Rotations in a shear beam model of a seven-story building caused by nonlinear waves during earthquake excitation

We model a seven-story, reinforced-concrete building in Van Nuys, CA, which was damaged during the 1994 Northridge earthquake. We use a one-dimensional, layered, shear-beam model with bi-linear material properties, and we examine how the rotations (local strains and drifts) in this model depend upon the distribution of the stiffness along the building height, the nonlinear properties of the reinforced concrete, and the nature of strong motion. We show how, following the powerful waves propagating up and down the building, point rotations take place that differ from the corresponding average drift angles. These point rotations are larger near the rigid floor slabs (near the top and bottom ends of the columns, shear walls, and nonstructural members found at all floors) and propagate as slow waves up and down the building. These slow rotational waves occur only while the material is experiencing large nonlinear deformations, and their amplitudes grow with ductility. We note that recording these rotational waves in real time may provide a powerful new vehicle for health monitoring of full-scale structures excited by large transient forces when their structural members enter large nonlinear deformations