This paper presents a stiffness separation method for the static response parameter identification of multispan rigid frames. The stiffness separation method segments the global stiffness matrix of the overall structure into the stiffness matrices of its substructures, which are to be computed, thereby reducing the computational workload and improving the efficiency of parameter identification. Loads can be applied individually to each separate substructure, thereby guaranteeing obvious local static responses. The veracity and efficacy of the proposed methodology are substantiated by applying it to three- and eight-span continuous rigid frame structures. The findings indicate that the proposed approach significantly enhances the efficiency of parameter identification for multispan rigid frames.

Shear deformation plays an important role in certain structures, and neglecting shear deformation can affect the accuracy of structural response. This paper proposes a non-destructive damage evaluation method that considers shear deformation, based on static response, for identifying corrosion in beam-like structures. The influence of shear deformation on nodal displacement for simply supported beams with different cross-sections was analyzed. The results indicate that even small errors yield inaccurate identification results when neglecting shear deformation. To solve this problem, analytical displacements of the structure were determined based on the Timoshenko beam theory, and the objective function was established. Additionally, the damage identification results were obtained by minimizing the objective function using the interior point method. Several progressively complex examples were used to demonstrate the effectiveness of the proposed method in identifying damage in beam-like structures.

Optimization-based damage identification in continuous rigid frame (CRF) bridges faces challenges. As the degrees of freedom of the structure increase, the complexity of the objective functions increases significantly, making convergence more difficult to achieve. This study introduces a stiffness separation method for damage identification in CRF bridges. This method decomposes the overall stiffness matrix of the bridge into the required stiffness submatrices, which greatly simplifies the objective function for identifying structural damage. By dividing the stiffness matrix into smaller stiffness submatrices, the proposed method reduces computational complexity and improves damage detection efficiency. Two CRF bridges are presented to verify the effectiveness of the proposed method.