Extraction of horizontally curved beam influence lines based on a unilateral step-by-step loading inversion algorithm

Abstract

The influence line is widely used as one of the main characteristic indicators for bridge health monitoring. However, horizontally curved bridges have bending and torsion coupling, and it is difficult to extract the influence line of its lateral distribution. To address this problem, an influence line extraction method based on the unilateral step-by-step loading inversion algorithm is proposed in this paper, which obtains the unilateral wheel-induced influence line by obtaining the increment of the influence line affected only by the additional overturning moment. The influence lines during loading are extracted using Tikhonov regularization, which effectively improves the stability of the results. Using a modified analytical method, horizontally curved beams under statically indeterminate structures are analyzed to obtain the inner and outer wheel bending moment and torque influence line algorithms. A horizontally curved beam vibration and deformation test bed is constructed for step-by-step loading experiments. The results show that the strain influence line under unilateral step-by-step loading is increasing. The deviations between the theoretical influence lines of the inner and outer wheels and the actual influence lines obtained using the RMSE evaluation index are 0.0072 and 0.0047, which proves that the strain influence line extraction algorithm of the unilateral wheel is basically consistent with the trend of the theoretical influence line under the horizontally curved beam of the statically indeterminate structures. The influence line decreases as a whole with the increase of curvature of horizontally curved beams.