Cylindrical shells longitudinal stress

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

Figure 8.7 Stresses in a thin cylinder snbjected to an internal pressure, P (a) cylindrical shell nnder internal flnid pressure (b) longitudinal stress development (c) hoop stress development. Reprinted, by permission, from G. Lewis, Selection of Engineering Materials, p. 139. Copyright 1990 by Prentice-Hill, Inc.

Similarly, the total downward pressure on the semicircular portion of the cylindrical shell below the diametral plane XX is also 2prL. These two equal and opposite pressures act to burst the cylinder longitudinally at the plane XX. The resisting force comes from the hoop stress. Thus... 

Cylindrical shell with longitudinal stress circumferential joints... 

The hoop stress in a cylindrical shell with closed ends is pR/t and the longitudinal stress is pR/(fit), where p is the internal pressure, R the mean radius and t the thickness. If the shell is of diameter 0.5 m and a thickness of 12.5 mm, and is subjected to an internal pressure of 7 MPa, determine the maximum shear stress, the stress intensity and the von Mises equivalent stress. What is the factor of safety corresponding to (a) Tresca criterion, and (b) von Mises criterion if the material yield strength is 160 MPa ... 

Let us consider a long thin cylindrical shell of radius R and thickness f, subject to an internal pressure p. By thin shells we mean the ones having the ratio R/1 typically greater than about 10. If the ends of the cylindrical shell are closed, there will be stresses in the hoop as well as the axial (longitudinal) directions. 

Let us take the special case of discontinuity at a juncture between a cylindrical vessel and a hemispherical head subjected to internal pressure p. For simplicity let us assume the spherical head and the cylindrical shell are of the same thickness. If the mean radius and the thickness of the shell are denoted by Pm and t respectively, then the hoop and the longitudinal stresses in the cylindrical shell are given by ... 

The stress concentration caused by a hole in a plate due to uniaxial tension or biaxial tension will be considered. The biaxial tension would correspond to a cylindrical shell or a spherical shell subject to internal pressure. For the case of a cylindrical shell, the biaxiality is 2 1 corresponding to hoop and longitudinal strain for the case of a spherical shell, the biaxiality ratio is 1 1. 

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. 

As in Problem 11.2, what is the distance from the edge of the opening along the longitudinal axis in a cylindrical shell under internal pressure if required to have a stress of l.lSm ... 

Example 11.15. A cylindrical shell that is 84-in. ID by 1.0-in. nominal thickness contains a nozzle 8-in. ID by 1.0-in. nominal thickness. The design pressure is 400 psi and the allowable stress of the material is 17.5 ksi. The nozzle is subjected to an inward radial loading of 12,000 lb and an applied moment in the longitudinal direction of 150,000 in.-lb. What are the combined stresses on the longitudinal axis due to these two external loadings using the Mershon method and the curves in Appendix K The vessel is not subjected to cyclic loading, and therefore no stress concentration factors need be considered. 

I lxample 16.6. For the vessel described in Example 16.1, determine the total longitudinal stress in the cylindrical shell above and below the support line that IN at the lower shell-to-head junction. The value of SE = 15,000 psi. 

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 shell is subjected to internal hydrostatic pressure P and all resulting forces are carried by the fibers, which are considered to constitute an undeformable membrane. Tj and T2 are the normal components of stress in the latitudinal and longitudinal directions at a point r, 6, z). Because of cylindrical symmetry, Tj and T2 are independent of 6 and because there are equal numbers of fibers inclined at a, and r - a, (f = 1,2,. .. ), the shearing components of stress are zero. 

---