Sudden lateral asymmetry and torsional oscillations in the original Tacoma suspension bridge

The original Tacoma suspension bridge was completed on 10 June 1940 and opened to traffic on 1 July 1940. The bridge was stable with respect to torsional oscillation until 7 November 1940. That day at 10 a.m. the diagonal tie attached to the midspan band of one main cable loosened and the cable began to slip through the band. Just after the loosening of the tie torsional oscillations appeared, lasted for more than 1 h, and resulted in the collapse of the center span at 11:10 a.m. In this paper a continuous model of the original Tacoma suspension bridge is proposed. This model describes the mutual interaction of the main cables, central span, and hangers. The reaction of the ties attached to the midspan bands is included in the model, so it is possible to study the situation when only one midspan band loosens. The model is described by a system of variational equations which are derived from the Hamilton variational principle. Three different eigenvalue and eigenvector problems are formulated and analyzed. The problems correspond to the situations when the both midspans are loosened, the both midspan bands are fixed, and one midspan band is fixed and the other is loosened. The analysis of the three eigenvalue and eigenvector problems against flutter is carried out, which reveals possible reasons of the collapse.