Proceedings of the ASME 2013 Pressure Vessels and Piping Conference PVP2013 July 14-18, 2013, Paris, France
PVP2013-97814
Improved Analysis of External Loads on Flanged Joints Warren Brown Integrity Engineering Solutions Dunsborough, Western Australia
[email protected]
external loads and results in an under-loaded gasket, by comparison to the aligned joint case. If the external loads are reacted by external means (alignment pins, chain-blocks, hydraulic alignment tools, etc…) then once the joint is assembled to the appropriate bolt stress, upon release of the external means of alignment, the residual external bending moments will have little effect on the joint integrity.
ABSTRACT
External loads on bolted flanged joints must be assessed in order to be in compliance with ASME and other international pressure vessel and piping codes. However, in the case of the ASME B31.3 piping code or ASME VIII, Division 1 pressure vessel code, there is not specific guidance on how to assess these loads. This has created a situation where piping designers have employed a variety of methods, ranging from very conservative to possibly non-conservative. A review of historical joint external load experiments is made in this paper, which highlights the relatively low risk of joint leakage due to external loads. In addition, an improved method of assessing the acceptability of external loads for any given joint is introduced and compared to both test results and existing assessment methods. The method presented is based on probability of leakage for standard piping joints using the method outlined in Appendix O of ASME PCC-1 [1]. This allows, in some cases, a much higher acceptable load than typically employed when using traditional methods such as the Equivalent Pressure method. By allowing higher external loads, it is possible to reduce the footprint of a process unit, which saves money, while maintaining safety.
However, this does not mean that allowing high levels of external load on joints is a good idea. At the design phase it is prudent to limit the external loads on a joint due to the fact that not all joints are properly assembled and the design piping loads are often increased in the field due to underestimation of pipe or insulation weight, or fabrication tolerances and fit-up issues. In addition, forcing the piping designer to consider (and limit) external loads on bolted joints encourages good piping layout practice (e.g.: not using the joint joi nt as the base b ase for a cantilever that supports the entire piping system, for example). Without conservative limits on allowable joint external loads, the piping designer is allowed to resort to poor piping layout practices. So the selection of an appropriate method for assessing the effect of piping bending moments and external loads during the design phase becomes a task in trying to set a limit that encourages good piping design, but is not so conservative so as to require a significant increase in the number of piping supports or expansion loops. This paper examines previous test results and existing methods of assessing the effect of external loads. In order to address limitations in current approaches, a new method of assessing the maximum
INTRODUCTION
The effects of external loads on joint integrity can be summarized with the following statement: “with the exception of joints at high temperature, external forces and bending moments will have little effect on the integrity of a properly assembled joint until the loads exceed normal piping allowable design stress levels”. The more significant effect is where an external load is applied during assembly, which requires some of the bolt load to go into overcoming the
1
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acceptable level of external loads is outlined. The method results in a simple modification to the Equivalent Force method that is easily incorporating into piping and flange design procedures. The goal is to demonstrate demonstrate an approach that can be applied industry wide, or specifically tailored on a custom basis for each site or project by taking into consideration not only the actual operating conditions of the piping system, but also the gasket selection and joint assembly parameters used. The level of conservatism of the method can be adjusted, in order to suit the risk profile versus design optimization goals of a project or site. BACKGROUND
There have been many tests conducted to determine the maximum acceptable bending moment or external load that may be applied to a joint prior to leakage occurring. Table 1 outlines a summary of several joint leakage tests that have been performed on varying sizes and classes of standard piping joints. It can be seen that the majority of tests did not record any increase in leakage with applied bending moments, even though the applied moment was often in excess of 50% of pipe yield (well above the allowable piping design bending moment). In the cases where leakage was recorded, either the joint was purposefully assembled with a very low assembly bolt load and/or the applied internal i nternal pressure was in excess of twice the rated flange pressure. The reason why the bending moment has little effect on the sealing of the joint is that the flanges act to smooth the reduction in load over the gasket perimeter, as the flange must bend prior to coming out of contact with the gasket. In the traditional treatment of external loads (Equivalent Force or Equivalent Pressure) outlined in Koves [2], the force-balance is performed assuming a rigid flange and that the outer bolts transfer the entire load. In the updated methods used in ASME VIII, Div. 2 [3] and outlined in Koves [2] and Koves [4], the deformation of the flange in spreading the reaction of the external load around the bolt circumference is included. A comparison of different methods of analysis of external loads as shown in Koves [3] indicates that the Equivalent Pressure method is very conservative when used within ASME VIII, Div. 1 flange analysis. This is due to the double effect of the equivalent pressure acting as a force in the equation and also being applied to the stress required to seal the gasket via the “m” factor. If the same equation is used, but it is applied as a force only (i.e.: the Equivalent Force method) then the method is less conservative than the Equivalent Pressure method, but still quite conservative by comparison to
Rodabaugh [5]. The methods employed in that study incorporated the effects of mechanical interaction to establish the amount of conservatism for traditional methods such as the Equivalent Pressure method. It was identified that there was significant conservatism in the traditional methods and an alternative method was proposed based on the bolt and flange strength. That method was incorporated into ASME III, Subsection NC [6] as NC-3658.3. In addition, more recent studies have shown that the effect of external loads can be accurately confirmed with FEA and that prediction of leakage, which is found to be proportional to gasket deformation, can be achieved (Takagi [7]). However, it is typically impractical to rely on FEA for general piping design. EXAMPLE CASE
To illustrate the significance of some of these limitations on existing methods, an actual joint leakage case caused by bending moments will be examined. In t his case, a NPS 26, cl. 300, ASME B16.47 Series B flange leaked after only a few months in operation at around 510°C (950°F). An analysis of the piping system and joint indicated that a severe bending moment was present at the joint. An outline of the FEA model used and the analysis results obtained for this case are shown in Fig. 1 and Fig. 2. In this case, case, if the residual pressure between the operating pressure and the flange rating is translated into an allowable moment using the Equivalent Pressure method, then the allowable bending moment is only around 5% of the operating pipe yield. At the other end of the spectrum, the allowable moment in accordance with NC3658.3 is equal to 26% of ambient pipe yield. The actual applied load which caused the leakage was about 20% of ambient pipe yield. The NC-3658.3 method is not conservative in this case, since it is coupled to material yield and therefore doesn’t consider the effects of creep/relaxation on the likelihood of joint leakage. This is acceptable in the context of ASME III Subsection NC, since design in the creep range is not allowed. This example highlights the risk with applying the ASME III approach to other codes of construction. Conversely, the Equivalent Pressure method is tied to the flange rating, which does consider the effects of creep, due to the significantly reduced flange rated pressures once creep/relaxation becomes significant. This reduction is shown in Fig. 3, where the flange rating reduction ratio is plotted in addition to the material yield reduction ratio for grade 1.1 material. It can be seen that the flange pressure rating reduces rapidly once creep becomes
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original design not considering bending moment limits on the joint (resulting in twice the Equivalent Pressure limit being applied, per a later piping assessment). In addition, the piping insulation became wet in the field and doubled the piping sustained load case (resulting in a further doubling of the weight load). From this example, it can be seen that it is important to consider creep relaxation when looking at allowable bending moments and that external piping loads at the design stage should be set conservatively, as they can easily be exceeded in the field by unforeseen circumstances.
the design stage and allowing sufficient tolerance between the imposed limit and the actual system integrity limit in order to ensure that the other operational, fabrication and assembly variables that act to reduce the design limit do not result in system integrity being compromised. In summary, it is possible to demonstrate that the joint will take significant external loads, however, the question that should be asked is: “given the other variables that come into play with assuring joint integrity, what is an acceptable level of external load at the piping system design stage?”.
It is noted that as a high temperature joint, this case is more susceptible to external loads than normal piping systems, but this raises the question of what level of conservatism is appropriate at the design stage. A more conservative method such as using the Equivalent Force method to determine the joint bending moment limit by taking the remaining pressure between the flange rating and the line operating pressure has generally been found to be acceptable and has found good usage and successful operational history within industry. This method is generally found to be workable in most piping design scenarios, however on occasion it will force the piping designer to employ the next pressure class of flange (cl.300 in a nominal cl.150 system, for example). However, this will be to the benefit of the operational integrity of the system. It should also be kept in mind that it is easier to rectify leakage issues at the design stage, rather than once the plant is operational.
PROBLEMS WITH CURRENT APPROACHES
However, using the Equivalent Force method will result in a more complex and costly plant. The higher the complexity of the plant, then the more potential there is for maintenance costs and longer term operating problems which may impact safety. For example, piping spring hangers are a maintenance item, which may cause joint leakage if they fail. Therefore reducing the number of spring hangers used in a piping system will positively impact system maintainability and safety in the longer term. With all of the above analysis methods and test results, it should be remembered that they are based upon the “perfect joint” scenario, where the assembly is monitored, the flanges are aligned, flat and in good condition. All of these additional factors that act to reduce the achieved gasket stress will come into play in the actual field case and they will reduce the margin of tolerance that the joints have for external loads. In addition, sustained external loads will act to increase the amount of gasket relaxation that occurs (particularly at higher temperatures). Therefore, while a joint may see no leakage in
If the ASME III approach is applied to other applications, then it must be ensured that the applicability limits of ASME III (particularly at high temperature) are recognized. In addition, it should be recognized that the ASME III limits are applied to the piping analysis cases used in the nuclear industry, which are potentially significantly more conservative than the load cases and combinations used in other industries. Therefore it is likely that if the ASME III approach is applied in another context it may well not be conservative. In addition, it is based only on the flange and bolt strength and therefore neglects the likelihood of joint leakage, which should be assessed based on gasket stress levels. It also neglects any advantage associated with the joint operating at a pressure lower than the rated pressure (since the external load limits are established without consideration of the operating pressure). However, offsetting that advantage is the potential for needing to redo the piping assessment if the system design pressure is increased at a later date. The use of the Equivalent Pressure or Equivalent Force methods is likely to result in a very conservative limit being established, which will result in unnecessary complexity in the piping system. The approach outlined in ASME VIII, Div 2 uses the Equivalent Force method to establish the required bolt area for the joint and then the Koves method to determine the effect of the external loads on the flange stresses. In those methods, the effects of mechanical interaction are neglected. This is a significant oversight, since depending on the joint component relative stiffness, the bolt load may not change, may reduce or may increase as the bending moment is applied. In simple terms, the flange system has three loads acting on it once the external external loads are applied (Fig. 4). As the external loads are applied, the gasket load is reduced and depending on the component flexibilities, the bolt load may increase or decrease. This effect may be best envisaged by looking at extreme
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stress. Therefore, from a practical perspective the external loads will have a significant effect on flange stresses and no effect on joint leakage. Conversely, if the bolts are extremely flexible and the gasket is extremely stiff, then when the external load is applied, the bolt load will not change and the gasket stress will reduce in proportion to the applied load. In this case, the flange stresses will not change, but the likelihood of joint leakage will increase in proportion to the applied external loads. The actual case will be somewhere in between these two extreme cases. If the change in bolt and gasket stress for the previous example (NPS 26, 2 6, cl.300 Series B) joint is examined with a kamprofile gasket fitted (Fig. 1), it can be seen that the applied bending moment has very little effect on the flange stresses and mostly results in the gasket stress reducing. This means that if the method used in ASME VIII, Div. 2 is applied to this joint with a kamprofile gasket, then the flange stress levels will be significantly over-predicted. Therefore, ideally ASME VIII, Div.2 would be revised to incorporate joint component mechanical interaction, such that unnecessary conservatism is removed from the method. NEW APPROACH PREREQUISITES
Given the preceding cautions regarding the use of the current methods, the following points were considered important in establishing a new method: a) Should be based on flange rating in order to account, in a rough non-conservative way, for creep/relaxation b) Should include the effects of mechanical interaction on the gasket and flange loads. c) Limit should be established based on the likelihood of the joint leaking, since that is the predominant failure mode. d) Due to a variety of unknown factors at the design stage (assembly efficiency, additional loads, poor fabrication tolerances, etc…) the method should be conservative. e) In addition, conservatism is also desired in order to encourage better piping design. NEW APPROACH OUTLINE
The basis of the development of the new approach was to incorporate two established joint analysis methods in order to determine the acceptable level of external loads on standard piping joints. The mechanical interaction effect s were assessed using the methods outlined in Brown [12]. The level of effect of the load transfer from the gasket and bolts as a consequence was determined for each flange size and class. An example of how the inclusion of elastic interaction improves the results of
Rodabaugh and Koves also indicated a preference for including elastic interaction effects in the analysis, for this same reason. The second phase of the development of the new approach was to use the methods outlined in ASME PCC-12010 Appendix O to calculate the required assembly bolt load for each joint size and class using a spiral wound gasket and A193-B8 cl.2 bolt material. The bolt material was selected such that the results would be applicable to the widest range of joints and will be conservative compared to B7 or B16 bolting in the class 150 to class 600 ratings. The method was used, as outlined in Brown [13], to determine the buffer against leakage for each joint when assembled to the calculated assembly bolt stress and with the full ASME B16.5 rating ceiling pressure applied (from ASME B16.5 Table A-1). An example of this is shown in Fig. 7 for the NPS 14, cl.600 example case. It can be seen that the buffer against leakage for this case is 14% of bolt yield, which corresponds to a reduction in gasket stress of 82.7 MPa (12 ksi) before leakage is expect. If the gasket stress buffer is divided by the gasket stress lost due to hydrostatic end force from the rated pressure, then a ratio is established that represents the fraction of the rated pressure above which the joint maybe taken prior to leakage occurring (F M). The below Eq. 1 is then used to determine if the applied external loads are acceptable or not.
16 + 4
≤ 3�(PR − PD ) + FM PR
[1]
Where: ME = Operating external moment FE = Operating external tensile force G = Gasket reaction diameter PR = Flange pressure rating at design temperature PD = Flange design pressure FM = Moment factor, in accordance with Table 2. This moment factor (FM), without conservative adjustment, is plotted for each of the joints examined in Fig. 8 for B16.5 flanges, Fig. 9 for B16.47 Series A flanges and Fig. 10 for B16.47 Series B flanges. It can be seen that in some cases, there is significant additional capacity of the joint above what would typically be considered when using the Equivalent Pressure or Equivalent Force methods alone. However, the graph is somewhat deceptive, since a large value of FM for a class 150 joint will likely still be a small additional external load when compared to the smaller values associated with higher pressure classes (since the value of F M is multiplied by PR ).
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half the raw FM value for expansion loads. The corresponding selected values of F M are shown in Table 2. It is also recommended that these values be reduced again for the sustained load case (since the sustained load case will have a greater impact on joint relaxation). Therefore, for sustained load cases, the values shown in Table 2 should be divided by two.
B16.5 pressure rating. Therefore, it is envisaged that the method outlined in this paper should be extended to include actual assessment of the effects of flange and bolt creep relaxation using the methods outlined in Brown [13]. Unfortunately, due to the lack of good material data for assessing creep/relaxation in joints, this is only possible in relatively few material combinations at the moment.
This approach meets the previously stated prerequisites, in that it is tied to the flange ratings, is based on a method that includes mechanical interaction and is based on a limit obtained versus the likelihood of flange leakage. The nominal safety margin of 2 used to establish the values of F M shown in Table 2 could, of course, be adjusted to suit site preferences. In addition, the assembly bolt loads used for the calculation are based on ASME PCC-1 Appendix O calculations, where the bolt load is maximized. If another approach is used, then it may be necessary to adjust the values of F M downward in order to ensure that the desired level of conservatism exists.
In addition to addressing piping analysis, the methods used in this paper (mechanical interaction and leakage buffer) can also be applied to custom designed flanges. The advantage of incorporating that approach is that it reduces the level of conservatism in the method, since presently the ASME VIII, Div. 2 method uses a conservative assumption for determining both bolt area and flange strength. In addition, it is worth noting that the current method included in that code, which allows for force re-distribution due to flange distortion, was found to be less significant than allowing for component flexibility and mechanical interaction. Mechanical interaction affects both flange and gasket stress levels.
If the new approach is applied to the NPS 26, cl.300 leakage case, the calculated acceptable external load is equivalent to 11% of pipe yield for thermal expansion cases and 7% of pipe yield for sustained load cases. Therefore, if it had been applied, the new method would have avoided leakage, since external loads at the flange would have had to have been much lower, necessitating piping re-design. In addition, it can be seen that the new method is less conservative than applying just the Equivalent Pressure method, since the sustained case limit is 40% higher and the thermal expansion case limit is 120% higher. One final interesting note is that if the effects of mechanical interaction were not included, some of the results would be significantly different. The ratio of FM including mechanical interaction divided by FM without including mechanical interaction is shown in Table 3. It can be seen that, as expected, since the higher classes of joints have much stiffer bolts and flanges, the bolt load is predicted to increase on those joints with the application of pressure (for a spiral wound gasket) and therefore there is a higher buffer against leakage indicated once mechanical interaction is included. Conversely, for some of the larger diameter joints in lower classes, the bolt load is predicted to decrease as the external load is applied, which means that the buffer against leakage is much smaller (by up to 30%) if the effects of mechanical interaction are included in the analysis. FUTURE WORK
CONCLUSIONS
The method presented in this paper allows for additional conservatism to be removed from the use of the Equivalent Pressure and Equivalent Force methods, while still allowing some conservatism in order to encourage good piping design practices to be followed. The method does assume however that the bolt material strength is A193-B8 cl.2 or stronger and that the joints are assembled to a reasonably high assembly bolt stress, based on ASME PCC-1 Appendix O. Adjustment of the method would be required if either one of those assumptions is not correct for the case in question. The approach used can also be applied to custom flange design, however this requires the incorporation of principals from both ASME PCC-1 Appendix O and mechanical interaction.
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REFERENCES [1] ASME, 2010, PCC-1, “Guidelines for Assembly of Pressure Boundary Bolted Joints”, ASME, NY, NY, USA [2] Koves, W.J., 1996, “Analysis of Flange Joints Under External Loads”, Journal of Pressure Vessel Technology, Feb, v.116, p. 59-63 [3] ASME VIII, Division 2, 2010, “Rules for Construction of Pressure Vessels – Alternative Rules”, ASME, New York [4] Koves, W.J., 2005, “Design for Leakage in Flanged Joints under External Loads”, Proceedings of the ASME PVP Conference, Denver, USA, PVP2005-71254 [5] Rodabaugh, E.C., Moore, S.E., 1976, “Evaluation of the Bolting and Flanges of ANSI B16.5 Flanged Joints – ASME Part A Design Rules”, ORNL NRC-5 Publication 2913-3 [6] ASME, 2010, ASME III, Division 1, Subsection NC, Class 2 components, “Rules for Construction of Nuclear Facility Components” , ASME, NY, NY, USA [7] Takagi, Y., Tori, H., Sawa, T., Omiya, Y., 2010,”Effect of External Bending Moment on the Sealing Performance of Pipe Flange Connection”, Proceedings of the ASME PVP Conference, Bellevue, USA, PVP2010-25180 [8] Nash, D.H., Abid, M., 2000, “Combined External Load Tests for Standard and Compact Flanges”, International Journal of Pressure Vessels and Piping, v.77, p.799-806 [9] Bibel, G., Fath, T., Palmer, W., Reidesel, R., Westlind, T., 2001, “Experimental Leak Testing of 16-inch Class 300 RFWN Flange With and Without External Bending Moment”, Welding Research Council Bulletin 461, NY, USA [10] Birembaut, Y., Ledauphin, T., Masi, V., Bouzid, H., Derenne, M., Martelli-Garon, P., 2002, “The Effects of Bending Moments on Bolted Gasketed Joints”, Welding Research Council Bulletin 473 Part A, NY, USA [11] Marchand, L., Derenne, M., 2002, “Effect of the Gasket Type on the Behavior of NPS 4 Class 150 Bolted Flanged Joints Subject to External Bending Moments”, Welding Research Council Bulletin 473 Part B, NY, USA
[12] Brown, W., 1993, “Design and Behaviour of Bolted Joints” 3rd International Conference on Fluid Sealing, CETIM, Nantes, France, pp. 111-121 [13] Brown, W., McKenzie, W. Ryan, S., 2007, “Obtaining LeakFree Bolted Joint Operation by Returning to Basics”, Proceedings of the NPRA RCM-2007 conference , San Diego, USA, RCM-07-85 [14] Brown, W., 2010, “High Temperature Flange Design", ASME STC-LLC Project , STP-PT-036, ASME, NY, NY, USA
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Table 1 – External Load Test Result Summary
Source
Flange NPS
Flange Class
Gasket Type
Test Medium
Test Press. (barg)
Bolt Assembly Stress (MPa)
Maximum Applied Moment (Nm)
Leakage Moment (Nm)
Estimated % of Pipe Yield
Rodabaugh [5]
12
150
Asbestos
Water
43
275
79,100
50,840
29
28
275
79,100
79,100
45
Nash [8] Bibel [9]
Birembaut [10]
Marchand [11]
3
150
Asbestos
Water
43 26 110
68 68 138
4,745 4,745 4,745
2,034 4,745 No Leak
29 68 68
4
300
Asbestos
Water
30 10 110
60 60 123
7,344 7,344 11,299
3,954 7,344 No Leak
30 56 86
4 16
900 300
Spwd Graph Spwd Graph
He
230 50
361 276
15,800 154,563
No Leak No Leak
47 42
Sheet Graph
He
50
207
154,563
No Leak
42
Sheet Fiber
He
50
130
154,563
No Leak
42
300
Fiber Sheet
He
40
162
3000
No Leak
148
8
300
Graph Sheet Spwd Graph Fiber Sheet
He He He
40 40 40
162 243 162
3000 3000 32,000
No Leak No Leak No Leak
148 148 47
4
150
ePTFE
He
22
172
8600
7000
52
Corrugated Graph
He
22
172
8600
No Leak
66
vPTFE
He
22
172
8400
No Leak
66
Spwd Graph Spwd Graph
He He
22 22
172 345
9000 8900
No Leak No Leak
66 66
1.5
Table 2 - Flange moment factor (F M) Flange pressure class 150
300
600
900
1500
2500
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Table 3 - (FM) including interaction divided by (F M) without mechanical interaction included; Spiral Wound gasket
) . n i ( 0.5 e z 0.75 i S 1 e p 1.5 i P 2 l a n 2.5 i m 3 o N 4
5 6 8 10 12 14 16 18 20 24 26 28 30 32 34 36 38 40 42 44 46 48
Flange Class 150 300 600
1500
25 2 500
1.1
1.1
1.1
1.2
1.0
1.1
1.1
1.2
1.4
1.0
1.1
1.1
1.2
1.4
1.0
1.0
1.1
1.1
1.2
1.5
1.0
1.0
1.2
1.1
1.3
1.5
1.0
1.0
1.0 1.0
900
1.0
1.1
1.2
1.1
1.2
1.6
1.0
1.0
1.2
1.2
1.4
1.9
1.0
1.0
1.1
1.2
1.4
1.9
1.0
1.1
1.1
1.2
1.5
2.0
1.0
1.0
1.1
1.2
1.7
2.1
1.0
1.0
1.1
1.3
1.8
2.2
1.0
1.0
1.1
1.5
2.0
2.0
1.0
1.0
1.1
1.3
1.8
2.4
1.0
1.0
1.1
1.4
1.7
1.0
1.0
1.1
1.5
1.6
1.0
1.0
1.0
1.3
1.6
1.0
1.0
1.1
1.5
1.6
1.0
1.0
1.0
1.5
1.6
1.0
1.0
1.1
1.2
0.9
1.0
1.1
1.1
1.0
1.0
1.1
1.2
1.0
1.0
1.1
1.2
0.9
1.0
1.1
1.2
0.9
1.0
1.1
1.3
1.0
0.9
0.9
1.1
0.9
0.9
0.9
1.1
1
0.9
0.9
0.8
1.1
0.9
0.7
0.8
1.2
0.9
0.7
0.8
1.1
0.9
0.9
0.8
1.2
o i t 0.8 a R n o 0.6 i t c u d e0.4 R
Figure 2 – NPS 26, cl.300 ASME B16.47B FEA Model
1.2 cl.150
0.2
cl.300 & higher Material Yield
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Min. Min. Op.
Hydro Hydro
Thermal Thermal
Relaxati Relaxation on
Seating Seating
Buffer Buffer
Target arget & Spread Spread
Flange Flange Limit Limit
EXTERNAL LOAD 1
14%
0%
5%
10%
15%
2 0%
25%
30%
35%
40%
45%
50%
Percentage of Bolt Yield
Figure 7 – NPS 14, cl.600 Appendix O Calculation Graph B16.5, cl.150
5.00
B16.5, cl.300
4.50
B16.5, cl.600 4.00
B16.5, cl.900 B16.5, cl.1500
3.50 ) M
B16.5, cl.2500
F ( r 3.00 o t c a F2.50 t n e m2.00 o M
1.50 1.00 0.50 0.00 0
Figure 4 – Flange Load Equilibrium Under External Loads
1.1
2.2
3.3
4.4
) i s k ( s s e r t S t l o B n i e g n a h C
35
Eq. Press
242 207
S8D2
25
173
20
138
15
104
10
69
5
35
0
0 0
1
2
3
4 -6
Bending Moment Applied (in.lb x 10 )
10
12
14
16
18
20
22
24
Pipe NPS
Figure 8 – Moment Factor Results; B16.5 Flanges B16.47A, cl.300
276
Elast. Inter.
30
8
B16.47A, cl.150
311 E-P FEA
6
5.5
45 40
4
2.50
Bending Moment Applied (N.m x 10 -5) 0
2
5
B16.47A, cl.600
2.00
) a P M ( s s e r t S t l o B n i e g n a h C
B16.47A, cl.900 ) M F ( r 1.50 o t c a F t n e m1.00 o M
0.50
0.00 26
28
30
32
34
36
38
40
42
44
Pipe NPS
46
48
50
52
54
56
58
60
