›› 2014, Vol. 36 ›› Issue (4): 478-482.DOI: 10.6052/1000-0879-13-300

• 应用研究 • 上一篇    下一篇

一端外伸梁对称弯曲弹性位移的置换法确定

喻晓今   

  1. 华东交通大学土木建筑学院, 南昌330013
  • 收稿日期:2013-07-17 修回日期:2013-10-15 出版日期:2014-08-08 发布日期:2014-11-13
  • 通讯作者: 喻晓今,1959年生,男,工学硕士,教授,主要从事各种结构、构件(零件)_的力学性质研究.E-mail:yuxj_59@163.com
  • 基金资助:
    国家自然科学基金(51368019),江西省科技厅科技(20122BBG70186),江西省教育厅科技(赣教技字[08]257 号)资助项目.

DETERMINATION OF DISPLACEMENT OF A BEAM WITH ONE END OVERHANGING IN SYMMETRIC BENDING WITH CONVERSION METHOD

YU Xiaojin   

  1. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China
  • Received:2013-07-17 Revised:2013-10-15 Online:2014-08-08 Published:2014-11-13

摘要: 置换法应用于求解一端外伸梁,在对称弯曲的条件下,根据直梁挠曲线所在平面内其与切线所成图形的边角几何关系,推导出求解该形梁的挠度和转角的置换法位移方程,其变量是相应的置换梁自由端的挠度、梁长、梁轴线位置坐标等. 对具体载荷梁的求解过程是:先以具体量值填充左、右置换梁自由端的挠度,再将其代入该置换法位移方程的统一表达式,即得到所求梁段的挠度、转角的方程全解. 所用的计算为代数方程的分式四则运算,只需挠曲线和叠加原理概念,无需积分,一般无需查挠度表,结果精确. 给出工程背景的算例.

关键词: 梁挠度和转角|约束反力|置换法|悬臂梁|外伸梁

Abstract: The Conversion Method is used to determine the displacement of a beam with one end overhanging in symmetric bending. According to the relation between angles and normal lines of the beam, the displacement equation of the conversion method (DECM) is derived to obtain the deflection and the slope of this type of beams. The variables of the equation are the deflections of the free end of the corresponding Conversion Beam, the length of the beam converted, and the coordinate of the axis of the beam. The deeetailed process of computation for a specific beam is shown. The deflections of the free ends of the left, right conversion beams are computed, then they are put in a unified formula of DECM. The complete solution of the equation of deflection and slope is obtained. Only the knowledge of the deflection curve and the superposition method is required, without differentiation and integration, and without the need to consult the table of deflections. The result is accurate. Some instances of calculation with engineering background are given.

Key words: deflection and slope of a beam|constraint force|conversion method|cantilever|overhanging beam

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