本文推導了首見於文獻之變斷面變曲率拱面外運動之動態勁度矩陣；此矩陣乃建立於該拱面外運動控制方程之解析級數解。然後，結合此動態勁度矩陣與不連續系統多重輸出與多重輸入之關係，建立變斷面變曲率拱受多支承運動之平穩隨機面外反應分析程序。此程序優於傳統模態疊加法，在於不需知道系統模態而可輕易地求得精確之位移和內力反應。最後，利用此程序分析與探討單跨變斷面拋物線拱受兩端支承不同輸入關係下之反應均方值的差異。A systematic and accurate approach for studying the out-of-plane stochastic responses of a system consisting of curved beams with arbitrary shapes and cross-sections subjected to earthquake is presented in this paper. This approach combines the dynamic stiffness matrix for the curved beams with the multiple output/multiple input relation for discrete systems. The first known dynamic stiffness matrix for out-of-plane motion of a curved beam with arbitrary shape and cross-section is developed based on an analytical series solution. The main advantage of the present solution over the conventional modal superposition method is that it simply gives accurate results for displacement as well as for stress resultant responses without any knowledge of the natural frequencies and vibration modes of the system. Finally, the proposed procedure is applied to investigating the variances of the out-of-plane responses for two single span parabolic arches with variable cross-sections subjected to support motions with spatial variation.
