Identification of cable tension through physical models and non-contact measurements

Determining the static and dynamic response of structural cables is a mechanical problem of theoretical and practical interest in many aspects of civil engineering. In particular, the cable tension is a fundamental variable to be assigned in direct design problems, as well as a fundamental unknown to be assessed in inverse identification problems. The present paper outlines an original analytical strategy for identifying the axial tension of inclined sagged cables in cable-stayed structures, based on static measurements. Starting from the classic formulation of an inextensible, perfectly flexible model of catenary suspended cables, a perturbation-based low-order polynomial approximation of the static configuration under self-weight is achieved (direct problem). The quadratic and cubic coefficients of the configurational function are tension-dependent quantities, whose analytical expressions can be mathematically inverted to define consistent parametric formulas for tension identification (inverse problem). The experimental assessment of the static cable configuration, which serves as input for the inverse problem, is provided by the geometric data acquired by modern and noninvasive techniques of non-contact measurement. The methodological advantage is that the laser scanner acquisition of point cloud models can efficiently and economically provide precise and redundant three-dimensional geometric descriptions of the cable configuration, which is suitable for a highly accurate and statistically robust data treatment. Lastly, the identification strategy is successfully applied to a real-scale structure, for tension identification in the stays of a cable-stayed footbridge. The results are discussed from a qualitative and quantitative viewpoint, and finally validated through a comparison with the outcomes of a dynamic identification procedure based on high-speed camera acquisitions.