1. Introduction
The objective of this study is to examine the properties of the stability index SI, and the relations among the effective length factors obtained from different buckling conditions. Overview of the relations among the stability indexes (SI and GSI) and the effective length factors (γexact, SIγ, SIγ *, Gγ, Gγ˜ and Gγ˜* ) is shown in Fig. 1. The targets are rectangular 2-span plane frames, and total 96 frames are examined, taking the condition of the column base, number of story, stiffness ratio, stiffness ratio reduction factor and distribution of the story shear as the parameters.
2. Stability index and effective length factors
Stability indexes SI and GSI are calculated by Eqs. (1) and (12). For the overall structural system, the effective length factors SIγ and Gγ˜ are calculated by Eqs. (5) and (17), respectively. For the buckling of the story, the effective length factors SIγ* and Gγ˜* are calculated by Eqs.(9) and (19), respectively. The exact effective length factors γexact are calculated by the buckling slope-deflection method or the finite element method.
3. Results
Effects of story shear distribution and column base are shown in Figs. 6, 7 and Fig. 8, respectively. Comparison between the stability index SI obtained by the first-order lateral load elastic analysis and approximate GSI obtained by G factor is shown in Figs. 9, 10, 11, and 12. Comparison of effective length factor between SIγ and γexact is shown in Fig. 13, and comparison of effective length factor between Gγ˜ and γexact is shown in Fig. 14.
4. Conclusions
The conclusions derived from this study are as follows:
1) The effects of the story shear distribution on the stability index are hardly observed (see Figs. 6 and 7). For frames with four stories or more, the stability index above the 4th story is almost same among the fixed base and pin base frame (see Fig. 8).
2) In the intermediate-stories, the approximate stability index GSI obtained by G factor can be applicable as the stability index (see Figs. 9 10, 11, and 12).
3) The buckling-associated-story obtained from stability index GSI agrees well with that obtained from stability index SI (see Table 3).
4) Effective length factors obtained by using the stability index agree fairly well with the exact factors about within 5% error (see Fig. 13).
5) The effective length factors Gγ˜ estimate the exact values γexact up to 1.12 times (fixed base) and 1.2 times (pin base) (see Fig. 14).
6) In the intermediate-stories, the effective length factors Gγ˜* can estimate the factors SIγ*.
