Evaluation of error of deformed shape determined from strain measurements and double integration of curvature

Excessive deformations of beam-like structures and structural members (beams) may result in user distress, adversely affect neighbouring structural members, and even imperil structural safety. Therefore, determination of deformed shape of beams is of particular interest. Direct on-site long-term monitoring of the deformed shape is difficult, mostly due to limitations in available practical sensing technologies. As an alternative, indirect methods can be applied. As an example, strain can be monitored on-site and in long terms (e.g., using fibre optic sensors), converted into curvature by using appropriate equations, and curvature can be numerically double integrated to obtain the deformed shape. However, this method faces an important challenge, which is an accurate evaluation of error in the determined deformed shape. The error depends on several factors such as the accuracy measures of the monitoring system, geometrical and mechanical properties of the monitored beam, and in particular on the topology of the sensor network – number and spatial distribution of strain sensors. This research proposes a method for evaluation of error in deformed shape determined from strain measurements and double integration of curvature. As a result, it is possible to design sensor network, i.e., to determine minimum number of sensors needed to realize a wanted accuracy in deformed shape. Important finding is that error at a point depends on the value of curvature at that point, a constant related to curvature distribution along the beam, and the square of longitudinal distance between the sensors (i.e., density of the sensors). The method was validated in a laboratory and on a real structure – Streicker Bridge.