Abstract
This paper presented an accurate response reduction factor for non-stationary elastic response which was modified from the past reduction factor in Ref. 6). In the modification, the influence of the asymmetry of the response of the absorbed energy by the damping factor of one cycle just before the maximum response was taken into account, and the influence of the damping factor on the building period was also taken into account.
Furthermore, the paper proposed the simplified formula for response reduction factor.
Finally, the compatibility was examined for both the modified formula and the simplified formula using the response analytical results by actual earthquake motions and earthquake motions in notification.
The major findings obtained in this paper were as follows.
1) The correction coefficient of the equivalent damping factor for evaluating the response reduction factor in non-stationary response is (y1/y1-)^2. Here, y1 is the peak value before the maximum response, and y1- is the average of y1 and the opposite peak value before the maximum response. The average value of (y1/y1-)^2 is approximately 0.7.
2) It is proved that the new modified factor β0' of the absorbed energy by damping factor which taken the influence the asymmetry of the response into account is less influenced by the period of the buildings than the modified factor β0 of absorbed energy by damping factor proposed in Ref. 6).
3) The modified formula for response reduction factor in non-stationary elastic response isexpressed as Fh = [ {β0'/γ0^2·4πh0 + (1-1/γ0^2)} / {β0'/γ0^2·4πh+(1-1/γ0^2)} ] · ζ. Here, γ0 is the projected ratio at the maximum response, and h0(=10%) and h are damping factors.
4) The modified formula for response reduction factor using β0'/γ0^2 and 1/γ0 for each building period shows better compatibility with the response analytical results using actual earthquake motions and earthquake motions in notification than the past approximate formula of response reduction factor of Ref. 6) does.
5) The simplified response reduction factor can be expressed as Fh = [ {10h0+2.7(1-1/γ0^2)} / {10h+2.7(1-1/γ0^2)} ] · ζ in which β0'/γ0^2 is set to be 0.3 considering safety side. The simplified formula shows excellent correlation with the results of the response analysis than the past approximation formula dose. When 1/γ0 is set to 0.4, it is close to Akiyama Formula, and when it is set to 0.6, it is close to Kasai formula, and when it is set to 0.8, it is close to Kenken formula.
