建築物於風力的作用下，產生順風向、橫風向與扭轉向風力載重效應，向量載重效應是前述三種效應之非線性組合，其中建築物頂層角隅處之總振動加速度是本文研究的重點。我國耐風設計規範中，總振動加速度的公式是基於順風向與橫風向及扭轉向效應不相關，而橫風向與扭轉向效應完全相關之假設估計而得；本研究嘗試推導新的設計公式，以考慮三個方向載重效應的部分相關性。首先利用流體數值模擬求得不同矩形建築三個方向之風力頻譜與交頻譜，再代入以隨機振動理論所推導公式，計算三個方向結構加速度之相關係數，最後代入本文所推導公式，估計總振動加速度最大值之平均值。其中，數值模擬是針對地況B的風場下，深寬比為1、0.5與2及高寬比為6、5與4的矩形建築；將結果與所蒐集之風洞資料比較，發現模擬之結果整體趨勢表現上跟風洞實驗是一致的，但是兩者頻譜值大小仍有差距。這導致在不同建築物特性參數及設計風速下，利用數值模擬與風洞實驗結果會得到不同的加速度相關係數。本研究推導出兩種設計公式，公式1為橢圓解析解法配合橢圓八邊形法推導而得，公式2為橢圓解析解法配合CQC法推得；將風洞資料所得之相關係數分別代入二公式後，可以估計出建築物角隅處總加速度最大值之平均值。本研究發現公式2會提供最準確的估計，現行規範公式稍微保守，而公式1最為保守。當風速越高或建築物高度越低，或橫風向與扭轉向頻率相差越大時，公式2之估計與現行規範公式之差距會越大。

Buildings under wind loads result in along-wind, across-wind and torsional wind load effects; vectorial wind load effects are their nonlinear combinations. This study concerns the building top floor corner maximum acceleration and derives new formula considering the correlation between the wind load effects. First, wind load spectra are obtained by numerical simulations, and the results are compared with those from wind tunnel tests. The correlation coefficients between accelerations depend on the normalized wind load spectra, the fundamental natural frequencies and damping ratios. In this study, two formula have been derived; the difference is that formula 1 adopts an octagonal approximation while formula 2 adopts a CQC rule. Finally, the results of the above two formula are compared with those from design code. It is found that formula 2 provides the most accurate results; the results based on design code are slightly conservative; formula 1 generally yields the most conservative results.

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