格子梁の差分法による解法

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タイトル別名
  • AN ANALYSIS OF GRIDWORKS BY DIFFERENCE EQUATION
  • コウシリョウ ノ サブンホウ ニ ヨル カイホウ

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抄録

In the previous reports, various references were made to the studies of the statically determinate spaced trusses by introducing difference equation for solving the problems. However, in addition to the conditions of equilibrim, the statically indeterminate structures must be checked on the basis of deformation theory together with the grid girders which bring forward the problems of resemblance in conditions of stress with the statically indeterminate spaced trussed flat plates. To deal with the problems, firstly, the equilibrim of bending moments and shears at the intersecting grid points are obtained by difference equation neglecting the twisting moments and assuming that grid girders are in isotropy conditions. Secondly, by using the "method of elastic weights" in the grid points, the relations of bending moments and vertical displacements are expressed in form of difference. Then, we obtain the difference equations of displacements or bending moments by substituting the former equation into the latter. Thus its approximate formulas are obtained by assuming the shearing rigidities. To ascertain the probability, we have checked "difference pattern" at each points in accordance with the various boundary conditions on the several examples by computing the linear equations to determine these difference equations and the results obtained on each case proved that the suggested approximate formula can be used with ease and its error may be considered negligibly small compared with the values obtained from the established formulas. The above method is excellent especially in case of multiple grids as the use of electronic computers broaden in scope, and is considered to be most useful for wider and practicable application.

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