Flexural Stiffness Determination Using Mode Shape Derivative

Flexural stiffness of a single load-induced crack is determined. Modal analysis is performedon the beam prior and after each load stage. Mode shapes are extracted and eigenvectorsused to determine the mode shape equations. Global flexural stiffness is derived by utilizingthe regressed variable λ and the local flexural stiffness is derived by applying the centeredfinite- divided-difference formula on the regressed data. The global stiffness decreases with increasing severity of the crack. Results compared with values computed using the loaddeflection plot showed similar trends. The algorithm may be used as a technique for detecting crack damage in reinforced concrete.