Bending of an Eccentric Circular Ring with a Cut Out Portion Undergoing Forces and Bending Couples at the Both Ends

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  • 切口に荷重または曲げ偶力をうける偏心円環
  • キリクチ ニ カジュウ マタハ マゲ グウリョク オ ウケル ヘンシンエンカン

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Abstract

To solve the problem of bending action of piston rings or crane hooks, we considered an eccentric circular ring with a cut out portion undergoing forces and bending couples at the both ends. Using the theory of elasticity for plane stress and applying bipolar coordinates, we obtained correct solutions for the above problem and compared the solutions with those by the usual elementary theory for curved bars. From the results of calculations, we have a conclusion that the solution by the usual elementary theory is very reliable, only when the eccentricity between the centers and the difference between the radii of two circles of the boundaries are small.

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