4 三次元撓角法とその立体骨組への応用に関する研究

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タイトル別名
  • 4) THE GENERALIZED SLOPE DEFLECTION EQUATION METHOD AND ITS APPLICATION TO SPACE FRAME ANALYSIS
  • 三次元撓角法とその立体骨組への応用に関する研究
  • 3ジゲンドウカクホウ ト ソノ リッタイ ホネグミ エ ノ オウヨウ ニ カンスル ケンキュウ

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The generalized slope deflection equation method to analyze any type of space frames is discussed herein. The equations for an arbitrary member are drawn from Castigliano's theorem and are set up with matrix forms which are based on one to one correspondence between vector quantities in space to column matrices of order three. Consequently one can observe every members in a space framework are in a system of co-ordinantes. Once the coefficients belonged to the members are established, the procedure of analysis will be the same for any type of frameworks and is essensially smilar to Wilson's slope deflection equation method. Provided that the joints of a framework structure are rigid, the equilibrium of forces and moments yield two equilibrium conditions for each joint. If a joint in the framework is not rigid, which may lead to other conditional equations instead of equilibrium equations. Then the general solutions for frameworks are also obtained in the form of matrices. In the case that the both ends of every members are assumed spherical hinged, the solution becomes truss analysis. It may be mentioned, therefore, that this method is applicable to all type of framework structures.

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