APPLICATION RANGE OF TWO-MODE BASED STATIC SEISMIC LOAD FOR SINGLE LAYER RETICULATED SHELLS

Abstract

　The present paper discusses statically equivalent seismic force distributions for single layer reticulated shells. To analyze the relationship between a shell geometry and its vibrational properties, a vibration database is constructed. The database contains the results of natural vibration analysis for about 200 structural models, each of which is generated by parametrically varying the span, slenderness ratio of the member, number of partitions of the shell, and so on. The overall shape of the structure is based on three basic types: cylindrical shell, spherical shell, and free form shell. From the analysis of the database, the two-mode SRSS method reveals the effect of the effective mass ratio and strain energy ratio on the response evaluation of shell structures. Finally, the range of applicability of the two-mode static seismic load distributions, as shown in eq.(5.1), is investigated. The conclusions of this study can be summarized as follows:

　

1)　The response estimation using SRSS with two modes e1with the largest strain energy ratio and e2 with the second largest strain energy ratio can evaluate the response accurately in the range where the sum of the strain energy ratios of the two modes _εe1+_εe2 is greater than 0.8. In addition to this condition, it is confirmed that the bending moment can be evaluated accurately if the sum of the bending strain energy ratios of mode e1 and mode e2 _bεe1+_bεe2 is more than 0.2.

2)　It is confirmed that the response evaluation based on two modes using mode e1with the largest strain energy ratio and mode e2 with the second largest strain energy ratio is more accurate than that using mode r1 with the largest effective mass ratio and mode r2 with the second largest effective mass ratio. This is because the vibrational modes of in-plane deformation that appear in very short natural periods may have large effective mass ratio, and such modes do not contribute significantly to the overall response.

3)　For some cylindrical and free-form shapes, it is possible to evaluate the results of CQC considering all modes with two-mode SRSS. On the other hand, it is difficult to simulate the response of spherical shapes with two modes.

4)　For structures where _εe1+_εe2 >0.8 and _bεe1+_bεe2 >0.2, it is clarified that the two-mode based seismic load distribution can evaluate seismic response with high accuracy. Furthermore, the sum of the effective mass ratios of the two modes varies from 0.1 to 0.8. For this reason, it is concluded that when calculating two-mode based seismic load distributions, it is necessary to focus on the magnitude of strain energy ratio and bending strain energy ratio rather than effective mass ratio.