受震建築意外扭矩放大係數之可靠度評估

Reliability Assessment of the Torsional Amplification Factor for Accidental Torsional Moment of Buildings Subjected to Earthquakes

王韋竣(Wei-Chun Wang)

指導教授 ： 蔡克銓

國立臺灣大學/工學院/土木工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00527

摘要

當工程師進行結構設計時，為了節省分析時間，經常採用靜力分析取代動力分析來模擬結構的受震反應。由於質量中心位置、勁度中心位置、材料性質以及旋轉向地表加速度等不確定性因素，在結構分析時除了考慮質量中心與勁度中心之間的原始偏心量，無論是靜力分析或是動力分析，耐震設計規範規定需要再加上與地震力施加方向垂直之建築物平面尺度±5%的意外偏心量，以考慮上述之不確定因素。在考慮意外扭矩效應下，為降低靜力分析結果與動力分析結果之差異，耐震設計規範更將靜力分析中的意外偏心量再乘以意外扭矩放大係數。因此在考慮意外扭矩效應下，本研究評估以靜力分析估算建築物位移之可靠度，並且對於意外扭矩放大係數作出修正建議，期望使靜力分析所估算之位移能夠位於保守側。
本研究首先使用美國SAC計畫中三層、九層以及二十層樓建築做為示範構架，藉由調整結構之質量慣性矩來改變示範構架之頻率比，將頻率比調整至0.7、1.0、1.3以及1.6，並藉由改變結構質量中心在長向上的位置以改變其原始偏心量，將其長向之原始偏心量調整為0%至30%(每1%增量一次)，分別對示範構架進行靜力分析及動力分析，並且計算這兩種分析方式所得到之位移的差異值。採用易損性曲線之概念發展出差異曲線評估方法，將前述之位移差異值的絕對值表示成在各差異狀態下之超越機率，並且藉由此位移差異值的平均值來判斷靜力分析所得到的位移為高估或低估。研究發現，當考慮意外扭矩效應時，採用+5%意外偏心所得到的質量中心及柔度側位移較為保守、採用-5%意外偏心所得到的勁度側位移較為保守；當考慮原始偏心加上意外偏心效應時，靜力分析所估算的位移，除了對於三層樓建築稍微不保守外，對於九層及二十層建築均為保守，並且當建築總樓層數越高，靜力分析估算的位移就越保守。最後藉由計算靜力分析及動力分析位移差異值的標準差來顯示分析結果之變異性。第二部份對於意外扭矩放大係數提出改善方案，確保在考慮原始偏心加上意外偏心時，靜力分析估算所得之位移不小於動力分析所得之位移。本研究提出對於低矮樓層建築及中等高度樓層建築在頻率比小於一及等於一時的意外扭矩放大係數修正建議。

關鍵字

意外偏心 ； 扭轉不規則 ； 意外扭矩放大係數 ； 可靠度分析 ； 差異曲線

並列摘要

In order to reduce the analysis time, static analysis procedure is often used to compute the seismic response on structures. Due to the uncertainty of the location of center of mass, the location of center of rigidity, material properties, and rotational components of ground motions, it is necessary to consider ±5% accidental eccentricity in addition to the inherent eccentricity in both static and dynamic analyses. In order to reduce the discrepancy in the estimated responses resulting from static and dynamic analyses, the seismic design codes stipulate using the torsional amplification factor to amplify the accidental eccentricity in static analysis to account for the dynamic torsional effects. The objective of this study is the reliability assessment of the displacement estimates obtained from static analyses when the accidental torsion effect is considered. In addition, this study provides recommendations for possible modification of the torsional amplification factor in order to reduce the discrepancy between the static and dynamic responses.
Both static and dynamic analyses are conducted first on 3-story, 9-story, and 20-story buildings with various frequency ratios and eccentricity ratios. The discrepancies on displacements between the static and dynamic analyses are computed. Discrepancy curves analogous to the fragility curve are constructed to show the exceeding probability of the absolute values of the aforementioned discrepancies corresponding to each discrepancy state. The mean of the discrepancy is computed to represent the overestimation or underestimation of the statically estimated displacements. The standard deviations are also computed in order to gain insights into the consistency of the analysis results. It’s found that statically estimated displacements computed for the center of mass and the flexible side are conservative when the +5% accidental eccentricity is considered. Similarly, displacements of stiff side are also found conservative when the -5% accidental eccentricity is applied in the static analysis. The statically estimated displacements computed for high rise buildings are overly conservative when the inherent and accidental eccentricities are considered. Based on the analysis results, this paper provides improved torsional amplification factors to account for the dynamic torsional effects, and to prevent underestimation of the statically estimated displacements.

並列關鍵字

accidental eccentricity ； torsional irregularity ； torsional amplification factor ； reliability assessment ； discrepancy curve

參考文獻

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