Small detached wooden houses typically have eccentric arrangement of shear walls, which results in torsional vibration when subjected to earthquake. In addition, flexible floor diaphragm of wooden structures complicates the dynamic behavior. Since eccentricity ratio, which is originally defined in Japanese Building Standard Law, is a simple index to confirm adequacy of arrangement of shear walls, such a complicated behavior is not accurately simulated.
In this paper, index of torsion taking dynamic effect and flexibility of floor diaphragm into account is proposed based on dynamics model. In chapter2, structural model and the precondition in this study is stated. Translational behavior is assumed to be dominant rather than rotational behavior. In chapter3, 1x1-span flexible floor model is considered, and the dynamic properties are derived. The particular solution for rigid floor model is also dealt with as a kind of the general solutions for flexible floor model. In chapter4, 2x2-span flexible floor model is considered, and the dynamic properties are derived. In chapter5, eccentricity ratio is developed to address dynamic effect and flexibility of floor diaphragm. The range of application of the method is discussed in appendix.
The followings are findings of this research.
1) Modal shape of infinitely-rigid floor model is expressed by a parameter which is defined as "dynamic torsion index". It is the same as the one proposed by Ohami
12) et al. when the structure has infinitely rigid floor diaphragm. In addition, it is nearly the same as the one proposed by Fujii
13) when the structure suffers small torsion.
2) The index is theoretically related to modal shape of 1st mode obtained by eigen value analysis. The corresponding natural circular frequency is also estimated with acceptable accuracy.
3) Conventional static analysis, which generally considers mass-proportional lateral load, gives smaller torsion compared to 1st mode shape obtained by eigen value analysis due to so-called dynamic effect.
4) When a floor diaphragm is quite flexible, the structure is modeled by 2DOF system and defined as perfectly-flexible floor model. Dynamic torsion index for perfectly-flexible floor model is also defined similar to the infinitely-rigid floor model.
5) Dynamic properties of general 1x1-span flexible floor model, which is 3DOF system, is obtained by interpolation by the ones of infinitely-rigid floor model and perfectly-flexible floor model.
6) Dynamic properties of 2x2-span flexible floor model, which is 4DOF system, is obtained by interpolation by the ones of reverse symmetric shear model(reduced 2DOF) and symmetric shear model(2DOF). It insists that the effect of flexible floor diaphragm can be separated into the ones related/non-related to torsion.
7) The tendency of the dynamic behavior is compared to eccentricity ratio, and the key parameters to control torsional coupling is pointed out. The dynamic effect is reflected by the radius of gyration in the equivalent elastic radius.
As a future plan, inelastic torsional behavior derived from plasticity of shear walls will be addressed.
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