農業土木構造物に用いられる面構造の解法に関する研究
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概要
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The slabs are widely used in engineering structures of various kind types such as water tanks, retaining walls, floor slabs, reinforced-concrete breast walls, footing slabs, buttress dams and others. The studies of the deflection and moment of slab are most important part of the structural engineering and have been carried out since Sophie Germain obtained the fundamental eqution of thin-plate. In recent time, the study of slab has become to be perform more accurately for the ratioalization of design with construction of the massive structures. As is well known, however, the problems of the deflection caused by transverse loading of a wall of variable thickness and of a slab with an arbitrary external form and a circular hole involves considerably complex problems of boundary value. It is very difficult to obtain exact solutions to these problems and the author attempted to obtain an approximate practical solution for the deflection and moment of the slab as an integral part of these structures. Chapter 1 In this chapter, the process of development of the theory of slab is investigated and new topics for the discussion are taken up. Chapter 2 The solution of the problem of the variable thickness wall under earth pressure or hydraulic pressure is useually given by the solution of the cantilever beam. More precisely, however, the solution of the problem must be obtained from the theory of the plate of variable thickness with any boundary condition along the side and subjected to a transverse loading. In this chapter, deflections and bending moments of the zonal retaining wall under earth pressure are found. When the horizontal dimension of the wall is [enough large in comparison with its vertical dimension, the influence of the edge condition at both vertical sides can be neglected except for the neighbourhood of both sides by Saint Venant's principle. Therefore, we can assume that the wall is a semi-infinite cantilever wall of variable thickness clamped at the bottom edge. Solving the differential equation of equilibrium of walls of variable thickness [numerical formula] so as to satisfy the boundary conditions of semi-infinite cantilever wall, we can determine the deflection and moment of this wall. In the next place, a rectangular wall of variable thickness that is entirely free at the top edge, perfectly fixed along the other edges and subjected to a transverse traiangular loading is analyzed. These walls of variable thickness are of particular interest as an integral part of water tanks or retaining walls. If we assume that there is no abrupt variation in thickness of the wall, the deflection of wall w can be represented in the form of power series [numerical formula] by using Baker, Cowley-Levy's method. Substituting eq. (2) into eq. (1) and equating to zero the coefficients of succssive powers of λ, we obtain a sequence of differential equations [numerical formula] By solving the eq. (3) so as to satisfy the boundary conditions of this problem, the author gave an approximate solution with high precision for the deflection of wall. Chapter 3 In this chapter, the problems of the deflection caused by transverse loading of a rectangular slab with a circular hole are analyzed. It is very difficult to obtain exact solutions to these problems, and the author proposes an approximate solution by reffering to the Collocation method and a general solution of a differntial equation of slabs in polar coordinates system and Cartesian coordinates system. In this paper, arbitrary constants in general solution of a biharmonic differential equation of a slab are determined by exact boundary conditions on the edge of a circular hole and approximate boundary conditions which require exact boundary conditions only at the finite number of points selected on the external edge of the slab. The slabs with various kind of boundary conditions are analyzed by this method, and numerical examples for this analysis method are given. The model tests which are used steel plates and mortar slabs are carried out, and the stresses on model plates are measured by mean of wire strain gages. The stresses on the edge of a circular hole in rectangular slab are calculated by given method and compared with experimental stress values. Chapter 4 When the thickness of the slab increses finitely, the deformation due to the transverse forces such as shearing forces through the thickness of the slab which has been neglected in establishing the relation between stress and deflection of the slab can not be disregard. The inaccuracy of the customary thin-plate theory becomes of practical interest in the edge zones of plates and around holes that have a diameter which is not large in comparison with the thickness of the plate. The new fundamental equations governing the deflections and moments of the thick plates when shear deformation included have been developed by E. Reissner. In this chapter, the author derived an approximate analysis method for the thick rectangular slabs with a circular hole by using Reissner's new differential equations and the Collocation method in previous chapter.
- 大阪府立大学の論文
- 1971-03-31