., ' " J Cl .a SECTION 1 Q ' .c c C) 0 \ ~ 0 ~ 9 ' ') C) 0 0 .u () 0 Q 0 Q () 1.0 1.1 1.2 1.3 1.4 1.5 COADE Pipe Stress Analysis Seminar Notes Section 1 Table of Contents Introduction to Pipe Stress Analysis........................................................................ I Theory and Development of Pipe Stress Requirements ........................................... 8 1.1.1Basic Stress Concepts ............................................................................... 814 1.1.23-D State of Stress in the Pipe Wall ....................................................... 14-15 1.1.3Failure Theories ........................................................................................... 16 1.1.4Maximum Stress Intensity Criterion ..................................................... 1819 Fatigue Failure....................................................................................................... 20 1.2.1Fatigue Basics .............................................................................................. 20 1.2.2Fatigue Curves ............................................................................................. 22 1.2.3Effect of Fatigue on Piping ..................................................................... 2425 1.2.4Cyclic Reduction Factor ............................................................................... 25 1.2.5Effect of Sw;tained Loadson Fatigue Strength .......................................... 26 Stress Intensification Factors ............................................................................Welding Research Council Bulletin 330................................................................. 34 CodeCompliance ..................................................................................................... 43 1.5.1Primary vs.Secondary Loads ................................................................. 43-45 1.5.2Code Stress Equations ......................-...................................................... 4546 1.5.3B31.1 Power Piping ..................................................................................... 46 1.5.4B31.3 Chemical Plant and Petroleum Refinery Piping .............................. 4 7 1.5.5ASME Section III, Subsections NC&ND (Nuclear Class 2 &3) ......... .49-50 1.5.6B31.4 Fuel Gas Piping ................................................................................. 51 1.5. 7B31.8 Gas Transmission and Distribution Piping Code ............................. 52 1.5.8 .Canadian Z183/Z184 OiVGas Pipeline Systems ......................................... 54 1.5.9RCC-M C ...................................................................................................... 55 1.5.10Stoomwezen ................................................................................................. 56 1.5.11Special Considerations of CodeCompliance ........................................... 56-59 ' 1.5.12Evaluation of Multiple Expansion Range Cases ......................................... p9

s, Figure 16 internal axial forceacting on section, lb metal area of pipe, in2 Jt(do2.di2J I 4 1t dm t outer diameter, in inner diameter, in mean diameter,= (d0 + dil I 2 18 Cll 0 o . " 0 Cl ,

0 "' C>. " ' Q 0 0 0 Q 0 0 () 0 .__) ; 0 (,) 0 0 () COADE Pipe Stress Analysis Seminar Notes A specific instance oflongitudinal stress is that due to internal pressure: Figure 1-7 SL = PA;!Am Where: p = design pressure, psig A; = intemal area of pipe, in2 = 1tdi2 I 4 / Replacing the terms for the internal and metal areas of the pipe, the previous equation may be written as: SL=Pd;2/ (d02- d;2),or: For convenience, the longitudinal pressure stress is often conservatively approximated as: 81=Pd0/4t Another component of axial normal stress is bending stress.Bending stress is zero at the neutralaxisof the pipeandvarieslinearlyacrossthefromthemaximum compressive outer fiber to the maximum tensile outer fiber.Calculating the stress as linearly proportional to the distance fromthe neutral axis: VariationinBendingStressThru CrossSection Maxcompressivestress 1/2maxcompressivestress NeutralAxis f----:..:::C:.:.c.:c---'-==---or Ze robe n d i n gs t re s s 1/2maxtensionstress L ____.L"::::::::iMaxtensionstress Figure 1-8 1-9 COADE Pipe Stress,l\.nalysis Seminar Notes Where: .Mb=bending moment acting on cross-section, in-lb c =distance of point of interest from neutral axis of cross-section, in I=moment of inertia of cross-section, in4 =rr (d,4- d;4) I 64 Maximum bending stress occurs where cis greatest- where it is equal to the outer radius: Smax= Where: R0 =outer radius of pipe, in Z=section modulus of pipe, in3 =I I R0 Summing all components of longitudinal normal stress: SL=Fax1Am+Pd,/4t+Mb/Z Hoop stress:There are other normal stresses present in the pipe,applied in directions orthogonal to the axial direction.One ofthese stresses, caused by internal pressure, is called hOopstress.This stress acts in adirection parallel to the pipe circumference. SH = ~ . pNI SH = ~ Figure 1-9 The magnitude of the hoopstress variesthrough thepipewall and can becalculated by Lame's equation as: SH=P(ri2 + ri2 r02 I r2) I (r02 ~rf2) 1-10 1.0 0.8(RIT)2i3(r/R), with i, > 2.1 intensification factor for branch (to be linearly interpolated for r/R ratios between 0.9and 1.0) mean radius of header pipe, in thickness of header pipe, in mean radius of branch pipe, in outer radius of branch pipe, in thickness of branch pipe, in intensification factor for run (header) pipe Additionally, if a radius of curvature r2 is provided at the connection, which is not less than the larger oft/2, (Tb'+Yl/2, or T/2, then the calculated values ofib andi, 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 be checked using Z = p (r2)t and i(t!T) in place ofi, with i(t/T) > 1.0. 1-35 COADEPipe Stress Analysis Seminar Notes 11) 12) ,, TherewasnotsufficientdataavaliableonreinforcedfabricatedteesforRodabaugh tomakeanydefmitivereco=endationsregardingthem.Rodabaughdoes however suggest that tbe normal usage whereby tbe width of the pad is taken to be at least equal tothe radii>Sof the nozzle should be observed even tbough not explicitly directed by the code. For tiT ratios ofaboUtOne or more, stresses tend to be higher in the header, and are fairly independent of the wall thickness of the nozzle.As the tiT ratio gets much smaller than one,the largest stresses shift tothe branch.(This fmding originally came out of the research for WRC297.) ofWRC330's proposalsforstress intensification factors for various types of tees, ;versUsB31.3 calculated values are shown on the following pages. 136 15 (") , " e 0 '.) - . d o G 0 0 " @ 0 @ 0 0 D o 0 0 " Q Q COADE Pipe Stress Analysis Seminar Notes lJQ INTERSECTIONRADIUS "831.3"VS. "WAC 330" UNREIN FORCED, FABRICATED TEE STRESS INTENSIFICATION FACTORCOMPARISON HEADER NOM ... 34e. ,. 41!. ''41!. ... 541!. 41!. 5u. 41!, 548. 6411. 48. 641!. 48. 641!. 8-41!. 8.fll. B.41!. g 841!. 10n. lBU. IB48. u41!. !I!41!. 12e. l240. 1246. 1249. 1740, J 48. !448. 1'4@, H48. 1448. BfiANCH SCH WRC 330b 2.U3 -831.3- i iblob 2.874 140. 240 . 5.598 4.H?5.5'1!1 4.5. 598 4.H'15.591! 330h 1.667 L:m 1.123 1.1122 '1194 - 1.581 1.263 J. H11 l,

4.DU5.8ll!: .. I.H-3 4.68\1.277 4.6al5.9311.!17 4.68l5.831,993 4.6\H5.!l8!4. 717 4. 797 4. 797 4. 7117 5.141 5.148 5. 67B 5.679 S.67t1 5.i19'1 5.999 5.:199 s. 798 5.1Sa 5'.7SS 6.481 6.41B '"' ' 418 6.481 S.'H3 5.1143 S.'H3 5. 943 L:m I. 191 J,lm .891 6.szaiLm 6.521i.887 7. 227: 7.227 7.2Z7; ' 7.532t 7.532I 7.532: 7.384j i .384 7.384 7.)8-4 S.2Bi 9.2111 8.2118l S.2tal 8.281t !. 186 945 .883 .nr .sat 1.8.;3 .993 ,33 ,1.231! 1.157 1.187 t.r.s .878 ioh 330h 2. !08 1.67t J.H3 !. 286 1.989 l.SS9 !.4H I. 206 1.769 1.6!11 !.4!9 I. 252 L !25 "!.&9:!. [. 504 I. 125 1.411 I. 511 1.284 1.125 1.281_ l. 197 I. 125 i..-!56 1.260 1.198 1.125 1.587 1.462 1.393 !.316 1.125 i o 0 9 0 o r] .!!I (} 0 0 0 'z " 9.8 " 12.& l;:z

> "" gg JO " 10.1..13.4 m .NOTE:(I) FOR SPACING SUPPORTS INCORPORATING TYPE40 SHIELDS, SEE TABLES. {2)DOES NOTAPPLYWHERESfANCALCULATIONS ARE MADE OR WHEIU!TitRE ARECONCEm'RATEO LOADSBETWEENSlli'I'OkTS SOCII ASFLANGES,VALVES, SPECIALTIES, ETC., OR CHANGES IN DIRECTION REQUIRINGADDITIONAL SUPf'ORTS. 3: l:l ., ---------------------.., e "d 1-d' ro [ r; 'j .. m r z COADE Pipe Stress Analysis Semmar Notes 3- The standard span doesn't apply on risers, since no moment (and thus no stress) developsregardlessof 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 oflongrisers 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 be illustrated with an exanlple.In Figure 2-11, the system consists of a 12" diameter, standard schedule steel pipe fille'd with water, with a design pressure of 150 psi, and a design temperature of35QOF, which runs between two equipment nozzles. The engineerflrstmust determine the standard span for the system.For 12" diameter, water filled pipe, the standard span is shown in MSS SP-69 to be 23 feet.For changes of direction, 3/4 of this span is 17 feet-4 inches. Next, the engineer locates supports.The first concern isto locate them near concentrated loads- supports should be located as close as possible to the two valves (for example, near node points 20 and 70).The first of these is optional, depending on whether the nozzle at node point 10 is assumed toact as an anchor,and whether it isdesirable 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 buildingsteeldictatesthat theweight of theriser be split between twosupports.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 feet-4 inches. The next run of pipe accommodates a full23 foot run, so two supports can be located between node points 30 and 40.The line of action of the supports on the riser provide support to the end of the horizontal30-40 run, so noadditional support is required at node point 40. Support locations can be continued to be selected in this manner until all locations meet the selection criteria; one solution is shown in the Figure 2-12. Oncecompleted,whatdoesthisaccomplish?Byusingthestandard 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 of the stress equation: Ssus=PA/Am + 1500 = 150(113.1)/14.58 + 1500 =2664 psi< 20,000psi 2-16 0' .. c o -. 0 0 It 0 Ill C\ ~ q. 0 Ill 0 0 QCOADE Pipe Stress Analysis Seminar Notes 0 0 0 0 0 j)

0 0 0 0 (l) Now it is necessary to compute the relative displacements between the ends ofthe expansion joint. This is often nota simple task since the rotations oftheex:pansionjointends can cause lateral translations which don't produce axial deformation of the joint.In the event that displacements and rotations are small, and the expansion joint runs along a global axis, the relative displacements of the expansion joint can be fairly closely approximated: X e y =(DX1-DX2) =0.3- (-0.1) = 0.4 in =[(RY 1-RYz)2+(RZ1-RZ2)2]112=[(1.23-(-0.02))2+(0.03-Q.89)2]112= 1.52' =[(DY1-DY2)2+(DZ1-DZ2)2JII2= [(0.25-0.12)2+(0.0-0.0)2]112 =0.13 in Using the interaction formula,the range of expansion movementsis checked as: X+ 0.00872665 De +3 D Y /1 1.5&=19/j>Z.S&=ZB/j>4,B&=513/j>G.Z&=>1138 URC297NOZZLECALCULATIONS URCNOZZLENODE=5 UESSELDMean= NOZZLEO.D.Cin.>= 47.751:1 18.000 UESSELTHK.= NOZZLETHK.(in,)= .250 .zse AXIALTRANSLATIONALSTIFFNESSCOADE Pipe Stress Analysis Seminar Notes 0 - 0 c 0 0 ') 0 0 0 Iii 0 . 3- Contributory area should be calculated for each nodeas: 'Where: A = contributory area, in2 L; = length of the pipe "i", in D; = outsidediameter of pipe "i",in n = number of pipes framing into the node For example, the contributory area for node 20 of the 12" nominal diameter pipe shown in Figure 3-119 is calculated as: A = 1/2(10X12 X12.75+30 X12 X12.75) = 31J!l0in2 10 -,-l10-030.-0 25 Figure 3119 4- Thesubgrademodulusof elasticityforthetypeof soilisthendetermined, preferably from actual soil tests.In lieu ofbetter information, the following data (taken from Joseph E. Bowles, "Foundation Analysis and Design", 3rd Edition, 1982) is available: SoiltypeSubgrademodulus(kips/ft3) 1 oosesand mediumdensesand densesand clayanddensesand siltyanddensesand clayqu< 4ksf clayqu< 800ksf clayqu> !600ksf 30100 60500 400-800 200500 250700 75-150 150-300 >300 ~ - 1 2 7 .. COADE Pipe Stress Analysis Seminar Notes (where qu is the unconfined compressive strength of the soil) If otherwise not known, the subgrade modulus, e, can be calculated from k=eD= 33.336 x rCH+ D)2tan2(45+~/2), or: e=(33.336 ID)x r(H +D) tan2(45+ ~12) 5The effective soil restraint stiffness for each node is calculated by multiplying the contributory area for each node times the soil subgrade modulus. 6~Lateralrestraints(andpossiblyrotationalrestraintsrepresentingrestraint forcecouples)with thecalculated stiffriesses should then be inserted intothe piping model at the appropriate nodes. 7Next the density of the pipe should be set to zero, since the weight of buried pipe is uniformly supported along its length. Weight loads in buried pipe do not cause deflections, stresses, or forces in the pipe.(Note that this step should be skipped when doing dynamic analysis of underground pipe, since the mass distribution is important in the dynamic analysis.) 8- Any axial stops in the form oflarge flanges or concrete anchors, designed to resist the thermal expansion of buried pipe, should then be coded into the model.If these arepresent,it isrecommended that therestraint stiffnesses calculated abovebereducedbyapproximately25%in ordertoyieldmoreconservative anchor loads. 3.6.3.2AutomatedUndergroundPipingModeler CAESAR II providesan automatic undergroundpipemodeler,- accessedfromthe main ~ e n u ,which markedly simplifies this modeling process. The undergrourid modeler provides two services to the user: 1- If soil properties are not known, or if a good mathematical model ofthe soil is not available,CAESAR IIprovidesadefaultsoilmodelthatmaybeusedto approxinl.ate "typical" soil support characteristics. 2Given soil support stiffnesses either from user input or from the default model, CAESAR ll distributes the buried restraint stiffo.esses over the buried part of the pipingsystem.This isprobably the most useful part of theburied pipe modeler.Properly breakingdownthemodelintoafinerelement meshand distributing restraints over the piping system is a very time consuming task to doaccurately by hand, which the buried pipe modeler can doin seconds.The distributionof restraintstiffnessesoverlateralbearinglengths,transition lengths, and over axial bearing lengths is described in detail in the CAESAR ll user's manual. Seldom are soil properties known very accurately.Often there is absolutely no quantitative data available on the soil at the site.In these situations, the default soil model will probably provide as good an estimate of the actual soil properties as any.This model is based on-a 3128 0 Gl o . - e