静不定梁的拉普拉斯变换解法.PDFVIP

科學與工程技術期刊 第五卷 第四期 民國九十八年 69 Journal of Science and Engineering Technology, Vol. 5, No. 4, pp. 69-76 (2009) 靜不定樑的拉普拉斯變換解法 鍾文貴 王弘祐 胡竣傑 屏東科技大學土木工程系 91207 屏東縣內埔鄉學府路 1 號 摘 要 靜不定樑是常見的工程結構，連續樑即是典型的例子，其特徵為樑的約束反力多於靜力平 衡方程式，用一般方法求解較繁雜且易出錯。本文用拉普拉斯變換將均質等截面樑的撓曲曲線 方程式 Ely(4)=−q(x) 化為代數方程式，推導得包含作用在樑上的載重函數 Q(x) 與樑的端點邊界 條件 y (0), y ′(0), y ″(0) 及y ″′(0) 等輸入參數之解析公式，並以四個範例說明應用此公式求解靜不 定樑的具體方法與步驟。計算過程簡潔且方便應用，具有實用價值。 關鍵詞：靜不定樑，拉普拉斯變換，撓曲 A Solution to Indeterminate Beams Using the Laplace Transform WEN-GUEY CHUNG, HUNG-YU WANG and JIUNN-JYE HWU Department of Civil Engineering, National Pingtung University of Science Technology No. 1, Hseuh Fu Rd., Nei Pu, Pingtung, Taiwan 91207, R.O.C. ABSTRACT Statistically indeterminate beams such as continuous ones are commonly applied to practical engineering structures. A solution to such indeterminate beams, based on the Laplace transform, is presented in this report. A facilitating formula with loading functions and boundary conditions upon the beam was derived; moreover, four examples were used for testing the formula. The computational results from these examples show that this formula can easily and efficiently solve the problem of indeterminate beams, thereby evidently demonstrating the practicability of the