Application of residuals from regression of experimental mode shapes to locate multiple crack damage in a simply supported reinforced concrete beam

The objective of the study was to propose an effective, simple and reliable technique to determine the location of triple-crack damage in a simply-supported reinforced concrete beam using the method of mode shape regression. The study required simply supported finite element reinforced concrete beam models to be constructed with one as control and another as the test beam with predetermined triple-cracks along the length of the beam. The technique necessitated the performance of linear and Eigen analyses on the control beam, and nonlinear analysis on the beam with triple-cracks. Residuals obtained from regression of the mode shape using the Chebyshev series rational on the modal frequencies and transformation and application into the fourth order centered finite divided difference formula were used. The use of the regressed mode shapes for the reinforced concrete beam model showed large residuals around the areas of the crack damage. The results showed that the method was successful in determining the locations of the triple cracks and was comparable with other techniques proposed by other researchers in terms of its simplicity and reliability.

► Regression of the frequency mode shape could be used to detect crack damage.
► Chebyshev’s series rational is suitable to use for the curve fitting process.
► Curve-fitting process is effective and sensitive even for small damage.
► Method is versatile and useful as an aid to experimental design.