Buildings are made up of beams and plates which are much stiffer in tension-compression than in bending. Thus, the vertical modes of a building (governed by the tension-compression of the walls at the macroscopic scale) can appear in the same frequency range as the bending modes of the floors. In the absence of bending resonance, the vertical vibrations are described at the macroscopic scale by the usual equation for beams in tension-compression. When there is resonance, the form of the equation is unchanged but the real mass of the structure is replaced by an effective mass which depends on the frequency. This induces abnormal response in the neighbourhood of the natural frequencies of the floors. By considering idealized buildings made up of the periodic repetition of frames, this phenomenon is evidenced theoretically thanks to the homogenization method of periodic discrete media and numerically.
