Abstract
A practical solution is derived on the following assumptions for an isotropic cylindrical shell roof which has stiffening ribs either in the transverse direction or in the axial direction, or in the both directions. (1) Poisson's ratio is assumed to be zero. (2) The eccentricity of the stiffening rib is assumed as negligible. (3) The radial shear is assumed as negligible in the differential equation of equilibrium for the transverse sectional forces acting on the shell's infinitesimal elements. The characteristic values in this approximation are given by Equation (16) in the text, and the sectional forces and the displacements are given by Equations (27) and (28) respectively. The characteristic values are determined only by the parameter √<Rt/l>(R=radius, t=thickness and l=longitudinal span), the axial extensional rigidity ratio d_x=D_x/D_<xφ> and the transverse flexing rigidity ration k_φK_φ/K_<xφ>. Consider an isotropic cylindrical shell having the exactly same characteristic values as an anisotropic cylindrical shell. This isotropic shell is called the equivalent isotropic cylindrical shell of the anisotropic cylindrical shell. The radius, thickness and longitudinal span of the anisotropic shell are represented by R, t, l and those of the equivalent shell by R_0, t_0, l_0. If the radius and the central angle of the equivalent shell are, taken as the same as those of the anisotropic shell, and 1/k_φ is neglected in comparison to 1 because k_φ is very large, the characteristic equation of the anisotropic shell is equal to that of the isotropic shell. This can be seen by Equation (29) in the text. Then the dimensions of the equivalent isotropic shell can be given by the following equation. [numerical formula] Now the relation expressed in Equation (37) in the text is possible between the sectional forces and the displacements of the anisotropic shell and those of the isotropic shell. This makes it possible to find out the sectional forces and the displacements of the anisotropic cylindrical shell by just obtaining those of the equivalent shell without taking the trouble of finding a solution for the anisotropic cylindrical shell which are subjected to the edge loads. With this method followed, and if use is made of the numerical tables relevant to isotropic shells already published, it should be a simple procedure to perform the numerical calculations for the sectional forces and the displacements of any anisotropic cylindrical shell. In Equation (37), (F) represents the edge loads of the isotropic shell and [F]_i is given by Equation (36).
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More From: Transactions of the Architectural Institute of Japan
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