Four boundary conditions,such as fixed clamp,moving clamp,hinge support and simple support,are considered. The load of homogeneous distribution and the load of homogeneous loundary bending moment are considered in examples of calculation.

Two methods for analyzing caisson-beams are introduced in this paper.One is the well-known method of redundant forces. The author has simplified this methed by using couples of redundant forces to set up a typical equation and pointing out the rule that the matrix of the coefficients of simultaneous linear equations which are organized from the expansion of that typical equation. This method can be easily solvd when the number of unknown redundant forces, or that of equations, is less than 3 or 4; but it will...

Two methods for analyzing caisson-beams are introduced in this paper.One is the well-known method of redundant forces. The author has simplified this methed by using couples of redundant forces to set up a typical equation and pointing out the rule that the matrix of the coefficients of simultaneous linear equations which are organized from the expansion of that typical equation. This method can be easily solvd when the number of unknown redundant forces, or that of equations, is less than 3 or 4; but it will be difficult when the number is more than that. In order to solve this difficulty the author suggests another kind of method of which the essential principle is mentioned in the following.Supposing that the distance between the beams is sufficiently short in comparing with their spans, we can set up a partial differential equation for its deffiection W, as we often do in the theory of elasticity. In this way we can solve it with its boundary conditions of simple supporting by sine series. From this we can easily get the formulas of bending moments, shears and twist moments of each beam by partially differentiating the function of deffiection. The result of the calculation proves that it quite agrees with the method of redundant forces when the distance between beams is no longer than 1/5 of their spans.There are some tables given in this raper for practical use.

The paper deals with a new approach of the limit analysts of conical shells subjected to internal uniform pressure. On the basis of carrying-capacity from membrane theory, a rational correction is made for the bending effect according to the nature ofactual supporting condition. If the characteristic number of shell is suf-ficiently small, very simple formulae are obtained for the carrying capacity in the case of unmovable simple support as well as in the case of fixed support. The comparison with...

The paper deals with a new approach of the limit analysts of conical shells subjected to internal uniform pressure. On the basis of carrying-capacity from membrane theory, a rational correction is made for the bending effect according to the nature ofactual supporting condition. If the characteristic number of shell is suf-ficiently small, very simple formulae are obtained for the carrying capacity in the case of unmovable simple support as well as in the case of fixed support. The comparison with experimental data gives satisfactory result. The formula of the carrying-capacity is:where p-internal pressure, a-yield limit stress, h-thickness of shell, a-radius of shellbottom, r-half of vertex angle, , a= 1.45 of 1.65 according to casesof unmovable simple support or clamped support on the bottom of shell respectively.

This paper deals with the calculation or deflections and internal forces of shallow spherical shells under external uniform pressure by means of finite element method. Comparing with the well known approximate formula that of the boundary effect superposing to membrance solution, the cause producing a considerable error in the formula had been fond for an example of shallow spherical shell clamped on square bottom, Consequently, a modified fornmla has been proposed by producting a sum of infinite geometric progression....

This paper deals with the calculation or deflections and internal forces of shallow spherical shells under external uniform pressure by means of finite element method. Comparing with the well known approximate formula that of the boundary effect superposing to membrance solution, the cause producing a considerable error in the formula had been fond for an example of shallow spherical shell clamped on square bottom, Consequently, a modified fornmla has been proposed by producting a sum of infinite geometric progression. Results obtained in this paper for the above example are identical to that obtained by finite difference method. Additionally, for the singularity at corners or shallow spherical shells simple supported on hexagonal bottom, successive and automatic computation in fine mesh has been made using a transformation of similitude.