Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (7): 933-941 .doi: https://doi.org/10.1007/s10483-008-0712-x

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Exact solution for warping of spatial curved beams in natural coordinates

ZHU Li-li 1,2, ZHAO Ying-hua1   

  1. 1. Institute of Road and Bridge Engineering, Dalian Maritime University,Dalian 116026, Liaoning Province, P. R. China;
    2. School of Mechanical Engineering, Dalian Jiaotong University,Dalian 116028, Liaoning Province, P. R. China
  • Received:2008-01-14 Revised:2008-04-28 Online:2008-07-03 Published:2008-01-01
  • Contact: ZHAO Ying-hua

Abstract: The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present
theory are demonstrated by comparing its numerical results with Heins' solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

Key words: curved beam, multiple loads, warping, natural coordinate, analytical solution

2010 MSC Number: 

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