喻晓今. 求超静定等直梁的置换法[J]. 工程力学, 2007, 24(增Ⅰ): 66-069.
引用本文: 喻晓今. 求超静定等直梁的置换法[J]. 工程力学, 2007, 24(增Ⅰ): 66-069.
YU Xiao-jin. CONVERSION METHOD FOR CALCULATION OF STATICALLY INDETERMINATE STRAIGHT BEAMS WITH UNIFORM CROSS-SECTION[J]. Engineering Mechanics, 2007, 24(增Ⅰ): 66-069.
Citation: YU Xiao-jin. CONVERSION METHOD FOR CALCULATION OF STATICALLY INDETERMINATE STRAIGHT BEAMS WITH UNIFORM CROSS-SECTION[J]. Engineering Mechanics, 2007, 24(增Ⅰ): 66-069.

求超静定等直梁的置换法

CONVERSION METHOD FOR CALCULATION OF STATICALLY INDETERMINATE STRAIGHT BEAMS WITH UNIFORM CROSS-SECTION

  • 摘要: 解超静定梁,用力矩分配法不失为一种手算的良方,然其亦有记忆转动刚度、分配系数、传递系数等要求;力法、位移法等法对弯矩图形面积、固端弯矩等图表的依赖性又较强。以悬臂梁置换法求超静定等直梁,依悬臂梁挠曲线可置换任一梁者之原理,在列写变形协调关系时采用置换法位移方程,由于该方程所涉及的荷载作用于悬臂梁自由端产生的挠度、转角较易记住,其格式重复运用可补足补充方程,故得梁的反力,进而内力、位移等量的精确解析解。

     

    Abstract: The method of moment distribution is one of the better ways to solve a statically indeterminate beam. However, it has to depend on the memorization of rotational stiffness, distribution factor and carry-over factor of the different supports. The force method and the displacement method are dependent on moment area, fixed-end moment and so on. Conversion method is based on the theorem that the deflection of any beam can be converted into that of a cantilever beam. Deformation compatibility equations can then be established by the conversion method. Since it is easy to memorize the deflection and rotation of a cantilever beam at the fixed end, the precise solutions of the reaction, the internal force and the displacement of a beam can be achieved.

     

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