COADE Pipe Stress Analysis Seminar Notes

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PIPE STRESS ANAL YSIS

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.

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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 of design and engineer-ing standards for pipengineer-ing systems. The B31 pressure pipengineer-ing 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 of the hands of the highly-paid 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 official-looking 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:

1 In order to keep stresses in the pipe and fittings within code allowable levels.

2 - In order to keep nozzle loadings on attached equipment within allowables of

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3 In order to keep vessel stresses at piping connections within ASME Section VIII allowable levels.

4 - In order to calculate design loads for sizing supports and restraints.

5 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:

1 define geometry (system start, end, direction changes, intersection, etc.)

2 - note changes in operating conditions (system start, isolation or pressure

reduc-tion valves, etc.)

3 define element stiffness parameters (changes in pipe cross section or material,

rigid elements, or expansion joints)

4 - designate boundary conditions (restraints and imposed displacements)

5 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,

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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

Haterial A186 Gr.B tUI

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

tower-:'~[

,~~.y

..

SUpport ...

rD_

'i

A

~3S

~

..

COl!lputed therl!lal expansion of the vessel is

~145

17.268E-6 in/in/deg.F. at a telllp of 828 deg.F.

j;

Exchanger

Node 188 is 28.88 ft. above vessel skirt 0

Disp. @ 188 = (828-7B)deg.F(17.268E-6)in/in/deg* (28.88)(12)ft.in/rt. = 3.121 in.

Z X D isp. D 128 = (B28-78) (17.268E-6)(28.88+6.5-15)(12)

= 1.8 in.

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~

t.:.:I ANSI/ASME 831.3-1984 ROmON ASME CODJ! FOI. PIUlSSUIUI PlPINO ASMJ! COD! fOI. 'IU!SSUIUI'IPINO A

." TABLEA·I CHEMICAL PLANT AND PBTROLBUM Rl!FlNBIlY 'IPINO CIIEMICAL PLANT AND PBfR.OLEUM lEFINI!IlY.IPINO

...

'"0

00 TABLE A-1 (CONT'OI TAlLE A-1 (CONT'O) (!)

BASIC ALLOWABLE STRESSES IN TENSION FOR METALS lU BASIC ALLOWABLE mESSES DI TENSION FOR METAl UJ.

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CAESAR II VERS 3.18 JOBNAME:SSEM1 PIPE DATA

From 100 To 105 DY= 3.500 ft. PIPE

DEC 10, 1992 3:05 am

Dia= 20.000 in. Wall= .375 in. Insul= 2.000 in. GENERAL

T1= 700 F P1= 125.0000 lb./sq.in. Mat= (l)LOW CARBON STEEL E= 27,900,000 lb./sq.in. v = .292 Density= .2899 lb./eu.in. RIGID Weight= 3,290.00 lb.

DISPLACEMENTS

Page 1

Node 100 DX= .000 in. DY= 3.121 in. DZ= .000 in. RX= .000 RY= .000 RZ= .000

ALLOWABLE STRESSES

B31.3 (1990) Se= 20,000 lb./sq.in. Sh1= 16,500 lb./sq.in. From 105 To 110 DY= 3.000 ft.

BEND at "TO" end

Radius= 30.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 109 Angle/Node @2= .00 108

From 110 To 115 DX= 12.000 ft. BEND at "TO" end

From 115 To 120 DY= -15.000 ft. DISPLACEMENTS

Node 120 DX= FREE DY= 1.800 in. DZ= FREE RX= FREE RY= FREE RZ= FREE

From 120 To 125 DY= -3.000 ft. BEND at "TO" end

Radius= 30.000 in. (LONG) Bend Angle= 90.000 Angle/Node @1= 45.00 124 Angle/Node @2= .00 123 From 125 To 130 DX= 35.000 ft. RESTRAINTS Node 130 +Y From 130 To 135 DX= 35.000 ft. RESTRAINTS Node 135 +Y From 135 To 140 DX= 35.000 ft. RESTRAINTS Node 140 +Y From 140 To 145 DX= 20.000 ft. BEND at "TO" end

From 145 To 150 DY= -12.000 ft. RESTRAINTS

Node 150 ANC

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CASE 3 (EXP)D3=D1-D2 FILE:SSEI11 DEC 4.1992 12:4?am

"~'"

~"

1'I0DE= 123 OUERSTRESSED l'IODES ~,

Figure 1-4

CASE 1 (OPEJW+DIS+T1+P1 F1LE:SSEnl DEC 4.1992 12:49am

ItODE= 125 I1AX. DISPS. X

Figure 1-5 QUIT nODES OURSTR I1AXSTR BHDlltG TORS AXIAL STRESS S'inBOL BI'IDUIG TORS AXIAL STRESS COLOR BI'IDItIG TORS AXIAL STRESS RESET QUIT l'IODES DEFU SPECFY I1AGnIF GROW COLORS ORIGI'IL BLArtK Iml:'I}" HRDCP'i

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What are these Stresses?

The stresses calculated are not necessarily real stresses (such as could be measured by a strain gauge, for example), but are rather "code" stresses. Code stress calculations are based upon specific equations, which are the result of8 decades of compromise and simplification. The calculations reflect:

1 Inclusion or exclusion ofpiping loads, based upon convenience of calculation or

selected failure. In fact the result may not even represent an absolute stress value, but rather a RANGE of values.

2 Loading type - these are segregated, and analyzed separately, as though they

occur in isolation, even though they actually are present simultaneously.

3 - Magnification, due to local fitting configuration, which may in reality reflect a

decrease in fatigue strength, rather than an increase in actual stress.

4 - Code committee tradition - every code is a result of a different set of concerns

and compromises, and therefore may appear to be on a different branch of the evolutionary ladder. Because of this, every code gives different results when calculating stresses.

A summary of significant dates in the history of the development of the piping codes is presented below:

1915 Power Piping Society provides the first national code for pressure piping.

1926 The American Standards Association initiates project B31 to govern

pressure piping.

1955 Markl publishes his paper ''Piping Flexibility Analysis", introducing

piping analysis methods based on the "stress range".

1957 First computerized analysis ofpiping systems.

1968 Congress enacts the Natural Pipeline Safety Act, establishing CFR 192,

which will in time replace B31.8 for gas pipeline transportation.

1969 Introduction of ANSI B31.7 code for Nuclear power plant piping.

1971 Introduction of ASME Section III for Nuclear power plant piping.

1974 Winter Addenda B31.1 moves away from the separation ofbending and

torsional moment terms in the stress calculations and alters the intensi-fication factor for moments on the branch leg of intersections.

1978 ANSI B31.7 is withdrawn.

1987 Welding Research Council Bulletin 330 recommends changes to the

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1.1 Theory and Development of Pipe Stress Requirements

1.1.1 Basic Stress Concepts

Normal stresses: Normal stresses are those acting in a direction normal to the face of the crystal structure of the material, and may he either tensile or compressive in nature. (In fact, normal stresses in piping tend more to tension due the predominant nature of internal

pressure as a load case.) Normal stresses may be applied in more than one direction, and

may develop from a numher of different types of loads. For a piping system, these are discussed below:

Longitudinal stress: Longitudinal, or axial, stress is the normal stress acting parallel to the longitudinal axis ofthe pipe. This may he caused by an internal force acting axially within the pipe:

- - -... - FAX

Figure 1-6

SL = Fax/ Am

Where:

SL = longitudinal stress, psi

Fax = internaI axial force acting on cross-section, lb

Am = metal cross-sectional area of pipe, in2

= 1t(do2 - di2) / 4

= 1t dm t

do = outer diameter, in

di = inner diameter, in

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A specifie instance of longitudinal stress is that due to internaI pressure:

Figure 1-7

SL

=

PAil Am

Where:

P

₌

design pressure, psig

Ai

₌

internaI area of pipe, in2

=

1t di2 1 4

Replacing the terms for the internaI and metal areas of the pipe, the previous equation may be written as:

For convenience, the longitudinal pressure stress is often conservatively approximated as: SL

=

P do 1 4 t

Another component of axial normal stress is bending stress. Bending stress is zero at the neutral axis of the pipe and varies linearly across the cross-section from the maximum compressive outer fiberto the maximum tensile outer fiber. Calculatingthe stress as linearly proportion al to the distance from the neutral axis:

M

Variation in Bending Stress Thru Cross Section

Neutral Axis

Max compressive stress 1/2 max compressive stress Zero bending stress

1/2 max tension stress Max tension stress

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Where:

Mb

=

bending moment acting on cross-section, in-lb

c

=

distance ofpoint ofinterest from neutral axis of cross-section, in

l

=

moment ofinertia of cross-section, in4

Maximum bending stress occurs where c is greatest - where it is equal to the outer radius:

Smax

=

Where:

Ro

=

ri

=

inner radius of pipe, in

ra

=

outer radius of pipe, in

r = radial position where stress is being considere d, in

-p

Figure 1-10

Where:

SR = radial stress due to pressure, psi

Note that radial stress is zero at the outer radius of the pipe, where the bending stresses are maximized. For this reason, this stress componenthas traditionally been ignored during the stress calculations.

Shear stresses: Shear stresses are applied in a direction parallel to the face of the plane of the crystal structure of the material, and tend to cause adjacent planes of the crystal to

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slip against each other. Shear stresses may be caused by more than one type of applied load. For example, shear stress may be caused by shear forces acting on the cross-section:

'tmax

=

VQ/Am Where: Shear Distribution Profile

---~)

---~=

j

- - - -~ V

/MAX

~IN=O Figure 1-11

'tmax = maximum shear stress, psi

v

= shear force, lb

Q = shear form factor, dimensionless (1.333 for solid circular section)

These shear stresses are distributed such that they are maximum at the neutral axis ofthe pipe and zero at the maximum distance from the neutral axis. Since this is the opposite of the case with bending stresses, and since these stresses are usually small, shear stresses due to forces are traditionally neglected during pipe stress analysis.

Shear stresses may also be caused by torsionalloads:

T

Figure 1·12

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Where:

MT

=

internaI torsion al moment acting on cross-section, in-lb

c

=

distance of point ofinterest from torsional center (intersection ofneutral axes)

of cross-section, in

R

=

torsional resistance of cross-section, in4

=

2I

Maximum torsional stress occurs where c is maximized - at the outer radius:

'tmax

=

Summing the individual components of the shear stress, the maximum shear stress acting on the pipe cross-section is:

'tmax

=

v

Q /

Am + MT / 2 Z

Example Stress Calculations:

As noted above, a number of the stress components described above have been neglected for

convenience during calculation ofpipe stresses. Most V.S. piping codes require stresses to

be calculated using some form of the following equations:

Longitudinal stress: SL

=

Mb / Z + Fax / Am + P do / 4 t

Shear stress:

₌

Hoop stress:

₌

Calculations are illustrated for a 6-inch nominal diameter, standard wall pipe (assuming the piping loads are known):

Cross sectional

5999 psi Hoop stress: SR = 600 x 6.625/2 (0.280) = 7098 psi

1.1.2 3-D State of Stress in the Pipe Wall

During operation, pipes are subject to aIl ofthese types of stresses. Examining a small cube

ofmetal from the most highly stressed point of the pipe wall, the stresses are distributed as so: SR

S4

1

_{SH

: SL ' .... SH S R Figure 1-13

There are an infinite number of orientations in which this cube could have been selected, each with a different combination of normal and shear stresses on the faces. For example, there is one orientation of the orthogonal stress axes for which one normal stress is maximized,

and another for which one normal stress is minimized - in both cases all shear stress

components are zero. In orientations in which the shear stress is zero, the resulting normal components of the stress are termed the principal stresses. For 3-dimensional analyses, there are three of them, and they are designated as SI (the maximum), S2, and S3 (the minimum). Note that regardless of the orientation of the stress axes, the sum of the orthogonal stress components is always equal, i.e:

SL + SR + SR = SI + S2 + S3

The converse ofthese orientations is that in which the shear stress component is maximized (there is also an orientation in which the shear stress is minimized, but this is ignored since the magnitudes of the minimum and maximum shear stresses are the same); this is

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in a three dimensional sta te of stress is equal to one-half of the difference between the largest and smallest of the principle stresses (SI and S3).

The values of the principal and maximum shear stress can be determined through the use of a Mohr's circle. The Mohr's circle analysis can be simplified by neglecting the radial stress

component, therefore considering a less complex (i.e., 2-dimensional) state of stress. A

Mohr's circle can be developed by plotting the normal vs. shear stresses for the two known orientations (i.e., the longitudinal stress vs. the shear and the hoop stress vs. the shear), and constructing a circle through the two points. The infinite combinations of normal and shear stresses around the circle represent the stress combinations present in the infinite number of possible orientations of the local stress axes.

A differential element at the outer radius of the pipe (where the bending and torsional

stresses are maximized and the radial normal and force-induced shear stresses are usually zero) is subject to 2-dimensional plane stress, and thus the principal stress terms can be computed from the following Mohr's circle:

TMAX T S2 _S,

'"

/ S -T TMAX

T

Figure 1-14

The center ofthe circle is at (SL + SR) / 2 and the radius is equal to [[(SL - SR) / 2]2 + 't2 ]1/2.

Therefore, the principal stresses, SI and S2, are equal to the centerofthe circle, plus or minus

the radius, respectively. The principal stresses are calculated as:

SI

=

(SL + SR) /2 + [ [(SL - SR) / 2]2 + 't2 ]1/2 and

S2

=

(SL + SR) / 2 - [ [(SL - SR) / 2]2 + 't2 ]1/2

As noted above, the maximum shear stress present in any orientation is equal to (SI - S2) / 2, or:

'tmax = [(SL - SR)2 + 4 't2 ]1/2

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1.1.3 Failure Theories

To be useful, calculated stresses must he compared to material allowables. Material

allowable stresses are related to strengths as determined by material uniaxial tensile tests, therefore calculated stresses must also be related to the uniaxial tensile test. This

relationship can he developed by looking at available failure theories.

Unixial Tensile Test Machine Tensile Test Specimen crYield Figure 1-15 Strain Tensile Test Results

There are three generally accepted failure theories which may he used to predict the onset

of yielding in a material:

1 - OCTAHEDRAL SHEAR, or VON MISES THEORY 2 - MAXIMUM SHEAR, or TRESCA THEORY

3 - MAXIMUM STRESS or RANKINE THEORY

These theories relate failure in an arbitrary three dimensional stress state in a material to

failure in a the stress state found in a uniaxial tensile test specimen, since it is that test that

is most commonly used to determine the allowable strength of commonly used materials.

Failure of a uniaxial tensile test specimen is deemed to occur when plastic deformation occurs; i.e., when the specimen yields.

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The three failure theories state: Octahedral 8hear - Von Mises Theory:

"Failure occurs when the octahedral shear stress in a body is equal to the octahedral shear stress at yield in a uniaxial tension test."

The octahedral shear stress is calculated as:

'tact

=

1/3 [ (SI - 82)2 + (82 - 83)2 + (83 - 8 1)2 ]112

In a uniaxial tensile test specimen at the point ofyield:

81 = 8Yield; 82 = 83 = 0

Therefore the octahedral shear stress in a uniaxial tensile test specimen at failure is calculated as:

'tact

=

1/3 [ (8Yield - 0)2 + (0 - 0)2 + (0 - 8Yield)2 ]1/2

=

2 112 X 8Yield / 3

Therefore, under the Von Mises theory:

Plastic deformation occurs in a 3-dimensional stress state whenever the

octahedral shear exceeds 21/2 x 8Yield / 3.

Maximum 8hear 8tress - Tresca Theory:

"Failure occurs when the maximum shear stress in a body is equal to the maximum shear stress at yield in a uniaxial tension test."

The maximum shear stress is calculated as:

'tmax

=

In a uniaxial tensile test specimen at the point ofyield:

81 = 8Yield; 82 = 83 = 0

80:

'tmax

=

(SYield - 0) / 2

=

8Yield / 2 Therefore, under the Tresca theory:

Plastic deformation occurs in a 3-dimensional stress state whenever the maximum shear stress exceeds 8Yield / 2.

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Maximum Stress - Rankine Theory

"Failure occurs when the maximum tensile stress in a body is equal to the maximum tensile stress at yield in a uniaxial tension test."

The maximum tensile stress is the largest, positive principal stress, SI. (By definition, SI is always the largest of the principal stresses.)

In a uniaxial tensile test specimen at the point of yield:

SI

=

SYield; S2 = S3 = 0

Therefore, under the Rankine theory:

Plastic deformation occurs in a 3-dimensional stress state whenever the maximum principal stress exceeds SYield.

1.1.4 Maximum Stress Intensity Criterion

Mostofthe CUITent piping codes use a slight modification of the maximum shear stress theory for flexibility related failures. Repeating, the maximum shear stress theory predicts that failure occurs when the maximum shear stress in a body equals SYield/2, the maxim um shear stress existing at failure during the uni axial tensile test. Recapping, the maximum shear stress in a body is given by:

'(max

=

(81 -S3) / 2

For the differential element at the outer surface of the pipe, the principal stresses were computed earlier as:

SI

=

(SL + SR) / 2 + [ [(SL - SR) / 2]2 + '(2 ]1/2

=

As seen previously, the maximum shear stress theory states that during the uniaxial tensile test the maximum shear stress at failure is equal to one-half of the yield stress, so the following requirement is necessary:

tmax = [(SL - SR)2 + 4 12 ]112 2

<

2

Multiplying both sides arbitrarily by two saves the time required to do two mathematical operations, without changing this relationship. Multiplying by two creates the stress in tensity, which is an artificial parameter defined sim ply as twice the maximum shear stress. Therefore the Maximum Stress Intensity criterion, as adopted by most piping codes, dictates the following requirement:

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Note that when calculating only the varying stresses for fatigue evaluation purposes (as discussed in the following section), the pressure components drop out of the equation. If an allowable stress based u pon a sui table factor of safety is used, the Maximum Stress In tensity criterion yields an expression very similar to that specified by the B31.3 code:

[ Sb2 + 4 S~ ] 1/2 < SA

Where:

Sb

=

longitudinal normal stress due to bending, psi

St

=

shear stress due to torsion, psi

SA

=

allowable stress for loading case, psi

Example Stress Intensity Calculations:

Calculation of stress intensity may be illustrated by returning to our 6-inch nominal diameter, standard wall pipe for which longitudinal, shear, and hoop stresses were calculated. Reviewing the results ofthose calculations:

=

15547 psi

Shear stress:

₌

5999 psi

Hoop stress:

₌

7098 psi

Assuming that the yield stress of the pipe material is 30,000 psi at temperature, and a factor of safety of 2/3 is to be used, the following calculations must he made:

[(SL - SH)2 + 41:2 ]112 < 2/3 x SYield, or:

[(15547 - 7098)2 + 4 x 59992 ]1/2 < 2/3 x 30000, or:

14674 < 20000

The 14674 psi is the calculated stress intensity in the pipe wall, while the 20000 is the allowable stress intensity for the material at the specified temperature. In this case, the pipe

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1.2 Fatigue Failure

The fail ure modes discussed above were sufficient to de scribe catastrophic failure based upon one time loadings. However, piping and vessels were also found to suffer from sudden failure following years of successful service. The proposed explanation for this phenomenon was fatigue failure ofthe material, resulting from propagation of cracks on the material crystal structure level due to repeated cyclic loading.

1.2.1 Fatigue Basics

Steels and other metals are made up of organized patterns ofmolecules, known as crystal structures. However, these patterns are not maintained throughout the steel producing an ideal homogenous material, but are found in microscopic isolated island-like are as called a grains.

Inside each grain the pattern of molecules is preserved. From one grain boundary to the next the molecular pattern is the same, but the orientation differs. As a result, grain boundaries are high energy borders. Plastic deformation begins within a grain that is both subject to a high stress and oriented such that the stress causes a slippage between adjacent layers in the same pattern. The incremental slippages (called dislocations) cause local cold-working. On the first application of the stress, dislocations will move through many of the grains that

are in the local area ofhigh stress. As the stress is repeated, more dislocations will move

through their respective grains. Dislocation movement is impeded by the grain boundaries, so after multiple stress applications, the dislocations tend to accumulate at grain boundaries, and eventually becoming so dense that the grains "lock up", causing a loss of ductility and thus preventing further dislocation movement. Subsequent applications of the stress cause the grain to tear, forming cracks. Repeated stress applications cause the cracks to grow. U nless abated, the cracks propagate with additional stress applications until sufficient cross sectional strength is lost to cause catastrophic failure ofthe material. Figure 1-16 illustrates this process.

(24)

•

Molecular pattern in unstressed grain

•

...-Slipping of one molecular surface over another after first application of stress

~_

Slipping of a second molecular surface after a second application of

§§§§§§§§

~ocati'"

-+

§§§§§§§§

Slip' ' \ stress

Dislocations beginning to interact and tangle

.~

~

After many repeated applications of stress the dislocations are

completelytangled and the grain is 'Iocked".

With another application of the stress, the grain "tears' and a fatigue crack is initiated.

Figure 1-16

Tensile Test Specimen

Figure 1-17

One Cycl e TEST LOADING CURVE

(25)

One important consideration is the fact that fatigue cracks usually are initiated at a free surface. Corrosive attack on a material often produces pitting ofmetal surfaces. The pits act as notches and produce a reduction in fatigue strength. In those specifie cases when corrosive attack occurs simultaneously with fatigue loading, a pronounced reduction in fatigue properties results which is greater than that produced by prior corrosion of the surface. When corrosion and fatigue occur simultaneously, the chemical attack greatly accelerates the rate at which fatigue cracks propagate.

U nfortunately, fatigue failures can occur even when the stress in a material is below the yield stress. This is because localized stress concentrations can cause plastic deformation in a relatively few grains des pite the fact that the stress over a gross area ofthe section may be

far below the material yield stress. If the section is subjected to a sufficient number of stress

cycles, cracks can initiate in highly stressed grains and then propagate throughout the material, ultimately resulting in a fatigue failure of the section as a whole.

The fatigue capacity of a material can be estimated through the application of cyclic extensive/compressive displacement loads with a uni axial test machine, as shown in Figure 1-17.

Sam pIe results for typical ferrous material (with a yield stress of5 7 ,000 psi) are shown below:

Applied Cyclic Cycles ta Stress (psi) Fa il ure

300,000 23 200,000 90 100,000 550 50,000 6,700 30,000 38,000 20,000 100,000 1.2.2 Fatigue Curves

A plot of the cyclic stress capacity of a material is called a fatigue (or endurance) curve. These curves are generated through multiple cyclic tests at different stress levels. The number of

cycles to failure usually increases as the applied cyclic stress decreases, often until a

threshold stress (known as the endurance limit) is reached below which no fatigue failure occurs, regardless of the number of applied cycles. The endurance limit (for those metals that possess one) is usually quantified as the value orthe cyclic stress level which may be applied

for at least 108 cycles without failure. Typical ratios of the endurance limit to the ultimate

tensile strength of various materials are 0.5 for cast and wrought steels; about 0.35 for several nonferrous metals such as nickel, copper and magnesium; and 0.2 to 0.3 for rough or corroded steel surfaces (depending on the degree of stress intensification).

(26)

w Cl :::> 1-:::i c... ~ (f) (f) w cr: 1-(f) U :::i U >-U

tO'I:"""---r---T""""---r---T""""---.,

NOTH: 1" E- . . . IZI _ "" U1S 1II-1151to1.

131 T_5-11O.1 _ _ _ _ _ . _ ... _ _

-..--of __

FIG. 5-110.1 DESIGN FAnGUE CURVES FOR CARIION, Law ALLOY, SERIES ~IOC, HM ALLOY STEELS AllO HIGH

TENSILE S1ULS FDII TEMPERATURES NOT EXCEEDING 7UO'F

Figure 1-18

Note that according to the fatigue curve, the material doesn't fail upon ini tialloading, despite enormously high stresses that appear to be weIl above the ultimate tensile stress oftypical carbon and low alloy steels. The reasons for this are:

1 The highly stressed areas under fatigue loading are normally very localized.

Catastrophic failure under one-time loading will normally occur only when the gross cross-section is overloaded.

2 Fatigue curves are usually generated through cyclic application of displacement,

rather than force, loading. Displacement loads are "self-limiting". If a pipe is overloaded with an imposed displacement, plastic stresses will develop, deform-ing the pipe to its displaced position. At that point there will be no further tendency for displacements to occur, and therefore no continuation ofthe load, or further deformation leading to catastrophic failure. In the case of an applied force (which is not a self-limiting load), deformation of the pipe does not cause

the force to subside, so deformation continues until failure.

3 The stress shown in a fatigue curve is a calculated stress, based upon the

assumption that Hooke's law is applicable throughout the range of applied

loading; i.e., S = E E, where:

E

₌

modulus of elasticity ofmaterial, psi

(27)

In reality, once the material begins to yield, stress is no longer proportional to the induced strain, and actually is much lower than that calculated.

1.2.3 Effect of Fatigue on Piping

A. R. C. Markl investigated the phenomenon offatigue failure ofpiping during the 1940's and

1950's, and published his results in papers such as "Piping Flexibility Analysis", published in 1955. He tested a number of configurations (straight pipe, and various fittings, such as pipe elbow, miter bend, unreinforced fabricated tee, welding tee, etc.) by using cyclic displacements to apply alternating bending stresses. Plotting the cycles to failure for each applied displacement, he found that the results of his experiments followed the form of fatigue curves.

16"

~ 41"

f

1 (TYP, (TYP)

-a-~IL-,... _ _ _ _ _ ... Range of imposed displacements to

~ 1 impose complete stress reversaI.

~ Girth butt weld

-a-

RangeOfinPlaneL~

/

~t--...,IL.Ô.-J-I

____

- -...

I displacements ....

:...---.l~R

f t 1

~ _ • angeo ou pane

displacements

-a

... Range of inplane /

~~

...&...~ _ _ _ _ _ _ ...J displacements ~_ Range of outplane

• displacements

-a ...

Range of inPlane/

7'

{ ( - ' - - - . . . . displacement~ ... Range of outplane

ml!-

·

"'Placements

Figure 1-19

If an initially applied displacement load causes the pipe to yield, it results in plastic

deformation, producing a pre-stress in the system, which must be overcome by subsequent stress applications, resulting in lower absolute stresses during later load cycles. Because of the system "relaxation", the initial values of the thermal stress are allowed to exceed the material yield stress, with the aim being that the system "self-spring" during the first few cycles and then settle into purely elastic cycling. This "self-springing" is also called Elastic Shakedown. As shown in Figure 1-20, the maximum stress range may be set to 2SYieid (or more accurately, the sum of the hot and the cold yield stresses) in order to ensure eventual elastic cycling.

(28)

2Sy~~~"".r---2Sy -Sy~---~--~~~~----~~---~-- -2Sy~---Stress Time~ Figure 1-20

Based upon this consideration, the initial limitation for expansion stress design was set to the sum ofthe hot and the cold yield stresses - the maximum stress range which ensured that the piping system eventually cycled fully within the elastic stress range. Incorporating a factor of safety, this resulted in the following criterion:

SE <= F (SYe + Syh)

Where:

SE

=

expansion stress range, psi

F = factor of safety, dimensionless

SYe

=

material yield stress at cold (installed) temperature, psi

Syh

=

material yield stress at hot (operating) temperature, psi

1.2.4 Cyclic Reduction Factor

At sorne point, in the vicini ty of 7,000 cycles, the ( SYe + SYh)limi ta tion intersects the fatigue

curve for carbon and low alloy steel. The allowable stress range must therefore be reduced to fit the fatigue curve for cyclic applications with 7,000 cycles or more:

(29)

Where:

f

=

cyclic reduction factor, as shown in the accompanying table

CYCLIC REDUCTION FACTOR TABLE

Cycles N Factor f 1 7,000 1.0 7,001 14,000 0.9 14,001 22,000 0.8 22,001 45,000 0.7 45,001 100,000 0.6 100,001 200,000 0.5 200,001 700,000 0.4 700,001 2,000,000 0.3

1.2.5

Effect of Sustained Loads on Fatigue Strength

In almost an cases the material fatigue curves are generated using a completely alternating stress; i.e., the average stress component is zero. Research has shown that the magnitude of the mean stress can have an effect on the endurance strength of a material, the trend of which is shown below:

~ cr",

.. ..

;~

•

::

..

CIl ,5 d ·c

..

! Ci crllll < 17'IIIIZ < crllt, < 0"4 4 1 t05 _10' C~cles 10 foilure (b) For Design 1 107 cr Yield Figure 1-21 ~ ,~ 'j ~ ~ ~ Sa from endurance

=< ûS./ curve for completely ~ alternating stress

Mean Stress Axis

Tensile cr Yield

(30)

Note that as the mean stress increases the maximum permissible absolute stress (Sa + Sm) increases, while the permissible alternating stress decreases. The relationship between the allowable alternating stress and the average stress is described by the Soderberg line, which correlates fairly weIl wi th test data for ductile materials. The equation for the Soderberg line is:

SaCAllowed)

=

SaCfor R=-1) xCI - Sm/SYield)

Where:

R

=

Smin / Smax

Sa

=

(Smax - Smin) / 2

Sm

=

(Smax + Smin) / 2

Note that during the development of the ASME Boiler and Pressure Vessel Code Section III

rules and procedures for analysis ofnuclear piping, the Special Committee to Review Code

Stress Basis concluded that the required adjustments to a strain-controIled fatigue data

curve based on zero mean stress, occur only for a large number of cycles Ci.e. N > 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 im plemented 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:

(31)

1.3 Stress Intensification Factors

As noted previously, Markl's fatigue tests generated endurance curves for various fitting configurations, such as straight pipe, butt welded pipe, elbows, miters, welding tees, unreinforced and reinforced fabricated tees, mostly using 4" nominal diameter, size-on-size fittings. Markl noticed that the fatigue failures occurred not in the middle ofhis test spans, but primarily in the vicinity ofthe fittings, and in those cases, they also occurred at lower stress/cycle combinations than for the straight pipe alone.

Earlier theoretical work pointed to a possible explanation. It had been shown that elbows

tend to ovalize du ring bending, bringingthe outerfibers closerto the neutral axis ofthe pipe, thus reducing the moment of inertia (increasing flexibility) and the section modulus (increasing developed stress).

x

Ovalization of Bend

Section

Figure 1·22

The stress in tensifica tion factors (the ratio of actual ben ding stress to the calcula ted ben ding stress for a moment applied to the nominal section) for elbows was known to be:

10 = 0.75/ h2/3

li = 0.9/ h2/3

Where:

10 = out-of-plane intensification factor

li = in-plane intensification factor

h = flexibility characteristic

= t R/r2

t = pipe wall thickness, in

R = bend radius of elbow, in

(32)

Markl found this to correlate fairly weIl wi th his test data and so adopted it. Tests on mitered bends correlated weIl with those for smooth bends, providing an equivalent bend radius R was used in the above equation for h. Markl's estimates of equivalent bend radius are shown below:

Re

=

r(l + 0.5 sIr cot D) (for closely spaced miters)

Re

=

r(l + cot D) 1 2 (for widely spaced miters)

Where:

Re

₌

equivalent bend radius, in

s

₌

miter spacing at the centerline, in

D

₌

one-half of angle between cuts

Markl found that the unreinforced fabricated tees could be modeled using the same formula as that for single (widely spaced) miter bends could be use d, if a half angle of 45 degrees was used. This produces a flexibility characteristic of:

h =

tir

For butt welded tees (such as ANSI B16.9 welding tees) Markl again adapted the bend equations, this time computing an equivalent radius (Re) and an equivalent thickness (te). Markl's equation for weI ding tees was:

h

=

c ( te Re 1 r 2 )

1.35r (Markl's recommendation)

Inserting these values into the expression for h yields:

h

=

4.4 tIr

(33)

For reinforced fabricated tees, Markl used the expression he had previously used for welding tees, with different equivalent wall thickness and bend radius:

h = c ( te Re / r2 )

Where:

c

₌

(teft)3/2 (Markl's recommendation) te

₌

t + tp

tp

=

thickness of reinforcing pad or saddle, in

Re

=

r

The following tables compare the stress intensification factors suggested by Markl's test results versus the values calculated with his equations (results are for 4" nominal diameter, standard schedule pipe):

Bend in-plane

(in

tR/r 2 Test Calculated 0.062 4.49 5.7428 0.210 2.17 2.5476 0.129 4.38 3.5238 0.320 2.02 1.9238 0.319 2.10 1. 9286 0.316 1.90 1.9381 0.328 1. 70 1.8904 0.331 1.53 1.8809 0.324 1.36 1.9095 0.332 1.28 1.8762 0.328 1.46 1.8904

(34)

Unreinforced tee (io):

tir Test Calculated

0.0390 Il.04 10.84

0.0455 6.12 7.06

0.0947 2.95 4.33

0.1111 2.34 2.89

Reinforced tee:

in-plane (i;) out-plane (io)

tpad Test Calculated Test Calculated

0.12 2.21 2.63 2.43 3.17

0.237 1. 78 1. 74 1.83 1.98

0.5 1.10 1.14 1.08 1.18

These fonnulas for intensification factors were adopted (and expanded) by the piping codes. Specifie fonnulas and/or fittings recognized by the individual ASME/ANSI B31 codes are usually shown in Appendix D ofthose codes (see Figure 1-23).

(35)

APPENDIX D

FLEXIBILITY AND STRESS INTENSIFICATION FACfORS

TABLE 0-1'

FLEXIBIUTY FACTOR t AND STRESS INTENSIFICATION FACTOR 1

la)

fini"'"

fortor DoKrillllon k w~."'G .. _ or plpt _ 1.6~ CHotts 121. (C)-(711

"

Ill) ,-_Id _ _ 1.52 J < '2 Cl + bit " ~ CII_ (2). 1.). (5), m)

Si_ ""''''

bond .. ..w..,. _.!,g

---

,,'/1,. Ji ~ '2 (1 +

\In"

CHotts 121. 1.'. (7)) lb) W.ldlng lot .... ASIII E 81U_ '. ~ ~0t.. Tc. :i!: 1.5 T IN .... 121. 141. (6). Ill). (Ul)

I.~ Remforttd fabnc.t~ tn

tbt wrth pad .or !.adtllt

[Note' 121. 1.1. IBI. (12). Ill):

te) Urninforced f.ltricated Ue

lb) IN.m 1Zl. I~). IIZl. mll

lb) Exuvdod _1 ... too "Ith

'It ~ 0.0506

Tt < l..5T

{Notn (2), loC}, Cl})]

(b) Wtlded~ln contour InSfrt

wllII

r. '2:: 'tWL

T(~l.sr

(ffote1 en (4), i1l). (131]

(0) IIrIr1ch _Id· •• IiItlno IIn ... ...,torc;ocll INo ... (2). «l. I~). 1121) _ _ Ion r ... l _ 121. D)I 0Ut~_ i. 0.75 Jill' O.' "li' M Ir''' O., Ir''' ~ JiJi~ o .• Ii''' o., hW o .•

"'''

0.9 Ir''' 1 ... ;, O., -;m O., ,,:1./1 ~ Jil" :w.. i. + lit ~f" + ~-;. ~l()+ '" ~I~ + \.Ii

Bult -.eIdi!d joint. Nducer, or _t'Id neck fI"\1e

D " " b _ ... on lWtgo Cel

lb)

FI'" wtIdH jOint, or socttt M'!d ftarlge or fittlng

Up )oint """"" (wlth ASME B16.9 Iap j,nt .tub)

Tht'tAdfod pipe joint, Or U.rudfd flallQf

FledIllillJ thoozurlstk k TR, -;;;-coti sf 2 _r,' ~.f 2 li 4.~ _r, If + ",i)'" f 1) ~ F

r,

( r.)

1,+- -i 12 '2 •.• 1. _r,

~r2

fUlfS:,,7-

OOod _--.. .J! .~_. !J".J, _--y_Z

.---

'--2-~~.

~:r'2 .

'.

~~2

_{T t '} _{T' .,} Pad s.ddIe' StmI Flaibllty IlIlIn,ifiutioo

Factor k F _ ; INoto Illl

1.0 1.2

Note (14)

Lb Z.l

(36)

Subsequent research has demonstrated that Markl's formulas, having been based on a limited numher configurations (significantly having omitted reduced outlet tees) and disregarding any need to intensify torsional stress, are inaccurate in some respects. The major problem with reduced intersections tees lies in the out-of-plane bending moment

on the header. Stresses due to these moments can never he predicted from the extrapolation

of size-on-size tests. Figure 1-24 below illustrates the origin of this problem.

Mob Size-on-size Area of high bending ... stresses Mob Reduced Intersection Figure 1-24

Errors due to these moments can be non-conservative by as much as a factor oftwo or three. Furthermore, when the rlR ratio is very small, the branch connection has little impact on the header, so use oflarge stress intensification factors for the header can produce unreasonably large calculated stresses.

R.W. Schneider ofBonney Forge pointed out this inconsistency for reduced branch connec-tions. His paper on the subject states that the highest stress intensification factors occur

when the ratio ofthe branch to headerradiiis about 0.7, at which point the nonconservativism

(versus Markl's formulas) is on the order oftwo.

i from Markl

- 1.0

0.7 1.0 r/R

Ratio of Actual i to Markl's i vs Ratio of 8ranch to Header Radius

(37)

1.4 Welding Research Council Bulletin 330

The Wei ding Research Council's Bulletin 330, "Accuracy of Code Stress Intensification Factors for Branch Connections" documented a major attempt to re-assess the existing code requirements for the intensification of stresses at tees and other branch connections. The

difficulty ofthis task was summed up in the bulletin by author E. C. Rodabaugh, who stated:

''We would rate the relative complexity ofi-factors for pipe, elbows and branch connections by the ratios 1 :5:500. These comments on relative complexity, we think, are relevant at this point because at least sorne readers will be looking for simple answers to what they perceive to be a simple subject. They will not find any simple answers in this report."

Summarizing the findings ofWRC 330 in order ofincreasing importance:

1) The following note should be added wi th regard to branch connection flexibilities:

"In piping system analyses, it may be assumed that the flexibilityis represented byarigidjointatthebranch-to-runcenterlinesjuncture. However, the Code user should be aware that this assumption can be inaccurate and should consider the use of a more appropriate flexibility representation."

2) ASME 2/3 and B31.1 users can use the ''Branch Connection" expressions for

unreinforcedfabricated tees wheneverrlR< 0.5. (Markl's formulas specified that the same stress intensification factor be used on both the branch and header legs of a tee, regardless of relative sizes. The codes noted above permit the reduction

ofthe stress intensification factor at the branch for relative diameters. CAESAR fi

automatically considers the effects ofreduced intersections on the stress inten-sification factors for these codes unless directed otherwise by the user through the setup file.)

3) B31.1 erred when including the calculations for branch connection stress

intensification factors; instead they should have included the calculations as they appeared in ASME III. (Further clarification of this note is given in note 10 herein.)

4) B31.3 should include the stress intensification factors for branch connections as

per ASME III. (B31.3 uses Markl's original formulas, thus specifying the same stress intensification factor for both the branch and header of a tee, regardless of relative sizes.)

5) B31.3 should intensif y the torsional moment at branch connections, with the

torsional intensification factor estimated as: it

=

(rlR)io.

6) B31.3 should eliminate the use of ii = _0.75io+ 0.25 for branch connections and

tees. It can give the wrong relative magnitude for header moments, and may underestimate the difference between Mo and Mi for rlR ratios between 0.3 and 0.95, and perhaps over-estimates the difference for rlR ratios below 0.2 and for rlR

=

1.0.

(38)

7) B31.3 and B31.1 should add restrictions to the stress intensification factor tables

indicating that they are valid for RIT < 50.

8) The codes should add notes that indicate that the stress intensification factors

are developed from tests and/or theories based on headers being straight pipe with about two or more diameters length of pipe on either side of the branch.

9) The codes should also add notes to indicate that for branch connections/tees the

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 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

(39)

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.

(40)

NO INTERSECTION RADIUS

"831.3" VS. 'WRC 330' UNREINFORCED, FA8RICATED TEE STRESS INTENSIFICATION FACTORCOMPARISON

HEADER NOM 1 40. 1 48. 2 48. J 40. l 40. J 43. 4 40. 4 40. 4 40. 4 49. 5 40. S 48. ~ 411!. 5 40. 5 411!. 6 49. b 411!. 6 411!. 6 40. 6 4\J. S 48. a 48. B 411!.

e

49. B 48. 19 48. III! 4B. 18 48. lB 48. 19 48. 12 48. 12 48. 12 41. 12 48. 12 48. 14 48. 14 4B. 14 4B. 14 49. 14 4B. BRANCH SCH 40. 1 48. 2 40. 1 414. 2 414. 3 40. 1 48. Z 40. 3 4B, 4 414. 1 48. 2 48. 3 411. 4 48. 5 48. 2 48. :) 48. 4 U. 5 411. 6 48. :) 4f.1. .. 48. 5 411. b 4@. B 411. .. 411. S 48. b 48. 8 411. 18

n.

l 5 48. h 4B. B 48. 18 48. 12 48. b 48. 8 48. 10 48. 12 48. 14 48. WRC 330 b 2.433 4.184 3.359 3.479 4.769 3.4811 3.416 4.682 5.694 3.B92 3.348 4.589 5.5BII 6.359 4.255 4.477 5.444 6.282 6.919 4.548 5.187 5.918 6.592 7.218 4.94'1 5.642 6.294 6.884 7.875 5.284 6.834 b.bBB 7.549 8.443 5.523 6.383 7.382 B.IM 8.569 5.599 --B31.3---i --B31.3---ib iOb 2.874 2.433 2.769 3.359 2.769 3.359 2.860 3.488 2.860 3.488 2.868 3.488 3.169 3.892 3.169 3.892 3.169 3.892 3.169 3.892 3.441 4.255 3.Hl 4.255 3.441 4.255 3.441 4.255 3.44J 4.255 3.655 4.540 3.655 4.548 3.655 4.541 3.b55 4.541 3.655 4.541 3.961 4.949 3.961 4.949 3.961 4.949 3.9bl 4.949 3.961 4.949 4.213 5.284 4.213 5.284 4.213 5.284 4.213 5.284 4.213 5.284 4.392 5.523 4.392 5.523 4.392 5.523 ·40592 5.513 4.392 5.523 4.458 5.599 4.45B 5.599 4.458 5.599 4.4Se 5.599 4.4511 5.599 .853

.. m

.B24 .822 .U8 .822 .928 .677 .557 .814 1.1128 .758 .617 .54J .889 .816 .671 .589 .528 .885 .764 .671 .681 .549 .BU .747 .669 .612 .535 .797 .728 .666 .592 .52@ .795 .697 .689 .545 .5J9 .795 iob 330 b 1.081 .822 1.010 1.011 .738 1.881 1.139 .831 .684 l.0U 1.271 .927 .763 .669 Lltllll !.lm .834 .732 .656 1.81l@ .954 .837 .751 .686 1.811! .936 .839 .768 .671 1.l!ea .915 .837 .732 .654 1.all'! .877 .767 .686 .653 U188 . WRC 2. tHe 2.986 2.111 2.111 3.893 2.11111 2.lem 2.665 3.46m 2.nll 2.1111 2.342 3.14B 3,783

2.m

2.11111 2.711 3.374 4.836 2.111 2.258 2.811 3.361 4.399 2.111 2.399 2.871 3.755 4.697 2.118 2.523 3.312 4.138 4.919 2.328 3.847 3.811 4.538 4.977 --B31.3---2.769 2.769 2.86B 2.868 2.86" 3.169 3.169 3.169 3.169 3.441 3.441 3.441 3.441 3.441 3.655 3.655 3.655 3.655 3.655 3.961 3.961 3.961 3.961 3.961 4.zn 4.213 4.213 4.213 ~.213 4.392 4.392 4.392 4.392 4.392 4.458 4.45B 4.458 4.4511 4.458 ~ ioh 1 330 h 2.433 .959 3.359 3.359 3.488 3.481 3.4811 3.891

3.an

3.892 3.a92 ".255 4.255 4.255 4.255 4.255 4.548 4.548 4.548 4.540 4.541 4.949 4.949 4.949 4.949 4.949 5.284 5.284 5.28" 5.284 5.284 5.523 5.523 5.523 5.523 5.523 5.599 5.599 5.599 5.5'19 5.599 1.319 .927 1.362 1.362 .925 1.5119 1.5B9 1.189 .916 1.639 1.639 1.478 I.H2 .91B 1.741 1. 741 1.348 1.883 .986 1.886 1.754 1.410 I.PS .911 2.@86 1.756 1.468 1.122 .997 2.882 1.741 1.338 1.1163 .895 1.911 1.468 1. Ib8 .982 .894 ioh 330 h 1.125 1.6"" 1.125 l.b57 1.657 1.125 1.953 1.853 1.468 1.125 2.826 2.826 1.817 1.488 1.125 2.162 2.162 1.674 1.346 1.125 2.356 2.191 J.76J 1.472 1.125 2.516 2.282 l.a41 1.407 1.125 2.b18 2.189 1.673 1.337 1.125 2.405 1.839 1.469 1.236 1.125

(41)

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 8 40. I@ 48. 12 48. 14 40. lb 48. 18 4~. 18 40. 18 48. 12 40. 18 48. 14 48. lB 40. lb 40. 18 48. 18 40. 20 40. 20 48. 20 4". 2" 48. 20 48. 24 48. 24 40. 24 4@. 24 40, 12 40. 14 40. 16 4~. 18 4~. 20 40. 16 48. 18 40. 20 40. 24 40. WRC 330 b 6.825 7.633 8.322 8.723 5.595 -·831.3··· i ib iOb 4.446 5.595 4.446 5.595 4.446 5.595 4.446 5.595 4.446 5.595 7.281 4.449 5.598 7.B50 4.4~9 5.598 8.229 4.449 5.598 8.797 4.449 5.598 5.598 4.449 5.598 7.711 8.882 8.640 9.165 5.801 8.076 8.566 9.@37 5.943 4.681 4.681 4.681 4.681 4.601 4.707 4.707

4.m

4.707 5.BBI 5.a61 5.B01 5.881 5.8@1 5.943 5.943 5.943 5.943 i ib 330 b .651 .583 .534 .510 .795 .618 .567 .541 .586 .795 .597 .56Q .532 .592 .793 .583 .549 .521 .79'l. iob 330 b .928 .733 .672 .641 1.098 WRC 330 h 2.664 3.332 3.961 4.352 4.973 .777 : 2.964 .713 : 3.523 .6811 3.871 .636 '4.423 1. 80~

l

4.976 .752 .718 .671 ,633 Lel8 3.281 3.604 4.1lB 4.633 5.156 .736 3.512 .694 3.951 .658 4.391 1.009 ; 5.282 ···831 .3··· i ih 330 h I.6b9 1.334 1.123 1.822 i ih ioh 4.446 5.595 4.446 5.595 4.446 5.595 4.446 5.595 4.446 5.595 .894 4.449 4.449 4.449 4.449 4.449 4.601 4.601 4.681 4.601 4.601 4.797 4.787 4.7@7 4.707 5.598 1.5&1 5.598 1. 263 5.598 1. 1-49 5.598 1. "lib 5.598 1 .894

5.m

5.BiH 5.a81 5.BIH 5.801 1.483 1. 277 1.117 .'193 .B92 5.943: \,:)48 5.943

l

1.191 5.943 i !.lm 5.'143 .B'11 i ioh 330 h 2.1011 1.b79 1. 413 1.286 1.125 1.889 1.589 1.446 1.2116 1.125

1.m

!.b10 1.4&9 1.252 1.125 l.h92 1.504 Lm I.! 25 30 48. 24 4~. 9.782 5.140 6.520 39 48. 3" 40, 6.528 5.140 6.520 .530 .672 4.619 5.140 6.52(1

i

1.113 1.411 .788 1.800 5.796 5.140 6.520 i .887 1.125 32 41Ll. 32 49. 32 40. 14 40. 34 411. 34 48. .56 48. 36 41l. 36 48. 36 48. 42 48. 42 48, 42 40. 42 4@. 42 40. 24 4~. 36 40. 32 40. 30 4~. 32 411. 34 40. 30 -4B. 32 49. 34 48. 36 48. 30 40. 32 U. 34 48. 36 40. 42 40. 10.394 10.134 7.227 11.763 !lU17 7.532 11.210 11.599 9.902 7.384 11.5(18 11.9(17 12.231 12.633 8.209 5.670 5.670

5.m

5.899 5.899 5.899 5.788 5.788 5.788 5.788 b.UB b.400 6.488 b.m b.480 7.227 .546 7.227 .560 7. '227, .785 7.5321 .501 7.532. .572 7.532! .783 ~ 7.384 j .51l! 7. 384: • 49'1 7.384, .585 7.384 .784 8.208 ; 8.208 ; 8.20~ : 8.2@0 ; 8.209 .537 .521 .507 .780 .,m ' 4.783 .713 6.801 I.m 6.424 .640 5.879 .733 6.293 1.89B 6.695

.m

.637 .746 1.888 .713 .089 .6&8 .649 1.BS8 5.446 5.830 6.283 6.563 5.lbB 5.533 5.a86 6.228 7.289 5.6lB S.670 5.670 5.899 5.899 5.899 5.788 S.7B8 S.788 5.788 6.480 6.4110 6.40& 6.489 6.480 7.227· 1.186 7.227 .945 7.227 .883 7.532 1.083 7.532 .937 7.532 .B81 7.384; U63 1 7.3B4· .993 7.384 .933 7.384 .8B2 B.280 8.280

8.m

S.2U 1 B.2BILl 1 1.238 ! .157 1.087 1.828 .878 1.511 1.204 1.125 1.281 1.197 1.125 1.35a 1.266 1.198 1.125 1.587 1.482 1.393 1.316 1.125

COADE Pipe Stress Analysis Seminar Notes

PIPE STRESS ANAL YSIS

SEMINAR NOTES

Table of Contents

1.0 Introduction to Pipe Stress Analysis

Why do we Perform Pipe Stress Analysis?

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1.1 Theory and Development of Pipe Stress Requirements

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