ENGINEERING SOFTWARE PIPE STRESS ANALYSIS SEMINAR NOTES Notice: Unless otherwise noted herein, the information contai
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ENGINEERING
SOFTWARE
PIPE STRESS ANALYSIS SEMINAR NOTES
Notice: Unless otherwise noted herein, the information contained in these course notes is proprietary and may not be translated or duplicated in whole or in part without the expressed written consent of COADE Engineering Software, 12777 Jones Rd., Suite 480, Houston, Texas 77070. Copyright {c} 1985 - 1998 COADE, Inc.
1
COADE Pipe Stress Analysis Seminar Notes Section 1 Table of Contents
1.0 Introduction to Pipe Stress Analysis ........................................................................ 1 1.1 Theory and Development of Pipe Stress Requirements ........................................... 8 1.1.1 Basic Stress Concepts ............................................................................... 8-14 1.1.2 3-D State of Stress in the Pipe Wall ....................................................... 14-15 1.1.3 Failure Theories ........................................................................................... 16 1.1.4 Maximum Stress Intensity Criterion ..................................................... 18-19 1.2 Fatigue Failure ....................................................................................................... 20 1.2.1 Fatigue Basics .............................................................................................. 20 1.2.2 Fatigue Curves ............................................................................................. 22 1.2.3 Effect of Fatigue on Piping ..................................................................... 24-25 1.2.4 Cyclic Reduction Factor ............................................................................... 25 1.2.5 Effect of Sustained Loads on Fatigue Strength .......................................... 26 1.3 Stress Intensification Factors ............................................................................ 28-33 1.4 Welding Research Council Bulletin 330 ................................................................. 34 1.5 Code Compliance ..................................................................................................... 43 1.5.1 Primary vs. Secondary Loads ................................................................. 43-45 1.5.2 Code Stress Equations ............................................................................ 45-46 1.5.3 B31.1 Power Piping ..................................................................................... 46 1.5.4 B31.3 Chemical Plant and Petroleum Refmery Piping .............................. 47 1.5.5 ASME Section III, Subsections NC & ND (Nuclear Class 2 & 3) .......... 49-50 1.5.6 B31.4 Fuel Gas Piping ................................................................................. 51 1.5.7 B31.8 Gas Transmission and Distribution Piping Code ............................. 52 1.5.8 Canadian Z183/Z184 Oil/Gas Pipeline Systems ......................................... 54 1.5.9 RCC-M C ...................................................................................................... 55 1.5.10 Stoomwezen ................................................................................................. 56 1.5.11 Special Considerations of Code Compliance ........................................... 56-59 1.5.12 Evaluation of Multiple Expansion Range Cases ......................................... 59
COADE Pipe Stress Analysis Seminar Notes
1.0 Introduction to Pipe Stress Analysis In order to properly design a piping system, the engineer must understand both a system's behavior under potentialloadings, as weIl as the regulatory requirements imposed upon it by the governing codes. A system's behavior can be quantified through the aggregate values of numerous physical parameters, such as accelerations, velocities, displacements, internaI forces and moments, stresses, and external reactions developed under applied loads. Allowable values for each of the se parameters are set after review of the appropriate failure criteria for the system. System response and failure criteria are dependent on the type of loadings, which can be classified by various distinctions, such as primary vs. secondary, sustained vs. occasional, or static vs. dynamic. The ASME/ANSI B31 piping codes are the result of approximately 8 decades ofwork by the American Society ofMechanical Engineers and the American National Standards Institute (formerly American Standards Association) aimed at the codification ofdesign and engineering standards for piping systems. The B31 pressure piping codes (and their successors, such as the ASME Boiler and Pressure Vessel Section III nuclearpiping codes) prescribe minimum design, materials, fabrication, assembly, erection, test, and inspection requirements for piping systems intended for use in power, petrochemical/refinery, fuel gas, gas transmission, and nuclear applications. Due to the extensive calculations required during the analysis of a piping system, this field of engineering provides a natural application for computerized calculations, especially during the last two to three decades. The proliferation of easy-to-use pipe stress software has had a two-fold effect: first, it has taken pipe stress analysis out ofthe hands ofthe highlypaid specialists and made it accessible to the engineering generalist, but likewise it has made everyone, even those with inadequate piping backgrounds, capable of turning out officiallooking results. The intention ofthis course is to provide the appropriate background for engineers entering the world of pipe stress analysis. The course concentrates on the design requirements (particularly from a stress analysis point ofview) of the codes, as weIl as the techniques to be applied in order to satisfy those requirements. Although the course is taught using the CAESAR II Pipe Stress Analysis Software, the skills learned here are directly applicable to any means of pipe stress analysis, whether the engineer uses a competing software program or even manual calculational methods.
Why do we Perform Pipe Stress Analysis? There are a number ofreasons for performing stress analysis on a piping system. A few of these foIlow: In order to keep stresses in the pipe and fittings within code allowable levels.
1 2
-
In order to keep nozzle loadings on attached equipment within allowables of manufacturers or recognized standards (NEMA SM23, API 610, API 617, etc.).
1-1
COADE Pipe Stress Analysis Seminar Notes
3 4
In order to keep vessel stresses at piping connections within ASME Section VIII allowable levels. -
5
In order to calculate design loads for sizing supports and restraints. In order to determine piping displacements for interference checks.
6
-
In order to solve dynamic problems in piping, such as those due to mechanical vibration, acoustic vibration, fluid hammer, pulsation, transient flow, and relief valve discharge.
7
-
In order to help optimize piping design.
Typical Pipe Stress Documentation
Documentation typically associated with stress analysis problems consists of the stress isometric, the stress analysis input echo, and the stress analysis results output. Examples ofthese documents are shown in Figures 1-1 through 1-5 on subsequent pages. The stress isometric (Figure 1-1) is a sketch, drawn in an isometric coordinate system, which gives the viewer a rough 3-D idea of the piping system. The stress isometric often summarizes the piping design data, as gathered from other documents, such as the line list, piping specification, piping drawing, Appendix A (Figure 1-2) of the applicable piping code, etc. Design data typically required in order to do pipe stress analysis consists of pipe materials and sizes; operating parameters, such as temperature, pressure, and fluid contents; code stress allowables; and loading parameters, such as insulation weight, external equipment movements, and wind and earthquake criteria. Points of interest on the stress isometric are identified by node points. Node points are required at any location where it is necessary to provide information to, or obtain information from, the pipe stress software. Typically, node points are located as required in order to: define geometry (system start, end, direction changes, intersection, etc.)
1 2
-
define element stiffness parameters (changes in pipe cross section or material, rigid elements, or expansion joints)
3 4
note changes in operating conditions (system start, isolation or pressure reduction valves, etc.)
-
5
designate boundary conditions (restraints and imposed displacements) specify mass points (for refinement of dynamic model)
6
-
note loading conditions (insulation weight, imposed forces, response spectra, earthquake g-factors, wind exposure, snow, etc.)
7
-
retrieve information from the stress analysis (stresses at piping mid spans, displacements at wall penetrations, etc.)
1-2
COADE Pipe Stress Analysis Seminar Notes The input echo (Figure 1-3) provides more detailed information on the system, and is meant to be used by the engineer in conjunction with the stress isometric. The analysis output provides results, such as displacements, internal forces and moments, stresses, and restraint loadings at each node point of the pipe, acting under the specified loading conditions. CAESAR II provides results in either graphic or text format; Figures 1-4 and 1-5 present stress and dis placement results graphically. The output also provides a code check calculation for the appropriate piping code, from which the analyst can determine which locations are over stressed.
SSEMl tUI
tower-:'~[
Haterial A186 Gr.B SH @ 788 deg. = 16.588 psi SC @ 78 deg. = 28.888 psi t = 788 deg. F. Flue Gas P = 125 psi Dia = 28" Std.Wall Insul = 2" Calciul!I Silicate
,~~.y..
SUpport ......
rD_
~3S ~..~145 j;
COl!lputed therl!lal expansion of the vessel is 17.268E-6 in/in/deg.F. at a telllp of 828 deg.F. Node 188 is 28.88 ft. above vessel skirt 'i
A
Z
Disp. @ 188 = (828-7B)deg.F(17.268E-6)in/in/deg* (28.88)(12)ft.in/rt. = 3.121 in. X
Disp. D 128 = (B28-78) (17.268E-6)(28.88+6.5-15)(12) = 1.8 in.
Figure 1-1
1-3
Exchanger 0
0
0 ANSI/ASME 831.3-1984 ROmON TABLEA·I
ASME CODJ! FOI. PIUlSSUIUI PlPINO CHEMICAL PLANT AND PBTROLBUM Rl!FlNBIlY 'IPINO
ASMJ! COD! fOI. 'IU!SSUIUI'IPINO CIIEMICAL PLANT AND PBfR.OLEUM lEFINI!IlY.IPINO
TABLE A-1 (CONT'OI BASIC ALLOWABLE STRESSES IN TENSION FOR METALS lU Nurilers ln '-thKes Rtftr to Notes ,., ~ A TMIes; Specifications AIt ASTM Uilleu DIIIIIwIIt lIIdItaIId
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50,000 100,000) cycles for carbon and low-alloy steels, and are insignificant for 18-8 stainless steels and nickel-chrome-iron aIloys. Since these materials constitute the majority of the piping materials in use, and since most cyclic loading events comprise much fewer than 50,000 cycles, the effects of mean stress on fatigue life are negligible for piping materials with ultimate strengths below 100,000 psi. For materials with an ultimate strength equal to or greater than 100,000 psi, such as high strength bolting, mean stress can have a considerable effect on fatigue strength and should he considered when performing a fatigue analysis. For a piping application, the implication of the Soderberg line on the fatigue allowable is implemented in a conservative manner. The sustained stress Ci.e., weigh t, pressure, etc.) can be considered to be the mean component of the stress range after system relaxation, and as such is used to reduce the allowable stress range: SE 1.5
For (rlR) = 1.0: 0.9 (RIT)2/3 (r/rp ), with ib(tIT) > 1.0
And:
=
0.8 (RIT)2/3 (rlR), with ir > 2.1
lb
=
intensification factor for branch (to be linearly interpolated for rlR ratios hetween 0.9 and 1.0)
R
=
mean radius ofheader pipe, in
T
=
thickness ofheader pipe, in
r
=
mean radius ofbranch pipe, in
rp
=
outer radius ofbranch pipe, in
t
=
thickness ofbranch pipe, in
Ir
=
intensification factor for run (header) pipe
Ir
Where:
Additionally, if a radius of curvature r2 is provided at the connection, which is not less than the larger of t/2, (Tb'+Y)/2, or T/2, then the calculated values of ib and ir may be divided by 2.0, but with the restriction that ib>1.5 and ir >1.5. Also, where reduced outlets are discussed, branch ends should he checked using Z = p (r2)t and i(tIT) in place ofi, with i(tIT) > 1.0.
1-35
COADE Pipe Stress Analysis Seminar Notes
Il)
There was not sufficient data available onreinforcedfabricated tees for Rodabaugh to make any definitive recommendations regarding them. Rodabaugh does however suggest that the normal usage whereby the width of the pad is taken to be at least equal to the radius ofthe nozzle should be observed even though not explicitly directed by the code.
12)
For t/T ratios of about one or more, stresses tend to be higher in the header, and are fairly independent ofthe wall thickness ofthe nozzle. As the tlI' ratio gets much smaller than one, the largest stresses shift to the branch. (This finding originally came out of the research for WRC 297.)
Comparisons ofWRC 330's proposaIs for stress intensification factors for various types of tees, versus B31.3 calculated values are shown on the following pages.
1-36
COADE Pipe Stress Analysis Seminar Notes
NO INTERSECTION RADIUS "831.3" VS. 'WRC 330' UNREINFORCED, FA8RICATED TEE STRESS INTENSIFICATION FACTORCOMPARISON
HEADER NOM
BRANCH SCH
WRC
--B31.3---
330 b
i ib
WRC
iob iOb
--B31.3---
~
i oh
1 330 h
330 h
330 b
ioh
1 40.
40.
2.433
2.874
2.433
.853
1.081
2.433
.959
1.125
1 48. 2 48.
1 48. 2 40.
4.184 3.359
2.769 2.769
3.359 3.359
..m .B24
.822 1.010
2. tHe 2.986
2.769 2.769
3.359 3.359
1.319 .927
1.6"" 1.125
J 40. l 40. J 43.
1 414. 2 414.
3.479 4.769 3.4811
2.860 2.860 2.868
3.488 3.488 3.488
.822 .U8
1.011 .738
3.488 3.481 3.4811
l.b57 1.657
1.881
2.86B 2.868 2.86"
1.362 1.362
.822
2.111 2.111 3.893
.925
1.125
4 40. 4 40. 4 40.
1 48.
3.416 4.682 5.694 3.B92
3.169 3.169
3.892 3.892
.928
1.139
2.11111
.677
.831
3.169 3.169
3.892 3.892
.557
.684 l.0U
3.892 3.a92
1.5119 1.5B9 1.189 .916
1.953 1.853 1.468
.814
2.lem 2.665 3.46m
3.169 3.169 3.169 3.169
3.891
Z 40. 3 4B, 4 414. 1 48. 2 48.
4.589
3.441 3.Hl
1.1128 .758 .617 .54J .889
1.271 .927 .763 .669
3.441 3.441 3.441 3.441 3.441
".255 4.255 4.255 4.255 4.255
1.639 1.639
2.826 2.826 1.817 1.488 1.125
.816
!.lm
2.m
.671 .589 .528 .885
.834 .732 .656 1.81l@
2.11111
.764 .671 .681 .549
.954 .837 .751 .686
.BU
1.811!
.747 .669 .612 .535
.936 .839 .671
.797
1.l!ea
.915 .837 .732 .654
4 49. 5 40. S 48. ~ 411!. 5 40. 5 411!.
3 40.
3 411. 4 48.
5 48.
6 49.
2 48.
b 411!. 6 411!. 6 40. 6 4\J.
:) 48.
S 48.
:) 4f.1. .. 48.
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e
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19 48.
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III! 4B.
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8 411.
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14 14 14 14 14
48. 4B. 4B. 49. 4B.
b 48. 18
n.
5 48. h 4B. B 48.
18 48. 12 48. b 48. 8 48. 10 48.
12 48. 14 48.
5.5BII 6.359 4.255
3.441 3.44J
4.255 4.255 4.255 4.255 4.255
4.477 5.444 6.282 6.919 4.548
3.655 3.655 3.655 3.b55 3.655
4.540 4.548 4.541 4.541 4.541
5.187 5.918 6.592 7.218 4.94'1
3.961 3.961 3.961 3.9bl 3.961
4.949 4.949 4.949 4.949 4.949
5.642 6.294 6.884 7.875 5.284
4.213 4.213 4.213
5.284 5.284 5.284
4.213 4.213
5.284 5.284
6.834
4.392 4.392
.728 .666 .592 .52@ .795
5.599
.697 .689 .545
3.348
l
3.441
b.bBB 7.549 8.443 5.523
·40592 4.392
5.523 5.523 5.523 5.513 5.523
6.383 7.382 B.IM 8.569 5.599
4.458 4.45B 4.458 4.4Se 4.4511
5.599 5.599 5.599 5.599
4.392
.5J9 .795
Lltllll
.768
1.all'!
.877
.767 .686 .653
2.nll
2.1111 2.342 3.14B 3,783
2.711
3.374 4.836
3.655 3.655 3.655 3.655 3.655
3.an
1.478 I.H2
.91B
1.125
4.548
1.741
4.548
1. 741
4.548
1.348 1.883 .986
2.162 2.162 1.674 1.346 1.125
1.886 1.754 1.410 I.PS .911
2.356 2.191 J.76J 1.472 1.125
1.122
2.516 2.282 l.a41 1.407
4.540
4.541
3.961 3.961 3.961 3.961 3.961
4.949 4.949
2.111 2.399 2.871 3.755 4.697
4.zn
2.@86 1.756 1.468
~.213
5.284 5.284 5.28" 5.284 5.284
.997
1.125
2.118 2.523 3.312 4.138 4.919
4.392 4.392 4.392 4.392 4.392
5.523 5.523 5.523 5.523 5.523
2.882 1.741 1.338 1.1163 .895
2.b18 2.189 1.673 1.337 1.125
2.328 3.847
4.458 4.45B 4.458 4.4511 4.458
5.599 5.599 5.599 5.5'19 5.599
1.911 1.468
2.405 1.839
1. Ib8
1.469
.982 .894
1.125
2.111 2.258 2.811
3.361 4.399
3.811
4.538 U188 . 4.977
1-37
4.213 4.213
4.213
4.949
4.949 4.949
1.236
COADE Pipe Stress Analysis Seminar Notes
NO INTERSECTION RADIUS "B31.3" VS. 'WRC 330" UNREINFORCED, FABRICATED TEE STRESS INTENSIFICATION FACTOR COMPARISON
HEADER NOM
16 40.
16 48.
lb 4". 16 4@, lb 48.
8RANCH SCH
WRC
-·831.3···
330 b
i ib
6.825 7.633 8.322 8.723 5.595
4.449
18 40.
7.281 7.B50 8.229 8.797 5.598
8 40. I@ 48.
12 48. 14 40. lb 48.
18 18 18 lB 18
48. 48. 40. 48.
20 20 20 2" 20
40. 48. 4". 48. 48.
12 40. 14 40. 16 4~. 18 4~. 20 40.
7.711 8.882 8.640 9.165 5.801
24 48. 24 40.
16 48. 18 40.
4~.
18 40. 12 40. 14 48. lb
40.
i ib
iob
WRC
···831 .3···
iOb
330 b
330 b
330 h
i ih
4.446
5.595
.928
2.664
4.446
5.595
4.446
5.595 5.595
.651 .583 .534
.733 .672
.510 .795
.641 1.098
.618 .567
4.449 4.449 4.449
5.598 5.598 5.598 5.598 5.598
4.681 4.681 4.681 4.681 4.601
5.BBI 5.a61 5.B01 5.881 5.8@1
.597 .56Q .532 .592 .793
4.707
.583 .549 .521
4.707
5.943 5.943 5.943 5.943
4.446 4.446
4.4~9
5.595
.541
.586 .795
3.332
I.6b9 1.334
2.1011 1.b79
3.961 4.352
4.446 4.446
5.595 5.595
1.123 1.822
1. 413 1.286
4.973
4.446
5.595
.894
1.125
.777 : 2.964 .713 : 3.523 .6811 3.871 .636 '4.423 1. 80~ l 4.976
4.449
5.598
5.598 5.598 5.598
1.5&1 1. 263 1. 1-49 1. "lib
1.889
4.449
.752 .718 .671
5.156
4.601
.736
3.512
.694 .658
3.951
6.52(1 6.520
i
1.113 .887
1.411 1.125
4.783 6.801
5.6lB 5.670
1.186 .945 .883
1.511
6.424
7.227· 7.227 7.227
.783
.640 .733 1.89B
5.879 6.293 6.695
5.899 5.899 5.899
7.532 7.532 7.532
1.083 .937 .B81
.51l!
.m
5.446
• 49'1 .585 .784
.637 .746
5.830 6.283 6.563
5.788 S.7B8 S.788
7.384;1 U63 7.3B4· .993 7.384 .933
5.788
7.384
6.480 6.4110 6.40& 6.489 6.480
B.280 8.280
.788
1.800
4~.
10.394 10.134 7.227
5.670 5.670
5.m
7.227 7.227 7. '227,
.546 .560 .785
11.763 !lU17 7.532
5.899 5.899 5.899
7.5321
.501
7.532. 7.532!
.572
7.384 j 7. 384: 7.384, 7.384
.56 48. 36 41l. 36 48.
30 -4B. 32 49. 34 48.
36 48.
36 48.
42 42 42 42
30
48. 48,
40. 4@.
42 40.
40.
32 U. 34 48.
36 40. 42 40.
11.210
5.788
11.599
5.788
9.902 7.384
5.788 5.788
11.5(18 11.9(17
b.400
12.231 12.633 8.209
b.UB 6.488
b.m b.480
.79'l.
~
8.208 ; 8.208 ; 8.20~ : 8.2@0 ; 8.209
1.252 1.125
5.140 5.140
.672
34 40.
.'193
.B92
4.619 5.796
.530
30 4~. 32 411.
!.b10
1.4&9
4.707
6.520 6.520
34 411. 34 48.
1.m
1.483 1. 277 1.117
5.BiH 5.a81 5.BIH 5.801
4.391
5.140 5.140
14 40.
5.m
1.009 ; 5.282
9.782 6.528
32 40.
5.598 1 .894
1.446 1.2116 1.125
5.943 5.943 5.'143
24 4~. 3" 40, 24
4.601
1.589
4.797 4.787 4.7@7
30 48. 39 48.
36 40. 32 40.
4.601 4.601 4.681
,633
20
32 41Ll.
4.449 4.449
Lel8
24 40.
32 49.
3.281
4.449
3.604 4.1lB 4.633
24 40,
4.m
330 h
5.595 5.595
24 4@.
40.
330 h
ioh
4.446 4.446
8.076 8.566 9.@37 5.943
4.707
i ih ioh
.,m ' .713 I.m
1.888 .713
.537 .521 .507
.780
1-38
.089 .6&8 .649 1.BS8
5.lbB 5.533 5.a86 6.228 7.289
S.670
5.943:
\,:)48
l.h92
1.191
1.504
!.lm
Lm
.B'11
I.! 25
l i
i i
1.204 1.125 1.281
1.197 1.125
1.35a 1.266
.8B2
1.198 1.125
1.238 ! .157 8.m 1.087 S.2U 1 1.828 B.2BILl 1 .878
1.587 1.482 1.393 1.316 1.125
COADE Pipe Stress Analysis Seminar Notes
NO INTERSECTION RADIUS
"831.3" VS 'WRC 330" WELDOLET STRESS INTENSIFICATION FACTOR COMPARISON HEADER NOM
BRAN CH SCH
3 48. 3 48. 3 48.
..·931.3..i ib
i ib iOb
WRC
iOb
---B31 ,3---
i ih
i Oh
330 b
330 h
i ih
i oh
330 h
330 h
40.
1
2.433
1.097
1.897
.~51
.451
2.162
1.Il97
l.097
.588
.518
1.516 1.516
.371 .451
2.1110
1.516
1.516
1 ;::::
1.516 1.516
.371
:::
.451
2.986
1.516
1.516
.722 .588
.722 • SilS
411. 2 4B. 3 411.
3.363 4.769 3.483
1. 570 1. 578 1.5711
1.570 1.570 1.570
.467 .329 .451
1 2.1110
.748
.748
1 2.11l0
1.571 1.571
.748
.748
i 3.093
1.57@ 1.570 1. SHI
1.578
.329 .451
.508
.588
1 3.366 1 1 4.682
1.756 1. 756
1.756
.522
.522
2.110
1,756
1.75b
.83b
.B3b
1.756
.375
1. m
5.694
1.756
1.756 1.756
.308
.375 i 2.18e .308: 2.665
1. 756 1. 756
.836 .659
.836 .659 .588
A0. '1 40. 2 48.
WRC
, 330 b
,
330 b
.467
1
4 48. 4 411. 4 48.
1 40. '1 411. 3 40.
4 41l.
4 40.
5 S 5 5 5
48. 4@, 48. 4@. 411.
il
40.
6 ~8. 6 4@. 6 4@.
1 411. '1 411. 3 411. -4
411.
5 411. 2 40. 3 40. 4 40.
1
I
!.?Sb
l :. :9: 1
.::r • .) __,
1.920
1 4.589
1. 920 1.928 1. 920 L92@
1.920 1.928 1.920 1.920 1.920
2.848 2.048 2.B48
2.048 2.848 2.048
2.848 2.048
2.848 2.1148
i 5.580 [ 6.358 : 4.255 4.47i ,5.444 • 6.2112 6.919 4.540
6 40.
5 40. 6 411.
8 40.
3 48.
,5,187
2.233
2.233
8 40.
4 5 b S
! 5.910
2.233
6.592 7.210 4.'149
2.233
2.233 2.233 2.233 2.233
8 40. Il 40. B 40.
40. 4iJ.
48. 40.
10 40.
4 U.
10 40. 10 4~. 10 40. !~ 40.
S 48.
5.642 6.294
12 12 12 12 12
40. 40. 40. 41l. 40.
14 14 14 14 14
40. 40.
n.
40. 40.
2,233 2.233
il 40.
6.884
2.384 2.384 2.384
B 411.
7.S75
2.384
III U.
5.284
2.384
S 40. (, 4@. 8 40.
6.034
III 41l.
8.443
2.492 2.492 2.492 2.492
6.6@0
7. 54'?
2.492
12 411.
6 40.
UB3
8 40. 10 40. 12 40.
7.3112 8.1bb S.569
2.526 2.526 2.526 2.526
14 40.
5.599
2.526
.451 ~5t
2.492 2.492 2.492 2.492 2.492 2.526
I.ni 1. 928 I.cm 1. 928
.579
2.188
.418 .344
2.11'" 2.342
.382 .451
3.11411 3.783
Lm
t.m
1.920
2.1148 2.1148 2.848 2.1148
'4.@3b
2.848 2.848 2.148 2.848 2.148
2.1811
2.233
.451
.458
.458
2.108
.376 .3311 .296
.376 .331 .296 .451
2.101l 2.711 ! 3.374
i
.451
.430 .378 .339 .318 .451
.422
.422
.379
.379
.451 .4311 .378
.339 .318
.346
.346
.303
.303
.m
.451
.378
.413 .378
.3311
.338
.~ .J
.295
1 .451
.451
\ .396
.346
.346
2.526
l
.396
i
.319
2.526
1
.309 .295
2.526
1 .451
2.526
l.·m 1.92i! 1. Ç7~
.579
.302
.~13
;!
3.m_~ ._1!756_~_~~m8
.418 .344
2.384 2.384 2.384 2.384 2.384
1
1.756
'9~
.295 .451
' 2.258 \ 2.811
3.361 ~.399
2.233 2.233 2.233
.975 .755
2,848
.5118
.5118
2.233
!.IIb3
t.m
2.233 2.233
.989 .794 .664 .598
,989 .794
1.135 .994 .831 .635 .588
L 135 .994 .831 .635 .588
1.181 .987 .755
1.181
2.233
.., ,.,.,..,. L.J..0·~1
2.492
2.492
2.492
2.492
2.492
2.492
2.492
2.492 2.492
2.328 3.847 3.811
2.526 2.526
4.5311
2.526 2.526
4.917
1-39
2.526
.588
.755 .687
\2.lH!
2.492
.B20
.975
i 2.8711 ! 3.755 ! 4.697 2.523 '3.m 4.138 4.9119
.914
.'m
2.384 2.384 2.384 2.384
i
.914
.975
2.384 2.384 2.394 2.394 2.384
2.lBB 2.399
.914 .914 .820 .632 .528
2.384
2.526
2.526 2.526 2.526
2.526
.b~3
•sile 1.885 .829 .663 .558 .588
.607
.664 .58B
.987 .152 .603 ,588 1.885
.829 .663 .558 .508
COADE Pipe Stress Analysis Seminar Notes t:l.Q INTERSECTION RADIUS "831.3" VS 'WRC 330" WELDOLET STRESS INTENSIFICATION FACTOR COMPARISON
HEADER NOM
1& 48. 16 48. 16 48.
16 4@. 16 48.
8RANCH SCH
WRC
·-831.3..·
330 b
i ib
330 b
330 h
8 11 12 14 lb
6.825 7.633 8.322 9.723 5.595
2.524 2.524 2.524 2.524 2.524
2.524 2.524 2.524 2.524 2.524
.3711 .331 .383
.371 .331
.289 .451
.289 .451
2.664 3.332 3.961 4.352
1 l 7.2111 ; 7.858
2.526 2.526 2.526
2.52l, 2.526 2.526 2.526 2.526
.351 .322 .387 .287 .451
.351 .322 .387
2.9/,4 3.523 3.871
.287
4.423
.451
.339 .324 .383 .286
.339 .324 .31113 .286 .451
.332 .313 .297
.332 .313 .297 .451
48. 4a. 48. 48.
48.
1
i ib iob
330 b
WRC
iob
.313
-831.3..·
i oh
i oh
330 h
330 h
2.524 2.524 2.524 2.524 2.524
2.524 2.524 2.524 2.524 2.524
.947 .758 .637 .5B8 .509
.947
2.526 2.526 2.526 2.521: 2.526
.952
4.976
2.526 2.526 2.526 2.526 2.526
3.28B
2.617
3.6114
2.617
4.118 4.633 5.156
2.617
4.973
i ih
~
.759 .637 .588 .519
i
19 48.
18 40. 18 4B.
18 41. lB 40.
28 48. 20 41. 20 4!1.
21 40. 28 48.
24 48.
24 48. 24 48. 24 40.
10 12 14 16
• ,II. 4". 48. 46.
i1 8.229 ! 8.797 18 411.! 5.598
2.~m
2.526
7.71l 8.182 8.648 18 411. 1 9.165 28 4&. i 5.811
2.617 2.617 2.617 2.617
2.617 2.617 2.617 2.617 2.617
8.176 8.566 2" 40 •. 9.137 5.943 24 48.
2.681 2.681 2.691 2.6Bl
2.681 2.681 2.691 2.681
12 48. 14 n. 16 48.
16 40.'
18 48.
2.617
.451
.451
33 U. 38 48.
24 48.; 38 40.,
.6S3 .571 .588
.653
.798 .726 .635 .565 .518
.;98 .726 .635
2.617
2.617 2.617 2.617 2.617 2.617
3.512 3.951 4.397 5.282
2.681 2.681 2.681 2.681
2.6Bl 2.681 2.681 2.681
.763 .679
.763 .679 .619 .5@8
2.617
.618
.568
.383 .451
.383 .451
4.619 5.796
2.942 2.942
2.942 2.942
.51B
10.3114 [email protected]
3.261 3.261 3.261
.314
.m
4.783 6.881 6.424
3.261 3.261 3.261
3.261 3.261 3.261
.692 .543 .518
.682
.322 .451
.314 .322
7.227
3.261 3.261 3.261
.578 .549 .508
.6l]
24 40.
34 40.
3" 40.
11. 763
3.:m
3.398
.289
34 48. 34 40.
32 40. 34 40.
18.317 7.532
3.39!l 3.398
3.:m
.329 .451
.289 .329 .451
5.879 6.293 6.695
3.398 3.398 3.398
3.3118 3.399 3.398
.578 .540
36 40. 36 48.
3.331 3.:)31
3.331 3.331 3.331
.297 .287 .336 .451
.297 .287 .336 .451 ·
5.446
5.8311 6.283 6.563
3.331 3.331 3.331 3.331
3.331 3.331
.612 .571
56 40. 36 40.
30 40. ; Il.218 32 40. 1 II. 599 34 41!1. 1 9.962 7.384 36 40,
3.331
.:)37
3.331
.sltS
42 48. 42 40.
38 48. 1 11.588 32 40. 1 11. 9117
.321 .311 .381
.321
5.168
.311 .3U
i 5.533 i 5.886
.293 .451
.293 .451
6.228 1.289
3.699 3.699 3.699 3.699 3.699
3.699 3.699 3.&99 3.b99 3.&99
.716 .669 .628 .594 .5"8
4~.
42 48. 42 48.
i
34 4@.! 12.28!
12.633 42 48. 1 8.2111
36 40.
.637 .508
2.942 2.942
31 40. 32 4111.
42
.5&8
2.942 2.942
32 48. 32 43.
,
•SilS
9.782 6.528
32 40.
!
.571 .588
1
l
i
.717
.852 .717
3.331 3.:331
3.699 3.699 3.699 3.6119 3.699
3.398
3.331
3.6119 3.699 3.699 3.699 3.699
1 1
"
1-40
.sIB
.543
.58a
.612 .571 .537 .508 .716 .669 .628 .594 .516
COADE Pipe Stress Analysis Seminar Notes
NO INTERSECTION
RADIUS "831.3" VS 'WRC 330" SWEPOLET STRESS INTENSIFICATION FACTOR COMPARISON HEADER
8RANCH
NOM
SCH
WRC
-·831.3···
330 b
i ib
iob
330 b
i ib
WRC
-.. 831.3..·
330 b
330 h
i ih
ioh
iob
i ih 330 h
ioh 330 h
1 48.
1
48.
2.43;>
.929
.986
.382
.372
2.1b2
.929
.9ib
.43i
.419
2 48. 2 48.
48. 2 48.
4.884 3.359
1.188 1.188
1.251 1.251
.291
.354
.316 .372
2.188 2.986
1.188 1.188
1.251 1.251
.566 .398
.596 .419
3 48. 5 48. 3 48.
48. 2 48.
2.618 4.155
1.222 1.222
1.296 1.296
.467 .294 .551
1.296 1.296 1.296
.617
1. 296
1.222 1.222 1.222
.582
1. 222
2.188 2.188 3.893
.582
3 40. 1 3. 480
.495 .312 .372
.395
.617 .419
4 48. " 48. 4 48. -4 48.
1 48. 2 48. 3 41.
1.337 1.337
1.450 1.450
.372
3.461
1.337 1.337 1.337 1.337
1.458 1.4SB 1.45" 1.450
.637 .582 .386
.544
1.458
.;m
2.188 2.188 2.665
.698
1.458
.566 .356 .255
.637
1.337 I •.n?
.522 .329 .235
5 4t1.
1 48.
.685
1.585
1.585
1.439
1.585
1.439
1.585 1.585
.4112 .284 .249 .372
1.439 1.439
1.439
.579 .365 .258 .226 .338
1.585
2 3 4 5
1.439 1.439
1.585
5 48.
1.439
1.585 1.585
.685 .614 .473 .380
.416 .279 .245
.311 .273
.219
.244
2.111 2.108 2.711 3.374
.334
.372
4.036
1.518 1.518
.355 .312 .290 .256 .372
2.1'8 2.258 2.B18 3.361 4.399
1.632 1.632 1. 632 1.632 1.632
.349 .313 .286 .258 .372
2.188 2.399 2.87i 3.7:15 4.697
1.726 1.726 1.726 1.726 1.726
.341
2.m
.312
2.523
.272
3.382
1.793 1.793 1.793
.244 .372
4.138
5 48. 5 48. 5 40. il 4@. il 48.
b 40.
,
4
2.563 4.868 5••m
48'1 3.sn
! 2.483 41. i 3.940 411. , 5.588 41. ~ 6.358 48. : 4.255
3.738 2 40. 3 40. 5.444 ., 41. ; 6.282 •
1.439
1.518 1.518 1.518 1.518
1.585
1.691 1.691
Lm
:; 48. i 6 48. !
6.919 4.540
l.m
1.691 1.691
3 48. ,
5.187
1.632
1.843
4 5 6 8
.,8. 48. 48.!
5.910
1.632 1.632
1.843
48.
4.949
10 48.
4 48.
10 48. 18 48.
5 48. b 411.! 1 8 48.! UI 411'1
ô 48.
ô
4~.
a 48. 8 4m. B 48.
a 4m. 3 40.
10 48. 10 48. 12 48.
12 48. 12 48. 12 48.
5 b 8 111
1.632 1.632
1.843 1.843 1.843
.315 .276 .248 .226 .330
5.M2 6.294 6.884 7.875 5.284
1.726 1.726
1.968 1.968
.3@b .274
1.726
1. 96B
1.726 1.726
1. 968 1.968
.251 .219
6.834 48. 1 6.688 41. 7.549
1.793 1.793
.297 2.857 2.857 .272 2.857 .237 2.857 1 .212 2.857 .325
!
6.592 7.218
48.\
48. Ii
8.443
12 48.
12 48.
14 4I!. 14 40.
48. i 6.3S3 7.382 8.166 18 48. 12 48. 8.569 14 4B. 5.599
14
40.
14 40. 14 41.
5.523
1.193
1.793 1.793
6
1.814
Il 48.
1.814 1.814
1.814 1.S14
2.885 2.885 2.885 2.885 2.085
.~27
.2B4 .248 .222 .212 .314
.638
.452
! i
2. IIi
2.1811 2.342 3.848 3.783
4.989
.327 2.328 .286 3.847 .255 3.811 .243 . 4.530 .372 1 4.977
1-41
1.439
1.518 1.518 1.518
1.793 1.793
1.814 1.814 1.814 1.814 1.B14
Lm
.6911 .419
.755 .755 .677
.521 .419
.723 .723
.805 .885
.568 .458
.624
1.691
1.691
.376
.419
1.843
.i77 .723
1.691 1.691
.581
1.843
.581
.878 .816 .656
1.843
.486
.548
1.843
.371
.419
1.968
.828
1.843
.937
L968
.822 .719 .681
1.9b8 1. 968
.468 .367
2.1157
.850 .719
.975 .815
.543 .434
.623
1. 968
2.i57 2.1157 2.857 2.857 2.085 2.885
2."85 2.885
2.885
.365
.6B6 .524 .419
.498 .419
.779
.896
.595
.684 .547 .46"
.476 .480 .364
.419
COADE Pipe Stress Analysis Seminar Notes
NO INTERSECTION
RADIUS "831.3" VS 'WRC 330" SWEEPOLET STRESS INTENSIFICATION FACTOR COMPARISON HEADER
9RANCH
WRC
-931.3---
NOM
SCH
330 b
i ib
!6 40.
8 48,
6.825
1.813
16 48. 16 48. 16 411.
18 411. 12 48. 1-4 48. 16 48.!
7.633
l.813
8.322 8.723 5.595
1.813 1.813
2.884 2.IS4 2.884 2.184
1.813
2. B84
18 48.
18 48.:
;.2111
18 4f1.
18 48. lB 4f1.
7.858 J.C 1 8.229 16 41. i 8.797
1.814 1.814 1.814
2.885
1.814
18 40.
18 48.,
5.:5'18
1.814
1.@8S 2.885
1.878 1.878 1.878 1.878 1.B78
2.168 2.168 2.160 2.160 2.160
1. 9t8 1.918 1. 918
2.213 2.213
16 48.
12 41.
4".
i
28 48.
12 48.
7.711
28 48.
14 48.
8.882
2S 48. 28 48.
16 4e.
a.bU
28 48,
28 49.!
24 24 24 24
lb 48. i 8.176 18 4111.! 8.566 2e 48.: 9.1137 24 U.! 5.943
48. 48. 48. 40.
lB
48. 1
9.165 5.881
330 b
.2116
.231
--931.3---
330 b
330 h
i ih
ioh
330 h
330 h
.385 .273 .258
3.:m
2.664
1.813
2.884
1.813
.680 .544 .458 .417 .364
.782 .625 .479 .419
.612
.704
.515 .469 .418 .364
.592
3.961
l.813 1.813
.372
4.352 4.973
1.813
2.884
2.964
1.814
.zn
3.:i23 3.871
1. 81~
.2211 .286
.291 .266 .253
1.814
.324
.372
4.423 4.976
2.885 2.885 2.1185 2.085
1.814
2.885
.243 .231
.28S .267 .251 .236 .372
3.288 3.614 4.118 4.633 5.156
1.878 1.878 1.878
2.168 2.163 2.163
.214 .372
3.512 3.951 4.:591 5.282
.25111 .372
.218
.288 .324
.239
2.885
.252
2.085
.231
2.213 2.213
.216
.284 .322
.236 .223 .211 .321
.258
.245
2.1b'
2.168
t.918 1. 918 1.910
2.213 2.213 2.213 2.213
.544 .483 .434 .362
.503' .419
4.619 5.796
2.971 2.171
2.428 2.428
.448 .357
.419
4.783 6.811 6.424
2.269 2.269 2.269
2.692
2.692 2.692
.474 .378 .353
.563 .449 .419
2.354 2.354 2.354
2.B!5 2.885
.4r18 .374
.477 .446
2.B85
.352
.419
2.750 2.756 2.750 2.751
.425 .397
.585 .472 .443 .419
3.854 3.1154 3.854 3.854
.492 .459 .432 .418
.519 .4911
3.854
.349
.419
.213
UI.394
2.269 2.269 2.269
2.692 2.692 2.692
.218 .224 .314
.259 .266 .:512
2.354 2.354
2.885 2.885 2.885
.28M .228 .315
.238 .272 .572
5.879
18.134
32 48.
32 48.
t 7.227
34 48.
48.! 11.763 32 48.1 10.317 34 48.! 7.532
1
2.354
.539 .471 .419
1.878
2.428 2.428
24 41l. 3111 48.
.526
1.870
2.m
.318
1.814
ioh
.570 .519 .454 .404 .363
2.1m
32 4i1. 32 48.
i ih
2.884 2.884 2.884
9.71l2
24 48,' 30 41l.
34 48. 34 48.
iob
WRC
iob
6.528
38 4!11. 38 48.
30
1.918
i ib
6.293 6.695
1.911
.659
.633 .560
.599
.525 .466 .419
.526
1
36 48.
J
3b 4f1.
30 48. f 11. 218 32 48. 1 Il. 599 34 48. i 9.982 7.384 36
2.312
42 48. 42 40.
32 48.
3B 48., 11. 588 11. 987 34 48. 1 12.281 3& 48. i 12.633 42 4@. f 8.28@
2.548 2.548 2.540 2.541 2.540
3b 48.
36 40.
42 48.
42 48. 42 48.
48.1
2.312
2.312 2.312
2.751 2.758 2.751 2.750 3.054 3.854
3.854 3.854 3.854
.2116
.245
15.446
.199
.237
5.838
.234.
.279
8~;) 3·
.372
6.213 6.563
2.312 2.312 2.312 2.312
.221 .213 .287 .2S1 .310
.265 1 5.168 .256 i 5.533 .249 5.886 .242 1 6.228 .:m l 7.289
2.548 2.548 2.548 2.548 2.548
1-42
l
.373
.352
.591 .552
COADE Pipe Stress Analysis Seminar Notes
1.5 Code Compliance 1.5.1 Primary vs. Secondary Loads
Markl's investigation of the fatigue problem, following the earlier recognition of the maximum stress theory offailure, led to identification of the basic problem in the design of piping systems. Not one, but two different criteria must be satisfied, one for primary loads, which may lead to single application catastrophic failure, and one for cyclic, dis placementdriven loads that may lead to fatigue failure (especially in the vicinity offittings and other discontinuities) after repeated applications. The main characteristics ofthese two different types of loads are described below:
Primary Load Characteristics: 1 -
Primary loads are usually force driven (gravity, pressure, spring forces, relief valve, fluid hammer, etc.).
2
-
Primary loads are not self-limiting. Once plastic deformation begins it continues unabated until force equilibrium is achieved (through change of the external boundary conditions or through material strain hardening), or until failure of the cross section results.
3 -
Primary loads are typically not cyclic in nature (and those that are, such as pulsation or pressure variation, show characteristics of both primary and secondary loads).
4
-
Allowable limits for primary stresses are related, through failure modes such as those advanced by the Von Mises, Tresca, or Rankine theories, to the material yield stress (i.e. the point where plastic deformation begins), the ultimate strength, or, for sustained loads only, to time-dependent stress rupture properties (such as creep characteristics).
5 -
Excessive primary load causes gross plastic deformation and rupture. Failure may occur with a single application ofthe load. Note that failures that occur due to single load applications usually involve pressure (hoop stress) design failures and are not directly addressed by CAESAR n or by the flexibility stress requirements ofthe codes. Such pressure design requirements are encompassed in the minimum wall thickness requirements discussed in detail in separate sections of the codes.
Secondary Load Characteristics: 1 -
Secondary loads are usually displacement driven (thermal expansion, imposed anchor movements, settlement, vibration, etc.).
2
-
Secondary loads are aImost always self-limiting, i.e. the loads tend to dissipate as the system deforms through yielding or deflection.
3
-
Secondary loads are typically cyclic in nature (except settlement).
1-43
COADE Pipe Stress Analysis Seminar Notes
4
Allowable limits for secondary stresses are based upon cyclic and fatigue failure modes, and are therefore limited based upon requirements for elastic cycling after shakedown and the material fatigue curve.
5
A single application of the load never produces failure. Rather catastrophic failure can occur after some (usually high) number of applications of the load. Therefore, even if a system has been running successfully for many years, it is no evidence that the system has been properly designed for secondary loads.)
Several examples should help illustrate:
Primary Stress Failure: Springs were improperly sized to support the weight of the valve operator on a system. When the line was fùled for hydrotest, everything (stresses and displacements) appeared fme, since the pipe could support the moment imbalance at ambient temperature. However, heating up the fluid (and pipe) during startup, the valve sagged and the guardrail was crushed in less than 30 minutes due to the decrease in strength at the operating temperature. Steps ta failure: 1
Weight loads were improperly accounted for. (The primary stresses were tao high.)
2
At operating tempe rature there was a resulting drop in material strength.
3
Gross deformation began almost immediately and continued until force equilibrium was achieved (the spring bottoming out).
Secondary Stress Failure: After 12 years of successful operation, inspection of the inside surface of a vessel revealed fatigue cracks in the vicinity of a piping nozzle connection. A subsequent analysis showed that a temperature increase in the adjacent vessel and piping system (alongwith a relocation of pipe restraints for the new operating conditions) made several years ago caused the stresses to exceed the expansion allowables. Even though the calculated stress range at the
1-44
COADE Pipe Stress Analysis Seminar Notes junction was weil over 470,000 psi, thejunction survived several years hecause of the selfrelieving nature of the thermalload, and the fact that the system cycled fewer than a dozen times over the two year period. Steps to failure: 1
Thermal allowables were exceeded by mistake.
2
After about a dozen applications of the excessive load, cracks formed on the highly stressed inside surface of the vessel at the junction with the nozzle.
Therefore, code compliance requires that the piping system be checked for both types of loading - primary and secondary. The basic steps involved in doing code compliance are outlined below: 1
Compute the primary stresses, i.e. the stresses due to the sustained primary loads, usually weight and pressure, and those due to the occasional primary loads, such as earthquake, wind, fluid hammer, etc.
2
Compute the range of the varying stress, i.e. the expansion stress range.
3
Compare the primary stresses to their allowables, which is based on a factor of safety times the hot yield stress.
4
-
Compare the expansion stress range to its allowable, which is a factor of safety times a value varying with the number of cycles such that it fits the material fatigue curve (adjusted for mean stress), but never exceeds the sum of the hot and cold yield stresses.
Note that due to the shakedown effect, and the fact that the primary and secondary stresses have different failure criteria, these two load types are reviewed in isolation. Therefore, it should he stressed that, as far as most codes are concerned, there is no such thing as "operating stress".
1.5.2 Code Stress Equations The piping code stress equations are a direct outgrowth of the theoretical and investigative work discussed above, with specific limitations established by Markl in his 1955 paper. The stress equations were quite similar throughout the piping codes (i.e., between B31.1 and B31.3) until the winter of 1974, when the power codes, having observed that Markl was incorrect in neglecting intensification of the torsional moment in a manner analogous to the bending component, combined the bending and torsional stress terms, thus intensifying torsion. It should be noted that the piping codes exactly calculate the stress intensity (twice the maximum shear stress) only for the expansion stress, since this load case contains no hoop or radial components, and thus becomes an easy calculation. Including hoop and radial stresses (present in sustained loadings only) in the stress intensity calculation makes the
1-45
COADE Pipe Stress Analysis Seminar Notes
calculation much more difficult. When considering the hoop and radial stresses, it is no longer clear which of the principal stresses is the largest and which is the smallest. Additionally, the subtraction of Sl-S3 does not produce a simple expression for the stress intensity. As it turns out, the inclusion of the pressure term can be simplified by adding only the longitudinal component of the pressure stress directly to the stress intensity produced by moment loadings only. This provides an equally easy-to-use equation and sacrifices little as far as accuracy is concerned. The explicit stress requirements for the piping codes addressed by CAESAR II follow below. Note that most codes allow Pdi2 / (d0 2 - di 2 ) to be used in place ofPdo / 4t.
1.5.3 831.1 Power Piping The B31.1 code requires that the engineer calculate sustained, expansion, and occasional stresses, exactly as defmed below:
Sustained: 0.75i MA
P do +
z
4t
Where: Ssus, SI
=
sustained stress, psi
1
=
intensification factor (single factor for aIl types of moments), as per Appendix D ofB31.1 Code (note that 0.75i may not be less than 1.0)
MA
=
resultant moment due to sustained (primary) loads, in-lb
=
[Mx2 + My2 + M z 2 ]1/2
=
basic allowable material stress at the hot (operating) temperature, as per Appendix A ofB31.1 Code. Sh is roughly defined as the minimum of:
Sh
1)
1/4 of the ultimate tensile strength of the material at operating temperature;
2)
1/4 of the ultimate tensile strength of the material at room temperature;
3)
5/8 ofthe yield strength ofthe material at operating temperature (90% of the yield stress for austenitic stainless steels);
4)
5/8 ofthe yield strength of the material at room temperature (90% of the yield stress for austenitic stainless steels); and
5)
100% of the average stress for a 0.01 % creep rate per 1000 hours.
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COADE Pipe Stress Analysis Seminar Notes
Expansion: iMc
z Where: SE
=
expansion stress range, psi
Mc
=
resultant range ofmoments due to expansion (secondary) loads, in-lb
SA
= =
Allowable expansion stress, psi
Sc
basic allowable material stress at the cold (installation) temperature, as per Appendix A ofB3!.1 Code.
Occasional: Soce
=
z
Pdo
0.75iMB
0.75i MA +
z
+
4t
Where: Soce = occasional stresses, psi MB
=
resultant moment due to occasionalloads, in-lb
k
=
occasionalload factor
=
1.2 for loads occurring less than 1% of the time
=
1.15 for loads occurring less than 10% of the time
1.5.4 831.3 Chemical Plant and Petroleum Refinery Piping
Sustained: B31.3 does not provide an explicit equation for sustained stress calculations, but only requires that the engineer compute the longitudinal stresses in the pipe due to weight and pressure, and then ensure that these do not exceed Sh. This is most commonly interpreted to mean:
Fax +
+
z
4t
1-47
COADE Pipe Stress Analysis Seminar Notes
Where: Fax
=
axial force due to sustained (primary) loads, lb
Mi
=
in-plane bending moment due to sustained (primary) loads, in-lb
Mo
=
out-plane bending moment due to sustained (primary) loads, in-lb
li> 10
=
in-plane, out-plane intensification factors, as per Appendix D ofB31.3 Code
Sh =
basic allowable material stress at the hot (operating) temperature, as per Appendix A of B31.3 Code. Sh is defined as the minimum of: 1)
1/3 of the ultimate tensile strength of the material at operating temperature;
2)
1/3 ofthe ultimate tensile strength of the material at room temperature;
3)
2/3 of the yield strength of the material at operating temperature (90% of the yield stress for austenitic stainless steels);
4)
2/3 ofthe yield strength ofthe material at room temperature (90% of the yield stress for austenitic stainless steels);
5)
100% of the average stress for a 0.01% creep rate per 1000 hours;
6)
67% of the average stress for rupture after 100,000 hours; and
7)
80% of the minimum stress for rupture after 100,000 hours.
Expansion: [(ii Mi)2 + Cio Mo)2 + 4MT2]1/2
z Where: Mi
=
range of in-plane bending moments due to expansion (secondary) loads, in-lb
Mo
=
range of out-of-plane ben ding moment due to expansion (secondary) loads, inlb
MT
=
range oftorsional moment due to expansion (secondary) loads, in-lb
Sc
=
basic allowable material stress at the cold (installation) temperature, as per Appendix A ofB31.3 Code.
1-48
COADE Pipe Stress Analysis Seminar Notes
Occasionsl: The equation for calculating occasional stresses is undefined by B31.3, which simply states that the sum of the longitudinal stresses due to sustained and occasionalloads shall not exceed 1.33Sh. The default interpretation ofthis requirement is to calculate the sustained and occasional stresses independently (as per the equation given for sustained stresses above) and then to add them absolutely. Note the differences between these two codes: 1
-
B31.I intensifies torsion, while B31.3 doesn't.
2
-
B31.3 calculation methods are undefined for sustained and occasionalload cases, while they are explicit for B31.1.
3
-
In its most common interpretation, B31.3 neglects torsion in the sustained case, while B31.I includes it.
4
-
B31.I neglects all forces, while in the default interpretation, B31.3 includes Fax in the sustained case.
5
-
Allowable stresses are different for each code.
6
-
Stress increase for occasionalloads are different for each code.
Note that both codes additionally cite a conservative value of SA, f(1.25S c + O.25Sh), which may be used instead ofthe more liberal allowable off(1.25Sc + 1.25Sh - SI). This is a carry over from pre-computer days, when sustained stress calculations were rarely done, so SI was not known explicitly, and conservatively estimated to be at its maximum allowable level of Sh. Specific requirements of other common codes are shown below as weIl.
1.5.5 ASME Section III, Subsections NC & ND (Nuclear Class 2 & 3)
Sustained:
=
BI Slp + B2 Mal Z < 1.5 Sh
Bl,B2
=
primary stress indices for the particular product under investigation
Slp
=
longitudinal pressure stress
Ma
= =
resultant moment on the cross-section due to sustained (primary) loads rMx2 + M~ + Mz2]112, in-lb
Sh
=
basic aIlowable material stress at the hot (operating) temperature, as per ASME III Code. Sh is roughly defined as the minimum of:
Ssus Where:
= P di2 / (d0 2 - di2 ), psi
1-49
COADE Pipe Stress Analysis Seminar Notes
1)
1/3 of the ultimate tensile strength ofthe material at operating temperature;
2)
1/3 of the ultimate tensile strengthofthe material at room temperature;
3)
2/3 of the yield strength of the material at operating temperature (90% of the yield stress for austenitic stainless steels);
4)
2/3 of the yield strength of the material at room temperature (90% of the yield stress for austenitic stainless steels);
5)
100% of the average stress for a 0.01% creep rate per 100 hours;
6)
60% of the average stress for rupture after 100,000 hours; and
7)
80% of the minimum stress for rupture after 100,000 hours.
Expansion: SE
=
i Mc / Z < f( 1.25 Sc + 0.25 Sh ) + Sh - SL
=
resultant range of moments on the cross-section due to variations in loading (usually due to thermal effects)
=
[M~
Where: Mc
SL =
+ M; + Mz2]1I2, in-lb
Slp + 0.75 i Ma / Z (where 0.75 i >= 1.0)
Occasional: The occasional stress equations are: For Service Level C (Emergency): Socc = BI x Slpmax + B2 (Ma + Mb) / Z < 1.8 Sh n2, ng ... , nn consideration shall be given to the
1-61
COADE Pipe Stress Analysis Seminar Notes
superposition of cycles of various origins which produce the greatest total alternating stress range. For example, if one type of stress cycle produces 1000 cycles of a stress variation from zero to +60,000 psi and another type of stress cycle produces 10,000 cycles ofa stress variation from zero to -50,000 psi, the two cycles to be considered are shown below: (a) Cycle type 1: nl=1000; and Sa1tl=(60000+50000)/2 (b) Cycle type 2, n2=9000; and Salt2=(50000+0)/2 2
-
For each type of stress cycle, determine the alternating stress intensity Salt, which for our application is one half of the range between the expansion stress cycles (as shown above). These alternating stress intensities are designated as Saltl , Sa1t2, ... , Saltn.
3
-
On the applicable design fatigue curve fmd the permissible number of cycles for each Salt computed. These are designated as NI, N2, ... , N n.
4
-
For each stress cycle calculate the usage factors VI, V2, ... , Vn, where VI = nl/ NI, V2 = n21N2, ... , V n = nnlNn· Calculate the cumulative usage factor V as V = VI + V2 + ... + Vn.
5 6
-
The cumulative usage factor shall not exceed 1.0.
1-62
2
COADE Pipe Stress Analysis Seminar Notes Section 2 Table of Contents
2.0
Piping Design For Loading Types ............................................................................. 1
2.1
Designing For Sustained Loads - Pressure ............................................................ 2 2.1.1 Minimum Wall Thickness Requirements ...................................................... 2 2.1.2 Pressure Design ofElbows and Miters .......................................................... 4 2.1.3 Pressure Design of Flanges and Blanks ........................................................ 5 2.1.4 Pressure Design of Branch Connections ....................................................... 6 2.1.5 Restraint ofUnbalanced Expansion Joint Pressure Loads ....................... 8-9
2.2
Designing For Sustained Loads - Weight ............................................................. 10 2.2.1
Calculation ofWeight Stresses .................................................................... 10
2.2.2 Use of Standard Weight Spans .................................................................... 13 2.2.3 Consideration of Nozzle Loads .................................................................... 19 2.3
Designing For Expansion Loads ............................................................................. 22 2.3.1 Magnitude of Thermal Load ........................................................................ 22 2.3.2 Guided Cantilever Method .......................................................................... 24 2.3.3 Refining the Model Through the Use ofRestraint Stiffnesses ................... 26 2.3.4 Use of Expansion Loops ............................................................................... 27 2.3.5 Simplified Expansion Stress Check ........................................................ 29-30 2.3.6 Stress Reduction through Use of Expansion Joints .................................... 30 2.3.7 Expansion Stress - Other Solutions ..................................................... 33-33
2.4
Ranger Design ....................................................................................................... 34 2.4.1 Variable Spring Ranger Design Basics ....................................................... 35 2.4.2 Load Variation ............................................................................................. 37 2.4.3 Ranger Selection Table ............................................................................... 37 2.4.4 Ranger Design Process - Restrained Weight, Free Thermal, and More .. 39 2.4.5 Restraint Placement Using Distance to First Rigid Criteria ..................... 40 2.4.6 Notes on Ranger Design .............................................................................. 43 2.4.7 CAESAR II Ranger Design Control and Options .................................. 45-49
2.5
Designing For Occasion al Loads (Static Equivalent of Dynamic Loads) ............... 50 2.5.1 Wind Loading ............................................................................................... 50 2.5.2 Earthquake Loading ............................................................................... 54-56 2.5.3
Quickly Applied Loads ................................................................................. 56
COADE Pipe Stress Analysis Seminar Notes
2.0 Piping Design For Loading Types As described in Section 1.0, the pipe stress analyst is concerned with two types ofloadsprimary and secondary. Not only are the causes and the failure modes ofthese two loading types quite different, but not surprisingly, the solutions to these two types ofloading are usually different as weIl. In fact, the solution to a problem caused by one of the loading types often causes a problem with the other loading type. Therefore, a compromise must often be reached in order to find the solution to these two types ofloading.
Note that primary loads are usually classified further, according to their duration ofloading. Those primary loads which are nearly always present throughout operation are called sustained loads, while those which occur less frequently are called occasionalloads. The methods ofresisting these two types ofloads are similar, with the main difference beingfound in the use of a higher allowable stress for occasionalloads (as seen in Section 1).
2-1
COADE Pipe Stress Analysis Seminar Notes
2.1 Designing For Sustained Loads -
Pressure
AlI piping systems must be designed to withstand sustained loadings. Sustained loads are classified as those caused by mechanical forces which are present throughout the normal operation of the piping system. Therefore the se loads: •
Are force driven, as opposed to displacement driven, and
•
Are present for relatively extended periods of time, as opposed to those which change dynamically.
Typical sustained loads consist of: •
Pressure -loads due to operating (or design) pressure,
•
Weight - uniform loads due to the weight ofthe pipe, fluid, and insulation, and concentrated loads due to the weight of in-line components (such as valves, flanges, etc.), and
•
Spring hanger pre-Ioads and other applied forces.
2.1.1 Minimum Wall Thickness Requirements Since hoop pressure stresses are approximately twice as large as longitudinal pressure stresses, pipe wall thicknesses are initially sized for hoop stresses. Because ofthis, pressure design of components is usually done far before, and therefore in isolation, from the pipe stress analysis phase of piping design. Because of this, pipe stress software such as CAESAR II does not normally handle this part ofthe design effort. A discussion of pressure design of components is included here for the sake of completeness, and is based upon an amalgam of the requirements of various codes. Note that pressure design of piping components must be done according to the requirements of the user's specifie code, not to the rules described here! Because the pipe wall is sized for the large hoop stress, this usually provides sufficient margin between the allowable stress and the longitudinal pressure stress to accommodate the weight stresses. The requirement for the minimum pipe component wall thickness is:
=
t +c
tm
=
minimum wall thickness, in
t
=
minimum wall thickness required for pressure, in
c
=
sum of allowances for thread or groove depth, corrosion, erosion, and manufacturer's tolerance, in
tm Where:
2-2
COADE Pipe Stress Analysis Seminar Notes
For thin wall (t < D/6), straight pipe under internaI pressure, t may normally he calculated, through various approximations of Lame's equation, as: t
=
PD 1 2(SE + PY), or:
t
PD 1 2SE, or:
t
= =
(D/2) x (1 - [(SE - P) 1 (SE + P)]1/2), or:
t
=
P (Di + 2c) 1 [2(SE - P(l-Y)]
P
=
design pressure, psig
D
=
outside diameter, in
Di
=
inside diameter, in
S
=
basic allowable stress at design temperature, psi
E
=
casting or longitudinal weld quality factor (typically ranges from 0.8 to 1.0)
y
=
material coefficient, with a value (depending upon the specific code requirements) to he interpolated from:
Where:
Temperature. oF Material
1250
Ferriti c
0.4
0.5
0.7
0.7
0.7
0.7
0.7
0.7
Austenitic
0.4
0.4
0.4
0.4
0.5
0.7
0.7
0.7
Nickel All oys
0.4
0.4
0.4
0.4
0.4
0.4
0.5
0.7
Other ductil e
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
Cast iron
O.
Requirements for pressure design of other piping components are described in the following sections. (For B31.3 y = 0.0, for B3l.l y =.4. The CAESAR II check uses 0.4 for ail codes except B3l.3, where y = 0.0.)
2-3
COADE Pipe Stress Analysis Seminar Notes
2.1.2 Pressure Design of Elbows and Miters When using elbows, the minimum wall thickness after bending shall not fall below that calculated for straight pipe. For mitered elbows, the maximum allowable pressure is calculated differently depending on whether the angle of the miter cut is less than or greater than 22.5°. For 0 < 22.5 0 , the allowable maximum pressure is the lesser of: Pm
=
[SE(T - C)/r2]
X
[(T - c) 1 (T - c + 0.643 tan 0 (r2(T-c»1/2)]
or:
For 0 >= 22.5 0 , the allowable maximum pressure is:
=
[SE(T - C)/r2] x [(T - c) 1 (T - c + 1.25 tan 0 (r2(T-c»I/2)]
Pm
=
maximum allowable internaI pressure for miter, psig
T
=
minimum pipe wall thickness, in
r2
=
mean pipe radius, in
RI
=
effective radius of miter bend (defined as the shortest distance from pipe center line to the intersection of the planes of adjacent miter joints - see Figure 2-1), in
o
=
angle of miter cut (see Figure 2-1), degrees
Pm Where:
I - - H - - - R,,------i
Figure 2-1
2-4
COADE Pipe Stress Analysis Seminar Notes
2.1.3 Pressure Design of Flanges and Blanks Pressure design offlanges is a complex task, requiring consideration ofthe configuration and materials of the flange, bolts, and gasket. Potential causes of failure are bending stresses in the flange, localized stress concentrations in the hub, yielding of the bolts, or unloading of the gasket, causing leakage. Design offlanges is covered in detail in Section VIn of the ASME Boiler an Pressure Vessel Code; however, due to the complexity, it is rarely done by the pipe stress engineer. Instead, the most common piping codes endorse the use offlanges conforming to recognized standards such as ANSI B16.5 "Pipe Flanges and Flanged Fittings". This standard designates standard pressure classes of flanges, which are recognized by the codes to be acceptable for the following combinations of pressure and temperature:
Design Pressures (psig) for Flange Pressure Classes Pressure Class Temperature. oF 150
300
400
600
900
1500
100
275
720
960
1440
2160
3600
150
255
710
945
1420
2130
3550
200
240
700
930
1400
2100
3500
250
225
690
920
1380
2070
3450
300
210
680
910
1365
2050
3415
350
195
675
900
1350
2025
3375
400
180
665
890
1330
2000
3330
450
165
650
870
1305
1955
3255
500
150
625
835
1250
1875
3125
550
140
590
790
1180
1775
2955
600
130
555
740
1110
1660
2770
650
120
515
690
1030
1550
2580
700
110
470
635
940
1410
2350
750
100
425
575
850
1275
2125
800
92
365
490
730
1100
1830
850
82
300
400
600
900
1500
900
70
225
280
445
670
1115
950
55
155
220
310
465
770
1000
40
85
160
170
255
430
2-5
COADE Pipe Stress Analysis Seminar Notes
A more detailed discussion of flange analysis, with specific regard to determination of leakage under load, is provided in Section 3 of these seminar notes.
Blanks are designed based upon formulas for the calculation ofbending stresses for plates under pressure loading. The minimum thickness for a blank is calculated as: tm
=
dg [3P / 16SE]1/2 + C
=
inside diameter of gasket for raised or flat face flanges, or gasket pitch diameter for ring joint and fully retained gasketed flanges, in
Where: dg
2.1.4 Pressure Design of Branch Connections A pipe having a branch connection is weakened by the opening that is cut in it, so it may be necessary to provide reinforcement to replace the metal removed from the wall thickness at the opening. A typical fabricated tee is shown in Figure 2-2.
Limitlof
1
Nominollhickn...
M-_MiI__I I=__ -i-______ --:J~~t=-"-----..... pipe
--r--
1
ornozzr. Thicknes:ll. measured specification
.1 i
- - - - - - - - - t Pipe
------
Figure 2-2 For fabricated tees, with the angle between branch and header of at least 450, the area required to replace the area of the opening is calculated as:
2-6
COADE Pipe Stress Analysis Seminar Notes
Where: Al
=
area required to be replaced, in2
th
=
pressure design thickness ofheader pipe, in
dl
=
effective length of pipe wall removed from header at intersection, in
~
=
sm aller angle between axes ofbranch and run, degrees
This required area must he exceeded by the total available reinforcement area, or:
Where: A2
=
area resulting from excess thickness ofheader pipe, in2
d2
=
half-width of reinforcement zone, in
=
(Tb - c) + (Th - c) + dl/2, but not less than dl
Th
=
minimum wall thickness ofheader, in
Tb
=
minimum wall thickness of branch, in
Ag
=
area resulting from excess thickness ofbranch pipe, in2
L4
=
height ofreinforcement zone outside ofheader, in
=
lesser of 2.5(Th - c) or 2.5(Tb - c) + Tr
tb
=
pressure design thickness ofbranch pipe, in
Tr
=
minimum thickness ofreinforcing ring or saddle, if any, in
~
=
area ofwelds and reinforcement provided for the intersection within the area of reinforcement as defined as a parallelogram extending a distance of d2 on either side of the centerline of the branch, and from the inner wall of the header pipe to a distance ofL4 along the axis of the branch, measured from the outside of the header pipe.
2-7
COADE Pipe Stress Analysis Seminar Notes
2.1.5 Restraint of Unbalanced Expansion Joint Pressure Loads Pressure usually only creates stress in the pipe, rather than loadings on supports/restraints, because pressure loads are neutralized at the cross-section by the tension in the pipe wall. One exception to this is when the pipe is not continuous from anchor to anchor, such that tension is not present in the pipe wall at aIl locations of the system. (Note that a second exception occurs when the Bourdon effects of pressure are considered. The Bourdon effect is due to the axial extension of pipes either under high pressure or in long runs, causing displacements which must be absorbed by the piping system. Since this is a displacement load, it is a secondary load, and therefore is not considered here.) Tension in the pipe wall is not continuous when there are expansion joints or slip joints present in the system. These types of components are too flexible in the axial direction to transmit the pressure force, therefore the unbalanced pressure load must be handled by either tie rods or external pipe restraints. The unbalanced pressure load is calculated as: Fp
Ae
=
P
Fp
=
Pressure force, lb
P
=
Design pressure, psig
Ae
=
Effective area of expansion joint
De
=
Effective diameter of expansion joint, in
=
internaI diameter of pipe + depth of one corrugation, in
Where:
When using restraints to absorb the unbalanced pressure load, it is recommended that guides be located on the adjacent pipe runs in order to reduce the danger ofbuckling. The Expansion Joint Manufacturers Association recommends that the first guide be placed a distance no further than 4 pipe diameters from the expansion joint, with the second guide placed no further than 14 pipe diameters from the first. Figure 2-3 shows some typical piping layouts using expansion joints.
2-8
COf\DE Pipe Stress Analysis Seminar Notes
* O=Pipe ~-+--Vertical
....
0.0.
Support
/,f-----~-
/Pipe
Anchor
Expans~_11
Joint
--; C
~ Anchor
"" 1st Guide
'-----~E
Ail Other Guides
Figure 2-3 More information on the use ofexpansion joints is foundin Section 2.3.6 and Section 3 ofthese seminar notes.
2-9
COADE Pipe Stress Analysis Seminar Notes
2.2 Designing For Sustained Loads - Weight 2.2.1 Calculation of Weight Stresses Stresses due to weight loads acting on a supported pipe can be estimated through the use ofbeam theory. The simplest method of estimating pipe stresses due to weight is to first consider the pipe as being a continuous run, with supports located at constant intervals (this is a somewhat accurate model ofpiping traveling horizontally, mounted on racks, and with a minimum ofin-line components):
5
l l ~e
l L
·1· e--+-e~ Figure 2-4
Elementary beam theory can be used to determine stresses in a member due to loading on that member. Normally the member considered is one-dimensional, homogenous with respect to cross-sectional and material parameters, and restrained in a number of degreesof-freedom atone or bothends. This model can only be usedifthe effects examined are limited totwo adjacent support points and the straightrunofpipebetweenthose support points. The question is what beam stress equation should be used? Bearn theory states that ifboth support points are pinned (free to rotate):
w JJHHHHHBB BBUBBB!!. Figure 2-5 The maximum moment in the beam is in the center of the span, and has a value of:
=
w1 2/8
Mmax
=
maximum moment in the beam, in-lb
w
=
uniform weight of pipe, fluid, insulation, etc., lb/in
l
=
length of beam, in
M max
where:
2-10
COADE Pipe Stress Analysis Seminar Notes
Ifboth ends are fixed, or rigid (restrained against rotation):
~ 11/1II1Il!!!!Il III I!! 11111 Il ~ Figure 2-6 The maximum moment is at the ends ofthe span, and has a value of:
Mma
= w1 2/12
Which formula is more appropriate? Examining a typical pipe support detail:
@
@
Figure 2-7 The clamp/pin/rod hardware allows rotation of the pipe, therefore simulating a pinned connection. However, if an spans are of identicallength and loading, the reaction of the adjacent pipe span prevents rotation at the support, therefore simulating a fixed connection. The true condition is somewhere in between, so a compromise approximation is reached:
Mmax = w1 2/10 with the location of the maxim um moment being somewhere between the ends and the center (i.e., anywhere) on the span.
2-11
COADE Pipe Stress Analysis Seminar Notes
Ofcourse, there sometimes are concentrated loads (valves, flanges, etc.)in the pi ping system. The effect ofthese on the pipe stresses can he estimated as weil. For pinned connections: p lOI
"!"
a
C*J
LS.
e
1 ..
b----j h
.1
Figure 2-8 The maximum moment is located at the point ofloading, and has a value of:
=
Pab!l
a
=
longer portion of span, in
b
=
shorter portion of span, in
Mmax Where:
For fixed connections:
..-t-I-----
a -----t---
~I--------e------~
Figure 2-9 The maximum moment is located at the end nearer to the load, and has a value of: Mmax
=
pa2b!l2
In either case (or actually some case in between), the additional stress (MIZ) due to concentrated loads should be added to the stress from the uniform load in order to determine the total stress in the pipe. Or, examining the formulas above, it is evident that, as the shorter portion of the span (b) approaches zero length, the moment, and therefore the stress, approach zero as weIl. This points to an important rule of design - if supports are placed as near as possible to concentrated loads, the effect ofthese loads from a stress point ofview may be neglected. (They must still be considered for the support loads, of course.)
2-12
COADE Pipe Stress Analysis Seminar Notes
2.2.2 Use of Standard Weight Spans Implementation ofthe preceding analysis provides a simple way to design for weight loading. The engineer may first support all concentrated loads in the system as closely as possible, reducing the stresses due to those loads to near zero. Next, converting the formula Mmax = w1 2/10 into its corollary:
=
(10 Z SalI / w)1/2
LalI
=
allowable pipe span for weight loading, in
Z
=
section modulus of pipe, in3
SalI
=
approximate allowable stress ofpiping material for weight stresses (Sh, less pressure stresses, divided by intensification factor, for example), psi
LalI Where:
If the piping system is then supported, such that no straight span exceeds Lall, the engineer can be sure that allowable weight stresses are not exceeded in the system, and no analysis per se need be done. In order to save even the brief time required to calculate LaU, the Manufacturer Standardization Society of the Valve and Fitting Industry has calculated allowable piping spans for various piping configurations, and published them in their standard MSS SP-69 (Figure 2-10). They have calculated the maximum allowable piping weight spans based upon the following criteria: 1
the pipe is assumed to have standard wall, with insulation,
2
the maximum moment is calculated as Mmax =wI 2/10,
3
-
no concentrated loads are present,
4
-
there are no changes of direction in the spans, which are assumed to run in the horizontal plane,
5
-
the maximum allowable stress is assumed to be 1500 psi, combined bending and shear,
6
-
maximum deflection of the span under load is limited to 0.1", and
7
-
stress intensification factors of components are not considered.
Due to the low allowable stress value used, there is sufficient factor of safety that this standard span may he applied to a wide range of piping configurations. If the engineer supports a piping system such that no span in the system exceeds the standard spans listed in the table, it is virtually certain that the system is adequately supported for weight loading. However, it is rare that a piping system has no concentrated
2-13
COADE Pipe Stress Analysis Seminar Notes
loads, consists of only horizontal runs with minimal changes in direction, etc. Therefore, standard practice dictates that standard spans be applied subject to the following four caveats: 1
Supports should be located as close as possible to concentrated weights. The theoretically best location for a support is directly on the concentrated load; however, this is usually impractical.
2
A developed length of 3/4 of the standard span or less should be used when the piping run changes direction in the horizontal direction, in order to minimize eccentric moments. The theoretically best location for a support is on an elbow; however, this is not recommended due to the bend stiffening and increased local stresses associated with attachments on a bend.
2-14
TABLE 3.
o
MAXIMUM HORIZONTAL PIPE HANGER AND SUPPORT SPACING 3:
~
~....
'"d
1 NOMINAL PIPE OR TUBESIZE
t\:)
..... 1
01
l' ~
.....•
Q
4
J
5
COPPERTUBE
WATER SERVICE
VAI'OR SERVICE
ft
m
ft
m
ft
ft
m
1/4
7
2.1
8
2.4
5
I.S
5
I.S
J/8
7
2.1
8
2.4
5
I.S
6
1.8
1/2
7
2.1
8
2.4
5
I.S
6
1.8
WATER SERVICE
m
VAPOR SERVICE
7
2.1
9
2.7
5
I.S
7
2.1
1
7
2.1
9
2.7
6
1.8
2.4
1 1/4
7
2.1
9
2.7
7
2.1
8 9
2.7
1 1/2 2
9
2.7
12
J.7
8
2.4
.10
3.0
10
3.0
\J
4.0
8
2.4
21/2
Il
J.4
14
4.3
9
2.7
J/4
~
2
STD WT STEEL PIPE
FIRE OUCTILE PRO· ..ON TECTION PAESSlIRE
::lé! or-
:~ tri
1":11:1
g;.a as
i~
-tri
~~ ut
3
12
3.7
15
4.6
10
3.0
II 13 14
J 1/2
13
4.0
16
4.9
Il
3.4
15
4.6
4
14
4.3
17
5.2
12
3.7
16
4.9
5
16
4.9
19
5.8
13
4.0
18
5.5
6
~ r-
17
5.2
21
6.4
14
4.3
20
6.1
:!l
8
19
24
7.3
16
4.9
23
7.0
10
22
26
7.9
18
5.5
25
7.6
19
5.8
28
8.5
12
23
5.8 6.1 7.0
30
9.1
14
25
7.6
32
9.8
16
27
8.2
35
10.7
18
28
8.5
37
20
30
9.1
39
11.3 Il.9
24
32
9.8
42
12.8
30
33 10.1
44
13.4
3.4
6 psrlRoru
°"t'I
~ooj.~t.I zO~
1'1--
...
. ::1:
",
~ X
1ft III",
>:: "'n
~z
~e ~S; ~~
'"III
i ~
~
~
zZO ...... ...
. ::1:>
l'IX
III'"
>:: "'n ~z
>!i
~
Si
800j0°
~I 00
"'0
j!g
ASBESTOS CEMENT
ra
1ft
2:
CAST IRON SOIL
ra
4.J
:z:
8
Q~~ l''~;:' goi 5°9 ozz:z:- 300jiC
4.0
ooj
7
>"t'I n2: ::1: tri
Si!!3 r::~
~:s 2:;g
>g; ~Q
~~
>"t'I
... 0
~g
a~ trl
z OC') "1113 g
a~
ai! 2: tri
>'"
ilia
~a 1110
~n
~n
"'2
QG ~
"'2:
Qa
r-
~
'"III
=;; a: >
1ft
Z
!ii >
~ )III
tri
)III
rA )III
; !C
~
~
i
'"C CJ
10
Il
GLASS
PLASTIC
FIBERGLASS RJ:IN· FORCED
~OD
en ..,
l'I~
:IIIr-
§~ 0-
za: -> !",X
'"
j ~
1=
°1:lE > Z c ~
Q
"'~ triO
~i
~6 ."lE
8~ Zl"
"'> "'z >c ooj.., c> 'i:!:l c )III
...
tri
)III
rA :11:1
$q
i
~
rA )III
{3 CI
~
!C
!'>
c)III
~
i~
i ~
Q
~
:1 '"rA )III
~~
-z Oc z_
1
0
)III
~
~ ~
~
00 00
j....
:IIIr-
!è!;:: '"III!C
r:n
~
1'10
ooj:!
(1)
~
~
00
r:n
(1)
~
> zg >
'"
10
."
~
i
'""II i ~ 0
C'2:)
> ~
. NOTE: (1) FOR SPACING SUPPORTS INCORl'ORATING TYPE 40 SHIELDS, SEE TABLE S. (2) OOB NOT APPLY WHERE SPAN CALCULATIONS ARE MADE OR WHERE THERE ARE CONCENTRATED LOADS BE1WEEN SUPfORTS SUCH AS FLANGB, VALVES, SPECIALTIES, ETC., OR CHANGES IN DIRECTION REQUiRING ADDmONAL SUPI'ORTS.
~
s.I:S
~
Z
~
00
COADE Pipe Stress Analysis Seminar Notes
3
-
The standard span doesn't applyon risers, since no moment (and thus no stress) develops regardless of the riser length. The number and location of supports should be determined by the location and strength of building steel. However, it is preferable to locate supports above the center ofgravity oflong risers in order to prevent toppling.
4
-
Support locations should be selected as close to building steel as possible in order to simplify support configuration.
The steps involved in supporting a piping system for sustained loads can he illustrated with an exam pIe. In Figure 2-11, the system consists of a 12" diameter, standard schedule steel pipe filled wi th water, wi th a design pressure of 150 psi, and a design tem perature of 3500 F, which runs hetween two equipment nozzles. The engineer first must determine the standard span for the system. For 12" diameter, water filled pipe, the standard span is shown in MSS SP-69 to he 23 feet. For changes of direction, 3/4 of this span is 17 feet-4 inches. Next, the engineer locates supports. The first concern is to locate them near concentrated loads - supports should he located as close as possible to the two valves (for example, near node points 20 and 70). The first ofthese is optional, depending on whether the nozzle at node point 10 is assumed to act as an anchor, and whether it is desirable to minimize the nozzle loads on the equipment. The next concern is the placement of supports on the riser. Assume that the capacity of the building steel dictates that the weight of the riser be split hetween two supports. It is recommended that one ofthese be placed above the center ofgravity ofthe riser (for example, 15 feet below the top of the riser). Now supports can be located elsewhere in the system, starting at the nozzle at node point 10. A support was located near node point 20 earlier; we now want to locate the next one downstream within the standard span. It is evident that pipe changes direction within 23 feet, so the developed length to the next support should be maintained as less than 17 feet4 inches. The next run ofpipe accommodates a full 23 foot run, so two supports can be located between node points 30 and 40. The line of action ofthe supports on the riser provide support to the end of the horizontal 30-40 run, so no additional support is required at node point 40. Support locations can he continued to he selected in this manner until alilocations meet the selection criteria; one solution is shown in the Figure 2-12. Once completed, what does this accomplish? By using the standard span criteria, the engineer can assume that the maximum stress in the piping system due to weight loading does not exceed 1500 psi. Therefore, substituting this value for the weight component ofthe stress equation: Ssus
=
PA/Am + 1500 = 150(113.1)/14.58 + 1500 = 2664 psi < 20,000 psi
2-16
COADE Pipe Stress Analysis Seminar Notes
12" DIA - STD SCH PIPE MAT'L - A106 GR B FLUID - WATER PRESSURE - 150 P~ TEMP - 350 DEGREES F ELBOWS - LONG RADIUS INSULATION - 2" CS VALVES - 150# GATE VALVES (WT =826#) NOZZLES (ANCHOR POINTS) @1 0 & 90 Sc = 20,000 PSI Sh = 20,000 PSI THERMAL CYCLES ,
= =
P(120)~3/12EI + P(240)~3/12EI P(120~3 + 240~3)/12EI
~10'-O
1
10'-0
i
10'-0
~
Figure 2-23 The expansion stress range in each ofthe legs is linearly proportional to the length ofthat leg, so: SEl
SE2
=
6 x 29E6 x 6.375 x 0.23 x 240/ (1203 + 2403 )
=
3937 psi
=
6 x 29E6 x 6.375 x 0.23 x 120/ (1203 + 2403 )
=
1918 psi
The stress range calculated in the longer leg is only 3937 psi (note that the maximum expansion stress is found in the longest leg resisting the displacement), compared to 17,700 psi without the loop. Generically, the stress range in a legj, due to thermal expansion in a direction perpendicular to that of leg j, is:
Where: SEj
=
stress range in a legj Oegj must be orthogonal to the direction of the thermal growth to be absorbed), psi
lj
=
length of leg j, in
li
=
length ofleg i (where leg i represents each leg helping to absorb the thermal growth; normally, aIl legs running orthogonally to the thermal growth), in
Therefore, the calculated stress range should always decrease if expansion loops are added in any direction perpendicular to a direction of thermal growth, since the denominator in the expression for the expansion stress will increase.
2-28
COADE Pipe Stress Analysis Seminar Notes
2.3.5 Simplified Expansion Stress Check The concept that addition ofexpansion loops reduces the expansion stress range in a system is recognized by the B31.3 code (and others). This is codified in the requirement that expansion analysis need not be explicitly done for a system meeting the following conditions: 1 -
the system is all of the same size, material, etc.,
2 -
the system has no branches, and consists of only a single run between two anchors,
3 -
there are no intermediate restraint points (note that hangers are traditionally excluded from consideration as restraints), and
4 -
D y / (L - U)2 < 0.03 Where: D
=
pipe outer diameter, inches
y =
resultant thermal growth to he absorhed, inches
L =
totallength of piping, feet
U
=
straight line distance between anchors, feet
The term (L - U) represents the amount of extra pipe (i.e.,loops) in the system. Examination of this equation reveals that, after factoring through constants, it is simply a form of the guided cantilever stress equation:
This simplified check can be illustrated by applying it to the system shown in Figure 2-12. It is clear that this system meets the first three criteria - the system is aIl of the same size, material, etc.; the system has no branches, and consists of only a single run between two anchors; and there are no intermediate restraint points except hangers. For the fourth requirement: D
=
12.75 in
y
=
[«(11+12)x12x1.88E-3)2+(50x12x1.88E-3)2+«45+33)x12x1.88E- 3)2]1/2 x-growth y-growth z-growth
=
2.154 in
=
11 + 45 + 50 + 33 + 12 = 151 ft
L
Dy / (L - U)2
= 12.75 x 2.154/ (151- 95.46)2 = 0.0089
.
DISTANCE TO FIRST RIGID
~
Figure 2-33
2.4.6 Notes on Hanger Design 1
-
In the event that a system which carries a fluid with a specific gravity less than 1.0 is to be hydro tested, the springs will generally have to remain pinned during the hydro test. The hanger hardware (clamps, rods, etc.) and supporting structure will have to he selected and/or designed to withstand the hydro test loads, which will normally he the controlling design loads for these supports.
2
-
When specifying the spring hanger's Hot and Cold Loads, the anticipated weight of additional hardware should be added to the loads calculated by CAESAR II, especially if it is expected to he significant (such as in the case of large stock clamps or a trapeze assembly made of structural steel). The spring must also support the hardware, and if this is not considered when specifying the spring parameters, the piping weight loading will he unbalanced by the weight of the hardware.
3
-
Horizontal movement at hanger locations must he considered when designing a support in order to assure that the pipe does not move 80 far that i t falls off of the support. Additionally, support manufacturers typically limit the range of a hanger rod's arc in to values such as 60, where the arc can be calculated as: Arc
= Tan-! (horizontal movement / rod length) 2-43
COADE Pipe Stress Analysis Seminar Notes
In cases where the horizontal movement is especially large, it may be advisable to install the support in an offset position to minimize the deviation of the line of support action from vertical in both the cold and hot positions. 4
-
In systems where installation is difficult due to flange fit-up problems caused by unbalanced cold loads, it may be preferable to adjust the springs in the field to carry the hot load once the system has been started up. In cases where nozzle operating loads are not critical, and fit-up problems are more of a concem, CAESAR II can provide Cold Load Design, where the weight loads are balanced in the cold, rather than the hot, condition. CAESAR II provides the option of calculating both the "theoretical" and the "actual" cold loads for springs. The theoretical cold load is the load to which the spring should be preset prior to installation (usually this is done at the factory, and the springis pinned tokeepitat this value). This is the load which the spring will exert on the piping system in the cold condition, as long as there is no vertical displacement ofthe system at this location. Since the cold load is almost always unbalanced vs. the piping weight load, there will be a net load on the system at this location in the cold condition. Ifthis net load is large, or the piping system is very flexible, the system may displace under the load, leading to extension or compression ofthe spring, and a corresponding change in the load plate reading. The new readingofthe spring load is what CAESAR II calculates as the "actual" cold load. Or more simply, the "theoretical" cold load is the cold load to be specified in the factory order of the spring, while the "actual" cold load is an approximation ofthe reading ofthe spring load after pulling the pins upon initial installation. The actual installed load case is important if the springs are to be adjusted or checked in the cold condition, or if the spring's cold load is being set in position, rather than at the factory.
5
6
-
Excessive use of spring hangers may create a dynamically unstable (low natural frequency) system due to lack of restraint stiffness. These systems have essentially no horizontal support, and typically small vertical stiffnesses resisting movement in the Y direction. Note that constant effort spring supports have no dynamic effect on a piping system.
7
-
Selected hanger locations may actually hold the pipe down during the restrained weight case due to unbalanced parts ofthe system pivoting about other supports. CAESAR II flags these with a warning during the analysis and reports them as zero load constant effort supports in the hanger table during output. When this occurs, the offending supports should be removed, or the support locations in the vicinity should be reconsidered.
8
-
There are special provisions to consider when cold spring and hanger design exist in the same job. Cold spring should be omitted from the restrained weight case, and included in the operating load case for hanger travel. The actual installed load case should be run with the cold spring in order to determine the installed hanger settings in the presence of cold spring. It is the user's responsibility to verify that the displacements during the actual installed case are still within the manufacturer's recommended load range. Problems usually only arise when
2-44
COADE Pipe Stress Analysis Seminar Notes
there is significant cold spring in a vertical run of pipe in the vicinity of one or more spring hangers. 9
-
In a liquid filled line, the springs may he installed when the system is empty. In this case it is necessary to ignore the "actual" cold load, and in some cases it may be preferable to adjust the springs in the field to carry the cold load once the system has been filled.
2.4.7 CAESAR Il Hanger Design Control and Options CAESAR II provides a number ofuser specified options for controlling its automatic hanger design. The control options may, for the most part, be applied to the system globally, or at specific locations. These options are fully descrihed in the CAESAR II U ser's Manual, but are discussed to some extent here: Actual cold load calculation - This is described in more detail above. The user should specify Yes, if: 1
-
The spring installation load is to he adjusted with the pipe resting on the spring and free to move vertically otherwise (i.e. there isn't a steel strap around the spring base and the load flange, preventing movement of the load flange when the spring is adjusted in the cold position).
2
-
The piping adjacent to the spring is very flexible and/or the stiffness ofthe spring is very high.
3
-
Fluid fùled systems are installed and set empty, and the user wishes to know the empty installation load.
Use short range springs - CAESAR II's hanger design algorithm first tries to select for an application a short range spring, followed by a mid-range, and then a long range, spring. On some construction sites short range springs are considered specialty items, and are only used where available spring installation clearance is small and where travel from cold to hot is small. In these cases, the user may instruct the design algorithm to bypass consideration of short range springs (and start with mid-range springs frrst) unless space limitations require it. Allowable Load Variation - As noted above, this is computed as: Var = 1 CL - HL 1 / HL = 1 k A th 1 / HL The maximum possible load variation inherent in recommended ranges of the spring tables approaches 100% when the Hot Load is less than the Cold Load, and is approximately 50% when the Hot Load is greater than the Cold Load. Typical values for the permissible load variation range from 10% to 25%. A constant support may he forced at a location by specifying a minuscule load variation requirement at that location.
Rigid Support Displacement Criteria - Where feasible, rigid supports are considered preferable to springs supports, for reasons of economy (purchase, installation, and mainte-
2-45
COADE Pipe Stress Analysis Seminar Notes
nance) and vibration prevention. Therefore, if a rigid support can be chosen instead of a spring at a location, the engineer will usually want this to occur. One definition of a spring support is: "a restraint that supports a given load through some thermal travel". If the thermal travel is zero, or very small, then it is hypothesized that a rigid support can he used in place of the spring. This is indeed true providing that the surrounding pipe is relatively flexible as compared to the rigid rod. The extent to which rigid supports are chosen can be controlled by this criteria. At any support location where the vertical displacement calculated during the operating load case for hanger travel is less than the specified Rigid Support Displacement Criteria, a rigid rod will be selected and used in subsequent load cases. Note that this may not be desired at spring locations in the vicinity ofpumps or other rotating equipment or on risers, since this may result in high nozzle loads or thermallockup/liftoff of the support. It is best ifthis criteria is used in conjunction with some pre-design of support locations, such as that discussed in Section 2.4.5 of these seminar notes.
Free AnchorslRestraints - Often a major objective ofhanger design is the minimization of equipment nozzle loads due to weight. This is done by forcing an unbalanced hot load (usually an overload) at the hanger location nearest to the equipment nozzle. This unbalanced force pulls on the nozzle, thus relieving it of some of the weight that would normally fall on it under a natural distribution - ideally, the hanger would be sufficiently unbalanced to make the load on the equipment nozzle as close to zero as possible. In an attempt to force this unbalance, anchors at equipment nozzles are often ''freed" during the restrained weight case, forcing all of its weight to the hot load of the nearest support. This technique should be used sparingly in those configurations where no hangers are located within three pipe diameters or so in a horizontal direction from the nozzle being released. It is also recommended that care be taken when releasing more than just the Ydirection force at a anchor/restraint, as release of additional degrees-of-freedom may cause gross angular and vertical displacements, resulting in unrealistic hanger design loads.
Manufacturer's Tables - This entry is used to designate the manufacturer of the springs (and thus the hanger table) to he used, as weIl as certain design criteria relating to selection of the hangers within this table. The selection criteria include: 1 -
use of maximum (vs. recommended) load range,
2 -
centering of the spring in the table, and
3 -
cold load (vs. hot load) design.
Most hanger vendors provide hanger tables with two ranges defined: 1) a restricted, or recommended load range, and 2) a maximum allowed load range. In order to provide margin against analytical uncertainties, it is best to use the recommended range. The maximum allowed load range may be used in certain situations, such as to permit the use of variable support hangers instead of the more expensive constant effort support, or when an alreadyowned spring is to be used over a new one.
2-46
COADE Pipe Stress Analysis Seminar Notes
In cases where the expected analytical uncertaintyis especially high, maximum margin may he provided by selecting the spring which most closely centers the loads in the hanger table. Cold load design balances the weight loads in the cold, rather than the hot, condition. This may he desired in those systems where installation is difficult due to flange fit-up problems caused by unbalanced cold loads, and where nozzle operating loads are not critical.
Available Space - In certain cases, the distance between the top ofthe pipe and the steel overhead; or between the bottom of the pipe and the foundation or platform below, govern the type (and number) of springs which may he used at a specific location. This value may be specified at individual hanger locations for use in spring selection. Figure 2-34 defines the available space as used in the CAESAR II spring design.
Available clearance for hanger. (Input positive number for hanger available space.)
Available clearance for cano (Input negative number for Cab available space.)
--1;.-
j Figure 2-34
The available space option together with the "number of springs allowed" option lets the user design multiple spring support systems.
2-47
COADE Pipe Stress Analysis Seminar Notes
Number of Allowed Springs - Ifthere is physicaUy more than one spring can at a given hanger location, that numher may be specified here. Likewise, the maximum number of springs that the user will permit may be specified (in the event that CAESAR II has to split the load in order to meet space criteria). In the case of multiple springs, CAESAR II will split the load evenly among aU springs. User Defined Operating Load - In some piping configurations the program selected operating (or hot) load on the spring doesn't unload the equipment nozzle sufficiently to satisfy manufacturers aUowables. In these situations the user can force a hot load (higher or lower), overriding the program calculated value in an attempt to tune weight distribution and bring the equipment loads within the allowables. The user's entry in this case should normaUy be a variation of the value initially proposed by the program spring selection algorithm. Before adjusting the operating load the user should determine if a preferable course of action is freeing the problem nozzle during the restrained weight case (as discussed above). Old Hanger Redesign - In cases where part of a piping system is redesigned, it is preferable that the hanger design algorithm re-select the existing springs in the system wherever possible. Where they can be re-used, new load ranges may he identified for them, and only a readjustment ofthe load flange in the field may be required. Where the existing springs can't be used, new ones will be recommended. The Old Ranger Redesign capability allows the user to do this. Multiple Load Case Spring Hanger Design - This option is useful whenever the piping system has multiple thermal states that are sufficiently different such that the results from each thermal state should he considered when doing the spring hanger design. Figure 2-35 illustrates this idea:
Figure 2-35
2-48
COADE Pipe Stress Analysis Seminar Notes
The hanger at "A" should he designed with the main pump running, and the hanger at "B" should be designed with the backup pump running. Once the springs are designed for their respective thermal cases they are inserted into the piping system and the various operating conditions run to check for stress or equipment overloads. The options available in CAESAR II for combining data from the various design load cases are shown below: 1
Design per thermalload case 1
2
-
Design per thermalload case 2
3
-
Design per thermalload case 3
4
-
Design for maximum operating load Design for maximum travel
5 6
-
Design for average load and average travel
7
-
Design for maximum load and maximum travel
2-49
COADE Pipe Stress Analysis Seminar Notes
2.5
Designing For Occasional Loads (Static Equivalent of Dynamic Loads)
As noted earlier, piping systems must he designed to withstand primary and secondary loadings. Sustained loads were discussed as beingthe most common types ofprimary loads. There are additional requirements for the evaluation of occasionalloads, or primary loads which are present for short time durations, typically 1% to 10% of the total operating time. Failure criteria are typically the same for occasionalloads as for sustained loads, except that creep failure is not a concern for occasionalloads. Because of this, the allowable levels for the absolute sum of sustained and occasional stresses are the same as those for sustained loads, but increased by a factor (typically 15% to 33%). For example, looking at the B31.1 equation for occasional stresses:
Slp + 0.75 i Ma/Z + 0.75 i MlIZ < k Sh Where:
=
longitudinal pressure stress, psi
l
=
stress intensification factor
Ma
=
resultant moment on cross-section due to sustained loads, in-lb
Z
=
section modulus of pipe cross-section, in3
Mb
=
resultant moment on cross-section due to occasionalloads, in-lb
k
=
occasional stress factor
=
1.2 for loads present less than 1% of time
=
1.15 for loads present less than 10% oftime
=
Basic allowable stress in hot condition
Slp
Sh
Typical of these types ofloads are wind loads, earthquake loads, and quickly applied loads (reliefvalve, fluidhammer, etc.). These are dynamic (meaningthat they change as afunction of time) loads, and are therefore discussed in greater detail in Sections 4 and 5 of these seminar notes. However, the easiest (but less accurate), and therefore most common means of analyzing dynamic loads is usually to model them as static (meaning that they are constant throughout time) loads, with the magnitude increased to reflect the dynamic load amplification.
2.5.1 Wind Loading Wind loading is caused by the loss ofmomentum of the wind striking the projected area of the pi ping system. The static linear force per foot generated by a steady-state, constant speed wind load can be calculated as: f
=
P eq * S
* D sine 2-50
COADE Pipe Stress Analysis Seminar Notes
Where: f
=
"pseudo static" wind force per length of pipe, lb/ft
P eq
=
equivalent wind pressure, psi
=
V2 /2g
=
densi ty of air, Ibm/ft3
=
0.0748Ibm/ft3 at 29.92 in Hg and 700 F
v
=
design velocity ofwind (usually the 100-year maximum wind speed), ft/sec
g
=
gravitational constant, 32.2 ft/sec 2
S
=
shape factor (or drag coefficient), based upon Reynolds number ofwind and shape of structure; this typically varies between 0.5 and 0.7, with a value of 0.65 characteristic ofpiping elements, dimensionless
D
=
pipe diameter (including insulation), ft
e
=
angle oforientation between pipe and wind, where 0 0 represents the pipe axis parallel to the wind direction
Since this represents the force associated with a steady-state flow of air, the calculated value is often increased by a gusting factor in the range of 1.0 to 1.3 to account for dynamic effects. The linear force per foot, f, is calculated for each end of the element and the average taken. The average is assumed to apply as a uniform staticload over the entire length ofthe element. ASCE #7 (formerly ANSI A58.1) modifies this concept slightly to consider facility importance, proximity of hurricanes, etc. Its formula for wind load is:
=
0.00256 Kz (1 V)2
Kz
=
Exposure coefficient, based upon height above ground level and congestion oflocal terrain (varies from 0.12 for 0-15 feet height in city environment to 2.41 for 500 feet height in wide open terrain), dimensionless
I
=
importance factor, based upon importance of structure and proximity to hurricane coast (varies from 0.95 for non-essential facility over 100 miles from a hurricane to 1.11 for essential facility on the hurricane coast), dimensionless
v
=
basicwindspeedCexcludingfrom theaverageabnormallyhigh windloading events such as hurricanes or tornadoes), from ANSI A58.1 map (rangingfrom 70 to 110), milhr
f
Gt Cd D sin
Where:
2-51
COADE Pipe Stress Analysis Seminar Notes
~
=
gusting factor, based upon height above ground level and congestion oflocal terrain (varies from 1.0 for 500 feet height in wide open terrain to 2.36 for 015 feet height in city environment), dimensionless
CAESAR II's ASCE #7 wind input screen requests a number ofparameters, from which the coefficients of the equation above are determined.
ASCE #7 provides a map of basic wind speeds in the Continental United States. The following is a crude summary of the map:
Region
Basic Wind Speed
California Other West Coast Areas Rocky Mountains Great Plains Non-Coastal Eastern U. S. Gulf Coast Florida - Carolinas Mi ami New England Coastal Areas
70 mph 80 mph 70 mph 80 mph 70 mph 100 mph 100 mph 110 mph 90 mph
ASCE #7 adjusts the importance factor according to the site's Distance from Hurricane Ocean line. This typically translates into the distance from the east coast or the Gulf of Mexico in the Continental U .S. Ifthe plant site is greater than 100 miles from either the east or the gulfcoasts, then a value of 100 miles should be used (no credit may he taken for any plant site greater than 100 miles from any ofthese hurricane prone areas). The importance factor is further influenced by the Structural Classification, where the options are:
CateQor.v
Description
1
Everything except the options below Primary occupancy (greater than 100 people> Essential facilities. i.e. hospitals Failure represents low hazard
II III IV
The exposure coefficient and gusting factor are influenced by the terrain's Wind Exposure type, where the options are: 1 -
Large city center
2 -
Urban and suburban
3 -
Open Terrain
4 -
Flat coastal areas 2-52
COADE Pipe Stress Analysis Seminar Notes
Wind is a static, horizontal uniform load. Itmay act in any direction, and as such the engineer has several items to consider: How many directions should be analyzed for sensitivity to wind?
1 2
-
Should both positive and negative directions be evaluated?
3
-
Should sorne skewed direction be evaluated?
4
-
Do nonlinear supports (i.e. horizontal guides with gaps) and/or friction affect the wind load?
5
-
Should the wind act on the piping system in the cold or hot condition?
The logic diagram shown in Figure 2-36 should serve as a guideline when setting up and analyzing wind load cases to satisfy piping code requirements. (Note: The load cases shown here only contain the basic analysis components. Other items such as imposed displacements, concentrated loads, etc. may need to he added to the load cases shown above for the user's particular job.) DOES THE PIPING SYSTEM CONTAIN FRICTION, 1-D RESTRAINTS, AND/OR GUIDES WITH GAPS?
l
YES
NO~ IS THE MOST SENSITIVE WIND DIRECTION OBVIOUS?
YES~ RUN: JOB1 1 (OPE) 2 (SUS) (OCC) 3 4 (EXP) 5 (OCC)
T+P+W P+W WIND Di - D2 S2+S3
l
RUN: JOB1 (OPE) T+P+W 2 (SUS) P+W 3 (OPE) T + P + W + WIND1 4 (OCC) D3 - Di 5 (EXP) Di - D2 6 (OCC) S4+S2
1
NO
RUN: JOB1 1 (OPE) (SUS) 2 3 (OCC) (EXP) 4 5 (OCC)
T+P+W P+W WINDX Di - D2 S2+S3
JOB2 (SUS) P+W 2 (OCC) WINDZ 3 (OCC) Si +S2
JOB2 * 1 (OPE) 2 (SUS) 3 (OPE) 4 (EXP) 5 (OCC)
T+P+W P+W T + P + W + WIND 2 D3 - Di S4+S2
*REPEAT THIS LOAD SET FOR ALL OTHER WIND DIRECTIONS (BOTH + AND -) OF CONCERN
Figure 2-36 For nonlinear systems an additional algebraic case may be required to extract the occasional bending moments from the operating hending moments. In perfectly linear systems an occasionalload case can he run alone, with this used for the stress component due to the
2-53
COADE Pipe Stress Analysis Seminar Notes
occasionalload. With nonlinear systems, the effect the occasionalload has on the system is linked to the effect of the operating loads on the system. The algebraic load cases shown in Figure 2-36 permits these two effects to be separated.
2.5.2 Earthquake Loading Earthquakes may be analyzed using either dynamic or static methods. Dynamicearthquake analyses, which will be covered in depth later, are not discussed here. Static earthquake loads are determined and applied in a manner very similar to static wind loads. The static loading magnitude is considered to be in direct proportion to the element's weight. Earthquake load magnitudes are given in terms of the gravitational acceleration constant, i.e. g's. If an earthquake is modeled as having a 0.5g load in the X direction, then a force equal to one-half of the system's weight is applied to the pipe uniformly in the X direction. Earthquake static load cases are set up and determined exactly as they are for wind occasional loads, i.e. by considering the same load case, non linearity, and directional sensitivity logic. In some cases the client specifies the magnitude of the earthquake loading in g's and the direction(s). In others, the analysis is left to the sole discretion of the engineer. It is not unusual to see only X or X-y components ofan earthquake. It is not uncommon to see Y only components, or X, Y and Z simultaneous components. When not provided by the client, there are a number of sources for obtaining the seismic gfactors:
Response spectrum: If seismic response spectra are available for the piping system, then, given the natural frequency of the lowest mode of vibration of a piping system, the analyst can find a corresponding acceleration from one of the curves. Ifthis acceleration lies on the right side of the peak, this acceleration may be conservatively used an overall g-factor. For more information on seismic response spectra, refer to Sections 4 and 5 of these seminar notes. Building code: Building codes provide ways to calculate seismic g-factors, based upon earthquake potential, structure type, and structure fundamental frequency. For example, the Uniform Building Code and the BOCA Basic/National Building Code calculates:
=
ZKCT
g
=
static equivalent g-factor to use for seismic design, multiples of gravity
Z
=
seismic coefficient based on earthquake zone, equal to 0.0 for Zone 0, 0.25 or Zone 1, 0.5 for Zone 2, and 1.0 for Zone 3
K
=
structure type constant, ranging from 0.67 to 3.0, dimensionless
C
=
0.051T 1/3 , but not greater than 0.1
T
=
fundamental period (inverse of frequency) of structure, sec
g Where:
2-54
COADE Pipe Stress Analysis Seminar Notes
ASCE #7: This standard calculates seismic g-factors in a manner similar to those of the building codes, based upon earthquake potential, structure importance, structure type, structure fundamental frequency, and soil parameters. The requirement is:
v
= ZIKCSW
Where:
v
= totallateral force or shear at the base, lb
Z
= seismic zone coefficient:
Seismic Zone
Coefficient, Z
4 3
1 3/4 3/8 3/16 1/8
2 1 0
I
=
occupancy importance factor:
Category
Description
1
1
Everything except the options below
1.0
II
Primary occupancy -
III
Essential facilities, i . e. hospitals
1.5
IV
Failure represents low hazard
NIA
> 100 people
1. 25
K
= structure type constant from Table 24 of ANSI A58.1, ranging from 0.67 to 2.5 (use K=2.0 for structures other than buildings)
C
= 1/(15 Tl/2), not greater than 0.12
T
= fundamental period (inverse of frequency) of structure, sec
S
= soil type coefficient from Table 25 ofANSI A58.1, ranging from 1. 0 to 1.5 (note that the product ofC and S neednot exceed the value 0.14, so this value should he used as a conservative maximum).
W
= total dead load
The "g'" factor can be found be dividing both sides ofthis equation by W, so: g
= V/W=ZIKCS
2-55
COADE Pipe Stress Analysis Seminar Notes
For piping, the generic equation for the maximum g-factor is: g
=
Z (1.0) (2.0) (0.14)
and, for the various values of Z:
Seismic Zone
Product
g-load
4
(1)(1)(2)(0.14)
0.28
3
(3/4)(1)(2)(0.14)
0.21
2
(3/8)(1)(2)(0.14)
0.105
1
(3/16)(1)(2)(0.14)
0.0525
o
(1/8)(1)(2)(0.14)
0.035
2.5.3 Quickly Applied Loads Loads that are applied near-instantaneously, and then remain constant for a reasonable duration oftime, such as fluid hammer and relief valve loads, effectively are applied with a DynamicLoadFactor(dynamicmultiplier)betweenO.Oand2.0. Thisisevidentbyassuming the worst case - no damping and instantaneous application of a constant force - and performing a time history analysis of the dynamic equation: M x(t) + K x(t)
= F(t)
Equating energies (where the kinetic energy added to the mass is Fx( t), while the crumpling energy of the spring is Kx(t)2/2): Fx(t) = Kx(t)2/2, or Kx(t) = 2 F(t) The term Kx(t) represents internally induced forces/moments within the system. The DLF is the ratio of the induced forces to the applied forces, or K x( t)max / F( t), which in this case has its maximum value of2.0. It is often highly conservative to apply twice the calculated force as a static load, but this is still often done. As the load ram p-u p time (such as the opening time of a relief valve) increases, or the load duration decreases (such as fluid hammer in a short piping leg), the DLF will decrease as well. In order to take advantage of the "true" (reduced) DLF, it is necessary to perform a dynamic analysis, such as a time history analysis or a response spectrum analysis. In lieu of a dynamic analysis, the user can only estimate a DLF, estimate the applied load, and apply a concentrated static force equal to the DLF times the applied load to the piping system.
Fluid Hammer: It is not always so easy to calculate the applied loads. One method of estimating fluid hammer loads is described in Crocker & King's Piping Handbook as: F
= P c dv A /144g
2-56
COADE Pipe Stress Analysis Seminar Notes
Where: F
=
fluid hammer force (exclusive ofDLF), lb
p
=
density offluid, Ibm/ft3
=
62.4 for water
=
0.0003 for saturated steam at atmospheric pressure
=
1.85 for superheated steam at 10000 F and 1500 psig
=
speed of sound in a fluid, ft/sec
=
for liquid: 12 [g Ef / (1 + D Ef / tEp)]
=
approximately 3000-4000 ft/sec for water in typical pipe sizes
=
for gas: (kgRT) 1/2
=
approximately 2000-2500 ft/sec for steam in typical pipe sizes
g
=
acceleration gravity, ft/sec 2
Ef
=
bulk modulus of fluid, psi
=
approximately 300,000 psi for water and other fluids
D
=
inside diameter of pipe, in
t
=
wall thickness ofpipe, in
Ep
=
modulus of elasticity of pipe material, psi
k
=
ratio of specifie heats for gas, dimensionless
=
1.3 for steam, 1.24 for ethylene, 1.27 for natural gas
=
gas constant, ft-Ib/lbm-oR
=
85 for steam, 55.1 for ethylene, 79.1 for natural gas
T
=
temperature of gas, oR
dv
=
change in fluid velocity causing fluid hammer, ft/sec
A
=
internaI area of pipe, in2
c
R
Relief valves: Relief valves are used in piping to provide an outlet on those occasions when pressure builds up beyond that desired for safe operation. When the pressure setting is
2-57
COADE Pipe Stress Analysis Seminar Notes
reached, the valve opens, allowing sufficient fluid to escape from the piping system to lower the pressure. This discharge initiates ajetforce, which must be resisted by the piping system. Valve opening time and duration of the jet load affect the dynamic response of the system, thus affecting the developed loads. Reliefvalve jet loads are normally provided by the valve manufacturer. Ifthis is not the case, the loads can he estimated by a thorough thermodynamic analysis. This methodis discussed in detail in Section 5 of these course notes. In lieu of thermodynamic and dynamic analyses, the B31.1 code provides a means of estimating the discharge force (as an equivalent static force) of a relief valve venting steam to atmosphere. The force is estimated as such:
=
DLF (M V 1 g + P A)
F
=
static equivalent discharge force, lb
DLF
=
dynamic load factor (as calculated helow), dimensionless
M
=
mass flow rate from valve x 1.11 (factor of safety), Ibm/sec
V
=
fluid exit velocity, ft/sec
=
[(2gJ)(ho - a) 1 (2b - 1)]1/2
J
=
conversion constant, 778.16 ft-Ib/Btu
ho
=
stagnation enthalpy ofsteam, Btu/lbm
a,b
=. steam constants as per following table:
F
Where:
Steam conditi on
a (Btu/lbm)
b (dimensionless)
Wet, 90% quality
823
4.33
Superheated
831
4.33
g
=
gravitational constant = 32.2 ft/sec 2
P
=
static pressure at discharge, psig
=
[M (b - 1) 1 A b ][ 2J (ho - a)/g(2b - 1) ]1/2 - Pa
2-58
COADE Pipe Stress Analysis Seminar Notes
A
=
internaI area of dis charge pipe, in2
Pa
=
atmospheric pressure = 14.7 psi M, V, P, A F
token at this location
--
W =Weight of entire assembly
Figure 2-37 The dynamic load factor (DLF) is used to account for the increased load caused by the sudden application of the dis charge force. (Note that DLFs are discussed in great detail in Sections 4 and 5 ofthese seminar notes.) For the purposes ofthis estimate, the DLF varies between 1.1 and 2.0, depending upon the rigidity of the valve installation and the opening time ofthe valve. If the piping system is relatively rigidly restrained, the DLF can he calculated by fin ding the natural period ofvibration ofthe valve installation, treating it as a single degreeof-freedom oscillator:
=
0.1846 [ W H3 / g E 1]112
T
=
natural period of vibration, sec
W
=
weight of relief valve installation, lb
H
=
distance, run pipe to center of outlet pipe (see Figure 2-36), in
g
=
gravitational constant = 386.4 in/sec2
E
=
modulus of elasticity ofpipe material, psi
1
=
moment ofinertia ofinlet pipe, in4
T Where:
Next, the ratio of the valve opening time, to, to the fundamental period of vibration of the valve installation, T, should be found. This ratio is then used to determine the DLF from the chart in Figure 2-37. (Note that in the event that the opening time is not known, a conservative value of 2.0 for the DLF should be used.)
2-59
COADE Pipe Stress Analysis Seminar Notes
2.2
2.0
\
1.8 u...
c5
~
1.6
\
1.4
\
1.2
0.1
\
r--- rl'- i'-
0.2
0.4 0.6 0.8 1.0
2.0
4.0 6.0 8.0 10
Ratia af volve apening time ta periad af vibration toiT
Figure 2-38
2-60
20
3
COADE Pipe Stress Analysis Seminar Notes Section 3 Table of Contents
3.0
Modeling And Analysis Of The Piping System .......................................................... 1
3.1
Computer Representation Of Basic Elements ........................................................... 2
3.2
Piping Configuration Modeling Techniques ............................................................. 19
3.3
Expansion Joint Modeling And Evaluation ............................................................. 20 3.3.1
Expansion Joint Stiffnesses .......................................................................... 20
3.3.2 Evaluation of Expansion Joint Allowable Movements ................................ 23 3.3.3 Use of the ERATE Program .......................................................................... 25 3.3.4 Modeling ofUnbalanced Pressure Force ...................................................... 28 3.3.5 Modeling ofTie Rods ...................................................................................... 35 3.3.6 Expansion Joint Assemblies .......................................................................... 35 3.4
Piping Nozzle Evaluation .......................................................................................... 43 3.4.1 Equipment Nozzle Load Analysis ................................................................. 43 3.4.1.1 NEMA SM23 Standard for Steam Turbines ................................. 44 3.4.1.2 API 610 Standard for CentrifugaI Pumps ..................................... 49 3.4.1.3 API 617 Standard for CentrifugaI Compressors ........................... 54 3.4.1.4 API 661 Standard for Air Cooled Heat Exchangers ...................... 54 3.4.1.5 HEl Standard for Closed Feedwater Heaters ............................... 57 3.4.2 Calculation ofVessel Stresses Due to Nozzle Loads .................................... 59 3.4.2.1 Calculation ofVessel Stresses Due to Nozzle Loads ..................... 60 3.4.2.2 Running a Sample WRC 107 Calculation ...................................... 65 3.4.2.3 Evaluating Vessel Stresses ............................................................. 75 3.4.2.4 Completing the Sample Calculation .................................. :........... 83 3.4.3
Estimation ofVessel Nozzle Flexibilities ...................................................... 84 3.4.3.1 Use ofWRC Bulletin 297 ................................................................ 86 3.4.3.2 Modeling Nozzles for Flexibility Calculations ............................... 92
3.5
Restraint Modeling .................................................................................................... 97 3.5.1 Restraint Types .............................................................................................. 97 3.5.1.1 Anchor .............................................................................................. 97 3.5.1.2 Restraint .......................................................................................... 98 3.5.1.3 Spring Hanger ................................................................................. 99 3.5.1.4 Hanger ........................................................................................... 100 3.5.1.5 Support .......................................................................................... 100
1
3.5.1.6 Snubber .......................................................................................... 101 3.5.1.7 Sway Brace .................................................................................... 103 3.5.2
Non-linear Effects ........................................................................................ 103 3.5.2.1 Friction ........................................................................................... 103 3.5.2.2 One-Way Restraints ...................................................................... 104 3.5.2.3 Gaps ............................................................................................... 104 3.5.2.4 Large Rotation Restraints: ........................................................... 105 3.5.2.5 Bi-linear Stiffnesses ...................................................................... 107
3.5.3 Evaluation of Restraint Stiffness ................................................................ 108 3.5.3.1 Use of the Structural Steel Modeler ............................................. 112 3.5.4 Use of CNODES When Modeling Restraints ............................................. 116 3.6
Miscellaneous Topics ............................................................................................... 118 3.6.1
Consideration ofCold Spring ...................................................................... 118
3.6.2
Fiberglass Reinforced Plastic Pipe .............................................................. 122
3.6.3 Underground Pipe ........................................................................................ 124 3.6.3.1 Modeling Soil Restraint ................................................................ 126 3.6.3.2 Automated Underground Piping Modeler .................................... 128 3.6.4 Jacketed Pipe ............................................................................................... 130 3.6.5 Flange Leakage Analysis ............................................................................ 132 3.6.5.1 Equivalent Pressure Calculation ................................................. 132 3.6.5.1 Flange Leakage Analysis Module ................................................ 133
2
COADE Pipe Stress Analysis Seminar Notes
3.0 Modeling And Analysis Of The Piping System The first two sections ofthese seminar notes have served to give the user an overview of the requirements of pipe stress analysis. This section presents the task on a detailed level, presenting ideas for modeling of various piping configurations and explaining specific analyses which may be performed to evaluate individual piping components. Included in this section is information on the following subjects: 1
Computer representation ofbasic elements
2
Piping configuration modeling techniques
3
Expansion joint modeling and evaluation
4
-
Nozzle evaluation, including evaluation of equipment loads, determination of nozzle/vessel stresses, and estimation of nozzle/vessel connection flexibilities
5
-
Piping restraints/structural modeling
6
-
Miscellaneous topics (coldspring, underground pipe, plastic pipe,jacketed pipe, flange leakage analysis, etc.)
3-1
COADE Pipe Stress Analysis Seminar Notes
3.1 Computer Representation Of Basic Elements Pipe stress analysis computer software algorithms are based upon certain assumptions. These assumptions serve to make the computer model (and its corresponding analytical results) only an approximation of reality. In many cases this approximation may be sufficiently close to reality to fall within the tolerances, margins, and factors of safety of the problem to be an adequate representation, while in other cases the user may find itnecessary to refine the model through more detailedmodeling. This section describes the assumptions used in the computer algorithms in order that the user may more fully understand the limitations (and the potential work-arounds) of the system. The "stiffness method" algorithm, which is used to perform the actual analysis done by CAESAR II and other prominent pipe stress/structural computer programs is described in detail in Section 6 of the se seminar notes.
o @ ~
•
•
•
Arbitrary Cross Section
Pipe Cross Section
Structural Cross Section
"Stick" Member
Figure 3-1 Piping basic elements are modeled as centerline, or "stick" members. These elements are defined by two node points (one at the "from" end, and the other at the "to" end), each with fixed spatial coordinates and six degrees of freedom (three translational and three rotational). The elements are further defmed by a constant (non-varying along the element length) set of stiffness parameters (i.e., material and cross-sectional properties). Response of the elements under load is governed according to recognized strength of material
3-2
COADE Pipe Stress Analysis Seminar Notes
relationships (as described in Section 6 ofthese notes), subject to certain limiting assumptions. These assumptions, described on the followingpages, govern the relationship between the mathematical model in the computer and the actual pipe existing in the power plant or refrnery. AlI elements remain stable under load (local buckling of cross-sections is ignored):
1
48" 00
0.375" Wall
Local Buckling of Cross Section
Section A-A
Figure 3-2
2
-
Plane sections remain plane:
Center of Bending
D
B
Figure 3-3 The computer algorithm assumes that points A and B (of Figure 3-3) always lie on the same cross-sectional plane, whether in the deformed or the undeformed state.
3-3
COADE Pipe Stress Analysis Seminar Notes
J
L
1
~
:~
B
1
0 F
L'
Figure 3-4 In reality, the moment F x L (in Figure 3-4) does not produce a uniform "plane-
sections-rem ain-plane" bending load at the cross-section A-B, since it causes local warping. 3
-
Hooke's Law is applicable across all fibers of the cross-section:
Compressive Normal Stress
"---.. Tensile Normal Uniform Bending Stress
Pipe Shoe W/Saddle
(Normal stresses very linearly from the neutral axis)
Saddle inhibits uniform bending and extension along ail fibers at the cross section.
Figure 3-5 4
-
Hooke's Law is applicable throughout the entire load range:
7
1
Stress Distribution Remains Unear
... Not Plastic
Figure 3-6
3-4
COADE Pipe Stress Analysis Seminar Notes
5 -
Moments and forces applied to the beam are assumed to act about the neutral axis:
L
Should not be modeled as: (Unless the F * L moment can be assumed negligible)
Figure 3-7 6
-
Element cross-sections do not ovalize under load (except as adjusted for bend elements):
A
-0-
~CTLA-A
A
This ovalization will make the pipe more flexible, i.e. the pipe will bend easier. Ovalization of this type for straight pipes is not considered.
Figure 3-8
The stresses at the ovalized section are intensified due to: 1 2
reduction in section modulus, and -
added local plate bending in the top and bottom fibers.
3-5
COADE Pipe Stress Analysis Seminar Notes
7
Applied loads are not affected by the deformed state of the structure (P-delta effect):
Np
6. =
F - -..-
0.25 in
=
1000 lb
1 1 1 1 1 1 1 1 1 1
Figure 3-9 In reality, there will be an addition al moment applied to the system, equal to the load times its displaced distance from the neutral axis ofthe structure (i.e., 1000 pounds x 0.25 inches = 250 in-lb). The computer software models this load as strictly a force with no applied moment. 8
Rotational deformations of the system are assumed to be small:
Sterling From y
Sequentiel 90· Rotetions About Z, Y, end X-Axes About Y About X About Z y
y
y
,~, ,~, /~, /~, Sterling From y
Sequentiel 90· Rotetions About Y, X, end Z-Axes About Y
About X
y
y
About Z y
,~, /~, /~, ,~, Figure 3-10
3-6
COADE Pipe Stress Analysis Seminar Notes
Node point rotations are added vectorially by the computer software. This is not a valid representation of reality for large rotations, as demonstrated in Figure 3-10 for three 900 rotations. 9
Boundary conditions are assumed to respond in a linear fashion:
Non-Linear Restraint Response Different for Up and Down Loads (OneWay Restraint)
Linear Restraint Response Constant Throughout Load Range
Figure 3-11 The stiffness algorithm cannot solve for non-linear restraint conditions, such as one-directional restraints, bi-linear restraints (soil or bottomed out springs), friction, etc. However, CAESAR II does include a procedure which overcomes this limitation; see point 8 below. These limitations are of the most concern when modeling the following situations (pointers for increasing accuracy in each situation are also given): Large Diameter/thin wallpipingorducts: In thiscase,itisadvisabletominimize localized loadings by distributing them with pads or saddles, or do plate buckling analysis (preferably with finite element software) when the loads cannot be altered.
1
2
-
3
4
Localized stress conditions not explicitly covered by an SIF, i.e. a saddle: The portion of the pipe impacted by the saddle may be modeled as a rigid element, while saddle/piping local stresses may be estimated through the use of finite element analysis or through the use ofWelding Research Council Bulletins, such as 107 and 198. Pipe connections to thin walled vessels: The flexibility of the connection may be modeled by a flexible element (such as that generated using Welding Research Council Bulletin 297), while stresses in the pipe and vessel may be estimated through the use offinite element analysis orthrough the use ofWel ding Research Council Bulletins 107 and 297.
-
Highly corrosive systems (especially when subjected to cyclic loadings): Corrosion of a pipe results in an irregular cross-section which is usually modeled by using the uncorroded cross-section for load generation (weight and thermal forces), and the fully corroded cross- section for calculation ofthe section modul us
3-7
COADE Pipe Stress Analysis Seminar Notes
(stress calculation). Corrosion is much more dangerous under fatigue loadings due to the fact that it provides many more opportunities for crack initiation; in order to compensate, a low cyclic reduction factor should be used to match the allowable expansion stress range to the fatigue curve for a highly corroded material. 5
Elbows: Elbows ovalize significantly when subjected to bending loads. This can be accounted for by increasing the flexibility ofthe elbow element in the computer model and multiplying the calculated stress by a stress intensification factor (this is done automatically by most programs such as CAESAR II). Code defined "flexibility factors" for bends have been determined theoretically and verified experimentally.
t--_~dline
= "\
Flange .A" 1
r - rnean raJ
~
p:l
th: r
(From BS 806-1975)
~tion
cross
Figure 3-12 The flexibility and stress intensification factors of bends must be reviewed in those cases where ovalization is inhibited (such as when the elbow is stiffened by flanges or welded attachments). The piping codes provide correction factors for bends with one or two flanges, but omit geometries such as shown in Figure 3-13.
(A)
(8)
(C)
Figure 3-13 These attachments almost certainly affect the flexibility, and more importantly, the stress intensification factors for the bends. The factors for heavily stiffened bends, such as that shown in Figure 3-13(A), could he estimated using finite element analysis, or stiffness could he increased by modeling the elbows as
3-8
COADE Pipe Stress Analysis Seminar Notes
flanged, or simply as straight pieces ofpipe (with increased stress intensification factors applied). In less pronounced cases such as those shown in Figures 3-13 (B) and (C), deviations from the response of an unstiffened bend is usually ignored. 6
-
Loadings which produce stresses which are weIl outside of the code allowable ranges: These loads will tend to produce stresses weIl beyond the material yield stress, stresses in the buckling range, large dis placements resulting in significant P-delta loads, or large rotations Oeading to inaccurate results). This limits programs such as CAESAR II as accurate analysis tools throughout the full range of potential loadings. However accuracy is not affected for those loads which are ofmost interest to the engineer- code allowables are based upon the fact that the analysis being done assumes linear material response.
7
-
Non-linear boundary conditions: The effects of non-linear restraints must be simulated through an iterative process aimed at convergence of the non-linear restraints inlegitimate states-forexample, with the pipe liftedoffataone-way support (and with the support function removed from the analysis), or with the pipe sliding along a frictional restraint (and with an appropriate force applied along that line of action in the analysis). This process is activated (during static analysis) automatically when a non-linear effect is detected by CAESAR II.
8
Non-homogenous elements: As noted, piping elements are modeled as stick elements ofconstant cross-section and material properties. In certain cases, such as with reducers, which have a variable cross-section, this is not a valid representation. An element such as this is usually modeled as a single, or as a series of elements, each having average parameters. For example, a l2x8 standard wall reducer may be modeled as a 10-inch standard wall pipe Capproximately the average of the inlet and outlet pipes), or as two segments, with outer diameters and wall thicknesses interpolated hetween the two. When using those codes which define a stress intensification factor for reducers, one would have to he calculated and specifically applied at that location.
9
Rigid elements: Rigid elements, such as valves and flanges are most difficult to model due to the inability to represent their geometry, and their stress distribution with stick elements. Therefore, pipe stress software cannot be used to accurately determine the effects ofthe piping system on rigid elements. Analysis of these components is best left to fmite element analysis, test, or other recognized methods. However, the effects of the rigid elements on the piping system can he simulated by providing an element ofhigh relative stiffness in the model (it is always more important to adequately model relative stiffnesses than absolute stiffnesses when constructing a model). This is done by providing an element with sufficiently large cross-section, and having the defined weight of the rigid item. In CAESAR II, a rigid element is modeled as having: a) aninsulationfactorof1.75Ccompared tothematchingpipe), unless a zero weight rigid Ca modeling construct) b) fluid weight of the matching pipe added, unless a zero weight rigid c) the same inside diameter and 10 times the wall thickness ofthe matching pipe 3-9
COADE Pipe Stress Analysis Seminar Notes
3.2 Piping Configuration Modeling Techniques Piping may he modeled in varying detail, depending upon how much accuracy is required. This section looks at the various ways (providing corresponding degrees ofaccuracy) in which sample piping configurations might he modeled. Consider the following geometry, of a large diameter pipe supported hy a dual spring assemhly:
1
\
t
J 1\
Vl L
_
50" diameter
1/2" wall -.J ____ _ 4· trunnion support shown. (Typ. both sides)
V
Figure 3·14
Simplest Method:
50" diameter pipe Flexible Restraint K at centerline K =2 Kspring
Figure 3·15 Limitations: 1
-
local stress calculations not considered for 50" pipe
2
-
stiffness of trunnions not considered
3
-
torsional resistance due to the restraint pair is not considered (see Figure 3-16)
4
-
local flexihility of the shell of the 50" pipe is not considered
3-10
COADE Pipe Stress Analysis Seminar Notes
Figure3-1G More Accurate:
L
Rigid element - zero weight Kspring
Kspring
Figure 3-17 Limitations: 1
local stress calculations not considered for 50" pipe
2
stiffness of trunnions not considered
4
local flexibility of the shell of the 50" pipe is not considered
Most Accurate:
Ksheillocal (WRC 297)
Kshell local (WRC 297)
\
~-------il,...------____
\
/
Pipe element
/ 'modeling trunion Kspring
Rigid element - zero weight Length = 1/2 00
Figure 3-18
3-11
COADE Pipe Stress Analysis Seminar Notes
Limitations: 1
local flexibilities and stresses only as close as WRC 297 and WRC 107 bulletins (see discussion in this Section 3.4 of these seminar notes)
Looking at another configuration, a he avy-wall forged WYE fitting:
Figure 3-19
Simplest Model:
~
Incoming pipe with branch properties coded to intersection
~point. Apply SIF's forwelding tee here. Incoming pipe with header~ properties coded to ~ intersection point.
Figure 3-20 Limitations: 1
weight offorged fitting probably underestimated considerably
2
rigidity of forged fitting probably underestimated considerably
3
stress intensification factors may be too conservative
3-12
COADE Pipe Stress Analysis Seminar Notes
More Accurate:
Rigid elements whose cumulative weights equal that ot the torged titting and tlanges.
Figure 3-21
Limitations: 1
no provision for stress calculations in forging, but this isn't usually a problem, because ofthe extra heavy wall of the fitting would ensure that the connecting pipe would probably fail first. Any questions regarding load capacity should probably be directed to the fitting manufacturer
Most Accurate:
Rigid element modeling tlange.
Figure 3-22
3-13
COADE Pipe Stress Analysis Seminar Notes
Comments: 1 2 3
the flexibility ofthis model will he more accurate (but only marginally so for a heavy fitting) -
stresses (unintensified) will be computed at the crotch; however, there will be sorne unknown intensification factor existing at the crotch this model probably does not yield any significant im provement overthe previous one
One of the most common types ofpipe support is shown in Figure 3-23:
6" dia. std. wall stanchion
Figure 3-23
Simplest Model:
·V" direction restraint applied at the bend point shown.
Figure 3-24
3-14
COADE Pipe Stress Analysis Seminar Notes
Limitations: 1
flexibility of the stanchion is not included in the model
2
-
the point of application of the stanchion is not at the correct location on the bend curvature
3
-
pipe may lift off of (or lock up with) modeled support due to thermal expansion between centerline of horizontal run and point of application on riser
4
-
stiffening effect on bend of stanchion not considered
5
-
local stresses at stanchion not considered
More Accurate:
~ Pipe between
·C·
t
nodes Cand D with properties of stanchion
Figure 3-25
Limitations: 1
stanchion doesn't act at the proper point on the bend curvature
2
-
stiffening effect on bend of stanchion not considered
3
-
local stresses at stanchion not considered
3-15
COADE Pipe Stress Analysis Seminar Notes
Most Accurate:
41.4 deg. For Long Radius Bend 48.2 deg. For Short Radius Bend
R(1 - cosa )--....-4
L LL U1' -SiOO}
el
1
Use WRC107 To Calculate Local Stresses
Aa
1
1
Ct
:'-------
1
Pipe Element Between Points "B" and ·C". Restraint at Stanchion Node "C"
Figure 3-26 Limitations: 1
points A and B aren't exactly at the same location (this can be resolved using CAESAR n's "OFFSETS" feature, but other pipe stress software may have a difficult time with this)
2
-
modeling the stiffening effect of the stanchion on the bend through the use of a single flange bend is an approximate solution
3
-
local stresses at the stanchion are only as accurate as WRC 107 bulletin
A few configurations which illustrate solutions to potentially tricky modeling situations follow below: The distance L in Figure 3-27 may become important if the gap on the guide closes and there is a horizontal restraint force which will cause a torsional moment to exist in both members.
3-16
COADE Pipe Stress Analysis Seminar Notes
Centerline of the pipe "stick" model
L Centerline of the structural 'stick" model
Figure 3-27 Because the elbow in Figure 3-28 connects directly to the equipment flange and the equipment flange is anchored, the stiffness ofthe model in this local region is very high. If the stanchion connects at A and the equipment centerline is at B, the differential thermal growth of the elbow between those points could put enormously high loads on both the stanchion and the equipment model. This is also in reality, a difficult problem to design for. Unless the user is willing to put a spring at the stanchion location, the differential thermal growth in this small area might result in large nozzle loads.
A Rotating Equipment Centerline
B
Figure 3-28 In the Figure 3-29, a small, but heavy process monitor and actuator is mounted on the line. The rigidity, weight, and moment due to the offset is best modeled using a weightless rigid element going from the centerline of the pipe out to the center of gravity of the process monitor, at which point a small rigid element with the weight ofthe equipment should be modeled. The rigidity ofthe body of the monitor (within the pipeline) should be modeled as
3-17
COADE Pipe Stress Analysis Seminar Notes
a rigid as weIl. (Note that some engineers may prefer to model the effects ofthis equipment by applying a force equal to the weight and a moment equal to the weight times offset at the centerline ofthe pipe. This approach, although acceptable for static analysis, is absolutely incorrect for dynamic analysis, and should therefore be avoided since it cannot be promised that no dynamic analysis will he conducted on a system in the future.)
ç Pump Figure 3-29 In Figure 3-30, the large 18 inch line comes directly from a flue-gas furnace, passes through a small exchanger and enters a waste heat boiler. This is a very stiffsystem relative to the vessel connections. Therefore, instead ofmodeling the connections as rigid anchors (which would give the same relative stiffness to the restraints and to the piping), WRC Bulletin 297 should he used to estimate and model the nozzle flexibilities. This method will provide the best approximation of the distribution of the piping loads to the vessels.
Soiler
--~~--~--~~
~ ~umace
Soiler and fumace nozzle flexibilities? (This is a very tight. stiff system)
Figure 3-30
3-18
COADE Pipe Stress Analysis Seminar Notes
In Figure 3-31, rectangular ducting connects the two separators, which are rigid relative to the ductwork. In order to size each spring for i ts share ofthe distributed weight ofthe whole assembly plus the connected piping, it is best to simulate the stiffness of the duct through the use of an equivalent structural member or piping element.
User defined cross section in structural
Separator
~{!Sprin9
stee'
Pi'"' ' ' '
"Ri9idElem7 ! Separators modeled as pipe
Location
Figure 3-31 An angle valve could be modeled as shown in Figure 3-32. It may be necessary to model it as three rigid elements if the weigh t of the operator is significant in com parison to the valve body.
Figure 3-32 The following sections of these seminar notes provide more detailed methods for modeling and analyzing specifie components of the piping model.
3-19
COADE Pipe Stress Analysis Seminar Notes
3.3 Expansion Joint Modeling And Evaluation Expansion joints are used when it is necessary to provide a large amount offlexibility in a small space. Expansion joints are constructed out of sheet metal, which, after rolling and welding to for a cylinder, has convolutions (also called corrugations) formed in it via either hydraulic pressure or rolling. Expansion joints may vary in terms of the number and type of convolutions, the material, the number of plies, all ofwhich effect the pressure capacity, the stiffness, and the allowable movement.
Figure 3-33 For the most part, these details are taken care ofby the expansion joint manufacturer. A typical expansion joint piping design proceeds: The decision is made to use an expansion joint in the piping system. (In many design problems the joint is used to protect a sensitive piece of equipment from excessive nozzle loads.)
1
2
-
Based upon the design temperature and pressure, a standard expansion joint is selected from a manufacturer's catalog. The properties ofthat bellows are then inserted into the piping model.
3
-
Ifthe bellows reduces loads and stresses as intended then the range ofexpansion
movements on the bellows must be checked. For each bellows there is a limit to the cumulative axial, bending and lateral displacement that can be absorbed by the joint without excessively deforming the convolutions or causing fatigue failure. These limits are presented in different ways in different manufacturer' s catalogs, but are always functions of the number of applied cycles, bellows material properties and convolution shape. Where excessive displacement is a problem, increasing the number of convolutions can be the solution. 4
-
Once the bellows movement is within the allowable range of movements, the design is completed. A competent expansion joint manufacturer should be able to provide assistance throughout the design stage as required.
3.3.1 Expansion Joint Stiffnesses Each particular combination of material, thickness, and convolution geometry has a different axial spring rate (per convolution) associated with it. Bending and lateral convolution spring rates can be computed from the axial spring rate.
3-20
COADE Pipe Stress Analysis Seminar Notes
The behavior of a bellows under load is described by the following equations:
Where: F
=
axial force in each convolution (also the axial force throughout the entire bellows), lb
f
=
axial stiffness per convolution, lb/in
= NKax N
=
number of convolutions in the joint
Kax
=
total expansion joint axial stiffness, ib/in
ex
=
axial displacement per convolution, in
=
X/N
=
total axial dis placement of joint, in
Mr
=
bending moment in each convolution (also the bending moment supported by the entire bellows), in-lb
D
=
is the effective diameter of the joint (equal to the inside diameter plus the height of one convolution), in
er
=
axial displacement per convolution resulting from a rotation of the convolu tion,in
=
(rxD)/(2N)
r
=
bending rotation of single convolution, radians
v
= fD
x
Where:
ey /
(2 1)
Where:
v
=
shear force in each convolution (also the shear force supported by the entire bellows), lb
3-21
COADE Pipe Stress Analysis Seminar Notes
=
axial displacement per convolution resulting from a lateral deflection of the convolution.
=
3Dy/(NI)
y
=
totallateral displacement of the joint, in
1
=
length of the bellows, in
ey
These expressions can easily be converted into stiffness and flexibility coefficients:
=
F/x
Bending Flexibility: MIr
=
(1/8) (Kax) (D2)
Lateral Stiffness:
=
(3/2) (D2) (Kax) / (12)
Axial Stiffness:
Kax
V/y
These stiffness values are provided in most manufacturer's catalogs. In the event that the manufacturer only gives axial stiffness, the other two can be calculated once the effective diameter and length are known. (Note that torsional stiffnesses are not usually provided, since unprotected expansion joints are not designed to carry torsionalloads and may fail catastrophically if inadvertently exposed to even moderate torsional moments.)
Note however that the bending flexibility coefficient should not he used in any piping program. The bending stiffness that should be used is exactly four times the hending flexibility. This is because the so-called bending flexibility is calculated by applying a moment (M r ) to the free end of an expansion joint and observing its end rotation (9). A computer model, however, expects a bending stiffness to be the ratio of the applied moment to the angular rotation at the end of an expansion joint that is fixed against translation - i.e., a representation of guided cantilever. This angular stiffness for a guided cantilever expansion joint model is calculated as:
Mrfr
=
(Kax) (D2) /2
FLEXIBILITY
STIFFNESS
Figure 3-34 Some pipe stress programs only offer "point", or zero-Iength expansion joint models. (In CAESAR II the user can define "fmite length" or ''point'' expansion joints.) There is a difference in terms of how the two models are entered. As seen above, for finite length expansion joints, the lateral and bending stiffnesses are related by the equation:
3-22
COADE Pipe Stress Analysis Seminar Notes
Bending Stiffness
=
M!r = Kax x D2/2
=V/y x 12/3
=
Lateral Stiffness x 12/3
Because ofthis exact relation, and since the length is known, the user can only enter one of these two values. CAESAR II computes the other value using this equation. For a "point" expansion joint, the length is unknown, so aIl three stiffnesses must be definedfor the model.
Example: Consider an expansion joint with the following parameters: Nominal diameter = 4 in Effective Area = 19.6 in2 Kax (from manufacturer) = 316 lb/in
Bellows Length = 4.447 in The expansion joint stiffnesses are calculated as: M!r
=
(1/8) (Kax) (D2)
D
=
[4 x 19.6/ pi
M!r
=
(1/8) (4.9955 2 ) (316) = 985.7 in-lb/rad = 17.2 in-Ib/deg.
]1/2
= 4.9955 in
The bending stiffness to use in a piping program would be: 4 x M!r V/y
=
4 x 17.2 = 68.8 in-Ib/deg
=
(3/2) (D2) (Kax) / (12)
=
(3/2) (4.9955 2 ) (316) / (4.447 2 ) = 598.14 lb/in
3.3.2 Evaluation of Expansion Joint Allowable Movements Since the failure mode of expansion joints is fatigue, the relative expansion displacements hetween the start and end ofthe expansionjoint must be checked against the manufacturer's allowables. Note that the allowables provided will not be absolute values, but will he based upon a specifie number of cyclic applications. The manufacturer must always provide a fatigue curve or some other type of adjustment factor in order to determine the allowable displacement for a different number of cycles. Occasionally, the manufacturer provides allowable movements only for axial displacements. In this case, the equations given in Section 3.3.1 can be used to calculate an equivalent axial displacement from lateral and rotational displacements: Er
=
R D / 2 , or:
Er
=
0.00872665
eD
3-23
COADE Pipe Stress Analysis Seminar Notes
=
3DY/l
Er
=
total equivalent axial displacement due to rotation, in
R
=
total rotation on expansion joint, radians
D
=
effective diameter of expansion joint, in
e
=
total rotation on expansion joint, degrees
Ey
=
total equivalent axial displacement due to lateral displacement, in
y
=
totallateral displacement on expansion joint, in
1
=
length of expansion joint, in
Ey Where:
Therefore, movements on an expansion joint are acceptable if:
x + Er + Ey