СПОСОБ Б.Н. ЖЕМОЧКИНА В РАСЧЕТАХ ПЛИТ В ФОРМЕ ЧАСТИ КРУГА ИЛИ КОЛЬЦА НА ПРОИЗВОЛЬНОМ УПРУГОМ ОСНОВАНИИ

Abstract

Abstract. Problems of calculating slabs on an elastic foundation in polar coordinates in the traditional formulation without taking into account the shear stresses in the contact zone are considered. The shape of the plates is taken in the form of a sector of a circle with an arbitrary angle or part of a ring. Analytical solutions for such problems are known for slabs of a circular or annular plan. The calculation is carried out by the Zhemochkin method, therefore, the deflections of the slab are first determined in the form of a sector of a circle with an arbitrary angle or a part of a ring with a clamped normal. This stage of the calculation is performed by the Ritz method, where the terms of the series by the product of the powers of the radius by the trigonometric functions of the angular coordinate are taken as the coordinate functions. The expressions obtained for the deflections of a slab with a clamped normal make it possible to form a system of resolving equations of the Zhemochkin method, the solution of which is the linear and angular displacements of the introduced clamping and the distribution of reactive stresses under the slab. Further, by known methods, the movements of the slab on the elastic foundation and the forces in it are determined. Two examples are given for slabs in the form of a semicircle and an annular sector with a right angle on an elastic half-space. The results obtained can find application in the calculation of circular and ring foundations for non-axisymmetric loads and slab foundations of complex shapes in polar coordinates.