Aerodynamic Stability of H Sections

A theory is developed for an H section under lateral wind loading to explain the dynamic stability of girder-stiffened suspension bridges. The mathematical model presupposes, as the most significant force, the aerodynamic loading on the windward girder and because the shear-center for an arbitrary section and the center-of-gravity are not colinear, a lateral force gives rise to vertical and angular displacements as well as a horizontal displacement. Based on the loading assumption a quasistatic approach to the time-dependent cavity flow problem is developed which yields a formula for moments and thrusts, with wind velocity as a parameter. Stability of the system is then investigated using the Routh-Hurwitz theorems and is found to be dependent on the structural properties, geometry, and free-stream wind speed. As a function of the latter, the model predicts regions of stability imbedded in an otherwise generally unstable situation. Observations of the behavior of the Tacoma Narrows Bridge appear to confirm, qualitatively at least, the validity of the model. Other comparisons of model behavior and observation are similarly compared, and the significant parameters contributing to instability are identified.