一种新的计算Timoshenko梁截面剪切系数的方法

王乐; 王亮

doi:10.3879/j.issn.1000-0887.2013.07.011

一种新的计算Timoshenko梁截面剪切系数的方法

doi: 10.3879/j.issn.1000-0887.2013.07.011

王乐,
王亮

中国运载火箭技术研究院,北京 100076

详细信息

作者简介:
王乐(1984—),男,湖北荆州人,工程师,硕士 (通讯作者.E-mail:aabeau@163.com).

中图分类号: O343.2
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- 被引次数: 0
出版历程
- 收稿日期: 2013-03-13
- 修回日期: 2013-05-23
- 刊出日期: 2013-07-15

A New Method of Obtaining Timoshenko’s Shear Coefficients

WANG Le,
WANG Liang

China Academy of Launch Vehicle Technology, Beijing 100076, P.R.China

摘要

摘要: Timoshenko梁理论中考虑了截面剪切变形的影响，推导了一种新的计算剪切系数的方法．首先采用悬臂梁纯弯曲变形条件下截面剪应力分布的精确解，并基于能量原理得到了各种梁截面的剪切系数新的表达式，然后推导了弯扭耦合变形条件下截面剪应力分布的精确解，进一步获得了该条件下截面的剪切系数．结果表明，悬臂梁端面作用力偏离截面的弯曲中心将使剪切系数变小，通过与Cowper计算结果的对比发现结果偏小，其原因是Cowper没有考虑与外力垂直的剪应力的影响，因此新的计算结果更优越．
- Timoshenko梁理论 /
- 剪切系数 /
- 弯曲 /
- 扭转 /
- 剪应力
Abstract: With the effects of shear deformation of slender beams considered in Timoshenko beam theory, a new method of obtaining Timoshenko’s shear coefficients was derived. First, the exact solutions of the cross section’s shear stress distribution of the cantilever beam under the action of pure bending were used, and the new expressions of various cross sections were obtained based on energy principle. Then, the exact solutions of the cross section’s shear stress distribution of the cantilever beam under action of bending and torsion were derived and the coefficients obtained. The results show that the coefficients decrease when the terminal force departs from the bending center. The results are smaller than those given by Cowper because his theory doesn’t include the influence of shear stress perpendicular to the terminal force, and solution of the new method proved better.
- Timoshenko beam theory /
- shear coefficient /
- bending /
- torsion /
- shear stress

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参考文献(13)

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