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本文所謂架空結構是指搁置在較高的支墩上的連續梁結構,例如高架橋梁或水電站的架空輸水管道等。這類結構在承受震動荷載(例如地震)時,常會引起較大的變形和应力。如支墩較粗矮,則在計算較低的頻率時,其作用可近似的以一彈簧支座代替之,而忽略支墩本身的結構震動影響。這是一個常用的假定,可以使計算工作充分簡化。本文首先對這一情况作了詳盡討論,給出较完整的解答,包括起始條件影響在内,並提出用“載常數”及“形常數”的觀念來進行計算。然后本文給出考虑支墩的震動影響時的精確解答,分別就縱横方向的震動進行討論,並指出近似計算公式和精確公式间的關係,近似公式只能在支墩較剛固和計算较低階的頻率時才適用。文中列出了結構作横向諧和震動時的特別解答,可見其計算工作量將比近似法增加不少。
In this paper, the overhead structure refers to the continuous beam structure resting on the tall abutment, such as the overhead bridge or the overhead water pipeline of the hydropower station. Such structures often cause large deformations and stresses when subjected to shock loads (such as earthquakes). If the pier is thick and short, then in the calculation of lower frequencies, its role can be approximated by a spring bearing instead of neglect of the pier itself structural vibration. This is a common assumption that simplifies computations. This paper first discusses the situation in detail, gives a more complete solution, including the influence of the initial conditions, and puts forward the concept of “load constant” and “shape constant” for calculation. Then the exact solution to the influence of the pier vibration is given in this paper. The vertical and horizontal vibration are discussed separately. The relationship between the approximate formula and the exact formula is pointed out. The approximate formula can only be used when the abutment stiffness is relatively low The order of the frequency is only applicable. In this paper, the special solutions of the structure for horizontal harmonic vibration are listed. It can be seen that the computational workload will increase a lot compared with the approximation method.