Framework for Flexural Rigidity Estimation in Euler-Bernoulli Beams Using Deformation Influence Lines

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Abstract
Structural degradation is an inevitable part of a structure’s service life. Detecting structural impairments and assessing their nature is a significant challenge. Degradations reduce structural system stiffness and subsequently affect system deformations. An appropriate structural health index that is able to capture these changes in deformation and relate them to a structural system stiffness may help engineers to adequately rate structural condition. This paper outlines a theoretical framework for the utilization of static deformation influence lines for estimating the flexural rigidity of Euler-Bernoulli beams. In the proposed technique, the relationship between the second derivative of the deformation influence line and the flexural rigidity for both statically determinate and indeterminate beam structures is presented. The proposed method provides a flexural rigidity estimate (FRE) over the entire span that is based on a single measurement location and estimates both the location and severity of impairments, regardless of the location of the measurement or the damaged zones. Noisy analytical simulations are presented with noise levels of 0%, 0.5%, 1%, 2%, 3%, and 4%; in all cases the modeled damage is quantified and localized using the FRE. A laboratory experiment is also presented that validates the theoretical framework.

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