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 引用本文: 王乐, 王亮. 一种新的计算Timoshenko梁截面剪切系数的方法[J]. 应用数学和力学, 2013, 34(7): 756-763.
WANG Le, WANG Liang. A New Method of Obtaining Timoshenko’s Shear Coefficients[J]. Applied Mathematics and Mechanics, 2013, 34(7): 756-763. doi: 10.3879/j.issn.1000-0887.2013.07.011
 Citation: WANG Le, WANG Liang. A New Method of Obtaining Timoshenko’s Shear Coefficients[J]. Applied Mathematics and Mechanics, 2013, 34(7): 756-763.

## 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

###### 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

## A New Method of Obtaining Timoshenko’s Shear Coefficients

• 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．
•  [1] Timoshenko S P.On the correction for shear of differential equation for transverse vibrations of bars of prismatic bars[J]. Philosophical Magazine,1921, 41(5):744-746. [2] 胡海昌.弹性力学的变分原理及其应用[M].北京：科学出版社, 1981: 139-147.(HU Hai-cang. Variational Principle for Elasticity and Its Application [M].Beijing:Science Press, 1981: 139-147.(in Chinese)) [3] Leibowitz R C, Kennard K H.Theory of vibrating nonlinear beams[R].David Taylor Model Basin, Reports, 1317, 1961:180. [4] Love A E H. A Treatise on the Mathematical Theory of Elasticity [M].Chapter 16. New York:Dover Publications, 1944. [5] Cowper G R.The shear coefficient in Timoshenko’s beam theory[J]. Journal of Applied Mechanics,1966, 33(3):393-398. [6] Stephen N G.Timoshenko’s shear coefficient from a beam subjected to gravity loading[J].Journal of Applied Mechanics,1980, 47(1):121-127. [7] 杜丹旭, 郑泉水.子空间变分原理的修正及其应用于确定梁的剪切系数[J].固体力学学报, 1996, 17(4):348-352.(DU Dan-xu, ZHENG Quan-shui.Revised subspace variational principle and its applications to determine shear coefficients of beams[J]. Chinese Journal of Solid Mechanics,1996, 17(4):348-352.(in Chinese)) [8] Hutchinson J R.Shear coefficients for Timoshenko beam theory[J]. Journal of Applied Mechanics,2001, 68(1):87-92. [9] Hull A J.Mindlin shear coefficient determination using model comparison[J].Journal of Sound and Vibration,2006, 294(1):125-130. [10] Kawashima H. The shear coefficient for quartz crystal of rectangular cross section in Timoshenko’s beam theory[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control,1996, 43(3):434-440. [11] Puchegger S, Loidl D, Kromp K, Peterlik H. Hutchinson’s shear coefficient for anisotropic beams[J].Journal of Sound and Vibration,2003, 266(2):207-216. [12] Omidvar B. Shear coefficient in orthotropic thin-walled composite beams[J]. Journal of Composites for Construction,1998, 2(1): 46-56. [13] 钱伟长, 叶开沅. 弹性力学[M].北京：科学出版社, 1956: 185198.(CHIEN Wei-zang, YEH Kai-yuan. Theory of Elasticity[M].Beijing:Science Press, 1956: 185-198.(in Chinese))

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##### 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

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