5 H.P.立体トラス曲面板の応力解析 : 立体トラス曲面板の理論的解析・その2

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タイトル別名
  • 5) THEORICAL ANALYSIS OF SPACE TRUSSED SHELLS (PART II) : STRESS ANALYSIS OF HYPERBOLIC PARABOLICAL SPACE TRUSSED SHELL
  • 立体トラス曲面板の理論的解析-2-
  • リッタイ トラス キョクメンバン ノ リロンテキ カイセキ 2

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In the last report, I presented the general solution of shallow space trussed shells. This solution, which consists of 3 differential equations of equilibrium and 2 equationns of compatibility, is derived on the following, assumptions. (a) All members are assumed to be perfectly elastic. (b) The thickeness is assumed to be very thin in comparison with other dimensions. (c) The meshes of the net are very numerous. This present paper is concerned with the stress analysis of a hyperbolic parabolical space trussed shell roof which is supported with hinge edges on the boundaries, under normal uniform load. Firstly, considering the transverse sectional forces acting on the small unit element which composes the space trussed shell itself, 3 differential equations of equilibrium are obtained respectively by Equations (2, a b c). Two equations of compatibility are determined by Equations (4) and (5). Now, the relations between the sectinal forces and the displacements are expressed in Equations (3, a b c d), (7, a b) and (8, a b c d). Finally, 3 equations of equilibrium and 2 equations of compatibility are transformed into 3 differential equations by the displacements u, v and w, as shown in Equations (12, a b c), which are calculated by the application of finite difference method. The stresses and the bending moments of the members are obtained by Equations (15, a b c d) and (16, a b c d). The deflections and the load carrying characteristics are shown in Fig. (7), (8), (9) and (10), which are compared with those of the space trussed plate under the same condition.

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