Ambient vibration tools to validate the rigid diaphragm assumption in the seismic assessment of buildings

Vibration tests are encountering a growing success in earthquake engineering as a valuable tool for the seismic assessment of buildings. Ambient vibration measurements, in particular, offer reliable support for the updating of mechanical models, as well as the enhancement of seismic mitigation strategies for existing buildings. In this respect, the common description of the floor diaphragms as planar rigid bodies tends to oversimplify the actual mechanical behaviour of some traditional structural solutions, especially in masonry buildings. This assumption can be violated even in modern concrete and steel buildings due to inadequate design, poor manufacturing, or damage. The paper addresses the mathematical validation of the rigid diaphragm simplification using vibration measurements. To this purpose, a model-based inverse kinematic problem is stated and solved to discriminate the in-plane rigid motion and the angular deformation time histories from vibration data. Simple formulas, leveraging the approximate solution in the case of problem under-determinacy, exploit the spectral content of vibration data to discuss the diaphragm deformability. Natural modes exhibiting different (rigid, quasi-rigid, or nonrigid) diaphragm behaviour are distinguishable by comparing the power spectral densities of the rigid motion and angular deformation. Modes of pure floor deformability can also be identified. The influence of adverse testing conditions is discussed through pseudo-experimental data simulating the dynamic response of a simple frame structure. As a complementary contribution, the procedure effectiveness is experimentally verified by analysing vibration data related to, first, laboratory tests on a scaled concrete-steel frame and, finally, full-scale tests on a masonry building.