ASME Section 1 Dished Head Calculations PDF

Code Calculations - ASME Section I • Chapter 2 ^ OBJECTIVE 3 Given the required specifications and operating conditions, use the formula in ASME BPVC Section 1, PG-29.1 to calculate the minimum required thickness of a seamless, unstayed dished head. DISHED HEAD CALCULATIONS A dished head is a cur...

Code Calculations - ASME Section I • Chapter 2 ^ OBJECTIVE 3 Given the required specifications and operating conditions, use the formula in ASME BPVC Section 1, PG-29.1 to calculate the minimum required thickness of a seamless, unstayed dished head. DISHED HEAD CALCULATIONS A dished head is a curved end-section that closes off cylindrical components such as shells and drums. There are several shapes of dished heads used for both boilers and pressure vessels, but the terminology differs slightly between Section I and Section VIII of the ASME Boiler and Pressure Vessel Code. There are three types of dished heads described in Section I as defined in Table 3. Refer to Figure 3 for illustrations of the three types. Table 3 - Dished Head Types Section I Section VIII Description Segment of a sphere Torispherical This is the standard dished head, also called a flanged and dished head. The curved portion, with radius L, is attached to a cylindrical flange through a knuckle with a PG-29.1 to PG-29.6 UG-32(d) transition section, which encompasses this comer radius, radius r, called the comer radius. A knuckle is simply the between the curved portion (the dish) and the cylinder. See Figure 4. Ellipsoidal In this design, the length of the long axis D is twice the PG-29.7 to PG-29.8 UG-32(c) length of the minor axis h. Full hemispherical Hemispherical PG-29.11 toPG-29.13 UG-32(e) Semi-ellipsoidal This type of head is a half-sphere where radius L equals one-half the diameter D. Figure 3 - Dished Head Types Segment of a sphere (torispherical) Semi-ellipsoidal (ellipsoidal) 3rd Class Edition 3 • Part A2 Full hemispherical (hemispherical) 83 ^ Chapter 2 • Code Calculations - AS ME Section I Figure 4 - Pressure Vessel Head Showing the Location of the Knuckle 0.06L ^. I. De_ ^ (outside diameter) L=DO CALCULATIONS FOR DISHED HEADS (SEGMENT OF A SPHERE) As noted in Table 3, a head dished to a segment of a sphere is also called a.flanged and dished head. The curved portion, with radius L, is attached to a cylindrical flange through a knuckle with radius r, called the corner radius. The calculations for dished heads that are shaped to a segment of sphere are found in Section I, PG-29.1 to PG-29.6. The following paragraphs from PG-29 must be considered when performing calculations on dished heads. Paragraph PG-29.1: The thickness of a blank, unstayed+ dished head with the pressure on the concave side, when it is a segment of a sphere, shall be calculated by the following formula: { = 5 PL 4.8 Sw PG-29.1 thickness of dished head (segment of a sphere) The symbols in this formula are defined as follows: t = minimum thickness of plates (mm) P = MAWP(MPa) L = radius (mm) to which the head is dished, measured on the concave side S = maximum allowable stress (MPa) using values in Section II, Table 1A w = welded joint strength factor per PG-26 84 3rd Class Edition 3 • Part A2 Code Calculations - ASME Section I • Chapter 2 ^ Note: PG-26 states that a weld joint strength reduction factor (w) shall be applied in the design of the following: 1. Cylinders containing longitudinal butt welds 2. Hemispherical heads or any other spherical sections that comprise segments joined by welding This means that for dished heads, w must be determined from Table PG-26 using material type and temperature values. Unlike the calculations for pipes or tubes, there is no efficiency factor (£) for a seamless head. The w factor is determined by material and temperature. As for cylinder calculations, Table PG-26, Note 3 does allow an exemption for components constructed of carbon steel. ^Note: A blank" head is a head with no openings. Dished heads do not require being stayed, unlike flat heads. Along with this basic calculation in PG-29.1, some additional calculations are required using paragraphs PG-29.2 to PG-29.6. Paragraph PG-29.2 The radius L to which the head is dished shall be not greater than the outside diameter D of the flanged portion of the head, as shown in Figure 5. Where two radii are used, the longer radius shall be used as the value of L in the formula. Figure 5 - Dimensions of Dished Head PG-29.2 Paragraph PG-29.3: When a head, dished to a segment of a sphere, has a flanged-in manhole or access opening that exceeds 150 mm (6 in) in any dimension, then the thickness must be increased by no less than 15% of the required thickness for a blank head, as calculated by the formula in PG-29.1, but in no case less than 3.0 mm (1/8 in) additional thickness. Note: This would apply to a manhole found on the end of a boiler drum. Paragraph PG-29.5: Where the radius L to which the head is dished is less than 80% of the outside diameter of a head, the thickness of a head with a flanged-in manhole opening shall be at least that found by making L equal to 80% of the outside diameter of the head and with the added thickness for the manhole. This shall be the minimum thickness t of a head with a flanged-in manhole for any form of head. (Note: The geometry for a small radius head is shown in Figure 6. In this case, the head is more extended and not as flat as the head in Figure 5.) 3rd Class Edition 3 • Part A2 85 ^ Chapter 2 • Code Calculations - ASME Section I Figure 6 - Low Radius Dished Head PG-29.5 Paragraph PG-29.6: No head, except a full-hemispherical head, shall be of lesser thickness than required for a seamless shell of the same diameter. Example 7: Calculate the thickness required of a seamless, unstayed dished head Calculate the thickness of a seamless, unstayed dished head with pressure on the concave side, with a flanged-in manhole that measures 300 mm by 400 mm. The head has a diameter of 1235 mm and is a segment of a sphere with a dish radius of 1016 mm. The MAWP is 1380 kPa, the material is SA-285-C, and the metal temperature does not exceed 204°C. Solution 7 The material is carbon steel plate as indicated in PG-6. For a dished head with a flanged-in manhole, first check that the radius L of the dish is at least 80% of the diameter of the shell (PG-29.5). 1016mm = 0.823 = 82.3% 1235 mm This is greater than 80%, so the value of L is in compliance with PG-29.5. Therefore, the value of L used in the formula will remain at 1016 mm. Use the formula from PG-29.1: { = Given 5 PL 4.8 Sw P = 1.380 MPa L = 1016mm (radius of curvature of the sphere) from Table 1A S = 108 MPa w = 1.0 (Table PG-26, Note 3 says carbon steel exempt, so w = 1.0) Substitute these values into the equation: t = 5 PL 4.8 Sw 5xl.380MPaxl016mm 4.8 x 108 MPa x 1.0 7010.4 518.4 13.52 mm 86 3rd Class Edition 3 • Part A2 Code Calculations - ASME Section I ' Chapter 2 This would be the thickness of a blank head. But in this case, there is a manhole, and it exceeds the 150 mm allowed by PG-29.3. Therefore, the thickness must be increased by 15% or by 3.0 mm, whichever is greater. 15% of 13.52 mm = 0.15x13.52 mm = 2.028mm Since this is less than 3.0 mm, the thickness must be increased by 3.0 mm. Therefore, the required thickness = 13.52 mm + 3.0 mm = 16.52 mm (Ans.) Example 8: Calculate the thickness required of a seamless, blank, unstayed dished head Calculate the thickness of a seamless, blank, unstayed dished head that has pressure on the concave side. The head has a diameter of 1067 mm and is a segment of a sphere with a dish radius of 915 mm. The MAWP is 2068 kPa and the material is SA-285-A (carbon steel). The metal temperature does not exceed 250°C. Solution 8 PG-6 indicates that the material is carbon steel plate. Use the formula from PG-29.1: t = 5PL 4.8 Sw Given P = 2.068 MPa L = 915 mm (radius of curviture of the head) S = 88.9 MPa (from Table 1A) w =1.0 (Table PG-26, Note 3 states that carbon steel is exempt) Substitute these values into the equation: = 5PL 4.8 Sw 5 x 2.068 MPa x 915 mm 4.8 x 88.9 MPa x 1.0 9461.1 426.72 = 22.17mm 3rd Class Edition 3 • Part A2 87 Chapter 2 • Code Calculations - ASME Section I From PG-29.6, the head in this example cannot be of lesser thickness than a seamless shell of the same diameter. Therefore, to confirm that the calculated thickness of 22.17 mm is adequate, determine the shell thickness. Calculate the shell thickness using the diameter formula from PG-27.2.2, Piping Drums, Shells, and Headers. t =_? ^C 2SE+2yP Given that P = 2.068 MPa D = 1067mm Find factors of formula C = 0 (from PG-27.4.3 no threads involved) S = 88.9 MPa y = 0.4 (PG-27.4.6 for ferritic steel at 250°C) E = 1.0 (PG-27.4.1 for seamless as per PG-9) 2.068 MPa x 1067 mm t = — — _ ^———""- -"" _____ + o mm (2 x 88.9 MPa x 1) + (2 x 0.4 x 2.068 MPa) 2206.56 179.45 12.30 mm Since 22.17 mm is greater than 12.30 mm, the head thickness of 22.17 mm, as calculated, is adequate. (Ans.) Example 9: Calculate required head thickness, with a flanged-in manhole Calculate the thickness of the head in Example 8 if it has a flanged-in manhole greater than 150 mm in one dimension. Solution 9 The first thing to check is whether the radius of the dish is at least 80% of the diameter of the shell (1067 mm) or not, per PG-29.5. ^mm- = 0.857 = 85.7% 1067 mm This is greater than 80%, so the value of L is acceptable in the calculation. The thickness of the blank head in Example 8 is equal to 22.17 mm. According to PG-29.3, this thickness must be increased by the greater of either 3.0 mm or 15%. 22.17mmx0.15 = 3.33mm Since this value is greater than 3.0 mm, increase the thickness by 3.33 mm head thickness = 22.17+3.33 = 25.50 mm (Ans.) 3rd Class Edition 3 • Part A2 Code Calculations -ASME Section I • Chapter 2 Example 10: Calculate required thickness of a seamless, blank, unstayed dished head Calculate the thickness of a seamless, blank, unstayed dished head with pressure on the concave side. The head has a diameter of 1067 mm and is a segment of a sphere with a dish radius of 827 mm. The MAWP is 2250 kPa and the material is SA-515-60 (carbon steel). The metal temperature does not exceed 325°C. The head has a flanged-in manhole greater than 150 mm in one dimension. Solution 10 The thickness of the head must comply with PG-29.5. We need to check if the radius of the dish is at least 80% of the diameter of the shell (1067 mm). s^mm- = 0.775 = 77.5% 1067 mm This is less than 80%, so the value of L used in the calculation must be made 80% of the diameter. 0.80 x 1067 mm = 853.6 mm Therefore, use L = 853.6 mm in the calculation. Using the formula from PG-29.1 for thickness of dished head (segment of a sphere): = 5PL 4.8 Sw The values to be used in the formula are as follows: t = minimum thickness of plates (mm) P = maximum allowable working pressure = 2.250 MPa L = 853.6mm S = 112 MPa from Section II, Table 1A w = 1.0 (Table PG-26, Note 3 says carbon steel exempt, so w = 1.0) Substitute the values into the formula for calculating plate thickness from PG-29.1 t =A^ 4.8 Sw t = t = 5 x 2.250 MPa x 853.6 mm 4.8xll2MPaxl 9603 537.6 t = 17.86mm 3rd Class Edition 3 • Part A2 89 ^r Chapter 2 • Code Calculations - ASME Section I •^ To d^eck that this value meets the requirement of PG-29.6, calculateth^sJ^lt^i^kness t for a cylindrteal vessel using the appropriate formula froi SE+2yP •+c Given that P - 2.250 MPa D = 1067mm C = 0 (Prom PG-27.4.3 no threads involved) S = 112 MPa y = 0.4 (PG-27.4.6 for ferritic steel at 250°C) E = 1.0 (PG-27.4.1 for seamless as per PG-9) 2.250 MPa x 1067 mm t = — — ..__"""" A'""^"~"/""\ ._ ._ . + 0 mm (2 x 112 MPa x 1) + (2 x 0.4 x 2.250 MPa) 2400.75 225.8 10.63 mm The value for shell thickness t using the formula from PG-27.2.2 is 10.63 mm. The value for head thickness calculated from PG-29.1 is 17.86 mm. This second value meets the criterion specified in PG-29.6 and is therefore acceptable as the minimum required thickness of the dished head. Therefore, the minimum required thickness for the dished head is 17.86 mm (Ans.) Ellipsoidal and Hemispherical Heads So far, we have dealt with calculations for heads dished to a segment of a sphere. The other two commonly-used head shapes are ellipsoidal and hemispherical. Ellipsoidal Heads The ellipsoidal head (PG-29.7 to PG-29.8) has a 2:1 ratio between the major and minor axis of the ellipse and is designed using the cylinder formulas from PG-27. If a flanged-in manhole is used, the thickness is the same as for a head dished to a segment of sphere (PG-29.1 and PG-29.5). Hemispherical Heads When a boiler head is in the form of a full hemisphere, the requirements of paragraph PG-29.11 apply. This paragraph states that the minimum required thickness for a blank, unstayed, full-hemispherical head with the pressure on the concave side shall be calculated with the following formula: t.—PL- 2 Sw - 0.2 P Paragraph PG-29.12 states that if a flanged-in manhole that meets code requirements is placed in a full-hemispherical head, the thickness of the head is calculated using the same formi the formula used for a head dished to the segment of a sphere (per PG-29.1 and PG-29.5)rwith a dish radius equal to 80% of the shell diameter and with the added thickness for the manhole (per PG-29.3). That is, the following formula is used, where the value of L in the formula is 80% of the diameter of the shell. = 5PL 4.8 Sw 90 3rd Class Edition 3 • Part A2