Local Loads 449 h typical tc b b b b See Note 2 C1 0.5b 0.3b 0.25b 0.3b C2 0.4h 0.4h 0.4h 0.4h h typical See Note 1 b b b b C1 0.4b 0.5b 0.3b 0.2b C2 0.5h 0.5h 0.5h 0.4h Figure 7-10. Attachment parameters for nonsolid attachments. Procedure 7-4: Stresses in Cylindrical Shells from External Local Loads [7,9,10,11] Mf ¼ internal longitudinal moment, in.-lb/in. VL ¼ longitudinal shear force, lb Vc ¼ circumferential shear force, lb Rm ¼ mean radius of shell, in. ro ¼ outside radius of circular attachment, in. r ¼ corner radius of attachment, in. Kn,Kb ¼ stress concentration factors Notation Pr ¼ radial load, lb P ¼ internal design pressure, psi ML ¼ external longitudinal moment, in.-lb Mc ¼ external circumferential moment, in.-lb MT ¼ external torsional moment, in.-lb Mx ¼ internal circumferential moment, in.-lb/in. C Mc Pr ML N N M N N M Rm N M M t Radial load–membrane stress is compressive for inward radial load and tensile for outward load N M Circumferential moment M Longitudinal moment Figure 7-11. Loadings and forces at local attachments in cylindrical shells. 450 Pressure Vessel Design Manual 0° σx 90° 270° 2CSQ σφ 180° 0° 2C2 90° 270° 2C1 180° rc 0° 90° 270° 180° Figure 7-13. Load areas of local attachments. For circular attachments use C ¼ 0.875ro. Figure 7-12. Stress indices of local attachments. Figure 7-14. Dimensions for clips and attachments. Figure 7-15. Stress concentration factors. (Reprinted by permission of the Welding Research Council.) Local Loads Kc,KL,K1,K2 ¼ coefficients to determine b for rectangular attachments Nx ¼ membrane force in shell, longitudinal, lb/in. Nf ¼ membrane force in shell, circumferential, lb/in. sT ¼ torsional shear stress, psi ss ¼ direct shear stress, psi sx ¼ longitudinal normal stress, psi sf ¼ circumferential normal stress, psi C ¼ one-half width of square attachment, in. Cc,CL ¼ multiplication factors for rectangular attachments 451 C1 ¼ one-half circumferential width of a rectangular attachment, in. C2 ¼ one-half longitudinal length of a rectangular attachment, in. h ¼ thickness of attachment, in. dn ¼ outside diameter of circular attachment, in. te ¼ equivalent thickness of shell and reinforcing, in. tp ¼ thickness of reinforcing pad, in. t ¼ shell thickness, in. g,b,b1,b2 ¼ ratios based on vessel and attachment geometry 452 Pressure Vessel Design Manual Geometric Parameters Rm t C b ¼ Rm Load area g ¼ 2C2 or for circular attachments: 2C1 0:875ro Rm Figure 7-16. Dimensions of load areas. For rectangular attachments: b1 ¼ C1 Rm b2 ¼ C2 Rm Procedure To calculate stresses due to radial load Pr, longitudinal moment ML, and circumferential moment Mc, on a cylindrical vessel, follow the following steps: Step 1: Calculate geometric parameters: a. Round attachments: Rm t 0:875ro b ¼ Rm g ¼ b. Square attachments: Rm t C b ¼ Rm g ¼ dimensionless membrane forces and bending moments in shell. Step 3: Enter values obtained from Figures 7-21 through 7-26 into Table 7-11 and compute stresses. Step 4: Enter stresses computed in Table 7-11 for various load conditions in Table 7-12. Combine stresses in accordance with sign convention of Table 7-12. Computing b Values for Rectangular Attachments b1 ¼ C1 Rm b2 ¼ C2 Rm b1 b2 b Values for Radial Load From Table 7-8 select values of K1 and K2 and compute four b values as follows: b If 1 1; then b b2 pffiffiffiffiffiffiffiffiffiffi 1 b1 1 ð1 K1 Þ b1 b2 ¼ 1 3 b2 c. Rectangular attachments: Table 7-8 b Values of radial loads Rm g ¼ t b values for radial load, longitudinal moment, and circumferential moment vary based on ratios of b1/b2. Follow procedures that follow these steps to find b values. Step 2: Using g and b values; from Step 1, enter applicable graphs, Figures 7-21 through 7-26 to K1 K2 Nf 0.91 1.48 Nx 1.68 1.2 Mf 1.76 0.88 Mx 1.2 1.25 Reprinted by permission of the Welding Research Council. b Local Loads .6 .7 .8 .9 1.0 1.1 1.2 50 .5 1.3 1.4 1.5 1.6 1.5 1.6 300 00 0,3 15 2.5 200 β1/β2 2.0 1.5 1.0 .75 20 15 .3 .4 .5 30 .2 15 0 .1 50 100 .9 1.0 10 300 200 .25 Mf 50 CL for NX 0 .5 0 b Nx .6 .7 .8 CL for Nφ 1.1 1.2 1.3 1.4 Figure 7-17. Graph of coefficients CL for values Nf & NX from Table 7-9. CL for Nx KL for Mf KL for Mx 3.5 0.75 0.77 0.80 0.85 0.90 0.43 0.33 0.24 0.10 0.07 1.80 1.65 1.59 1.58 1.56 1.24 1.16 1.11 1.11 1.11 3 0.25 15 50 100 200 300 0.5 15 50 100 200 300 0.90 0.93 0.97 0.99 1.10 0.76 0.73 0.68 0.64 0.60 1.08 1.07 1.06 1.05 1.05 1.04 1.03 1.02 1.02 1.02 1 15 50 100 200 300 0.89 0.89 0.89 0.89 0.95 1.00 0.96 0.92 0.99 1.05 1.01 1.00 0.98 0.95 0.92 1.08 1.07 1.05 1.01 0.96 15 50 100 200 300 0.87 0.84 0.81 0.80 0.80 1.30 1.23 1.15 1.33 1.50 0.94 0.92 0.89 0.84 0.79 1.12 1.10 1.07 0.99 0.91 15 50 100 200 300 0.68 0.61 0.51 0.50 0.50 1.20 1.13 1.03 1.18 1.33 0.90 0.86 0.81 0.73 0.64 1.24 1.19 1.12 0.98 0.83 15 50 100 50 CL for Nf 100 g KL for MX 200 300 b1/b2 15 2.5 β1/β2 2.0 1.5 1.0 .75 .5 100,200 .7 .8 .9 1.0 50 .6 1.1 15 .25 ,300 KL for MX ,200 100 Reprinted by permission of the Welding Research Council. KL for Mφ 4.0 200 Table 7-9 Coefficients for longitudinal moment, ML 300 Mx 4 .4 3 Nf 2 .3 20 KL .2 3.5 b Values for Longitudinal Moment From Table 7-9 select values of CL and KL and compute values of b as follows: qffiffiffiffiffiffiffiffiffiffi 3 For Nx and Nf, b ¼ b1 b22 qffiffiffiffiffiffiffiffiffiffi 3 For Mf, b ¼ KL b1 b22 qffiffiffiffiffiffiffiffiffiffi 3 For Mx, b ¼ KL b1 b22 CL .1 4.0 100 then b pffiffiffiffiffiffiffiffiffiffi 4 b1 ð1 K2 Þ b1 b2 ¼ 1 1 b2 3 15 50 b1 < 1; b2 100 If 453 1.2 KL for Mφ 300 1.3 1.4 50 1.5 1.6 15 1.7 Figure 7-18. Graph of coefficients KL for values Mf & MX from Table 7-9. 454 Pressure Vessel Design Manual b Values for Circumferential Moment From Table 7-10 select values of Cc and Kc and compute values of b as follows: qffiffiffiffiffiffiffiffiffiffi 3 For Nx and Nf, b ¼ b21 b2 qffiffiffiffiffiffiffiffiffiffi 3 For Mf, b ¼ Kc b21 b2 Table 7-10 Coefficients for circumferential moment, Mc b1/b2 g Cc for Nf Cc for Nx Kc for Mf KC for Mx 15 50 100 200 300 0.31 0.21 0.15 0.12 0.09 0.49 0.46 0.44 0.45 0.46 1.31 1.24 1.16 1.09 1.02 1.84 1.62 1.45 1.31 1.17 0.5 15 50 100 200 300 0.64 0.57 0.51 0.45 0.39 0.75 0.75 0.76 0.76 0.77 1.09 1.08 1.04 1.02 0.99 1.36 1.31 1.26 1.20 1.13 1 15 50 100 200 300 1.17 1.09 0.97 0.91 0.85 1.08 1.03 0.94 0.91 0.89 1.15 1.12 1.07 1.04 0.99 1.17 1.14 1.10 1.06 1.02 2 15 50 100 200 300 1.70 1.59 1.43 1.37 1.30 1.30 1.23 1.12 1.06 1.00 1.20 1.16 1.10 1.05 1.00 0.97 0.96 0.95 0.93 0.90 4 15 50 100 200 300 1.75 1.64 1.49 1.42 1.36 1.31 1.11 0.81 0.78 0.74 1.47 1.43 1.38 1.33 1.27 1.08 1.07 1.06 1.02 0.98 0.25 qffiffiffiffiffiffiffiffiffiffi 3 For Mx, b ¼ Kc b21 b2 Cc Kc b Nf Nx Mf Mx 1.875 15 1.75 CC for Nφ 50 1.625 100 1.5 Reprinted by permission of the Welding Research Council. 200 1.375 300 1.25 15 1.125 1.875 0 10 50 KC for Mφ 0 20 1.75 1.625 0 30 1.5 1 1.375 15 15 .875 50 0 10 .75 50 1.25 20 1.125 .625 0 30 15 0 1 200 .5 .875 .375 100 200 .625 .125 .5 KC for MX 300 100 300 .75 .25 50 CC for NX .375 .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 β1/β2 Figure 7-19. Graph of coefficients Kc & CC for values Nf & Mf from Table 7-10. .5 1.0 1.5 2.0 β1/β2 2.5 3.0 3.5 4.0 Figure 7-20. Graph of coefficients Kc & CC for values NX & MX from Table 7-10. Table 7-11 Computing stresses Figure b Value from Figure Forces and Moments Stress Radial Load Membrane 7-21A 7-21B Bending 7-22A 7-22B Nf Rm ¼ ðÞ Pr Nf ¼ ð ÞPr Rm sf ¼ Nx Rm ¼ ðÞ Pr Mf ¼ ðÞ Pr Mx ¼ ðÞ Pr Nx ¼ ð ÞPr Rm sx ¼ Mf ¼ ð ÞPr Mx ¼ ð ÞPr Kn Nf t Kn Nx t 6Kb Mf sf ¼ t2 6Kb Mx sx ¼ t2 Longitudinal Moment Membrane 7-23A 7-23B Bending 7-24A 7-24B Nf R2m b ¼ ðÞ ML Nx R2m b ¼ ðÞ ML Mf Rm b ¼ ðÞ ML Mx Rm b ¼ ðÞ ML Nf ¼ Nx ¼ ð ÞCL ML R2m b ð ÞCL ML R2m b ð ÞML Mf ¼ Rm b ð ÞML Mx ¼ Rm b sf ¼ Kn Nf t Kn Nx t 6Kb Mf sf ¼ t2 6Kb Mx sx ¼ t2 sx ¼ Circumferential Moment Membrane 7-25A Nf R2m b ¼ ðÞ Nf ¼ NX R2m b ¼ ðÞ MC Nx ¼ Mc 7-25B Bending 7-26A 7-26B Mf Rm b ¼ ðÞ Mc Mx Rm b ¼ ðÞ Mc ð ÞCc Mc R2m b ð ÞCc Mc R2m b ð ÞMc Mf ¼ Rm b ð ÞMc Mx ¼ Rm b sf ¼ Kn Nf t sx ¼ Kn Nx t 6Kb Mf t2 6Kb Mx sx ¼ t2 sf ¼ 456 Pressure Vessel Design Manual 7. The maximum stress due to a circumferential moment is 2–5 times larger than the stress due to a longitudinal moment of the same magnitude. 8. The maximum stress from a longitudinal moment is not located on the longitudinal axis of the vessel and may be 60 –70 off the longitudinal axis. The reason for the high stresses on or adjacent to the circumferential axis is that, on thin shells, the longitudinal axis is relatively flexible and free to deform and that the loads are thereby transferred toward the circumferential axis which is less free to deform. Figures 7-23 and 7-24 do not show maximum stresses since their location is unknown. Instead the stress on the longitudinal axis is given. 9. For attachments with reinforcing pads: This applies only to attachments that are welded to a reinforcing plate that is subsequently welded to the vessel shell. Attachments that are welded through the pad (like nozzles) can be considered as integral with the shell. Shear Stresses • Stress due to shear loads, VL or Vc . Round attachments: VL ss ¼ pro t VC ss ¼ pro t Square attachments: VL 4Ct VC ss ¼ 4Ct ss ¼ Rectangular attachments: VL 4C1 t VC ss ¼ 4C2 t • Stress due to torsional moment, MT. Round attachments only! ss ¼ sT ¼ MT 2pr2o t Notes 1. Figure 7-15 should be used if the vessel is in brittle (low temperature) or fatigue service. For brittle fracture the maximum tensile stress is governing. The stress concentration factor is applied to the stresses which are perpendicular to the change in section. 2. Subscripts q and C indicate circumferential direction, X and L indicate longitudinal direction. 3. Only rectangular shapes where C1/C2 is between 1/4 and 4 can be computed by this procedure. The charts and graphs are not valid for lesser or greater ratios. 4. Methods of reducing stresses from local loads: a. Add reinforcing pad. b. Increase shell thickness. c. Add partial ring stiffener. d. Add circumferential ring stiffener(s). e. Kneebrace to reduce moment loads. f. Increase attachment size. 5. See Procedure 7-3 to convert irregular attachment shapes into suitable shapes for design procedure. 6. For radial loads the stress on the circumferential axis will always govern. Moment loadings for nonintegral attachments must be converted into radial loads. This will more closely approximate the manner in which the loads are distributed in shell and plate. Stresses should be checked at the edge of attachment and edge of reinforcing plate. The maximum height of reinforcing pad to be considered is given by: For radial load: 2C2 d1 C1 For longitudinal moment: 4C2 d1 2d21 max ¼ 3C1 2d2 max ¼ For circumferential moment: 4C1 d2 2d11 max ¼ 3C2 Moments can be converted as follows: Pr ¼ 3ML 4C2 Pr ¼ 3Mc 4C1 or 10. This procedure is based on the principle of “flexible load surfaces.” Attachments larger than onehalf the vessel diameter (b>0.5) cannot be determined by this procedure. For attachments which exceed these parameters see Procedure 7-1. Local Loads 457 (a) 70 50 30 20 γ= 15 γ= 30 0 10 0 10 8 γ= 50 NφRm Pr 6 4 γ = 15 3 2 γ=5 1.0 0.8 0.6 0.5 0.05 0.1 0.15 0.2 0.25 β 0.3 0.35 0.4 0.45 0.5 0.3 0.35 0.4 0.45 0.5 (b) 70 50 40 30 γ=3 00 20 15 γ=1 00 10 γ = 50 NxRm Pr 8 6 4 γ = 15 3 2 γ=5 1 0.05 0.05 0.1 0.15 0.2 0.25 β Figure 7-21. Membrane force in a cylinder due to radial load on an external attachment. (Reprinted by permission from the Welding Research Council.) 458 Pressure Vessel Design Manual (a) 0.6 0.4 γ=5 0.2 γ=1 Mφ Pr 0.1 0.08 5 0.06 γ= 0.04 γ= 0.02 γ= 50 100 300 0.01 0.008 0.006 0.004 0.002 0.05 (b) 0.1 0.15 0.2 0.25 β 0.3 0.35 0.4 0.45 0.5 0.3 0.35 0.4 0.45 0.5 0.3 0.2 0.15 γ=5 0.1 0.08 γ= 15 0.06 Mx Pr 0.04 γ= 0.02 γ= 50 10 0 0.01 0.008 γ= 0.006 30 0 0.004 0.002 0.05 0.1 0.15 0.2 0.25 β Figure 7-22. Bending moment in a cylinder due to radial load on an external attachment. (Reprinted by permission from the Welding Research Council.) Local Loads (a) 459 40 30 20 15 γ=3 00 2β ΝφRm ML 10 9 8 7 6 5 γ=1 00 γ=5 0 4 3 γ = 15 2 1.5 1.0 0.7 0.5 γ=5 0.4 0.3 0.2 0.15 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.3 0.35 0.4 0.45 0.5 β (b) 10 8 6 γ= 4 γ = 10 300 0 3 γ = 50 2β ΝxRm ML 2 1 0.8 γ = 15 0.6 0.4 0.3 0.2 0.15 γ=5 0.1 0.08 0.06 0.05 0.1 0.15 0.2 0.25 β Figure 7-23. Membrane force in a cylinder due to longitudinal moment on an external attachment. (Reprinted by permission from the Welding Research Council.) 460 Pressure Vessel Design Manual (a) 0.1 0.08 0.06 γ=5 0.04 γ = 15 0.02 0.015 γ= 50 0.01 γ= MφRmβ ML 0.008 0.006 0.004 γ= 100 300 0.002 0.001 0.0008 0.05 0.1 0.15 0.2 0.25 β (b) 0.3 0.35 0.4 0.45 0.5 0.35 0.4 0.45 0.5 γ=5 0.1 0.08 γ = 15 0.06 0.04 γ= 50 MxRmβ ML 0.02 γ= 0.01 0.008 100 0.006 0.004 γ= 300 0.002 0.001 0.05 0.1 0.15 0.2 0.25 0.3 β Figure 7-24. Bending moment in a cylinder due to longitudinal moment on an external attachment. (Reprinted by permission from the Welding Research Council.) Local Loads (a) 461 14 12 10 8 γ=3 00 6 4 γ = 50 2 1.5 2β NφRm Mc 1 0.8 γ = 15 0.6 0.4 0.2 0.15 γ=5 0.1 0.08 0.06 0.05 0.05 0.1 0.15 0.2 0.25 β (b) 25 0.3 0.35 0.4 0.45 0.5 0.35 0.4 0.45 0.5 γ = 300 20 15 γ = 100 10 8 6 γ = 50 4 2β NxRm Mc 2 γ = 15 1 0.8 0.6 0.4 γ=5 0.2 0.15 0.1 0.05 0.1 0.15 0.2 0.25 0.3 β Figure 7-25. Membrane force in a cylinder due to circumferential moment on an external attachment. (Reprinted by permission from the Welding Research Council.) 462 Pressure Vessel Design Manual (a) 0.2 MφRmβ Mc 0.15 γ=5 γ = 15 0.1 0.08 γ = 50 0.06 γ = 100 γ = 300 0.04 0.03 0.05 0.1 0.15 0.2 0.3 0.35 0.4 0.45 0.5 0.3 0.35 0.4 0.45 0.5 0.25 β (b) 0.08 γ=5 MxRmβ Mc 0.06 γ = 15 0.04 γ = 50 γ = 100 0.03 0.02 γ = 300 0.015 0.01 0.05 0.1 0.15 0.2 0.25 β Figure 7-26. Bending moment in a cylinder due to circumferential moment on an external attachment. (Reprinted by permission from the Welding Research Council.) Maximum Allowable Nozzle Loads This procedure is an alternative work process for developing and analyzing nozzle loads on pressure vessels. It establishes the minimum criteria for design by providing the maximum allowable nozzle load by size and class of flange rating. This is an alternative work process to determining each individual nozzle load after the piping system is designed. This procedure eliminates much of the late design changes that occur when late data on nozzle loads impact either the design of the piping system or the stresses in the vessel shell. The allowable loads and moments listed in Table 7-14 do not represent any actual loading or a real maximum allowable load or moment. Rather they are “arbitrary” maximum allowable nozzle loads. This procedure does not take into account any of the vessel parameters such as diameter, thickness, material, temperature, allowable stress, internal pressure, etc. Since the basis of Table 7-14 is the “flange rating”, the associated nozzle loads are generic only. There are two reasons for the implementation of this procedure as follows; 1. To provide the vessel fabricator with nozzle loads with which to design the vessel shell or head to which the nozzle is attached, prior to design of the piping systems. 2. To provide the piping designer with guidelines for design of piping that terminates at a vessel nozzle. Therefore, as long as the piping does not exceed the loads in Table 7-14, they automatically know that the vessel shell or head is not overstressed for this condition. If the piping department cannot design the piping in such a way as to not exceed the values in Table 7-14, then the work process must revert back to the original work process of analyzing each specific, individual nozzle for the actual loads and resultant shell stresses. This would become an iterative work process between the vessel designer and the piping designer where actual loads will dictate the ultimate design. In the event that the nozzle loads still result in excessive shell stresses after the iterative work process is conducted, the loadings may be reduced by recalculating the piping loads utilizing the “vessel spring rate”. Often times the loads determined using the vessel spring rate will be much Local Loads less than that determined by the normal process of considering the vessel as a “rigid anchor”. In general the following notes apply to this procedure; 1. Each nozzle, including those designated as “spare”, but with the exception of manways and instrument nozzles, shall be designed to withstand the forces and moments specified in Table 7-14. The indicated loads are to be considered to act at the shell/head to nozzle intersection and to be true normal and tangential to the shell at that point. The effect on the shell/head shall be analyzed per an acceptable local load procedure such as WRC # 107. 2. With regard to radial load (Pr), calculations shall be made first with the force acting radially outwards in 463 conjunction with the internal pressure and then with the force acting inwards. In the second instance, the internal pressure shall not be used to oppose the compressive stresses due to the force acting radially inwards; for this load condition a null pressure condition is to be considered to exist. 3. Values in Table 7-14 were computed by the coefficients and equations given in Table 7-13. In Table 7-13, the variables shown are “D”, the nominal diameter in inches and “b”, the value listed against the nozzle flange rating. These variables and equations were used in the development of Table 7-14. 4. Whenever shell or head stresses exceed the allowable stress for local loadings, the vendor shall apply Table 7-13 Coefficients used for determination of maximum allowable nozzle loads Flange Rating Class 150 300 600 900 1500 2500 b Value 0.6 0.7 0.8 0.9 1 1.1 Equations: Longitudinal Bending Moment ( Ft- Lbs) Circumferential Bending moment ( Ft-Lbs) Resultant Bending Moment, (Ft-Lbs) Radial Load (tension or compression) (Lbs) ML ¼ b X 110 X D2 M4 ¼ b X 85 X D2 MR ¼ [M2L þ M24] .5 ¼ b X 140 X D2 Pr ¼ b X 500 X D Table 7-14 Maximum allowable nozzle loads FLANGE RATING CLASS 150 FLANGES Force, Lbs CLASS 300 FLANGES Bending Moment, Ft-Lbs Force, Lbs Bending Moment, Ft-Lbs NPS (Inches) Radial Load, Pr Longitudinal, ML Circumferential, M4 Resultant, MR Radial Load, Pr Longitudinal, ML Circumferential, M4 Resultant, MR 2 3 4 6 8 10 12 14 16 18 20 24 600 900 1200 1800 2400 3000 3600 4200 4800 5400 6000 7200 264 594 1056 2376 4224 6600 9504 12936 16896 21384 26400 38016 204 459 816 1836 3264 5100 7344 9996 13056 16524 20400 29376 336 756 1344 3024 5376 8400 12096 16464 21504 27216 33600 48384 700 1050 1400 2100 2800 3500 4200 4900 5600 6300 7000 8400 308 693 1232 2772 4928 7700 11088 15092 19712 24948 30800 44352 238 536 952 2142 3808 5950 8568 11662 15232 19278 23800 34272 392 882 1568 3528 6272 9800 14112 19208 25088 31752 39200 56448 464 Pressure Vessel Design Manual FLANGE RATING CLASS 600 FLANGES Force, Lbs CLASS 900 FLANGES Bending Moment, Ft-Lbs Force, Lbs Bending Moment, Ft-Lbs NPS (Inches) Radial Load, Pr Longitudinal, ML Circumferential, M4 Resultant, MR Radial Load, Pr Longitudinal, ML Circumferential, M4 Resultant, MR 2 3 4 6 8 10 12 14 16 18 20 24 800 1200 1600 2400 3200 4000 4800 5600 6400 7200 8000 9600 352 792 1408 3168 5632 8800 12672 17248 22528 28512 35200 50688 272 612 1088 2448 4352 6800 9792 13328 17408 22032 27200 39168 448 1008 1792 4032 7168 11200 16128 21952 28672 36288 44800 64512 900 1350 1800 2700 3600 4500 5400 6300 7200 8100 9000 10800 396 891 1584 3564 6336 9900 14256 19404 25344 32076 39600 57024 306 689 1224 2754 4896 7650 11016 14994 19584 24786 30600 44064 504 1134 2016 4536 8064 12600 18144 24696 32256 40824 50400 72576 FLANGE RATING CLASS 1500 FLANGES Force, Lbs CLASS 2500 FLANGES Bending Moment, Ft-Lbs Force, Lbs Bending Moment, Ft-Lbs NPS (Inches) Radial Load, Pr Longitudinal, ML Circumferential, M4 Resultant, MR Radial Load, Pr Longitudinal, ML Circumferential, M4 Resultant, MR 2 3 4 6 8 10 12 14 16 18 20 24 1000 15000 2000 3000 4000 5000 6000 7000 8000 9000 10000 12000 440 990 1760 3960 7040 11000 15840 21560 28160 35640 44000 63360 340 765 1360 3060 5440 8500 12240 16660 21760 27540 34000 48960 560 1260 2240 5040 8960 14000 20160 27440 35840 45360 56000 80640 1100 1650 2200 3300 4400 5500 6600 7700 8800 9900 11000 13200 484 1089 1936 4356 7744 12100 17424 23716 30976 39204 48400 69696 374 842 1496 3366 5984 9350 13464 18326 23936 30294 37400 53856 616 1386 2464 5544 9856 15400 22176 30184 39424 49896 61600 88704 adequate reinforcement and or increase thickness of shell and /or nozzle locally. 5. For nozzles on a formed head or sphere, the resultant bending moment is to be compared with MR. 6. Shear and torsion effects are omitted from consideration because they have negligible effects on final stress resultants. 7. The loadings computed from these equations shall be considered as caused by 67% thermal and 33% dead weight load. 8. Under vacuum conditions, the deflection. 2, adjacent to the nozzle should be limited to the following; 2 < .0025 R where R is the radius of the shell or head.
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