Dynamic response of multistory buildings

Two modern multistory buildings, one a five-story reinforced concrete building, the other a nine-story steel frame building, have been the subjects of an extensive series of dynamic tests. The vibrations of the buildings were induced by means of synchronized vibration exciters. The mathematical analysis needed in order to determine the stiffness and damping matrices from the experimentally determined modal properties of a structure has been developed. Three translational and one torsional mode of vibration of the reinforced concrete building were investigated in considerable detail. The damping in each mode and the resonant frequency was determined under various levels of excitation. Complete mode shapes were determined as well. The measurements of the resonant frequencies show a well-defined nonlinearity that can be well explained from the hysteretic material properties. The values of damping were for all modes approximately 276 with a tendency for the value of damping to increase with increasing force levels. A total of seven translational and three torsional modes of vibration of the nine-story steel frame building were investigated in detail. A mode in which the floor slabs vibrate horizontally as free-free beams was excited as well. The lowest translational modes in the two principal directions of the building had damping values of about 0.516. The second lowest translational modes had damping values of approximately 1.0016. For both buildings the damping values are considerably less than the values usually mentioned in the literature. Since most earlier tests used run-down tests rather than the steady-state tests used in the present work, comparison tests were run to explore possible differences in the test results. It was concluded that run-down tests could easily overestimate the values of damping by several hundred per cent. A new method for the measurements of natural periods of vibration of structures is proposed. The new method has several important advantages over wind-excited vibration tests which have been used extensively in the past to measure the natural periods of vibration of structures