為了兼顧安全性與經濟性，允許建築物產生塑性變形，可以降低地震力。採用韌性設計法時，國內建築物耐震設計規範以結構體的韌性容量估算地震力折減係數，以折減彈性設計地震力。地震力折減係數與韌性容量的關係隨不同地表振動而改變，故有必要依據規範的彈性設計震譜，探討或建立地震力折減係數的法規公式。
本研究改良Kaul之時間域人工地震修正法，在盡少更動原始地震紀錄的前提下，更有效率地產生與彈性設計震譜相容的人工地震。原始歷時採用中央氣象局自由場強地動監測網之實測地震紀錄，並依據測站之地盤分類及設計水平加速度反應譜係數進行分組，產生一千餘筆與彈性設計震譜相容之人工地表加速度歷時。經由單自度系統之非線性歷時分析，可得對應不同基本振動週期、韌性容量及勁度係數等參數之地震力折減係數。
經由參數敏感度分析，顯示地震力折減係數與系統特性高度相關。依據迴歸分析之結果，可歸納為對應不同勁度係數之正規化基本振動週期與韌性容量之三折線函數，其轉折週期與彈性設計震譜相同。原規範公式於短週期處過於保守，而本研究提出之地震力折減係數修正公式則在安全性與經濟性中取得較佳的平衡。
另一方面，經由多自度系統之非線性歷時分析，發現根據規範之靜力分析方法或反應譜分析方法，所得結果較為保守；而且在均勻層間剪力降伏強度下，往往只有低樓層充分發揮韌性效果。本研究提出層間剪力降伏強度計算流程，以使各樓層皆達相同韌性容量，並對均勻剪力屋架，建議層間剪力降伏強度之比例分佈公式，以進行多自由度系統之最佳化設計。

For the purpose of safety and economy, the plastic deformations of buildings are allowed to reduce seismic loads. When the ductility design is applied, the domestic building seismic design code provides formulas to estimate the seismic load reduction factor by the ductility capacity, and then the seismic load is reduced from the elastic design spectrum. The relationship of the seismic load reduction factor on the ductility capacity depends on the ground motions, so it is necessary to investigate the code formulas or propose a new one on the basis of the elastic design spectrum.
This paper proposes an improved Kaul’s method to efficiently generate artificial earthquakes compatible with the design spectra. The original ground accelerograms come from seismic records of TSMIP operated by CWB, and are modified as less as possible in our method. Over than one thousand artificial ground accelerograms are generated and then are classified by different site conditions and design spectra. Through the nonlinear response history analysis on SDOF systems, a lot of seismic load reduction factors corresponding to different parameters, such as natural vibration period, ductility capacity, and stiffness ratio, are obtained for further study.
Through the sensitivity analysis on parameters, it is found that the seismic load reduction factor is highly correlated to system properties. On the basis of regression results, a tri-linear relationship of the mean seismic load reduction factor on the normalized natural vibration period is proposed, and the two transition periods locate exactly at both ends of the platform in the elastic response spectra. The code formula generally underestimates the seismic load reduction factor on the short-period region, but our formula considers a compromise between safety and economy.
On the other hand, it is observed that the response results of MDOF systems by the static analysis and the response spectrum analysis are more conservative than those by the nonlinear response history analysis. It is also found in the nonlinear response history analysis that only the ductility capacities of the lower stories are well used if the building is designed with uniform story shear yield strength. This paper provides an optimum design procedure to calculate the story shear yield strength in order for achieving the same ductility capacity in each story. Finally, for uniform shear buildings a formula of optimal distribution of the story shear yield strength ratio is proposed.

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