SIMPLIFIED EVALUATION METHOD OF DYNAMIC PROPERTIES FOR SINGLE-STORY WOODEN STRUCTURE HAVING FLEXIBLE FLOOR DIAPHRAGM

Abstract

 Traditional-type boarding floor diaphragm of wooden structures consists of narrow boards fastened by nails and has low shear stiffness unlike plywood sheathing floor diaphragm. It is incapable of achieving so-called rigid floor assumption which is generally assumed in the current seismic design standard. In practical design and seismic diagnosis, when the structure has flexible floor diaphragm, three dimensional framing analysis is required. Therefore, the flexible floor diaphragm is believed to make the dynamic behavior quite complicated and to make the simulation difficult.
 In this paper, simplified evaluation method of basic dynamic properties such as natural circular frequency and mode shape for single-story wooden structures is proposed. A theory of 2x2-span flexible floor dynamics model which the authors has proposed is developed, and useful indexes indicating the effect on the dynamic properties are derived in the process. Although eigen value analysis requires matrix operation and numerical solver to obtain natural circular frequency and mode shape, the proposed method can provide them only with the four arithmetic operations of the indexes. The accuracy of the method is confirmed by comparison with numerical analysis solutions. In addition, applicability of conventional method such as sparsely discretized model (i.e. lumped mass model) and static pushover analysis is also investigated.
 The followings are findings of this research.
 1) Dynamic properties such as natural circular frequency and mode shape were estimated using the ones of simplified models with smaller number of degrees of freedom: reverse symmetric shear model and symmetric shear model. Regarding mode shape, another model might be included, and the accuracy was improved in particular cases.
 2) Dynamic properties of the simplified models stated above could be calculated using a controlling index.
 3) Lumped mass model was likely to give smaller natural circular frequency compared to strict solutions due to neglect of flexural stiffness of floor diaphragm and to sparsely discretized mass.
 4) Accuracy of static analysis for natural circular frequency(i.e. initial stiffness) was variable. Mode shape was well predicted except for particular cases.
 5) Natural circular frequency and mode shape of whole structure could be determined by the two controlling indexes, and the contours were drawn. If the criteria of dynamic properties are set, the acceptable range of the two indexes is clearly found out from the contours.
 By considering mode shape given by the proposed method as acceleration distribution, it can be applied to static force distribution in horizontal direction when static push-over analysis is conducted. As a future plan, two-story structures and inelastic behavior derived from plasticity of shear walls will be addressed.