Uncertainty in determining the deformed shape of beams using the conjugate beam method

The deformed shape of a structure can be defined as the curvature of the centroid line of the structure after deformation. This curvature can be used to indicate abnormal behavior in structures - particularly those with beam-like configurations. The deformed shape is an extremely useful tool in the field of structural health monitoring, as it can help with evaluating the serviceability and overall stability of a structure. However, monitoring the deformed shape over long periods of time has proven difficult to achieve with necessary levels of accuracy. The deformed shape can be analyzed using both direct and indirect monitoring techniques. Direct monitoring techniques are sensitive to environmental factors, and therefore accurate deformation measurement using such methods is difficult to achieve. Double integration of a structure's curvature, a method of indirect monitoring, is also limited in its scope, as it involves manually correcting the deformed shape after integration, and is difficult to use if sensors are not evenly spaced on the structure. Other indirect methods also require detailed knowledge of boundary conditions in order to determine the deformed shape. However, alternative methods exist for indirectly determining the deformed shape of the structure. The aim of this paper is to analyze the deformed shape of the beam via the conjugate beam method, which applies the measured curvature as a load on the structure in order to determine its deformed shape. This study presents an analysis of the uncertainties and errors associated with the conjugate beam method, as well as an evaluation of the number of sensors needed when using this method in order to obtain the desired degree of accuracy. The error in this method depends on the type and positioning of loading on the structure, the magnitude of the curvature of the structure, and the number of sensors that the structure is equipped with. This method is also tested on data from a laboratory specimen and a real structure in order to validate the method as a way of accurately determining the deformed shape.