Basic Equations

The allowable stress f  for mainly statically loaded construction components is equal to the material strength K divided by the safety factor S  

       f = K/S.                                                                                                                   (6.3-1)

Table 6.3-1: Material strength K and corresponding safety factor S for forged and rolled steels with mainly statically loading under internal pressure.

*) T is the minimum service life time, T > 100.000 hours. If the correct life time is not known use: T=200.000h. In exceptional cases with short loading (e.g. purging) T = 10.000 hours.

If only values for T=100.000 hours exist, the safety factor S=1.5 must be used.

When the creep characteristics for fully loaded weld seams are not available, the strength values for the basic material must be reduced by 20%, if they are used for the calculation of weld constructions with fully loaded weld  seams. (e.g. axially welded pipe).

For austenitic steels with R_p0,2/R_m < 0.5 at 20 °C the yield strength R_p1,0/tc (1% offset) can be used instead of R_p0,2/tc (0.2 % offset).

Table 6.3-2: Criteria for the design strength K and the corresponding safety factor S for cast iron and cast steel according to requirements of section 2 of the standard.

The allowable stress for test pressure is

       f' = K'/S'.                                                                                                                   (6.3-2)

Table 6.3-3: Strength value K' and allowable safety factor S' for test pressure p'

The required wall thickness of cylinders is defined in sections 7.1 and 7.2. Below follows the required wall thickness with allowances (7.1-1) and the required thickness for internal pressure without allowances

The weakening of the basic body can be compensated a) by an increased thickness of the basic body or b) a thick walled nozzle.

a)     Increased wall thickness of the basic body on a minimum length of l_rs.

b)     Increased wall thickness e_rb of the nozzle on a minimum length of l_b1; conditions for e_rb/e_rs:

c)     Thickening in the opening region (Forging, cutting)

d)     Reinforcement plates

Symbols:

For different variants of design type 1, the diameter d and depth h₁ can be so selected that the equivalent diameter in Eq. (8.2-7) corresponds with the required value in the European norm, see also Fig.2 to Fig. 6.

Fig. 2: Single opening with d1=d=opening diameter (Fig. 8.2-1 European norm 12952-3)

Fig. 3: Attached nozzle (d1=nozzle outside diameter)

Fig. 4: Roller expanded and seal welded pipe

Fig. 5: Roller expanded pipe with graded hole 

Fig. 6: Partial drill hole (d=0)

Adjacent openings can be calculated as single branches when the distance P_φ is larger than the theoretical support length given by eq. (8.1-4). Otherwise, the combined weakening factor ν_m can be calculated with eq. (8.2-12).

Section 8.3 of the Euronorm considers also the support effect of the nozzles. The calculation is performed in design type 2 with five variants according to Figure 7.

Fig. 7: Variants of the vertical nozzle of design type 2:

1 Set through nozzle with seal welding; 2 Set on nozzle; 3 Welded nozzle attached at extruded cylinder; 4. Conical transitions and roundings; 5 Integral branch. 

The detailed Figures for the variants are illustrated in Figures 8 to 12. Equations (8.3-2) and (8.3-4) for the allowable stress of the shell can be written in the form

Fig.8: Set through nozzle with seal welding. 

Fig.9: Set-on nozzle

Fig.10: Welded nozzle attached at extruded cylinder

Fig.11: Conical transitions and roundings

Fig.12: Integral branch

The strength conditions for the calculated circumferential stress f_a on the left and right side of the opening are

The variables f_s  and f_b signify the allowable stress in the shell and nozzle, respectively.

Fig.13: Single openings with oblique nozzle and reinforcement (design type 3)

Fig. 14: Loading diagram for a cylindrical shell with non-radial branch

The strength condition (8.3-2) holds, with the areas according to Fig. 14. For design type 4, one or two non-radial branches can be selected. When a single branch is calculated, the values for branch II will not be considered. Different additional variables for the calculation are illustrated in Fig.19.

Fig.15: Loading diagram for a Y-shaped branch

The strength condition (8.3-10) holds

Fig.16: Forged and drilled integral branches.

For this type of integral branch holds Eq. (8.3-10) for design type 5 with y=1.

Fig. 17a: Loading areas in the axial section.

Fig.17a&b: Loading diagram for cylindrical shells with adjacent nozzles placed at an angle  f  to the shell axis.

Fig.18: Loading diagram for cylindrical shells with  non-radial branch placed circumferentially

The circumferential stress f_aφ on the left and right of the opening and the weakening factor are