In this paper, the results of the basic study on the simplest model for torsional vibration, which had been carried out for several years, was applied to long-in-plan buildings and the basic property of their torsional response was inyestigated.
Firstly, the results of the basic study on the single story linear system with uniaxial eccentricity were arranged and summarized, for example, the formulae of peak response under simplified input ground motions derived in the explicit form, simple indices of the effects of the torsional coupling on response proposed in this study, and so on.
Secondly, the common property to all long-in-plan buildings with uniformly distributed mass was investigated. As a results, the followings were pointed out : If having the eccentricity in the transverse direction, the range, which the eccentricity factor and the stiffness radius factor of gyration can be taken respectively, is very wide. And the upper limit of the amplification factor of peak response to that of uncoupled system reaches to about 1.6 which is 20% larger than that of the square plan. On the other hand, if having the eccentrisity in the longitudinal direction, the effect of torsion appears mainly on response in the transverse direction, which has no eccentricity. Moreover, the upper limit of the amplification factor is very large ; i.e.about 1.2 which is 40% larger than that of the square plan.
Finally, such analytical model was investigated as a case study that has both uniformly distributed mass and stiffness and is attached by one eccentricity element. As a result, it was pointed out that there is some possibility that large torsion is induced in spite of small eccentricity, and that the stiff side of the floor vibrates largely than the other side, and their concrete conditions were made clear. Furthermore, indices proposed in this study, were confirmed effective to this analytical model, including torsion by small eccentricity mentioned above.