Cylindrical shells circumferential stress

Thick-walled cylindrical and spherical shells (internal pressure), minimum thickness based upon circumferential stress (longitudinal joints)... 

The exact calculation of radial and circumferential stresses in each layer requires the solution of N+2 linear equations in N-r2 unknowns, namely the N-H radial displacements of the layer boundaries, and the longitudinal strain of the vessel. We simplify by assuming that the internal pressure is applied only to the steel shell, and that the other layers follow the expansion of the steel. We also assume a condition of plane stress that is, no stress in the axial direction of the cylindrical vessel. We also consider the layer as being flat when layer stresses are being computed. 

The ellipsoidal shape is usual for closures of vessels that are six feet in diameter or greater. The hemispherical shape is preferred for vessels of a lesser diameter. The basic relationships for thin cylindrical shells under internal pressure assume that circumferential stress is dependent on the pressure and vessel diameter, but independent of the shell thickness. 

Cylindrical shell with circumferential stress long joints... 

Cylindrical shell with longitudinal stress circumferential joints... 

The design criteria of the ASME Code, Vni-1, and Section III, Division 1, Subsections NC except NC-3200, ND, and NE, are similar to those for Sections I and rv except that the ASME Code, VIII-1, and Section III, Division 1, Subsections NC, ND, and NE require cylindrical shell thickness calculations based on both the circumferential and the longitudinal directions. The minimum required thickness may be set by stresses in either direction. In addition, the ASME Code, VIII-1, permits the combination of primary membrane stress and primary bending stress to go as high as 1.5 5 at temperatures where tensile and yield strength control and 1.25 5 at temperatures where creep and rupture control, where 5 is the allowable tensile stress values. 

Example 8.2. A seamless cylindrical shell with an outside diameter of 30.0 in. is butt-welded to seamless ellipsoidal heads. The circumferential seams are not x-rayed. Find the required shell thickness if the allowable stress is 15,(XM) psi and the internal design pressure is 250 psi. Use Section Xni, Division 1 rules. 

Circumferential Stress in a Cylindrical Shell (Longitudinal Joints)... 

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