Cylindrical shells formulas

Although spherical vessels have a limited process application, the majority of pressure vessels are made with cylindrical shells. The heads may be flat if they are suitably buttressed, but preferably they are some curved shape. The more common types of heads are illustrated on Figure 18.16. Formulas for wall thicknesses are in Table 18.3. Other data relating to heads and shells are collected in Table 18.5. Included are the full volume V0 and surface S as well as the volume fraction V/V0 corresponding to a fractional depth H/D in a horizontal vessel. Figure 18.17 graphs this last relationship. For ellipsoidal and dished heads the formulas for V/V0 are not exact but are within 2% over the whole range. 

The ASME code formula for the thickness of a cylindrical shell is listed in UG-27, as t = PR/(SE — 0.6P)S In this formula, t is the minimum thickness of the shell (in.), P is the maximum allowable working pressure (MAWP) (psi), R is the internal radius of the vessel (in.), S is the allowable stress in the material listed in ASME Section II, and E is the weld joint efficiency. 

In the absence of corrosion, wind, and earthquake considerations and for internal pressures greater than the external pressure (i.e., excluding vacuum operation), the cylindrical shell wall thickness is computed from the ASME pressure-vessel code formula ... 

He et al. [48] 2005 Continuum cylindrical shell — Establishing an algorithm for buckling analysis of multi-waUed CNTs based on derived formula which considering Van der Waals interaction between any two layers of MWCNT... 

Figure 5.6 Comparison of formulas for hoop stress in a cylindrical shell. 

This appendix is a compilation of codes and standards for high-pressure vessels. The center of interest is the dimensioning and the lifetime evaluation of high-pressure vessels. Several codes and standards are evaluated detailed with a view to the applicability for high-pressure vessels. Primarily are described the respective formula for dimensioning of cylindrical shells under internal pressure. The limits of validity are a quite good indication for the application of the codes for high-pressure vessels. 

Internal-pressure design rules and formulas are given for cylindrical and spherical shells and for ellipsoidal, torispherical (often called ASME heads), hemispherical, and conical heads. The formulas given assume membrane-stress failure, although the rules for heads include consideration for buckling failure in the transition area from cylinder to head (knuckle area). 

Formula (1) is based on the static analysis of the shell of a cylindrical tank with constant wall thickness. Let us consider a thin-walled circular cylindrical tank of height //, internal radius r (distance from the vertical axis of symmetry to the wall surface) and wall thickness t, see Figure 3. 

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