Determining the deformed shape of beams using the conjugate beam method and strain measurements

Determining the deformed shape of a structure is an important aim of Structural Health Monitoring (SHM), as it can indicate damage or abnormalities in the behavior of structures. Moreover, the deformed shape is a parameter that is present in all beamlike structures. The deformed shape can be described as the shape of the centroid line of the structure after deformation, and is a result of loading patterns on the beam. Currently, options for determining the deformed shape of the structure include direct external measurement, for example, with radar, lasers, camera imaging, or GPS, or by indirect derivation from internally measureable parameters, such as strain and curvature. Accurate direct long-term monitoring is frequently difficult to achieve mainly due to the effects of environmental factors. Certain indirect methods of analyzing the deformed shape, such as the double integration of curvature, require specific knowledge of a structure's boundary conditions. This paper applies and analyzes another indirect monitoring technique for determining the deformed shape: the conjugate beam method. The main aim of this study is to evaluate the errors in using the conjugate beam method for determining the deformed shape. The error in this method depends upon the loading configuration, curvature magnitude, and quantity of sensors on the structure. Finally, the conjugate beam method is validated using laboratory test data and data collected from a real structure.