## Stresses in Shells |

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affine transformation angle applied arbitrary assume axial axis barrel vault beam bending moments bending stresses bending theory boundary conditions buckling coefficients components computation conditions of equilibrium const constant coordinate corresponding cross section curvature curve cylinder cylindrical shell deflection deformation derivatives determined diagram differential equations direction displacements distribution dome edge load elastic law external forces factor FlOgge following form force Nx formulas Fourier series functions harmonic HOOKE'S law hoop force hoop stress horizontal integration introduce line element magnitude membrane forces membrane theory meridian meridional force middle surface normal force numerical obtain parallel circle plane radial ring rotation shearing forces shearing stresses shell element shell of revolution shown in fig solution solve sphere spherical shell statically indeterminate strain stress resultants stress system Stresses in Shells symmetry tangent tank tions values variable vertical wall thickness yields zero