PRGiK

PRGiK™v1.1

PAULIN RESEARCH PAULIN RESEARCH GROUP

PRGiK™ User Manual

PRGiK™ v1.1* User Manual

 2013 – 2013 – Paulin Paulin Research Group

11211 Richmond Avenue • Suite 109 Houston, TX 77082 Phone +1 281.920.9775 • Fax +1 281-920-9739 www.paulin.com

PRGiK iK™ is part of PRG’s FEATools™ * - PRG FEATools™ is a collection of individual FEA-based programs developed by Paulin Research Group For the purposes of tracking and support, the version number used for FEATools™ Is the version number of the PRGiK Translator program incorporated into FEATools™

PRGiK™ v1.1* User Manual

 2013 – 2013 – Paulin Paulin Research Group

11211 Richmond Avenue • Suite 109 Houston, TX 77082 Phone +1 281.920.9775 • Fax +1 281-920-9739 www.paulin.com

PRGiK iK™ is part of PRG’s FEATools™ * - PRG FEATools™ is a collection of individual FEA-based programs developed by Paulin Research Group For the purposes of tracking and support, the version number used for FEATools™ Is the version number of the PRGiK Translator program incorporated into FEATools™

Table of Conten Contents ts

Chapter 1 Introduction to the

PRGiK™

Calculation Calculation Tool .............................. 1

Chapter 2 Detailed PRGiK™ Discussion ....................................................... 6

Chapter 3 PRGiK™ Examples .................................................................... 17

Chapter 4 Recommended Recommended use of k-factors ................................................. 34 Chapter 5 Stress Intensification Intensification Inconsistencies Inconsistencies in WRC 329 .................... 36 Chapter 6 Reference Reference Data .......................................................................... 38

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Chapter

1 Introduction to the PRGiK™ Calculation Tool This chapter will provide the user with a brief overview of what the PRGiK™ calculation tool does and when it should be applied.

T

he PRGiK™ calculation calculation spreadsheet computes stresses, i-factors and kfactors for branch connections using Code and correlation methods for comparison. The spreadsheet spreadsheet is intended to be part part of of the pipe stress analysts toolbox and should be available in important situations that can be identified by stress magnitude and cycles. Generally, some additional evaluation beyond the current (2012) B31.3 piping code is required when:

1) 0.5 < d/D < 1. 2) N > 5000 and f = 1; or N > 2200 and f = 1.2. 3) D/T > 50 4) Rotating equipment is present 5) The operating temperature is greater than 250F 6) SE > 0.5SA.

© Paulin Research Group – 2013 All Rights Reserved

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The PRGiK spreadsheet should be used: 1) To check Code branch connection SIFs against more applicable i-factor data per 319.3.6. B31.3 Appendix D Notes state that the Appendix D SIFs are to be used in the absence of more applicable data. If more applicable data is available the user is obligated to use it certainly in situations where it will impact the design or safety of the system. Several of those situations are listed below: a. When pressure contributes to the fatigue damage of the piping system. (Pressure cycling must be evaluated per 301.10, and is included in Equations P17 in Appendix P, and when present likely does add in some way to the fatigue damage from thermal cycling.) b. When torsional cyclic loads act on branch connection legs and d/D > 0.5. Paragraph 319.4.4 states that it = 1 in the absence of more applicable data. More applicable data is available in WRC 329, EPRI 110996, and ASME ST-LLC 07-02 and shows that i t can be much greater than 1. PRGiK can be used to eva luate the condition where it>1 if the pipe stress program being used makes this assumption. c. When run pipe i-factors for small d/D branch connections control the pipe design. (These i-factors can easily be off by more than four times.) d. When 0.5 < d/D < 1.0, B31.3 Appendix D Table D-300 Note 11 states that out-of-plane i-factor for unreinforced, pad reinforced, or integrally reinforced (olet) b ranch connections may be NOT conservative, and that selection of the appropriate SIF is the designers responsibility. More applicable data is available in B31.1, WRC 329, EPRI 110996, EPRI 110755, or ASME ST-LLC 07-02. The PRGiK stress calculation will also incorporate this more applicable data in a Code stress calculation. 2) When more than one stress component is high. How the high stress components are combined can significantly affect the stress result. The lower and upper bounds can be found from either of: Slower = MAX( |Spmax|, |Saxmax|, |Sinmax|, |Soutmax|, |Stmax| ) Supper = |Spmax|+|Saxmax|+|Sinmax|+|Soutmax|+|Stmax| When these numbers are significantly different, the user should determine if the combination method used in the Code calculation is appropriate for the loading condition.


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3) When the pipe stress program of choice does not permit for pressure ifactors or pressure stress components to be a part of the equation 17 Code stress calculation for fatigue for pressure cycling at a branch connection. (In this case the user must find some alternative approach to evaluate Paragraph 301.10.) 4) When the pipe stress program of choice does not permit entry of torsional i-factors greater than 1 as part of the equation 17 Code stress calculation for fatigue for torsional loads on branch connections. The PRGiK spreadsheet should be used when: 1) High stresses at a branch connection indicate that a system may be overstressed. 2) Pressure and torsional loads exist at a branch connection in a cyclic system. Some B31 piping codes do not adequately address these conditions. 3) The number of operating cycles for the system is greater than 5000 cycles when f = 1, or is greater than 2200 cycles if f = 1.2, where f is the cyclic reduction factor. 4) The D/T ratio for the piping system is larger than 40 and the temperature is greater than 250F and the number of cycles is greater than those indicated in note 3 above. 5) The pipe stress program user is concerned that a branch connection in the piping system may not have suitable i-factors computed by Appendix D correlations.


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How to Use:

Activate the PRGiK program from the main FEATools Start dialog (shown above on the left). The main PRGiK application (shown above on the right) should appear. Fill in, as a minimum, the first four data items as shown below:

Then press the Compute/Update I,k and K button:


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SIF and k-factor results will be generated for a number of correlations as shown below.

To compute stresses and compare to allowables and mean failure curves, press the “Pipe Stress Evaluation” button:

The user can see stress and cycle values compared to allowables or mean failure curves. More detailed examples are shown in later sections.


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Chapter

2 Detailed PRGiK™ Discussion This chapter will provide the user with a detailed technical discussion of the PRGiK calculation tool

T

he PRGiK calculation spreadsheet computes i-factors and k-factors for branch connections using a selected set of e quations so that the results can be compared and more applicable data selected per B31.3 319.3.6. The tool also allows the i-factors to be used in a stress and allowable calculations so that different stress equations and i-factor applications can be evaluated and so that different allowable and failure mechanisms can be compared. Some individual uses of the PRGik Tool are listed below: 1) Verification of the i-factors provided by the Code of choice. It is known that for certain geometries and branch connections particular Code guidelines can be non-conservative. The PRGiK spreadsheet provides ifactors from six different methods of calculation. When five of the methods agree and one method is different, it is li kely that the one method that is different is errant. 2) Evaluation of k-factor magnitudes for branch connections. When the pipe attached to branch connections are short, the affect of the branch connection flexibility factors can have a large affect on secondary calculated forces and moments. The WRC 329 Fig. 15 example shows an 800% reduction in bending moment at a branch connection when flexibilities were used for that particular piping configuration. The WRC 329 example demonstrates a moment reduction due to the selective location of the branch connection in the model. (k-factors don’t only have large effects when the pipe is short.) Changes on the order of 800% are © Paulin Research Group – 2013 All Rights Reserved

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not typical although the system shown in WRC 329 is not exceptional. Guidelines for use of k-factors for system evaluation are provided in Section 2.0. 3) Calculate B31 Stress S E using equation from Appendix P including a separation of axial, pressure and torsional SIFs. There are numerous ways to combine the up to five stress components that describe the stress state in a pipe. When stresses cycle and are relatively high, it is important to make the proper combination of stresses for comparison against the allowable to be sure the desired Code separation from failure is maintained. 4) Determine if given loads and cycles would likely cause a fatigue failure. Mean failure lines for several criteria are presented. Plotted results include the failure lines, the actual number of cycles and the calculated stress so that separation between failure and stress can be estimated. Each of the methods identified in the spreadsheet either provide i -factors or maximum membrane and bending stresses on the surface. Where only maximum membrane and bending stresses are available, the method of EPRI 110996 (Wais/Rodabaugh) is used to develop the stress intensification factor. The initial i-k screen is shown on the following page:


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Figure 1 – Main PRGiK Input Screen.

Only the branch and run pipe diameters and wall thicknesses need to be input. (First four items in the upper left corner of the form. All other entries will be defaulted.) To produce a calculation or recalculation of the stress and flexibility factors when any of the inputs are changed press the Calculate/Update Button:

A typical output PRGiK panel is shown in Figure 2 below. © Paulin Research Group – 2013 All Rights Reserved

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Figure 2 – Typical PRGiK Output Panel

The branch connection types used in the calculation are defined in Figure 3 below. A discussion of how the PRGiK results for the main screen might be used is provided in a later chapter of this manual.


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Applicable Notes: 1) Section III NB and NC equations are based on the worst case SIF for any direction. Generally this is the out-of-plane direction, and so the out-of-plane SIF is reported for the in-plane and torsional directions and so in some cases the Section III NB and NC in-plane and out-plane SIFs can be artificially higher than those from the other methods and should likely be ignored. 2) ST LLC 07-02, EPRI 110996 and 110755 SIFs are based on finite element regressed surfaces, adjusted to match fatigue test data. The first public use of this approach was described by Wais and Rodabaugh in EPRI 110996. WRC 497 gives the sum of membrane and bending stresses on the surface of the geometry in a manner similar to that used in EPRI 110996. The SIF determination method used in EPRI 110996 is then used to find the SIF from the regressed finite element data in WRC 497. 3) When the background is shown in red, at least one of the equation parameters is outside of recommended limits. 4) Wais model boundary condition lengths used in EPRI 110996 and EPRI 110755 are generally shorter than Widera models in WRC 497 and so for larger D/T branch connections some interaction of the boundary condition occurs, resulting in lower flexibility and SIF factors for Wais. 5) SIF factors are adjusted when effective section modulii are used as part of the Code B31 stress evaluation so that SIFs given are equal to (Stress)(Z/M); where M is the moment in the branch or run, and Z is the section modulus of the branch or run. Mb and Zb are always used together, and M r and Zr are always used together. 6) As recommended in WRC 329 and echoed by the finite element results in EPRI 110996, WRC 497 and ST-LLC 07-02, for the run pipe, the in-plane stress intensification factor is higher than the out-of-plane stress intensification factor. This is a reversal of the trend observed for in-plane and out-of-plane loads through the branch pipe, and is a reversal of the in-plane and out-of-plane SIFs for the run pipe in the B31.3 Code. Typical example uses are shown below with discussions and comparisons.


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The Pipe Stress Evaluation button permits the user to enter loads and/or stresses for probability of failure, safety factor and comparisons with allowables and mean failure curves. This capability is intended to let the user know when they are close to the allowables, and when they are far removed from allowables so that the actual magnitude of the SIF or calculated load is not that critical a part of design. This capability helps the designer know when to use “more applicable data”.


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Welding tee per ASME B16.9 Sketch 2.1 – WLT

Reinforced fabricated tee Sketch 2.2 – RFT

Fabricated tee Sketch 2.3 - UFT

Extruded outlet Sketch 2.4 - EXT

Welded-in contour insert Sketch 2.5 - SWP

Integrally reinforced branch welded-on fittings Sketch 2.6 – OLET

Figure 3 – Branch Connection Types


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Once the SIFs and k-factors have been computed, stresses may be evaluated by pressing the “Pipe Stress Evaluation” button:

A version of the following screen appears: (Different versions might appear, although each has essentially the same data. The PRGiK spreadsheet might be called in a variety of ways, and the differences result in slight changes in how the data is arranged on the form.)

Each area (Letter) is explained on the following page. © Paulin Research Group – 2013 All Rights Reserved

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Each major item on the screen is identified with a letter: A. Input and control. Entries in this section let the user test variations and see the instantaneous affect they have on the stress, allowable or predicted cycles to failure. B. Load Screen. Entries in section B are used to provide load components from the case under study for the stress evaluation. C. Stresses computed for each load or for the load combinations are plotted in this area and compared to a variety of allowables. The “C” Endurance Curve Window screen defaults as disconnected and is toggled on and off. D. Stress/Allowable Plot Control. Log-log plots can be deceiving. Various options for displaying the stress and allowables can be selected to look at the calculated values. In particular, the user may zoom in on the stress and allowable and switch to linear representations to get a clearer idea of the relationship between the stress and the various allowables. E. Selected tabular results are available for use and review. F. Various collective manipulation options are available to help make clearing joint text cells, or resetting parameters easier. The analyst that often uses this screen to compute stresses should explore this option to ease the repeated calculation effort. G. Various stress combination options. When combining the stresses there are several interpretations when multiple i-factors are used. Several of the options are available so that the user can see if there is much of a difference in the stress between the options.


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“Options” Panel

The options panel permits quick clearing and entry of commonly used loads and i-factors and it permits the user to enter stresses directly. By default, forces, i-factors and pipe properties are entered and the program computes stresses, allowables, probabilities, damage factors, etc. In some situations, the user would rather enter the stresses directly and have the downstream properties calculated directly. The “Expose Stress” button should be pushed for this option. When the user pushes the “Expose Stress” button, the stresses may be input, and loads will be back calculated based on the giv en ifactor and pipe cross section properties. Stress Combination Panel

Pressure, axial, inplane, outplane and torsional stresses can be combined in several common ways. The radio buttons in this panel let the user step throught the various options so that the accuracy of the selected approach can be reviewed in important instances. Of more importance in future analyses will be how the run loads combine with branch loads to possibly increase stresses at branch connections. Recent work suggests that the signs of the loads can affect this combination. Future updates to this screen will help the user evaluate these conditions. The intention here is to help the user understand how individual stress components are combined to form the final stress component that’s used by the Code.


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Chapter

3 PRGiK™ Examples This chapter will present a collection of examples of the use of the PRGiK calculation tool.

A

number of typical examples are given in this chapter. Each example provides the problem description, output from PRGiK and a discussion of how the results might be used.


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Example #1: Problem:

A piping system contains a fabricated 8x12 intersection with a schedule 20 wall thickness. The calculated stress is 91% of the B31.3 allowable of 42,250psi. Since the Appendix D Note 11 warns of a non-conservatism in the Code i-factor, would a more applicable value cause the system to show that the branch connection is overstressed?

Note 11 of 2010 B31.3 Appendix D is shown below.

Branch Connection: 12 x 8 Schedule 20. UFT Sketch 2.3 Input:

There are six correlation equations for unreinforced fabricated tees (Sketch 2.3) in the PRGiK spreadsheet. For this branch connection, the results from the six correlation equations are given below:


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The out-of-plane stress intensification factor for thru-branch loading referred to in Note 11 is given for each of the methods in the PRGiK spreadsheet in the table below: Table 1-1 iob stress intensification factors for 8x12 Schedule 20 fabricated tee.

Method

ST-LLC 07-02 B31.3 NC 3673.2 DNV RP C203 EPRI/TR 110996 WRC 497

i-factor

Fact/B31

11.486 7.694 10.19 11.859 13.41 9.377

1.492 1.000 1.324 1.541 1.743 1.219

Given that each alternative method indicates that the B31 method is low, it seems likely that, in accordance with Note 11, stresses computed using the B31.3 i-factors from the 2010 (and earlier) Appendix D will be non conservative by between 1.22 to 1.74 times. If the directional component causing the stress to be 91% of the allowable is ONLY the out-of-plane moment, then the increase will certainly cause the intersection to be overstressed according to the Code. If some of the 91% is due to other stresses at the intersection, then the increase in the out-of-plane moment might not be enough to cause a Code failure at the intersection. The user must evaluate each component of the stress to determine if the increase in the out-of-plane i-factor will cause the branch to be overstressed.


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If the stress distribution for the problem in Example 1 is given below. Will a 1.7 times increase in the out-of-plane stress intensification factor cause the intersection to be overstressed?

If the ST-LLC 07-02 out-of-plane i-factor is used, the Sout stress would increase from 27433 to 27433x11.486/7.694 = 40,930 psi. The bending stress is the square root of the sum of the squares of the in-plane and out-of-plane stresses, and so: 2

2 0.5

( 17968 + 40930 ) = 44,700 psi. 44,700 > 42250 psi, and so the increase in the out-of-plane stress intensification factor will cause this intersection to exceed the Code allowable stress.


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E. Rodabaugh in WRC 329 reviewed the i-factor calculations and noted that a number of inconsistencies existed in the thencurrent B31.3 piping code. The B31.3 Appendix D Table D-300 Note 11 only addressed the out-of-plane SIF problem. Are there any other issues identified in WRC 329 that might change the stress evaluation for loads through the branch at this intersection?

Section 6.0 in this document details a number of the points made in WRC 329 regarding i-factor errors. The inplane stress intensification factor for the branch connection is compared in Table 1-3 below, and it can be seen that what is more applicable data shows the in-plane SIF to be about one half of the B31.3 value. Table 1-3 iib Method ST-LLC 07-02 B31.3 NC 3673.2 DNV RP C203 TR 110996 WRC 497

i-factor 3.922 6.021 10.193 2.819 4.176 3.317

Fact/B31 0.651 1.000 1.693 0.468 0.694 0.550

The NC 3673.2 comparison to B31.3 is inappropriate since Section III NC uses the largest of the i-factors for ii, io and it, and so it is expected, when the io SIF is large, the ii and it SIFs will equally be large for Section III NC calculations, and similarly overly-conservative. The DNV, EPRI/Wais/110996, WRC 497 and STLLC07-02 methods all agree that the i-factor for the in-plane branch stress intensification factor for this b ranch connection should be between 3 and 4 and not 6. Adjust the in-plane stress calculation using the lower i-factor.


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Using 3.922 instead of 6.021 for the in -plane branch i-factor: 17968 x 3.922 / 6.021 = 11,704 psi. Recomputing the bending stress: 2

2 0.5

Sb = ( 11,704 + 40930 ) = 42,570 psi. The total stress at the intersection is computed using Eq. 17 from B31.3 and so the total stress will be: 48,224 psi > 42250 psi. The in-plane stress was too high, and the out-of-plane stress was too low, but the final result was still an overstressed branch connection.


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For the 12x8 Sch 20 branch connection the piping was rerouted due to stresses on the run. The result from that calculation is shown below. Does the pipe really need to be rerouted?

One of the inconsidtencies noted in WRC 329 is fo r the out-of-plane i-factor for loads through the run pipe. For the 8x12 Sch 20 intersection evaluated in this problem, the values of i or for the different methods are given in Table 1-2 below: Table 1-2 ior for 8x12 Sch 20 Fabricated Branch Connection Method ST-LLC 07-02 B31.3 NC 3673.2 DNV RP C203 TR 110996 WRC 497

i-factor 1.0 7.695 4.582 1.0 -

Fact/B31 0.13 1.00 0.59 0.13

The value for NC 3673.2 is known to be c onservative because it is the largest of the i-values at the junction, and so it is likely that the most realistic values of ior for the 8x12 intersection is much closer to 1.0 than 7.7. This suggests that in the B31.3 Code might be overestimating stress in the run pipe due to an out-of-plane moment by 7.7 times. All i-factors are defined with respect to a girth butt weld. An i-factor = 1.0 is with respect to the stress at a girth butt weld and not the stress in a plain pipe removed from welds. Many of the ior factors calculated by FEA for smaller d/D ratios are less than 1 since the high nominal stress is on the side of the pipe 90 degrees removed from the branch connection. The high stress location for the ior stress is shown in the figure below with the red star. EPRI TR 110996 and ST-LLC 07-02 agree that the out-of-plane i-factor for the run for this intersection is equal to one. The WRC 329 comment made regarding this stress component is included next to the figure below.


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WRC 329, p.22.

For the run the torsional SIF is at least 2.68 times greater than what’s used in B31.3, while the ior SIF used for B31.3 is probably about 7.7 times too high, and the iir is probably about 6.02 / 3.56 = 1.69 times too high. The adjusted stress calculation would be:


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Sin (Adjusted) = 21344 x 3.5595 / 6.021 = 12,618 psi. Sout (Adjusted) = 83243 x 1 / 7.695 = 10817 psi. 2

2 0.5

2

2 0.5

Sb = (Sin + Sout ) = (12618 + 10817 ) = 16620 psi. |Sa| + Sb = 8652 + 16620 = 25,272 psi << 41002 psi. The stresses in the run side were grossly overestimated since the run-side outof-plane i-factor for B31.3 is only based on size-o n-size branch connections. The pipe did not need to be rerouted due to stresses in this tee. The stress in the run side elements were 61% off the allowable, and not 230% of the allowable.


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The PRGiK table for the 8x12 Sch 20 fabricated branch connection includes k-factors for several of the references, but the k-factors for B31 are blank – why is that? Does that have any impact on the piping analysis?

The kob factors for branch connections in the PRGiK tables are a multiplier on the diameter. For branch side flexibility factors, the k-factors multiply the branch pipe nominal diameter, and for the run side flexibility factors, the k factors multiply the run pipe nominal diameter. The B31 Appendices for SIFs and k-factors give k-factors equal to 1.0 for all branch connections. ASME Section III NB3200 gives k-factors for fabricated tees when d/D < 0.5 and methods for installing those k-factors. The most important priority given by WRC 329 in t he recommendation section is that for the B31 Codes, that the meaningless k-factor of 1 should be deleted. The note from WRC 329 is provided in part below:

Since WRC 329 was written, E.Rodabaugh, E.Wais, Widera, PRG, and others have produced k-factor equations for branch connections. PRGiK compares the most common ones. For the 8x20 Sch 20 branch connection, the kob flexibility factor is given in the table below. Table 1-4 kob Method ST-LLC 07-02 B31.3 NC 3673.2 DNV RP C203 TR 110996 WRC 497

k-factor 33.2 29.96 38.60 28.60 37.7


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The out-of-plane flexibility factor for this branch connection is almost at least 30, and so at the surface of the branch connection, a point rotational stiffness that is as flexible as the rotational equivalent of 30 diameters of branch pipe should be present in the piping system. The analyst must look at the piping configuration and decide if 30 extra diameters of bending flexibility applied as a point rotational spring at the intersection of the branch centerline and run surface will further reduce the loads on the branch connection. Including flexibilities at branch connections provides more accurate flexibility models of the piping system. Pressing the “k – Per Elbow Basis” button: converts the kfactors to a “per elbow” basis, and gives the user a sense of how many elbows concentrated at the branch-run surface intersection, would be needed to simulate the intersection flexibility. Pressing the “k-per elbow basis” button gives the following k-factors for the 8x12 Sch 20 tee.

For the kob flexibility, omitting the local flexibil ity factor would be equivalent to leaving out the extra flexibility of 1.3 bends.


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Using the output for the 8x12 Schedule 20 tee, what conclusions can be drawn for the intersection?

The PRGiK table for the 8x12 Schedule 20 tee is shown below. Conclusions drawn from this result are included in the table below.


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Conclusions: Factor

iob ior iib

kob

iit

Cv

t/T

D/T

d/D

kor/kir/ktr

kob

B31.3 Evaluation

Discussion

Underpredicts stress 1.4 times Overpredicts stress 2 to 7 times Overpredicts stress by 1.7 times Local flexibility is equal to 1.3 elbows

B31.3 stress intensifcation factor for iob underpredicts stress by 1.4 times. B31.3 stress intensification factor for ior likely overpredicts stress by 2 to 7 times B31.3 stress intensification factor likely overpredicts stress by 1.7 times The schedule 20 branch connection provides local flexibility equal to approximately 30 equivalent diameters of branch pipe. This is the equivalence of adding an elbow at the branch connection. B31.3 stress intensification factor likely underpredicts stress by 2 times. The Bildy membrane factor is 1 for this branch connection, suggesting that the elastic calculation for pressure and external loads is reasonable. The Koves membrane factor is 0.8459 for this branch connection suggesting that the elastic calculation may be conservative for pressure and possibly also for ex ternal loads. The t/T ratio is 1. Even though this is a reduced branch connection, the i-factors for both the run and the branch are the same for B31.3, regardless of the d/D ratio. D/T=50. This is a point where high external loads may cause local failures of geometries and is the point where elastic analysis tends to be increasingly conservative. d/D=0.67 is the point where B31.3 Table D-300 Note 11 warns that the B31.3 iob may be nonconservative. Most other references show that this nonconservatism is on the order of 1.4. kib and kob from Section III are out-of-range for this branch connection. These flexibility factors are all close to 1. The run-side pipe does not gain any flexibility due to presence of this branch connection. Widera and ST-LLC 07-02 kob factors are 37 and 33 respectively. Wais(EPRI 110996) is 28.6. This is consistent with what is known about the boundary condition lengths used by each methods. Where the attached boundary condition lengths are less than D1.4T0.4, it is expected that they will begin to have an affect on calculated i-factors and k-factors. Shorter lengths will reduce k and i-factors.

Underpredicts stress by 2 times -


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EXAMPLE #7: Problem:

Small bore branch connections on a relatively low pressure gas pipeline, D=24”, T=0.25”, are experiencing cracking problems. A detailed evaluation of the fatigue life of the branch connection is to be performed in accordance with B31.3. The branch pipe is welded directly to the run pipe and is a 2” x Schedule 160 pipe. (2.375 x 0.344)

For the run pipe, B31.3 gives an: out-of-plane i-factor of 0.9/(h

2/3

2/3

) = 0.9(R/T)

.

R=(24-0.25)/2 = 23.75/2 = 11.875. Appendix P is the only section of B31.3 that explicitly includes pressure with applied external loads to compute fatigue, and s o the equations P17a and P17b will be evaluated to include the pressure stress as recommended in P319.4.4(a). In the definition of Fa = axial force, the axial force due to internal pressure is to be included. The resulting nominal stress is found from F/A, which for pressure in a pipe cross section is equal to PD/(4T). The stress Sa is found from ia x (F/A) or for the pressure part of the longitudinal stress will be i a x (PD/4T). In the definition for ia, ia is equal to io for components besides elbows and straight pipe. For the run pipe in the example problem, io = 2/3 (0.9)(11.875/0.25) = 11.804. The design pressure for the pipeline is 175 psig. The cyclic pressure stress according to Appendix P is (i a)(F/A) = (ia)(PD/4T) = (io)(PD/4T) = (11.804)((175)(24)/[(4)(0.25)]) = 49,577 psi. If the allowable thermal stress is 1.25(Sc+Sh) = 50,000 psi. The pressure stress component at a 2” branch in a 24” line is the limiting stress and no external loads would be permitted.


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The PRGiK spreadsheet uses existing correlations and so does not produce an i-factor for pressure. The FESIF program that is also a part of FEATools can be used to generate i-factors due to pressure. Two FESIF calculations are required. One analysis is performed to obtain the i-factors for branch side loads, and the other analysis is performed to obtain the i-factors for run side loads. The input for FESIF is shown below:


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The output from FESIF is shown below:

The shell FEA analysis suggest that all the i-factors for pressure in this thick, small connection are 1.0. NozzlePRO lets the user transform the shell model into a brick (volumetric – thru-thickness) model.


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The maximum linearized stresses (for only the two element through the thickness model is given below)

The nominal hoop stress is 175 x 24 / (2 x 0.25) = 8400 psi. The nominal longitudinal stress is 8400 / 2 = 4200 psi. From EPRI 110996, for use with external loads, (and failure at the edges of the fillets), the i-factor for use with pressure would be: ip = C2K2/2; where K2 = 1 when weld lengths are not entered and C 2 is computed using the shell type membrane and bending stress. C2 = 12,012 / 4200 = 2.86. ip = C2/2 = 1.43.

For a finer mesh (5 nodes through the thickness of the non-compatible shaped 11 noded, reduced integration brick element), the maximum linearized stresses are essentially the same as those above, confirming this result. This would lead us to believe that the ip should be 1.43 for pressure and not 11.804. The pressure stress in this case would be expected to be off by 11.804/1.43 = 8.25 times.


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Chapter

4 Recommended use of k-factors

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here are two common uses of k-factors for piping system analysis. These are discussed in detail in this chapter.

1. Comparative – Qualitative: The analyst computes the k-factor and then based on a qualitative evaluation of the piping system decides whether an analysis that does not include kfactors gives an adequate representation of the piping system. When kfactors are close to 1 and the piping attached to the branch connection is relatively long and flexible, then the k-factors will likely have little effect on the calculated forces, moments and stresses. When the k-factors are >> 1 and/or the pipe attached to the branch connection is relatively short – or otherwise not-flexible because of the support in the area, then the k-factors may have a large effect. Also when branch connection branches or runs are at the end of long runs of cantilevered pipe, and the maximum moment occurs at the branch connection due to support in the vicinity of the branch connection large differences in the calculated moments can occur. The example in WRC 329 Fig. 15 is of this type and shows an 800% reduction in the out-of-plane bending stress at the branch connection in the example. 2. Evaluative – Quantitative: The k-factors can be used in every situation to produce a more accurate stiffness model of any branch connection. Local stiffnesses for all three moment loading directions for both the run and the branch are generated and included in a beam model of the piping system. When the attached pipe is short and the loads applied are secondary and strain limited, moments can be reduced by an order of magnitude. Generally reductions are not by an order of magnitude but rather some moments increase while others decrease. © Paulin Research Group – 2013 All Rights Reserved

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Displacements in parts of the system generally increase due to the added flexibility in the piping system. The inclusion of k-factors in piping systems can also be important when rotating equipment is included in the piping system. Equipment is often placed close together to reduce the unit footprint. In this case the excessive use of loops to reduce loads on rotating equipment can be expensive in terms of pipe, added steel, and the t ime it takes to reroute the pipe, both in man-hours and scheduling. Including the local stiffness of branch connections can be equivalent to adding one or more bends at the branch connection, where bends are equivalent to concentrating many extra diameters of pipe at a single point in the piping system. Comparative Use of Flexibility Factors. Forces and moments are particularly important when rotating equipment is located in the vicinity of the branch connection or when the integrity of the piping system is critical and/or the stresses are relatively high. If there is no rotating equipment, and the system does not cycle, and the thermal stresses are low (25% of the allowable), and there are no other significant loads to evaluate, it is seldom worth the effort to include l ocal flexibilities at branch connections. When any of these conditions are not true, then including local branch connections can provide a more accurate analysis.


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Chapter

5 Stress Intensification Inconsistencies in WRC 329

M

ost of the recommendations made by E. Rodabaugh in WRC 329 have an influence on the use of SIFs and k-factors in the piping codes and were incorporated in the notes or guidance included in the ST-LLC 07-02. Excerpts taken from WRC 329 are given below. The page number listed is from WRC 329. A full reading of WRC 329 may be required. Comments by PRG are provided in braces {}. In the forward to WRC 329 written by Sam Moore, Mr. Moore writes: “[Mr. Rodabaugh] … identified a large number of problems with the different code’s usage of branch connection SIFs in their design procedures.” p.9 “… using i = 1.0 for Mt on full size outlet branch connections can lead to inaccuracies far greater than the Mob inconsistency.” p.12 “We would rate the relative complexity of i-factors for pipe, elbows and branch connections by the ratios of 1:5:500. … [readers] will not find any simple answers in this report.” p.12 “…pad or saddle reinforced branch connections may share the Mob inconsistency with other types of branch connections.” p.13 “Extruded outlets are somewhat related to ANSI B16.9 tees in that extruded outlets, like B16.9 tees, may vary significantly between manufacturers.” p.19 “… if a single, nonparametric exponent is to be used for (R/T) … this is a potent source of inaccuracy. … if a more accurate (R/T) exponent is 1.0 then the extrapolation would give if = 25, instead of 11.6.” © Paulin Research Group – 2013 All Rights Reserved

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p.19 “ [C’2bo] … suggests that the t/T variable for r/R between 0.5 and 0.95 is not very significant, and the Code assumption that /M is independent of t is not too bad.” p.21 “[B31.3 itb=1] may be nonconservative by a factor of 2.7 … and may be nonconservative by a factor of 12 or more.” p. 22 “For run moments on branch connections with small r/R, both intuition and Ref. 26 data indicate that the B31.3 relationship ii = 0.75io + 0.25 is at best, reversed in relative magnitude of iir and ior, … and in effect, [the] Code requirements are obviously silly.” p.24 “The available fatigue test data are inadequate to even guess at the general accuracy of Code i-factors for run moments or how they vary with R/T , r/R, t/T, r/rp or some other parameters.” p.24” .. values[for] M tr indicate that the B31.3 SIF i=1.00 for M tr is perhaps unconservative even for r/R < 0.5.” 2/3

p.27 “[using ib=0.9/h instead of 1.5(R/T) unnecessary changes.”

2/3

1/2

(d/D)

(t/T)(r/rp)] could result in

p.28 “The Mob tests indicate that there is a peak somewhere around 0.75.” p.29 “.. we do not necessarily achieve greater accuracy in Code ev aluations by using more accurate i-factors unless more accurate k-factors are also used.” p.32-33 “… delete the use of ii = 0.75io + 0.25 for branch connections tees, … [it] gives the wrong relative magnitude for Mor versus Mir, [and] it underestimates the difference between Mob and Mib for r/R between about 0.3 and 0.95 and perhaps over-estimates the difference for r/R below 0.2 and for r/R = 1.0.” p.33 “For branch connections with r 2 provided, use iib/2.” p.37 “[limits on the inside radius of the branch connection are] dropped because moment fatigue tests and theory indicate that the inside corner radius is not a critical consideration.”


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Chapter

6 Reference Data


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