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In this work, we present a two-step procedure for damage identification in beam structures exploiting modal curvature changes. The reconstruction of modal curvatures requires the knowledge of several mode shape components along the analyzed beam. This requirement is practically unachievable when mode shapes are identified via vibration-based monitoring using a limited number of accelerometers. To overcome this limitation, in the first step of the proposed procedure, we perform a mode shape expansion employing a reduced subset of measured modal components. The remaining measured components are used as control parameters to formulate a first hypothesis on damage location and extent. For this purpose, the expansion procedure is performed considering a number of possible damage scenarios, consisting of a location and a severity (loss of stiffness) of the damage. Using the Total modal assurance criterion (TMAC), we select the expanded modes with the highest degree of correspondence with the measured control components. These expanded modes are thus associated with a first guess of the damage location and severity. In the next step, this initial damage identification is verified through the computation of a modal curvature-based damage index. If the curvature-based damage identification confirms the previous identification, the damage location and extent are determined. The procedure can be easily extended to identify multiple simultaneously damaged elements. The approach is numerically validated using a benchmark beam modeled via finite elements, investigating the influence of different parameters such as noise, position of the control components and beam discretization on the identification success rate. Finally, the procedure is tested on two experimental specimens: a steel beam, with three different damage configurations and a concrete beam progressively damaged with multiple damage locations.

Despite more than a century of continuous effort, shear still remains one of the few areas of research into fundamentals of the behavior of concrete structures where dispute remains amongst researchers about the mechanisms that enable the force flow through a concrete member and across cracks. This paper firstly presents the results of 9 full-scale prestressed concrete I-shaped beams subjected to a four-point bending test until failure. Two stereo-vision digital image correlation (DIC) systems were used to discretely measure three-dimensional displacements in both zones where a shear force exists. A numerical technique has been adopted to generate optimized patterns for DIC and the resulting speckle pattern was applied onto each specimen using a stencil printing technique. Using the sectional shear design procedure from Eurocode 2, a severe underestimation of the experimentally observed shear capacity was found. Therefore, a parametric nonlinear finite element (FE) model was constructed to further investigate the mechanical behavior. The ability of the FE model to reconstruct the observed structural behavior was validated using the experimental data concerning failure load, failure mode and (full-field) displacement data. Finally, based on the numerically obtained stress fields, an internally statically indeterminate truss model was proposed which clearly visualizes the flow of forces and accurately describes the observed failure load and failure mode. A simple relationship between the applied shear force and the amount of shear force carried by the shear reinforcement was proposed. The proposed relationship was validated using the reported experimental data.

Damage can be detected by vibration responses of a structure. Damage changes the modal properties such as natural frequencies, mode shapes, and damping ratios. Natural frequency is one of the most frequently used damage indicators. In this paper, the natural frequency is used to monitor damage in a free-free beam. The modal properties of the intact free-free beam are identified based on a setup of 15 accelerometers. A finite element model is used to model the free-free beam. Three models are considered: beam (1D), shell (2D), and solid (3D). The numerical models are updated based on the first five bending natural frequencies. The free-free beam is damaged by a rectangle cut. The experiment is re-setup and the model properties of the damaged beam are re-identified. The cuttings are modeled in the numerical simulations. The first five numerical bending natural frequencies of the damaged beam are compared with the experimental ones. The results showed that the 1D beam element model has the highest errors, while the 2D and 3D models have approximately the same results. Therefore, the 2D representation can be used to model the damaged beam for fast computation.