3) ON THE MEMBRANE SOLUTIONS OF CANTILEVER AND OTHER CYLINDRICAL SHELL ROOFS

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  • 円筒シエル屋根の片持梁など2,3の薄膜解について
  • エントウ シエル ヤネ ノ カタモチバリ ナド 2 , 3 ノ ハクマクカイ ニ ツイテ

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Abstract

The membrane solutions of cylindrical shells are solved on the following probrems. 1) Differential settlement of supports of a simply supported roofs. 2) Shearing rigidity. 3) Cantilever shells loaded on the free edge by vertical and horisontal force, and torque. 4) Cantilever rectangular plates, as a limitting case. Conclusion: 1) A simply supported shell can be deformed without any extension by the differential settlement of supports. In this case, there is no bending stress according to this displacement even based on the bending theory, except St. Venant's twisting moment. 2) Shearing rigidity of a cylindrical shell is nearly equal to that of a plate, if the shell is shallow and the support does not move vertically. 3) On the cantilever shells, we find the following properties, when the shell becomes shorter. a) The shear center tends to move outside in case of ψ_1<π/2, and inside in case of ψ_1>π/2. b) Bending and shearing deformation can not be separated, exactly. But we can give a deformation formula for practical use as a sum of them. In this formula, the shearing deformation factor is not constant but depending on the span-radius ratio. c) The distribution of longitudinal stress tends to concentrate to edge, on the both cases of bending and Wagner's twisting, when the shell gets shorter.

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