Estimating fundamental frequencies of tall buildings

Empirical estimates of the fundamental frequency of tall buildings vary inversely with their height, a dependency not exhibited by the various familiar models of beam behavior. This paper examines and explains this apparent discrepancy by analyzing the consequences of using two models to estimate such natural frequencies: A two-beam model that couples the bending of a classical cantilever to that of a shear beam by imposing a displacement constraint; and a Timoshenko beam in which the Euler-Bernoulli beam model is extended by adding a shear-displacement term to the classical bending deflection. A comparison of the two beam models suggests that the Timoshenko model is appropriate for describing the behavior of shear-wall buildings, while the coupled two-beam model is appropriate for shear-wall-frame (e.g., tube-and-core) buildings, and that the coupled-beam model comes much closer to replicating the parametric dependence of building frequency on height.