Wind-Induced Fatigue and Asymmetric Damage in a Timber Bridge.

The transformation of a 30 m long timber pedestrian bridge into a wobbly (laterally swaying) bridge with a dramatically reduced first lateral modal frequency has been monitored by seven annual, multi-sensor surveys. This evidence, in combination with analysis of the wind record, observations of local damage and evidence of wind-induced excitations from other bridges, is used to present a multi-stage scenario of the extraordinary structural weakening of our study bridge in only a few years. Our analysis is constrained by observations of asymmetric damage (longitudinal splitting cracks around metallic connections along the south side of the deck, not explained by ordinary, essentially symmetric lateral oscillations) and over-threshold analysis of strong northerly wind events, including gusts. The proposed scenario is that an unexpected for the area icing event took advantage of construction vicissitudes and produced damage that reduced the lateral stiffness of the bridge, especially of the arch superstructure. In addition, strong winds sharing common direction with gusts produced a combination of semi-static lateral bending and of dynamic oscillations, leading to numerous cycles of asymmetric high amplitude lateral deflections producing tensile stress normal to grain, cracks localized in connections, and fatigue. The vertical stiffness of the bridge was only slightly affected.

Solution of underdetermined systems of equations with gridded a priori constraints.

The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy. The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an R(n) grid containing an approximation of the real solution. The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the R(n) containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.