flange design calculations - by abdel halim galala

DESIGN CALCULATIONS OF HEAT EXCHANGER Page : 36 of 136According to ASME Code, Sec. VIII, Div. 1, Edition 2001, Addenda 2002 / TEMA "R" 7th Edition 88. Sheet : 1 of 10Designed by : Eng. Abdel Halim Galala, Design General Manager (Assistant) Rev. : 0

Project : Design & Fabrication of Heat Exchanger for APRC Refinery Date : 4.7.2003Job No. : 7443-33 Location : Alex.Dwg. No. : 7443-33-1A, Rev. 0 Sheet : 5 Client : APRCExchanger : Residue Cooler, Type : AES Item : E-323A/B & E-514C/D

N. Integral Type (WN) Main Shell Flange Thickness (item no. 4) [Appendix 2] [FIG. 2-4, Sketch (6a)]Flange Material, [Attached by Bolts] ASME SA266 ClassSubjected to internal press.

Design Temperature (shell side) 302 oF 150 oCMin. Design Metal Temperature, MDMT 53.6 oF 12 oCBolt-up and Gasket Seating Temperature 86 oF 30 oCAssume no corrosion, C [UG-25] 0.19685 INCH 5 MMOperating Pressure (shell side) 241.477 PSIG 17 Kg/CM2GInternal Design Pressure, P (MAWP) 284.776 PSIG 20.0483 Kg/CM2G Allowable Stress of Bolt Material (ASME SA193 Gr. B7), SB : * at design temp.(operating condition), Sb 25000 PSIG 1760 Kg/CM2G * or at atmospheric temp./bolt-up temp. (gasket seating), Sa 25000 PSIG 1760 Kg/CM2G Allowable Stress of Flange Material (ASME SA266 Class 2) : * at design temp.(operating condition), SfH 20000 PSIG 1408 Kg/CM2G

* or at atmospheric temp./bolt-up temp. (gasket seating), SfC 20000 PSIG 1408 Kg/CM2G

Allowable Stress of Nozzle neck, Vessel or Pipe wall Material (ASME SA106 Gr. B) : * at design temp.(operating condition), SnH 17100 PSIG 1203.84 Kg/CM2G

* or at atmospheric temp./bolt-up temp.(gasket seating), SnC 17100 PSIG 1203.84 Kg/CM2G

[Table 1A , SubPart 1 , ASME Sec. II , Part D]

FIG. 2-4, Sketch (6a)

Figure (1)

No. of bolts 28Nominal bolt dia., dB 1 INCH 25.4 MM

Bolt Hole, d 1.10236 INCH 28 MMFlange outside diameter, A 26.9685 INCH 685 MMFlange inside diameter, B 19 INCH 482.6 MMBolt circut diameter (B.C.D.), C = B + 2(g1 + h1+ R) [Appendix 2-3] 24.5276 INCH 623 MMHup thickness at small end, go = Shell Thickness t 0.5 INCH 12.7 MMHup thickness at back of flange, g1 (assume g1 = 2 go) 1 INCH 25.4 MMR must not less than 1.5 the bolt hole (see TEMA Table D-5) 1.5 INCH 38 MMHup length, h (must greater than 1.5 go) [FIG. 2-4, Sketch 6] 1.5748 INCH 40 MMUse max. slope 1:3, h = 3.5 g0 1.73228 INCH 44 MMSlope angle, Y = arc Tan [(g1-go)/h] 16.1001 DegreeFillet radius, r = 0.25 g1 [but not less than 3/16"(4.7625 MM)] [FIG. 2-4, Sketch 6, Note a] 0.25 INCH 6.35 MMUse r 0.23622 INCH 6 MMh1 = r * Tan (45-Y/2) 0.17768 INCH 5 MME = (A-C)/2 (Check D292 ) 1.22047 INCH 31 MM



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)] [Attached by Bolts] Subjected to internal pressureNominal shell (pipe) size 20"Pipe Schedule 30No. of bolts 28Nominal bolt dia., dB 1 INCH 25.4 MMBolt diameter at root of thread 0.88189 INCH 22.4 MM

Actual cross-sectional area of each bolt, [TEMA Table D-5] 0.551 INCH2 355.483 MM2

Total actual cross-sectional area of bolts, Ab 15.428 INCH2 9953.53 MM2

Flange outside diameter, A 26.9685 INCH 685 MMFlange inside diameter, B 19 INCH 482.6 MMBolt circut diameter (B.C.D.), C 24.5276 INCH 623 MMGasket Details: - Flat metal, jacketed asbestos filled, iron or soft steel - Outside diameter = (B.C.D - d) - 2*13 22.0472 INCH 560 MM - Inside diameter = O.D - 2N 20.8661 INCH 530 MM - Width, N 0.59055 INCH 15 MMGasket Dimensions: Basic gasket seating width, bO = N/2 [Table 2-5.2] 0.29528 INCH 7.5 MM Since bo > 1/4 inch (6.35 MM), [Table 2-5.2] Effective gasket seating width, b = 0.5*SQRT(bO) [Table 2-5.2] 0.2717 INCH 6.90109 MM Gasket Factor, m [Table 2-5.1] 3.75 Min. Seating Stress, y [Table 2-5.1] 7600 PSIG 535.04 Kg/CM2G Facing Sketch [Table 2-5.1] (1a); Column II

Diameter at location of gasket load reaction, GWhen bo is larger than 1/4", G = O.D.of gasket contact face - 2 b 21.5039 INCH 546.198 MM [Appendix 2-3]

N.B. When b < 1/4", the effective gasket seating width, b = bo [Table 2-5.2]

N.B. When b > 1/4", the effective gasket seating width, b = 0.5*SQRT(bO) [Table 2-5.2]



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)] [Attached by Bolts] Subjected to internal pressure

1. Bolt loading and size of bolts: [Appendix 2-5(c)] (a) Total hydrostatic end force, H = 0.785 G2 P [Appendix 2-3] 103373 lb 46889.2 Kg (b) Total joint-contact surface compression load, Hp =2b*3.14GmP 39182.8 lb 17773 Kg [Appendix 2-3] (c) Min. required bolt load for operating conditions, Wm1 = H + Hp 142556 lb 64662.2 Kg Min. required bolt load for gasket seating, Wm2 = 3.14 b G y 139426 lb 63242.6 Kg

Allowable Bolt Stress at atmospheric temp., Sa 25000 PSIG 1760 Kg/CM2G Allowable Bolt Stress at design temp., Sb 25000 PSIG 1760 Kg/CM2G [Table 1A, SubPart 1, ASME Sec. II, Part D] (d) Total cross-sectional area of bolts at root of thread required for: - operating conditions, Am1 = Wm1 / Sb 5.70222 INCH2 3678.84 MM2

- Gasket seating, Am2 = Wm2 / Sa 5.57703 INCH2 3598.08 MM2

[Appendix 2-3] Total required cross-sectional of bolts, Am = the greater of Am1 & Am2 5.70222 INCH2 3678.84 MM2

Actual bolt area Ab 15.428 INCH2 9953.53 MM2

Since area Ab > area Am, the bolts are adequately enough. OK (e) Flange design bolt load, W : - For operating conditions, Wo = Wm1 [Appendix 2-5(d)] 142556 lb 64662.2 Kg - For gasket seating, Wa = 0.5(Am + Ab) * Sa [Appendix 2-5(d)] 264128 lb 119806 Kg

2. Total flange moment for design condition: [Appendix 2-5(c)]Flange Loads:Hydrostatic end force on area inside flange, HD = 0.785 B2 P 80701.4 lb 36605.6 Kg

Gasket load (flange design bolt load - total hydrostatic end force), HG

Gasket seating force HG = Wm1 - H 39182.8 lb 17773 Kg

Difference bet. total hydrostatic end force and the hydrostatic end force on area inside of flange, HT HT = H - HD 22671.4 lb 10283.6 Kg

Lever arms: hD = R' + 0.5 g1 [Table 2-6] 2.17768 INCH 55.3131 MM hG = (C - G) / 2 [Table 2-6] 1.51185 INCH 38.4011 MM hT = (R' + g1 + hG) / 2 [Table 2-6] 2.09477 INCH 53.2071 MM

Where R' = R + h1 1.67768 INCH 42.6131 MM



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)] [Attached by Bolts] Subjected to internal presureFlange Moments:Component of moment due to HD, MD = HD hD [Appendix 2-3] 175742 lb-in 2024.77 Kg-MComponent of moment due to HG, MG = HG hG [Appendix 2-3] 59238.6 lb-in 682.503 Kg-MComponent of moment due to HT, MT = HT hT [Appendix 2-3] 47491.3 lb-in 547.16 Kg-M

Total moment acting upon the flange, Mo: [Appendix 2-6] - For operating condition MO1 = MD + MG + MT 282472 lb-in 3254.43 Kg-M

23539.3 lb-ft3. Total flange moment for bolt-up condition (Gasket condition): [Appendix 2-6]Flange Load: HG = WA = 0.5 (Am + Ab) * Sa 264128 lb 119806 KgLever Arm., hG = (C - G) / 2 1.51185 INCH 38.4011 MMFlange Moment for gasket condition, MO2 = HG hG = WA (C - G) / 2 (5) 399323 lb-in 4600.7 Kg-M Mo2 * (SfH / SfC ) 399323 lb-in 4600.7 Kg-M4. MO = The greater of MO1 or MO2 (SfH/SfC) 399323 lb-in 4600.7 Kg-M

33276.9 lb-ft5. Shape constants for flange:

1.41939From Appendix 2, FIG. 2-7.1:

1.74578

2.97106

5.71057

6.27534

g1/go 2 ho = SQRT(B go) 3.08221 h/ho 0.56203From Appendix 2, FIG. 2-7.2: F 0.81225From Appendix 2, FIG. 2-7.3: V 0.21166From Appendix 2, FIG. 2-7.6: f 1.02557

d = (U/V) ho go2 (for integral type flanges) [APPENDIX 2-3] 22.8457 INCH3 374374 MM3

e = F / ho (for integral type flanges) [APPENDIX 2-3] 0.26353 INCH-1 0.01038 MM-1

KBA

=

T K Log kk k

=+ −

+ −

210

2

1 8 55246 1104720 19448 1

( . )( . . )( )

Z KK

=+

−

2 12 1

YK

K Log KK

=−

+−

⎡

⎣⎢

⎤

⎦⎥

12

1021

0 66845 5 716901

. .

UK Log K

K K=

+ −

− −

2

2

1 8 55246 10 1

136136 1 1

( . )

. ( )( )



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)] [Attached by Bolts] Subjected to internal pressure6. Calculation of flange actual stresses Assume t 1.45669 INCH 37 MM [Appendix 2-3] 0.928 Where t = flange thickness factor e = F/ ho (for integral type flanges) [Appendix 2-3] 0.26353 INCH-1 0.01038 MM-1

e = FL/ ho (for loose type flanges) [Appendix 2-3] NA F = factor for integral type flanges [Fig. 2-7.2] 0.81225 T = factor involving K [Fig. 2-7.1] 1.74578 d = (U/V) ho go2 [Appendix 2-3] 22.8457 INCH3 374374 MM3

For integral type flange, actual stresses (calculated) : [Fig. 2-4, Sketch (6a)]1. a. Longitudinal hub stress, operating SH = f Mo / L g1

2 B (6) [Appendix 2-7(a)] 23226.7 PSIG 1635.16 Kg/CM2G

b. Longitudinal hub stress, seating SH = f Mo2 / L g12 B (6) [Appendix 2-7(a)] 23226.7 PSIG 1635.16 Kg/CM2G

2. a. Radial flange stress, operating SR = (1.33 t e +1) Mo / L t2 B (7) [Appendix 2-7(a 16135.7 PSIG 1135.96 Kg/CM2G

b. Radial flange stress, seating SR = (1.33 t e +1) Mo2 / L t2 B (7) [Appendix 2-7(a16135.7 PSIG 1135.96 Kg/CM2G

3. a. Tangential flange stress, operating ST = (Y Mo / t2 B) - Z SR (8) [Appendix 2-7(a)] 8620.34 PSIG 606.872 Kg/CM2G

b. Tangential flange stress, seating ST = (Y Mo2 / t2 B) - Z SR (8) [Appendix 2-7(a)8620.34 PSIG 606.872 Kg/CM2G

4. a. Flange stress, operating 0.5 (SH + SR) [Appendix 2-8(a)(4)] 19681.2 PSIG 1385.56 Kg/CM2G

b. Flange stress, seating 0.5 (SH + SR) [Appendix 2-8(a)(4)] 19681.2 PSIG 1385.56 Kg/CM2G

5. a. Flange stress, operating 0.5 (SH + ST) [Appendix 2-8(a)(4)] 15923.5 PSIG 1121.02 Kg/CM2G

b. Flange stress, seating 0.5 (SH + ST) [Appendix 2-8(a)(4)] 15923.5 PSIG 1121.02 Kg/CM2G

6. a. Bolt stress, operating = Wm1 / Ab 9240.05 PSIG 650.5 Kg/CM2G b. Bolt stress, seating = Wm2 / Ab 9037.19 PSIG 636.219 Kg/CM2G7. a. Shear stress carried by the fillet weld 0 PSIG 0 Kg/CM2G

7. Actual Stresses (Calculated) Compared with Allowable Stresses [APPENDIX 2-8] 7.a. For Operating Condition : Allowable design stress of flange at operating condiotion, Sf 20000 PSIG 1408 Kg/CM2G Allowable design stress of nozzle/vessel at operating condition, Sn 17100 PSIG 1203.84 Kg/CM2GAssume flange thickness (without C.A), toperating 1.45669 INCH 37 MM

Allowable stresses Actual stresses (Calculated )

PSIG Kg/CM2 PSIG Kg/CM2

Longitudinal Hub Stress SH1 = 1.5 Sf [Appendix 2-8(a)(1)(b)] 30000Longitudinal Hub Stress SH2 = 2 Sn [Appendix 2-8(a)(1)(b)] 34200 The calculated (actual) hub stress SH < SH (min.) allowable 30000 > 23226.7

Radial Flange Stress SR = Sf [Appendix 2-8(a)(2)] 20000 > 16135.7 The calculated (actual) radial stress SR < SR allowable

Factor L tT

td

e=

++

1 3^



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)]Subjected to internal pressure

Tangential Flange Stress ST = Sf [Appendix 2-8(a)(3)] 20000 > 8620.34 The calculated (actual) tangential stress ST < ST allowable

0.5(SH + SR) = Sf 20000 > 19681.2 The calculated (actual) stress < Allowable stress

0.5(SH + ST) = Sf 20000 > 15923.5 The calculated (actual) stress < Allowable stressBolt stress = Wm1 / Ab 25000 > 9240.05 The calculated (actual) stress < Allowable stress

7.b. For Gasket Seating : Allowable design stress of flange at gasket seating, Sf 20000 PSIG 1408 Kg/CM2G Allowable design stress of nozzle/vessel at gasket seating, Sn 17100 PSIG 1203.84 Kg/CM2GAssume flange thickness (without C.A), tgasket 1.45669 INCH 37 MM

Allowable stresses Actual stresses (Calculated )

PSIG Kg/CM2 PSIG Kg/CM2

Longitudinal Hub Stress SH1 = 1.5 Sf [Appendix 2-8(a)(1)(b)] 30000Longitudinal Hub Stress SH2 = 2 Sn [Appendix 2-8(a)(1)(b)] 34200 The calculated (actual) hub stress SH < SH (min.) allowable 30000 > 23226.7

Radial Flange Stress SR = Sf [Appendix 2-8(a)(2)] 20000 > 16135.7 The calculated (actual) radial stress SR < SR allowable

Tangential Flange Stress ST = Sf [Appendix 2-8(a)(3)] 20000 > 8620.34 The calculated (actual) tangential stress ST < ST allowable

0.5(SH + SR) = Sf 20000 > 19681.2 The calculated (actual) stress < Allowable stress

0.5(SH + ST) = Sf 20000 > 15923.5 The calculated (actual) stress < Allowable stress

Bolt stress = Wm2 / Ab 25000 > 9037.19 The calculated (actual) stress < Allowable stress

The min. flange thickness, t = Max. (toperating, tgasket) 1.45669 INCH 37 MM



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)]Subjected to internal pressure

Since all actual stresses are less than the allowable stresses, the selection of t = 4.5 inch, is adequate. If an optimum min. thickness of flange is desired, calculations must be operated with a smaller value of t until one of the actual stresses or stress combination is approximately equal to the allowable stress even though other actual stresses are less than the allowable stress for that actual stress.

Flange thickness with C.A & RF = t + 2*corrosion all. + raised face 2.04724 INCH 52 MM

Use flange thickness for construction 2.16535 INCH 55 MM

BOLT SUMMARYFactor K = A/B 1.41939Gasket width, N 0.59055 INCH 15 MMTotal required cross-sectional area of bolts 5.70222 INCH2 3678.84 MM2

Actual bolt cross-sectional area, Ab 15.428 INCH2 9953.53 MM2

Nominal bolt dia., dB 1 INCH 25.4 MM

1. Actual Edge distance, E from drawing = 1/2 (A - C) 1.22047 INCH 31 MM Min. Edge distance, E (for bolt size 0.75") 0.8125 INCH 20.6375 MM Min. Edge distance, E (for bolt size 7/8") 0.9375 INCH 23.8125 MM Min. Edge distance, E (for bolt size 1") 1.0625 INCH 26.9875 MM Min. Edge distance, E (for bolt size 1-1/8") [TEMA Table D-5] 1.125 INCH 28.575 MM Min. Edge distance, E (for bolt size 1-1/4") 1.25 INCH 31.75 MM2. Actual Bolt spacing, B from drawing 2.74622 INCH 69.7539 MM Min. Bolt spacing, B (for bolt size 0.75") 1.75 INCH 44.45 MM Min. Bolt spacing, B (for bolt size 7/8") 2.0625 INCH 52.3875 MM Min. Bolt spacing, B (for bolt size 1") 2.25 INCH 57.15 MM Min. Bolt spacing, B (for bolt size 1-1/8") [TEMA Table D-5] 2.5 INCH 63.5 MM Min. Bolt spacing, B (for bolt size 1-1/4") 2.8125 INCH 71.4375 MM Max. Recommended bolt spacing, Bmax = 2 dB + 6 t / (m + 0.5) [TEMA RCB-11.224.05651 INCH 103.035 MM3. Actual Radial distance, Rh from drawing = (C-B)/2-(g1+h1) 1.56693 INCH 39.8 MM Min. Radial distance, Rh (for bolt size 0.75") 1.125 INCH 28.575 MM Min. Radial distance, Rh (for bolt size 7/8") 1.25 INCH 31.75 MM Min. Radial distance, Rh (for bolt size 1") 1.375 INCH 34.925 MM Min. Radial distance, Rh (for bolt size 1-1/8") [TEMA Table D-5] 1.5 INCH 38.1 MM Min. Radial distance, Rh (for bolt size 1-1/4") 1.75 INCH 44.45 MM



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)]FLANGE FACTORS Subjected to internal pressure(a) For Integral Flanges Factor F per Fig. 2-7.2 is then solved by 0.81225

Factor V per Fig. 2-7.3 is then solved by 0.21166

Factor f per Fig. 2-7.6 is then solved by f = C36 / (1 + A) 1.02557 h/SQRT(BGo 0.562026971

The values used in the above equations are solved using Eqs. (1) through (45) below based on the values g1, g0, h and hoas defined by 2-3. When g1 = go, F = 0.908920, V = 0.550103, and f = 1; thus Eqs. (1) through (45) need not be solved.

(b) For Loose Hub Flanges Factor FL per Fig. 2-7.4 is solved by

1.435

Factor VL per Fig. 2-7.5 is solved by 0.66229

Factor f per Fig. 2-7.6 is set equal to 1. f = 1 1The values used in the above equations are solved using Eqs. (1) through (5), (7), (9), (10), (12),(14), (16), (18), (20), (23), and (26) below based on the values of g1, g0, h, and ho as defined by 2-3.

go 0.5 INCH 12.7 MM g1 1 INCH 25.4 MM h 1.73228 INCH 44 MM ho = SQRT(B go), Effective hub length 3.08221 INCH 78.2881 MM B 19 INCH 482.6 MM

(1) A = (g1/go) - 1 1(2) C = 43.68(h/ho)4 4.35824(3) C1 = 1/3 + A/12 0.41667(4) C2 = 5/42 + 17 A / 336 0.16964(5) C3 = 1/210 + A/360 0.00754(6) C4 = 11/360 + 59 A/5040 + (1+3 A)/C 0.96006(7) C5 = 1/90 + 5 A/1008 - (1+ A)3/C -1.81953

FE

C AC

=+

6

1 43

2 731

[.

]( )/

VE

CA

=+

4

1 4 32 731[

.] ( )/

FC A C A C A A

C AC

L =+⎛

⎝⎜⎞⎠⎟+ +⎛

⎝⎜⎞⎠⎟+ +⎛

⎝⎜⎞⎠⎟− −⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

+

1 8 2 1 2 4

1 4 3

12 6

14

1 18 4

17 0 1 0 5

14 0 7 2

2 7 31

.( )/

V

C C C

CA

L =− − −

⎛⎝⎜

⎞⎠⎟

+

14 5

32

2 73 1

24 2118

1 43. ( )

/



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)]FLANGE FACTORS (CONT.) Subjected to internal pressure(8) C6 = 1/120 + 17 A/5040 +1 /C 0.24116(9) C7 = 215/2772 + 51 A/1232 + (60/7 + 225 A/14 + 75A2/7 + 5 A3/2)/C 8.80529(10) C8 = 31/6930 + 128 A/45045 + (6/7 + 15 A/7 + 12A2/7 + 5 A3/11)/C 1.19331(11) C9 = 533/30240 + 653 A/73920 + (1/2 + 33 A/14 + 39 A2/28 + 25 A3/84)/C 1.06991(12) C10 = 29/3780 + 3 A/704 - (1/2 + 33 A/14 + 81 A2/28 + 13 A3/12)/C -1.55598(13) C11 = 31/6048 + 1763 A/665280 + (1/2 + 6 A/7 + 15 A2/28 + 5 A3/42)/C 0.46941(14) C12 = 1/2925 + 71 A/300300 + (8/35 + 18 A /35 + 156 A2/385 + 6 A3/55)/C 0.28903(15) C13 = 761/831600 + 937 A/1663200 + (1/35 + 6 A /35 + 11 A2/70 + 3 A3/70)/0.09326(16) C14 = 197/415800 + 103 A/332640 - (1/35 + 6 A /35 + 17 A2/70 + A3/10)/C -0.12378(17) C15 = 233/831600 + 97 A/554400 + (1/35 + 3 A /35 + A2/14 + 2 A3/105)/C 0.04744(18) C16 = C1C7C12 + C2C8C3 + C3C8C2 - (C3

2C7 + C82C1 + C2

2C12) 0.46133(19) C17 = [C4C7C12 + C2C8C13 + C3C8C9 - (C13C7C3 + C8

2C4 + C12C2C9)] / C16 2.2676(20) C18 = [C5C7C12 + C2C8C14 + C3C8C10 - (C14C7C3 + C8

2C5 + C12C2C10)] / C16 -4.32293(21) C19 = [C6C7C12 + C2C8C15 + C3C8C11 - (C15C7C3 + C8

2C6 + C12C2C11)] / C16 0.55926(22) C20 = [C1C9C12 + C4C8C3 + C3C13C2 - (C3

2C9 + C13C8 C1 + C12C4C2)] / C16 0.0956(23) C21 = [C1C10C12 + C5C8C3 + C3C14C2 - (C3

2C10 + C14C8 C1 + C12C5C2)] / C16 -0.11503(24) C22 = [C1C11C12 + C6C8C3 + C3C15C2 - (C3

2C11 + C15C8 C1 + C12C6C2)] / C16 0.05056(25) C23 = [C1C7C13 + C2C9C3 + C4C8C2 - (C3C7C4 + C8C9 C1 + C2

2C13)] / C16 -0.13119(26) C24 = [C1C7C14 + C2C10C3 + C5C8C2 - (C3C7C5 + C8C10 C1 + C2

2C14)] / C16 0.15946(27) C25 = [C1C7C15 + C2C11C3 + C6C8C2 - (C3C7C6 + C8C11 C1 + C2

2C15)] / C16 -0.05919(28) C26 = - (C/4)1/4 -1.02168(29) C27 = C20 - C17 - 5/12 + C17C26 -4.90543(30) C28 = C22 - C19 - 1/12 + C19C26 -1.16343(31) C29 = - (C/4)1/2 -1.04382(32) C30 = - (C/4)3/4 -1.06644(33) C31 = 3 A/2 - C17 C30 3.91827(34) C32 = 1/2 - C19 C30 1.09642(35) C33 = 0.5 C26C32 + C28C31C29 - (0.5 C30C28 + C32C27C29) -2.03619(36) C34 = 1/12 + C18 - C21 - C18C26 -8.54118(37) C35 = - C18 (C/4)3/4 4.61016(38) C36 = (C28C35C29 - C32C34C29)/C33 2.05114(39) C37 = [0.5 C26C35 + C34C31C29 - (0.5 C30C34 + C35C27C29)] / C33 -2.16975(40) E1 = C17C36 + C18 + C19C37 -0.88522(41) E2 = C20C36 + C21 + C22C37 -0.02864(42) E3 = C23C36 + C24 + C25C37 0.01881(43) E4 = 1/4 + C37/12 + C36/4 - E3/5 - 3E2/2 - E1 1.50639(44) E5 = E1 (1/2 + A/6) + E2(1/4 + 11A/84) + E3(1/70 + A/105) -0.60061(45) E6 = E5 - C36(7/120 +A/36 + 3A/C) - 1/40 - A/72 - C37(1/60 +A/120 + 1/C) -1.67593



N. Integral Type (W.N.) Main Shell Flange Thickness, item no. 4 (cont.) [Appendix 2] [FIG. 2-4, Sketch (6a)]

Subjected to internal pressureAPPENDIX 2-3When B < 20 g1, it will be optional for the designer to substitute B1 in theformula stress SH = f * Mo /( L * g1

2 * B). 20 * g1 20 INCH 508 MM B 19 INCH 482.6 MM

B1 = B + g1 for loose & integral type flanges have f <1 ( the min. f permitted is 1) 20 INCH 508 MMB1 = B + go for integral type flanges when f = > 1 19.5 INCH 495.3 MM

flange design calculations - by abdel halim galala

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