交叉梁型版構造の一般的応力解析法 : その 1 一般式

Abstract

The authors deal with the methods of stress analysis of cross beam structures which behave as plates. The composing members of the system are assumed to be elastic, and the effects of shearing, twisting and bending deformations are included. While connections are assumed to be rigid. In this paper following three methods are described : (i) Slope-deflection method. At every joint there are three displacements, one deflection and two rotations, as unknowns and three equilibrium equations are brought out. (ii) Difference equation. If same structural units are repeated, simultaneous difference equations can be formulated. The number of equations is 3 N, where N is the number of joints included in one unit. The equations are presented by using linear operators, to which three rules, i.e. addition, subtraction and multiplication, are availabe. Using the matrix of these operators the authors propose "a parametric function", from which all displrcements can be derived by the difference operation without summing up procedure. (iii) Differential equation. As an approximate method, the differential equations are derived from the difference equations, developing the displacements into Taylor series and the accuracy on this procedure is discussed. Also "a parametric function" is used. The partial differential equation with respect to the displacement w is the 6th order, because it includes shearing deformation. When shearing deformation is neglected, the order of the above equation reduces to four. This 4th order equation corresponds to that of the anisotropic plate derived from Kirchhoff's assumptions.