Stresses in Spherical Shells Due to Local Loadings Over a Rectangular Area

Abstract

Analytical solutions for displacements, membrane stresses, and bending stresses in spherical shells due to local loadings over a rectangular area were developed. The three types of loading considered are radial load, overturning moment load, and tangential shear load.

Stresses from radial loads and external moments in spherical pressure vessels

“…This means that WRC 107, and thus American and British codes, give conservative estimates. The shell equations [12] used in this work are…”

“…where L and L are differential operators of coordinates (r, f, y), as de ned in the Appendix. Several authors [10,12,19] have presented these spherical shallow shell equations. In shallow geometry simpli cations, shear forces Q f and Q y are negligible in the meridional and tangential force equilibrium equations and membrane displacements u and are not considered in bending strain expressions.…”

“…However, until the work of Chao [12] this method had never been extended to spherical shells with rectangular attachments, although this type of attachment is often used for lifting and support legs (Fig. 1).…”

“…Analytical solutions for local displacements and stresses in cylindrical shells with loading over rectangular area were developed by Bijlaard [1][2][3] and other authors [4][5][6][7][8][9][10][11] using double Fourier series and different governing differential equations and models of attachments. However, until the work of Chao [12] this method had never been extended to spherical shells with rectangular attachments, although this type of attachment is often used for lifting and support legs (Fig. 1).…”

“…1). In the paper by Chao [12] the procedure to obtain the solution is described, but no results are presented. Therefore, the purpose of this investigation is to develop a computer program to determine displacements and stresses using this method and to validate the analytical results by comparison with numerical nite elements and experimental data.…”