Journal of Sound and <ibration (1999) 225(1), 153 } 170 Article No. jsvi.1999.2228, available online at http://www.idealibrary.com on DYNAMIC BENDING AND TORSION STIFFNESS DERIVATION FROM MODAL CURVATURES AND TORSION RATES J. MAECK AND G. DE ROECK Department of Civil Engineering, Division of Structural Mechanics, K.;. ¸euven, =. de Croylaan 2, B-3001 Heverlee, Belgium (Received 11 August 1998, and in ,nal form 26 February 1999) In order to maintain the reliability of civil engineering structures, considerable e!ort is currently spent on developing a non-destructive vibration testing method for monitoring the structural integrity of constructions. The technique must be able to observe damage, secondly to localize the damage; and "nally to give an idea of the severity of the damage. Within the framework of relating changes of measured modal parameters to changes in the integrity of the structure, it is important to be able to determine the dynamic sti!ness in each section of the structure from measured modal characteristics. A damaged structure results in a dynamic sti!ness reduction of the cracked sections. The dynamic sti!nesses provide directly an indication of the extension of the cracked zones in the structure. The dynamic sti!ness reduction can also be associated with a degree of cracking in a particular zone. In an experimental programme, a concrete beam of 6 m length is subjected to an increasing static load to produce cracks. After each static perload, the beam is tested dynamically in a free}free set-up. The change in modal parameters is then related to damage in the beam. The technique that will be presented in the paper to predict the damage location and intensity is a direct sti!ness derivation from measured modal displacement derivatives. Using the bending modes, the dynamic bending sti!ness can be derived from modal curvatures. Using the torsional modes, the dynamic torsion sti!ness can be derived from modal torsion rates. ( 1999 Academic Press 1. INTRODUCTION In the framework of developing a non-destructive vibration testing method for monitoring the structural integrity of constructions in civil engineering, a technique is elaborated to derive the dynamic bending and torsion sti!ness at a certain location of a structure using the measured mode shapes and the corresponding eigenfrequencies. One of the goals of non-destructive vibration testing is to relate a shift in measured modal characteristics to a change in material properties of the structure. 0022-460X/99/310153#18 $30.00/0 ( 1999 Academic Press