Section 2 Cylindrical shells and drums subject to internal pressure
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Clasifications Register Rules and Regulations - Rules and Regulations for the Classification of Ships, July 2022 - Part 5 Main and Auxiliary Machinery - Chapter 10 Steam Raising Plant and Associated Pressure Vessels - Section 2 Cylindrical shells and drums subject to internal pressure

Section 2 Cylindrical shells and drums subject to internal pressure

2.1 Minimum thickness

2.1.1 Minimum thickness, t, of a cylindrical shell is to be determined by the following formula:

where

t, p, Ri, c and σ are defined in Pt 5, Ch 10, 1.2 Definition of symbols,

J = efficiency of ligaments between tube holes or other openings in the shell or the joint factor of the longitudinal joints (expressed as a fraction). See Pt 5, Ch 10, 1.9 Joint factors or Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes, whichever applies. In the case of seamless shells clear of tube holes or other openings, J = 1,0.

2.1.2 The formula in Pt 5, Ch 10, 2.1 Minimum thickness 2.1.1 is applicable only where the resulting thickness does not exceed half the internal radius, i.e. where t is not greater than 0,5Ri.

2.1.3 Irrespective of the thickness determined by the above formula, t is to be not less than:

  1. 6,0 mm for cylindrical shell plates.

  2. For tube plates, such thickness as will give a minimum parallel seat of 9,5 mm, or such greater width as may be necessary to ensure tube tightness, see Pt 5, Ch 10, 14.6 Fitting of tubes in water tube boilers.

2.2 Efficiency of ligaments between tube holes

2.2.1 Where tube holes are drilled in a cylindrical shell in a line or lines parallel to its axis, the efficiency, J, of the ligaments is to be determined as in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.2, Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.3 and Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.4.

2.2.2  Regular drilling. Where the distance between adjacent tube holes is constant, see Figure 10.2.1 Regular drilling,

where
d = the mean effective diameter of the tube holes, in mm, after allowing for any serrations, counterboring or recessing, or the compensating effect of the tube stub. See Pt 5, Ch 10, 2.3 Compensating effect of tube stubs and Pt 5, Ch 10, 2.4 Unreinforced openings.
s = pitch of tube holes, in mm.

2.2.3  Irregular drilling. Where the distance between centres of adjacent tube holes is not constant, see Figure 10.2.2 Irregular drilling:

where
d = is as defined in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.2
s 1 = the shorter of any two adjacent pitches, in mm
s 2 = the longer of any two adjacent pitches, in mm.

2.2.4 When applying the formula in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.3, the double pitch (s 1 + s 2) chosen is to be that which makes J, a minimum, and in no case is s 2 to be taken as greater than twice s 1.

Figure 10.2.1 Regular drilling

Figure 10.2.2 Irregular drilling

2.2.5 Where the circumferential pitch between tube holes measured on the mean of the external and internal drum or header diameters is such that the circumferential ligament efficiency determined by the formulae in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.2 and Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.3 is less than one-half of the ligament efficiency on the longitudinal axis, J in Pt 5, Ch 10, 2.1 Minimum thickness is to be taken as twice the circumferential efficiency.

2.2.6 Where tube holes are drilled in a cylindrical shell along a diagonal line with respect to the longitudinal axis, the efficiency, J, of the ligaments is to be determined as in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.7.

2.2.7 For spacing of tube holes on a diagonal line as shown in Figure 10.2.3 Spacing of holes on a diagonal line, or in a regular saw-tooth pattern as shown in Figure 10.2.4 Regular saw-tooth patten of holes, J is to be determined from the formula in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.8, where a and b, as shown in Figure 10.2.3 Spacing of holes on a diagonal line and Figure 10.2.4 Regular saw-tooth patten of holes, are measured, in mm, on the median line of the plate, and d, is as defined in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.2.

2.2.8 For tube holes on a diagonal line:

where
A =
B =
C =
cos α =
sin α =
α = angle between centreline of cylinder and centreline of diagonal holes.

Figure 10.2.3 Spacing of holes on a diagonal line

Figure 10.2.4 Regular saw-tooth patten of holes

2.2.9 For regularly staggered spacing of tube holes as shown in Figure 10.2.5 Regular staggering of holes, the smallest value of the efficiency, J, of all ligaments (longitudinal, circumferential and diagonal) is obtained from Figure 10.2.7 Compensation of welded tube stubsThe calculated minimum thickness is to satisfy 7.1, where a and b, as shown in Figure 10.2.5 Regular staggering of holes, are measured, in mm, on the median line of the plate, and d is as defined in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.2.

2.2.10 For irregularly spaced tube holes whose centres do not lie on a straight line, the formula in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.3 is to apply, except that an equivalent longitudinal width of the diagonal ligament is to be used. An equivalent longitudinal width is that width which gives, using the formula in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.2, the same efficiency as would be obtained using the formula in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes 2.2.8 for the diagonal ligament in question.

Figure 10.2.5 Regular staggering of holes

2.3 Compensating effect of tube stubs

2.3.1 Where a drum or header is drilled for tube stubs fitted by strength welding, either in line or in staggered formation, the effective diameter of holes is to be taken as:

where
d e = the equivalent diameter of the hole, in mm
d a = the actual diameter of the hole, in mm
t = the thickness of the shell, in mm
A = the compensating area provided by each tube stub and its welding fillets, in mm2.

2.3.2 The compensating area, A, is to be measured in a plane through the axis of the tube stub parallel to the longitudinal axis of the drum or header and is to be calculated as follows, see Figure 10.2.7 Compensation of welded tube stubsThe calculated minimum thickness is to satisfy 7.1 and Figure 10.2.8 Compensation of welded tube stubsThe calculated minimum thickness is to satisfy 7.1:

  • The cross-sectional area of the stub, in excess of that required by Pt 5, Ch 10, 7.1 Minimum thickness for the minimum tube thickness, from the interior surface of the shell up to a distance, b, from the outer surface of the shell;
  • plus the cross-sectional area of the stub projecting inside the shell within a distance, b, from the inner surface of the shell;
  • plus the cross-sectional area of the welding fillets inside and outside the shell;
where
=
t b = actual thickness of tube stub, in mm.

2.3.3 Where the material of the tube stub has an allowable stress lower than that of the shell, the compensating cross-sectional area of the stub is to be multiplied by the ratio:

Figure 10.2.6 Efficiency of ligaments between holes

Figure 10.2.7 Compensation of welded tube stubs
The calculated minimum thickness is to satisfy 7.1

Figure 10.2.8 Compensation of welded tube stubs
The calculated minimum thickness is to satisfy 7.1

2.4 Unreinforced openings

2.4.1 Openings in a definite pattern, such as tube holes, may be designed in accordance with the Rules for ligaments in Pt 5, Ch 10, 2.2 Efficiency of ligaments between tube holes, provided that the diameter of the largest hole in the group does not exceed that permitted by Pt 5, Ch 10, 2.4 Unreinforced openings 2.4.2.

2.4.2 The maximum diameter, d, of any unreinforced isolated openings is to be determined by the following formula:

The value of K to be used is calculated from the following formula:

where
= p, D o and σ are as defined in Pt 5, Ch 10, 1.2 Definition of symbols
t = actual thickness of shell, in mm.

2.4.3 For elliptical or oval holes, d, for the purposes of Pt 5, Ch 10, 2.4 Unreinforced openings 2.4.2, refers to the major axis when this lies longitudinally or to the mean of the major and minor axes when the minor axis lies longitudinally.

2.4.4 No unreinforced opening is to exceed 200 mm in diameter.

2.4.5 Holes may be considered isolated if the centre distance between two holes on the longitudinal axis of a cylindrical shell is not less than:

where
d = diameter of openings in shell (mean diameter if dissimilarly sized holes involved)
D = mean diameter of shell
t = actual thickness of shell

Where the centre distance is less than so derived, the holes are to be fully compensated.

Where two holes are offset on a diagonal line, the diagonal efficiency from Figure 10.2.6 Efficiency of ligaments between holes may be used to derive an equivalent longitudinal centre distance for the purposes of this paragraph.

2.5 Reinforced openings

2.5.1 Openings larger than those permitted by Pt 5, Ch 10, 2.4 Unreinforced openings are to be compensated in accordance with Figure 10.2.9 Compensation for welded standpipes or branches in cylindrical shells(a) or (b). The following symbols are used in Figure 10.2.9 Compensation for welded standpipes or branches in cylindrical shells(a) and (b):

t s = calculated thickness of a shell without joint or opening or corrosion allowance, in mm
t d = thickness calculated in accordance with 7.1 without corrosion allowance, in mm
t a = actual thickness of shell plate without corrosion allowance, in mm
t b = actual thickness of standpipe without minus tolerances and corrosion allowance, in mm
t r = thickness of added reinforcement, in mm
D i = internal diameter of cylindrical shell, in mm
d o = diameter of hole in shell, in mm
L = width of added reinforcement not exceeding D, in mm
C = in mm
D = and is not to exceed 0,5d o, in mm
σ = shell plate allowable stress, N/mm2
σp = standpipe allowable stress, N/mm2
σr = added reinforcement allowable stress, N/mm2
σw = weld metal allowable stress, N/mm2
Note
σp, σr and σw = are not to be taken as greater than σ.

Figure 10.2.9 Compensation for welded standpipes or branches in cylindrical shells

2.5.2 For elliptical or oval holes, the dimension on the meridian of the shell is to be used for d o in Pt 5, Ch 10, 2.5 Reinforced openings 2.5.1.

2.5.3 Compensation is to be distributed equally on either side of the centreline of the opening.

2.5.4 The welds attaching standpipes and reinforcing plates to the shell are to be of sufficient size to transmit the full strength of the reinforcing areas and all other loadings to which they may be subjected.


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