Journal of South China University of Technology (Natural Science Edition) ›› 2008, Vol. 36 ›› Issue (6): 30-34.

• Mechanics • Previous Articles     Next Articles

Precision Analysis of Classical Bending Deflection Formulae of Simply-Supported Beams

Yang Yi1  Liu Ji-ke2   

  1.  1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, Guangdong, China; 2. Department of Mechanics, Sun Yat-sen University, Guangzhou 510275, Guangdong, China
  • Received:2007-07-13 Revised:2007-10-29 Online:2008-06-25 Published:2008-06-25
  • Contact: 杨怡（1975-），男，博士，助理研究员，主要从事振动理论及其应用研究． E-mail:yiyang@scut．edu．cn
  • About author:杨怡（1975-），男，博士，助理研究员，主要从事振动理论及其应用研究．
  • Supported by:

    国家自然科学基金资助项目（10772202,10672060）;中国博士后科学基金资助项目（20060400757）

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Abstract:

A new deformation mode of the simply-supported beam is presented, which considers not only the deflection and slope but also the plane transmutation in the cross section. Then, the plane bending of the simply-supported beam is analyzed by means of the U-transformation and the four-node rectangular element, and the analytical displacements on the upper and lower surfaces under a concentrated load of magnitude in a two-dimension finite element mode are obtained. The displacements are compared with the deflection calculated on the basis of the material mechanics. Moreover, the applicable field of the classical bending deflection formulae of the simply-supported beam is discussed, and the corresponding precision is quantitatively analyzed.

Key words: U-transformation, simply-supported beam, plain bending, deflection, precision, analytical solution