Section 4 Dished ends subject to internal pressure

4.1.1 The thickness, t, of semi-ellipsoidal and hemispherical unstayed ends, and the knuckle section of torispherical ends, dished from plate, having pressure on the concave side and satisfying the conditions listed below, is to be determined by the following formula:

4.1.2 For semi-ellipsoidal ends:

the external height, H ≥ 0,18 D _o

Figure 4.4.1 Shape Factor

4.1.3 For torispherical ends:

• the internal radius, R _i ≤ D _o
• the internal knuckle radius, r _i ≥ 0,1D _o
• the internal knuckle radius, r _i ≥ 3t
• the external height, H ≥ 0,18 D _o and is determined as follows:

4.1.4 In addition to the formula in Pt 15, Ch 4, 4.1 Minimum thickness 4.1.1 the thickness, t, of a torispherical head, made from more than one plate, in the crown section is to be not less than that determined by the following formula:

where t, p, R _i, σ and J are as defined in Pt 15, Ch 4, 1.7 Definition of symbols.

Figure 4.4.2 Typical dished ends

4.1.5 The thickness required by Pt 15, Ch 4, 4.1 Minimum thickness 4.1.1 for the knuckle section of a torispherical head is to extend past the common tangent point of the knuckle and crown radii into the crown section for a distance not less than mm, before reducing to the crown thickness permitted by Pt 15, Ch 4, 4.1 Minimum thickness 4.1.4,

4.1.6 In all cases, H, is to be measured from the commencement of curvature, see Figure 4.4.2 Typical dished ends.

4.1.7 For fusion welded pressure vessels the minimum thickness of the head, t, is to be not less than where D _i is as defined in Pt 15, Ch 4, 1.7 Definition of symbols.

4.1.8 For ends which are butt welded to the shell the thickness of the edge of the flange for connection to the shell is to be not less than the thickness of an unpierced seamless or welded shell, whichever is applicable, of the same diameter and material and determined by Pt 15, Ch 4, 2.1 Minimum thickness.

4.2.1 The shape factor, K, to be used in Pt 15, Ch 4, 4.1 Minimum thickness 4.1.1 is to be obtained from the curves in Figure 4.4.1 Shape Factor, and depends on the ratio of height to diameter .

4.2.2 The lowest curve in the series provides the factor, K, for plain (i.e. unpierced) ends. For lower values of , K depends upon the ratio of thickness to diameter, , as well as on the ratio , and a trial calculation may be necessary to arrive at the correct value of K.

4.3.1 Openings in dished ends may be circular, obround or approximately elliptical.

4.3.2 The upper curves in Figure 4.4.1 Shape Factor provide values of K, to be used in Pt 15, Ch 4, 4.1 Minimum thickness 4.1.1, for ends with unreinforced openings. The selection of the correct curve depends on the value of and a trial calculation is necessary to select the correct curve,

4.3.3 The following requirements must in any case be satisfied:

4.3.4 From Figure 4.4.1 Shape Factor for any selected ratio of the curve for unpierced ends gives a value for as well as for K. Openings giving a value of not greater than the value so obtained may thus be pierced through an end designed as unpierced without any increase in thickness.

4.4.1 The requirements in Pt 15, Ch 4, 4.3 Dished ends with unreinforced openings apply equally to flanged openings and to unflanged openings cut in the plate of an end. No reduction may be made in end plate thickness on account of flanging.

4.4.2 Where openings are flanged, the radius, r _m of the flanging is to be not less than 25 mm, see Figure 4.4.2 Typical dished ends. The thickness of the flanged portion may be less than the calculated thickness.

4.5.1 Unreinforced and flanged openings in dished ends are to be so arranged that the distance from the edge of the hole to the outside edge of the plate and the distance between openings are not less than those shown in Figure 4.4.3 Limits for reinforcement.

Figure 4.4.3 Limits for reinforcement

4.6.1 Where it is desired to use a large opening in a dished end of less thickness than would be required by Pt 15, Ch 4, 4.3 Dished ends with unreinforced openings, the end is to be reinforced. This reinforcement may consist of a ring or standpipe welded into the hole, or of reinforcing plates welded to the outside and/or inside of the end in the vicinity of the hole, or a combination of both methods, see Figure 4.4.4 Opening in dished ends. Forged reinforcements may be used.

4.6.2 Reinforcing material with the following limits may be taken as effective reinforcement:

1. The effective width, ₁ of reinforcement is not to exceed or 0,5d _o whichever is the lesser.

2. The effective length, ₂ of a reinforcing ring is not to exceed

   where

   R i	=	the internal radius of the spherical part of a torispherical end, in mm, or
   R i	=	internal radius of the meridian of the ellipse at the centre of the opening, of a semi-ellipsoidal end, in mm, and is given by the following formula:
   	=

   	=	where a, b and x are shown in Figure 4.4.2 Typical dished ends
   d o	=	external diameter of ring or standpipe, in mm 1 and 2 are shown in Figure 4.4.3 Limits for reinforcement
   t b	=	actual thickness of ring or standpipe, in mm

4.6.3 The shape factor, K, for a dished end having a reinforced opening can be read from Figure 4.4.1 Shape Factor using the value obtained from:

As in Pt 15, Ch 4, 4.3 Dished ends with unreinforced openings, a trial calculation is necessary in order to select the correct curve.

Figure 4.4.4 Opening in dished ends

4.6.4 The area shown in Figure 4.4.3 Limits for reinforcement is to be obtained as follows:

• Calculate the cross-sectional area of reinforcement both inside and outside the end plate within the length, ₁, plus the full cross-sectional area of that part of the ring or standpipe which projects inside the end plate up to a distance, ₂, plus the full cross-sectional area of that part of the ring or standpipe which projects outside the internal surface of the end plate up to a distance, ₂, and deduct the sectional area which the ring or standpipe would have if its thickness were as calculated in accordance with Pt 15, Ch 4, 5.1 Minimum thickness.

4.6.5 If the material of the ring or the reinforcing plates has an allowable stress value lower than that of the end plate, then the effective cross-sectional area, A, is to be multiplied by the ratio:

4.7.1 If an opening and its reinforcement are positioned entirely within the crown section, the compensation requirements are to be as for a spherical shell, using the crown radius as the spherical shell radius. Otherwise, the requirements of Pt 15, Ch 4, 4.6 Dished ends with reinforced openings are to be applied.