Reconstruction of the area-moment-of-inertia of a beam using a shifting load and the end-slope data

Abstract

In recent years, much concern has been reported about the condition of US infrastructure, particularly the bridges. These concerns have brought attention to the area of structural health monitoring and its significance in averting tragedies. The main focus of this study was to develop a mathematical model that could be used to determine the changes in the structural characteristics such as cross-sectional area-moment-of-inertia from the knowledge of a shifting load and the end-slope data. In this investigation, the cross-sectional area-moment-of-inertias of a scaled model of simply supported steel bridge are reconstructed using a shifting load scheme and the corresponding end-slope data. The end-slope data used in this inverse problem were numerically generated using the finite element method. The end-slope data and the loading were then used in the inverse problem to reconstruct the cross-sectional area-moment-of-inertias for the model. To solve the inverse problem, the solution domain was discretized into finite number of elements and nodes. A shifting uniformly distributed load was applied to each element, and the beam equation was integrated to create a set of linear equations in terms of loading and end-slope differences that could be solved simultaneously to recover the area-moment-of-inertia for each element. Comparison of the inverse solutions with the direct solutions confirms that the variations in the area-moment-of-inertia for a bridge cross section can be reconstructed, with a good accuracy, from the knowledge of the shifting load and end-point slopes.