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TRAINING MANUAL- PIPING

PIPING FLEXIBILITY ANALYSIS

Uhde India Limited

DOC No. : 29040-PI-UFR-0027

Rev. : R0

Page : 1

CONTENTS

Page

0.0 Cover Sheet 1

1.0 Scope 2

2.0 Piping Codes 2

3.0 Introduction 2-3

4.0 Definitions 3-4

5.0 Sustained and Displacement Stresses 4-6

6.0 Allowable Stresses 6-9

7.0 Stress Intensification 9-11

8.0 Easily Analyzed Piping Systems 11-18

9.0 Piping Flexibility Analysis 18-23

10.0 Analysis of Complex Systems 23

11.0 Support Selection 24-25

12.0 Reducing Stresses 25-26

13.0 Designing with Expansion Joints 26-28

14.0 Sample data for Expansion rate and Allowable stress 29-31

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1.0 SCOPE

This design guide presents concepts and principles for calculating the strains and resultant stresses in

piping system to determine whether the system has sufficient flexibility to safely accommodate

changes in length resulting from temperature variations while simultaneously providing adequate

support for all loadings present.

1.1 Limitations:

This guide is not applicable to the design of non-metallic piping systems or to systems which

incorporate brittle materials, e.g. glass lined steel.

1.2 Application:This guide is in conformance with the requirements of ASME B31. process piping, hereinafter

referred to as the code.

2.0 PIPING CODESIn addition to ASME B31.3, which is applicable to all piping within the property limits of a chemical

plant, petroleum refinery, gas processing plant or tank farm which is not covered by other codes, the

stress analysis methods set forth in this design guide can be used with the codes for other classes of

piping. The scope of each of these codes is briefly stated in the following.

ASME B31.1. Power Piping :

Covers piping directly associated with power boilers, i.e. vessels which conform to Section I of the

ASME Boiler and Pressure Vessel Code.

ASME B31.4 Pipeline Transportation System for Liquid Hydrocarbons and other liquids :

Applies to piping carrying liquid petroleum products between refineries, plants, tank farms, etc. outside

plant boundaries.

ASME B31.5 Refrigeration Piping :

Covers requirements for refrigeration piping for services as low as -320F, both field erected and

factory assembled.

ASME B31.8 Gas Transmission & Distribution Piping Systems :

Applies to fuel gas piping systems not federally regulated, from the source to the user's meter but

excludes piping on process plant property.

ASME B31.9 Building Services Piping :

This code, when issued, will cover piping normally associated with industrial, commercial and multi-

unit residential buildings.

ASME Boiler & Pressure Vessel Code, Section III :

Covers piping systems of nuclear power plants.

3. INTRODUCTION:Piping systems are stress analysed for three reasons :1) to prevent over-stressing the material of construction,

2) to prevent joint leakage caused by excessive forces and moments,

3) to prevent failure or malfunction of attached equipment caused by excessive piping reactions. Thisdesign method permits a designer to accomplish these objective by :

4) To calculate forces and displacements at support points for support design.

3.1 Assuring adequate support to prevent excessive sag and stresses in the piping system.

3.2 Incorporating sufficient flexibility to accommodate stresses resulting from changes in pipe length dueto thermal effects and movement of the connections at the ends of the pipe.


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Mo Outplane bending moment, in-lbf.

Mt Torsional moment, in-lbf.

P Concentrated force, lbf.

Pr Internal pressure, psi.

PT Test pressure, psi.

R Total reaction forces & moments, lbf or ft-lbf.

RT +P Variable reaction caused by thermal & pressure effects, lbf, ft-lbf.

RW Weight reaction, lbf or ft-lbf.S Basic allowable stress from Appendix A of B31.3, psi.

SA Allowable stress range, psi.

Sb Resultant bending stress, psi.

0.5

(iiMi)2 + (ioMo

)2

= _______________

z

Sc Basic allowable stress at minimum metal temperature during the displacement cycle, psi

SE Computed displacement stress range, psi.

Sh Basic allowable stress at maximum metal temperature during the displacement cycle, psi.

SL Sum of longitudinal stresses caused by pressure, weight and other sustained loadings, psi.

St Torsional stress, psi = Mt/ 2Z

Tp Pressure thrust of bellows expansion joint, lbf.t Pipewall thickness, inch.

y Deflection in y-direction, inch.

Z Section modulus of pipe, inch3.

5. SUSTAINED AND DISPLACEMENT STRESSES :

Piping flexibility analysis in accordance with the basic assumptions and requirements of B31.3 is

concerned with two types of stress called sustained stress and displacement stress. Each type of stress

must be considered separately; these are the two criteria by which the adequacy of a piping system is

evaluated. They are considered separately because sustained stresses are associated with sustained

forces while displacement stresses are associated with fixed displacements.

5.1 SUSTAINED STRESSES:Sustained Stresses are defined as stresses caused by loads that are not relieved as the piping system

deflects. An example is the stress induced by the weight of the valve at the end of the cantilevered pipe

segment shown below.

Regardless of the magnitude of the displacement !, the magnitude of the load (the weight of the valve)

which causes the stress is unchanged. Therefore, to avoid catastrophic failure, the magnitude of any

sustained stress must not exceed the yield strength of the material. Another example of a sustained stress is

the hoop and longitudinal stresses induced by pressure. The loadings, which induce sustained stresses, are

termed sustained loadings.

The sustained stress principle is expressed as a Code requirement . The sum of the longitudinal stresses due

to pressure, weight and other sustained loadings SL must not exceed the hot allowable stresses Sh.


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This requirement is written as :

SL " Sh (1)

SL is computed by the following equation :

FA

SL = Sb + ------ (2) Aw

5.2 DISPLACEMENT STRESSES:Displacement stresses are defined as those stresses caused by fixed displacements, i.e., caused by loads that

are relieved as the piping system deforms. Consider the cantilevered beam shown below.

Assume that the end of the beam is displaced, its elastic limit and its elastic range is #. As long as any

displacement cycle is within the elastic range of the beam, no yielding will take place.

Consider the same cantilever beam displaced from its original position to position (1).

Its elastic limit is exceeded and the beam will yield. However, as long as D does not exceed #, no further

yielding of the beam will take place provided all successive displacement cycles are within the displacement

range D. If the beam is made of a relatively ductile material, yielding only in the first half cycle will not

cause failure of the beam. Therefore, fixed displacements can be allowed to cause displacement stresses

that exceed the yield strength of the material as long as the elastic range of the material is never exceeded.

Consider the stresses induced in a piping system caused by thermal expansion, as illustrated by the following

example.


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In Figure 5A, if the pipe end at position (1) is assumed free, then when the piping is heated it would move to

the unrestrained hot shape with the free end at position (2). Figure 5B illustrates how an increase in

temperature of the restrained piping system is equivalent to displacing the unrestrained hot pipe from

position (2) to position (1). Therefore, stresses caused by thermal expansion are displacement stresses.

Any yielding or permanent strain, with attendant relaxation or reduction of stress in the hot condition, leads

to the creation of a stress reversal when the piping system returns to the cold position. This reversal of

stress, referred to as self-springing, is similar to cold springing in its effect. See Para.9.3.

The code requires that the calculated stress range SE(sometimes known as the expansion stress range) must

not exceed the allowable stress range SA.

SE " SA (3)

When piping system statisfies Eq.3, it is judged to be adequately flexible against thermal expansion andrestraint displacement because the elastic range of the system will never be exceeded even though the system

may yield.

Since the inherent flexibility is most piping systems is provided by changes in direction, the code considers

only bending and torsional stresses significant in the calculation of SE and gives the following equation for

its computation.

SE = (Sb2 + 4St

2) (4)

In summary, two types of stress are of concern in a piping flexibility analysis. Sustained stresses are limited

by Eq.1 and the displacement stress range is limited by Eq.3. All piping systems must satisfy Eqs.1 and 3

and a separate analysis must be performed for each equation.

6. ALLOWABLE STRESSES:

The stresses computed by the program must be compared to Code allowable stresses to determine the

adequacy of piping systems. The Code differentiates between stresses caused by pressure and other

sustained loads and stresses caused by displacement strains. These allowable values are a function of the

basic allowable stresses.


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The allowable stress values given in the code are, S = Sy/1.6

Sy = 1.6 S, therefore SR = 1.6 Sc + 1.6 Sh.

However to have safety factor, code (ASME B31.1 / 31.3) allows SR = 1.25 Sc+ 1.25 Shwhich includes all

stresses that is expansion, pressure and weight stress and other sustained loads. Therefore the stress range

due to Thermal Expansion SE shall not exceed the value given below :

SE = f [1.25 Sc + 0.25 Sh + ( Sh - SL )] = SA + f (Sh - SL)

where f = Stress range reduction factor for cyclic conditions for total number of full temperature cycle over

the design period.

Sc = Allowable stress at minimum (cold) temperature.

Sh = Allowable stress at maximum (hot) temperature.

SL = The sum of longitudinal stresses due to pressure, weight and other sustained loads. This value

shall not exceed the allowable stress Sh. i.e SL< Sh.

SA = f (1.25 Sc+ 0.25 Sh)

6.4 DUCTILE Vs BRITTLE MATERIALS:

Most piping failures of ductile materials are caused by repeated yielding at relatively low strains, i.e., the

pipe cracks after a successful period of operation; a small leak results. The failure is not catastrophic unless

the escaping fluid causes a hazardous situation. When large deformations in piping systems are present, the

deformations are generally noticed and the situation corrected.

Brittle piping materials (cast iron, glass) behave differently. Failures in these systems often occur shortly

after start-up and are catastrophic. The pipe breaks through its entire cross section. Large deformations

cannot occur without failure of the pipe. Consequently, there is no warning, as there often is, for ductile

piping materials. On this account, allowable stress ranges must be very cautiously applied to brittle

materials.

7. STRESS INTENSIFICATION:

Local stresses in fittings such as tees and elbows are generally higher than stresses in the adjoining pipe

segments. The code allows these stresses to be calculated by multiplying the stresses in the adjoining pipe

segments by a Stress Intensification Factor (SIF).

The stress analysis of elbows has been the subject of many studies since 1910 when a German named Bantlin

demonstrated that curved pipe segments behaved differently than predicted by simple curved beam theory.

The curved beam theory assumes the elbow cross section remains circular when subjected to bending

moments. In fact, the cross section becomes oval when subjected to load, increasing the flexibility and the

stress magnitude in the curved portion of the elbow.


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The figure below illustrates the cross section distortion of an elbow when subjected to bending moments.

The circumferential bending stresses caused by the cross sectional distortion of the elbow are generally higher

than the bending stresses in the adjoining pipe segments.

The magnitude of the stresses and the degree of flexibility of an elbow have been determined by a number of

researchers. These analytical solutions have been verified by full scale tests of pressurized and non

pressurized elbows.

The equations for SIFs for the different types of elbows and tees are given in Appendix D of the Code. These

formulas determine the flexibility characteristics h and then, using that value, calculate the inplane and

outplane SIFs.

The Code also includes equations for computing SIFs for branch connections.

There can be stress intensification at flange and other seemingly innocent connections because of the change

in geometry. The Code suggests the following :

Description SIF

Butt-welded joint, reducer or weld neck flange 1.0

Double welded slip-on flange 1.2

Socket weld flange or fitting, fillet welded joint 1.3 - 2.1

Lap joint flange 1.6

Threaded pipe joint or threaded flange 2.3


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Omission of appropriate SIFs from the input for any piping stress analysis can result in a gross under-

estimation of the actual stresses. It is important to recognise that SIFs should be applied at most locations in

the piping net work where there is a change in geometry or a hole in the pipe.

8. EASILY ANALYZED PIPING SYSTEMS:

A formal piping flexibility analysis using the computer is not required for every piping system. Analysis is

not required for systems that duplicate or replace existing systems which have a satisfactory service record or

for systems which may be readily compared to previously analysed systems. Also, approximate or simplifiedmethods may be used for configurations for which adequacy has been demonstrated thus obviating a formal

analysis.

For an approximate analysis, the two types of stresses, sustained and displacement, are calculated by different

methods and compared to different allowable stresses.

Stresses due to sustained loads are calculated by the weighted cantilever method which employs basic beam

equations.

Stresses resulting from displacement loads are calculated by the guided cantilever method for simple systems.

Caution must be exercised in applying approximate methods. Assumptions or simplifications for modelling

the piping system must be conservative. The stresses values generated by an approximate analysis are notnecessarily actual. They should be used only to indicate whether a formal analysis is necessary.

8.1 SUSTAINED LOAD STRESSES:The stresses resulting from sustained loads are calculated by the weighted cantilever method. Maximum

stress is determined by dividing the maximum moment by the section modulus of the pipe and adding the

longitudinal stress due to pressure. The weight of the pipe and its fluid contents is considered but the weight

of insulation is usually ignored for approximate analysis.

Figure 8 illustrates the application of two of the maximum moment equations to model a simple piping

system.

For which M = PL + WL (L/2)

From this maximum moment, the stress can be determined.

Frequently a piping system is too complicated to analyse as a whole. In these instances, it can be broken

down into sections for analysis.

In analysing the system shown in Figure 9, a conservative approach is to break it into three sections and

consider each separately as shown in Figure 9. For section 3, to assure conservatism, the moment for the

longer leg at its anchor, rather than that for the shorter one, is computed.


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Figure 11, illustrates the conservative consideration of another situation frequently encountered in piping

system analysis.

Because both cantilever legs deflect the same due to the weight of the vertical section, the moment is larger

at the anchor for the shorter cantilever. Therefore, to be conservative, only the moment on the leg is

considered for calculating the stress in the piping system. To conservatively calculate that moment, it is

modelled as a uniform load on the shorter cantilever plus a concentrate load acting at its end. Theconcentrated load P is composed of two components, viz, the actual weight of the vertical leg and the

conservatively estimated effective weight of the longer cantilever leg. Experience has shown that including

half the weight of the longer leg is sufficient to assure a conservative analysis.

wL2s + PLs

M= -------- 2

Where : P = w ( cLL + Lv)

c = 0.5


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8.1.1 MATHEMATICAL EXAMPLE:

Figure 12 shows the application of the foregoing concepts to an actual piping system numerical values.

20'

16'

Section A

15' 0

Data

Pipe NPS 12 Sch 10 S 30' Section B

w = 25 lb / ft

Z=22.0 inch3 24'

P = 200 psi

FIGURE 12 - EXAMPLE PROBLEM

To simplify the problem, the analyst separated the system into two sections at Point 0. The two ends at

Point 0 are both considered to be anchored. The maximum longitudinal stress in each section is calculated.

FOR SECTION A (Figure 12A) :In this case, the weight of the 16 feet section is ignored, and the maximum moment for the 20 feet length is

calculated on the basis of uniformly loaded cantilever beam.

20'

16' LL

FIGURE 12 A - SECTION A

wLL2

M =

2

25 ( 202 )

= 5000 FT-lb

2

M 5000 (12 in./ft.)

Sw= =

Z 22

= 2727 psi


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FOR SECTION B (Figure 12 B):

The weights of the 30 feet vertical leg Lv and the 24 feet horizontal leg L L are combined into a concentrated

load P acting at the end of the shorter 15 feet cantilever leg L S. In this case the analyst considered the

effective weight of LLto be one half its actual weight.

P = w (Lv + LL/2 )

= 25 ( 30 + 24/2 ) = 1050 lb

M = PLs + w ( Ls/ 2) Ls = (conc. load ) (uniform load)

= 1050 (15) + 25 ( 15/2 ) 15

= 18563 ft - lb

18,563 x 12 in / ft

Sw = M/Z = = 10,125 psi

22

The longitudinal stress resulting from internal pressure in the system is then calculated by the formula.

PrD 200 ( 12.75)

Sp = = = 3542 psi

4 t 4( 0.18)

This value is added to the largest calculated weight stress to give the total longitudinal stress in the system.

SL = Sw (max.) + Sp = 10,125 + 3542 = 13,667 psi.

SL is then compared to the allowable stress for the material used at operating temperature Sh to decide

whether a formal analysis is required because of sustained loads.


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8.2 DISPLACEMENT LOAD STRESSES:

Stresses produced by displacement loads are calculated by the guided cantilever method. Consider the

where LS= length of shorter leg

LL= length of longer leg

This system may be conservatively modelled as follows :

where M = bending moment at end of LS

P = force exerted by expansion of LL.

= free expansion of LL.

This is the "guided cantilever" model - a beam with one end fixed and other free to deflect but locked against

rotation.


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8.2.1 EXAMPLES:

The following illustrate the application of the guided cantilever method for evaluating flexibility.

Example in Figure 15

Header : NPS 6, A53 Gr.BBranches : NPS 2, A53 Gr.B

SA= 29.6 ksi

TCOLD= 70 F

THOT = 275 F

Expansion = 1.61 in/100 ft.

SIF at stub-ins (2), (3) & (4) = 3.36

3 E D !

f = ------------- where

144 L2

f = Stress. lb / in2

E = 30 x 106 lb / in2

D = Pipe OD, inches ! = Deflection, inches

L = Span, ft.


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The point on the system which will undergo the largest deflection is node (4). The horizontal deflection will

be :

4 = (30 + 15 + 15) (0.0161) = 0.966 inch

Considering branch 4-7 to be a guided cantilever, the approximate stress is f4 = 6370 psi from above

formulae including the SIF raises the stress to 21.4 ksi. This stress is less than SA, therefore the system isadequately flexible and need not be formally analysed for displacement stresses.

Example in figure 16 :

Pipe : NPS 4, Sch 40, A53 Gr.B.

SA = 29.0 ksi

TCOLD= 70 F

THOT = 550 F

Expansion = 4.11 in/100 ft.

SIF at LR ells = 1.95

Since the system is of uniform pipe size, an imaginary anchor may be assumed to exist at node (3). This

breaks the system into two parts and each part can be further simplified into a guided cantilever. The

horizontal movement at node (2) can be approximated as !2= (13) (0.0.411) = 0.53" and at node (4) it can

be approximated as !4= (12)(0.0411) = 0.49". From above formulae, the guided cantilever stresses are SE2= 80,740 psi and SE4 = 45,420 psi. Because SE2 and SE4 is higher than the allowable stress SA, a formal

analysis is required.

9.0 PIPING FLEXIBILITY ANALYSIS:Design of safe, functionally acceptable piping systems requires that they be adequately supported while

retaining sufficient flexibility to accommodate thermal and external displacements without imposing forces

and moments that will overstress the pipe, piping components or attached equipment. The design involves

three basic steps as described in Para3 and illustrated by Figure 1.

It is important to note that when one step in the design process exceeds its limit, the analysis must be

repeated beginning with Step 1 regardless of which step failed. Each step must be completed for every

analysis, but for some problems one step may be more significant than the others. For example, for theanalysis of an NPS 24 steam header on a pipe bridge, the thermal analysis would be the most important step.

When a piping system is connected to sensitive equipment, such as a pump, turbine etc., the reaction analysis

is the most important; but each step in the process must be successfully completed.


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9.1 WEIGHT-PLUS-PRESSURE ANALYSIS:

Purpose

The purpose of a weight-plus-pressure analysis is to determine whether the piping system satisfies EQ.1,

SL " Sh. If it does, the piping system is sufficiently stiff against weight and pressure loads.

Data requiredThe process and mechanical data required for the weight-plus-pressure analysis of a piping system include :

1. Appropriate piping drawings or sketches to give the geometry of the system (Isometric).

2. Piping specification to provide wall thickness, materials of construction, types of branch connections, etc.

3. Specific gravity of the fluid in the pipe.4. Maximum and minimum design temperature and pressure.

5. Insulation specification to obtain insulation density.

6. Ambient temperature.7. Young's modulus of elasticity 'Ec' at ambient temperature.

8. Young's modulus of elasticity 'Eh' at flex. temperature.

9. Bend radius.10. Weight of valves, control valves, flanges & other items.

11. Support locations and type.12. Allowable stress ranges SA, Sh, Sc.13. End point movements, and type of restraints.

14. Weight of valves and special items.

15. Type of fittings.16. Operating requirements

9.2 THERMAL ANALYSIS:

Purpose

A thermal analysis determines whether the piping system satisfies Eq.3, SE " SA . If it does, the system is

sufficiently flexible against thermal expansion and fixed anchor displacements.

Data required

The process and mechanical data required for the thermal analysis of a piping system consist of :

1. All data as listed for weight-plus-pressure analysis.

2. Other process information pertaining to expected number of cycles and possible extremes or upset

conditions.

After a thermal analysis has been performed, the system is checked for adequate flexibility by comparing the

displacement stress SE to the allowable stress range SA.


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9.2.1 RESTRAINST:

The restraints are the most difficult components to model adequately in the thermal analysis of a piping

system. Restraints are hangers, guides, anchors, attached equipment, or other devices which can constrain a

piping system. A restraint can impose a displacement on a piping system and cause displacement stresses;

and it can respond to loads imposed by the system if the restraint has inherent flexibility. Both displacement

and inherent flexibility should be incorporated in a thermal analysis. However, because the flexibility of a

restraint is usually very small when compared to that of the piping system, it may be ignored withoutintroducing too much conservatism into the analysis. This is not the case with displacements.

Spring hangers are restraints which usually are very flexible relative to the piping system. Therefore their

stiffness may be ignored without the analysis becoming too unconservative. See Para11.2 Spring hangers.

Restraints usually have the effect of raising the levels of thermal stresses and lowering the levels of weight

stresses. Therefore it is important to include all hangers, guides, and anchors in the thermal analysis.

Figure 17, below illustrates how restraint displacements affect the thermal analysis of a piping system.

The pipe is attached to heat exchanger "A" at nozzle (1) and to vessel "B" at nozzle (2). These nozzles are

restraints which constrain the piping system. When a cycle begins, the heat exchanger will thermally

expand from its point of fixed support in the +X direction and the vessel will grow upward from its point of

support attachment. Vessel "B" will grow in a direction that will tend to reduce the displacement stresses in

the pipe, while heat exchanger "A" grows in the direction that increases these stresses. Sometimes the hot

fluid in the pipe can cause the pipe to heat up much more quickly than either the heat exchanger or the

vessel because they are more massive than the pipe. If that is the case, the extremes of the thermal cycle can

be conservatively approximated by including the movement of the heat exchanger but not the movement ofthe vessel in the thermal analysis.


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9.3 REACTION ANALYSIS:

A piping system is adequate stress-wise if it satisfies Eqs. 1 & 3. However, unless the restraints are at least

as strong as the pipe, they may be overstressed or overstrained even though the piping is not. Often

allowable loads on certain pieces of equipment are very low relative to the strength of the pipe attached to

it.

Therefore, for piping systems connected to load-sensitive equipment such as pumps, a complete analysisincludes the calculation of maximum restraint reaction loads.

Weight, temperature, and pressure superimpose reaction loads on the restrains. Weight is always present,

but thermal and pressure loads may or may not be present. It may be necessary to analyse several cases to

find the loading combination that produces the maximum restraint reactions. For instance, the forces in the

system caused by weight can partially or completely cancel the forces caused by temperature. Therefore, the

magnitude of the sum may be less than the magnitude of one or more of the individual forces. This means

that to determine the maximum value of reaction loads, each load combination that the system may encounter

must be separately examined.

The constant portion of the reaction analysis consists of a weight only analysis. This generates the weight

reaction Rw.

A thermal reaction analysis of a piping system differs from a thermal stress analysis in that the installation

temperature is used as the cold temperature instead of the design minimum temperature. Either the design

maximum or design minimum temperature, depending upon which produces the greatest temperature

difference, is used as the other temperature.

The forces and moments on the restraints determined by a thermal-plus-pressure reaction analysis comprise

the reaction range R. A thermal-plus-pressure analysis can always be used to find the reaction range unless

the change in pressure and the change in temperature have opposite signs. In this case the effect of pressure

and of temperature must be evaluated separately.

To accommodate variation in the modulus of elasticity caused by temperature change, the maximum reaction

forces and moments at design temperature can be estimated by multiplying RT+Pby the ratio of the modulus

of elasticity at design temperature Em to the as-installed modulus Ea, that is

EmRT+P

Ea

This total reaction R is obtained by adding the constant and variable reactions.

EmR = RW + RT + P ( 7 )

Ea

This equation assumes elastic behaviour of the entire piping system. This assumption is sufficiently accurate

for systems where no plastic deformation occurs or where it takes place at many points in the piping system.It does not reflect the actual strain distribution in an unbalanced system where only a small portion of the

piping system undergoes plastic strain, or where creep is uneven. Under these conditions, the weaker or

more highly stressed portions of the sytems will suffer strain concentrations due to an elastic follow-up of

the stronger or lower stressed portions. This local overstrain can be produced by :

1) The use of small branches with larger headers with the branch lines relatively highly stressed.

2) Local reduction of pipe size or cross-sectional area or the transition to a weaker material.


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Local overstrain should be avoided where possible, especially when using materials of relatively low

ductility. Where unavoidable, its effects can be lessened by cold spring or controlled by expansion joints.

Following is an illustration of local overstrain and how it can affect the estimation of reaction loads.

Assume, a thermal-plus-pressure analysis has been performed and the reaction range at anchors A, B and C

determined, i.e. RA, RB and RC. By inspection, it can be seen that branch intersection point (1) will

thermally displace to the right. The displacement is caused by the expansion of branch A and is resisted by

branches B and C. Branch B will plastically deform at smaller displacements than branch C. For such

inelastic displacement, the actual reaction R at point B will be less than the calculated reaction RB, evenwhen modified by Eq.7. That is, the actual reaction R at anchor C will be greater than the calculated

reaction RCwhen modified by Eq.7. R at anchor A will be about equal to the value calculated by Eq.7.

Cold spring is defined by the code as the intentional deformation of piping during assembly to produce a

desired initial displacement and stress. Some of the benefits of intentional cold spring are :

1) It can serve to limit the amount of initial overstrain in the system. This is especially good for pipingmaterials of limited ductility.

2) It helps to assure minimum departure from as-installed hanger settings.

3) Credit for cold spring can be taken when calculating the total reaction load R. See Eq.8.

On the negative side :

1) Credit for cold spring is not permitted in stress range calculations. This restriction applies because the life ofa system under cyclic operation depends on the stress range rather than on the stress level at any given time.

When the effect of cold spring is included in Eq.7 it becomes :

EmR = RW + RT + P (1 - 2/3 C) (8)

Ea

The value of C, the cold spring factor, ranges from zero for no cold springing to 1.0 for 100% cold

springing. The additional 2/3 factor is included because a specified cold spring cannot be assured even withelaborate precautions.

The effect of misalignment during erection is similar to that of intentional cold spring except it may be

detrimental instead of beneficial because misalignment may be in a direction opposite to that produced by

thermal expansion. (Note that piping design may have to include special inspection requirements or the

piping designer must arrange to do the necessary inspection where alignment can be critical.

The possibility of non-simultaneous or uneven heating of a piping system must always be kept in mind when

performing an analysis because this condition can significantly affect the results. The piping stress analyst

should be sufficiently familiar with the process under normal and upset conditions to determine the worst

possible combination of uneven equipment and pipe branch heating. If the worst case is not obvious, such

combination should be analysed individually.


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In summary, a reaction analysis is performed to find the maximum reaction loads on the restraints. The

maximum reaction load on the system results from the highest combination of loads to which the piping is

exposed and, except for weight, can be modified by cold spring and the ratio of the module, Em/Ea, in

accordance with Eq.8.

10.0 ANALYSIS OF COMPLEX SYSTEMS:

Frequently piping systems are so geometrically complicated that a stress analysis of the system as a whole

would be impossible, even with the help of the computer program. The solution is to make simplifyingassumptions which permit considering a part of the piping system at a time.

One common technique is to separately consider branches in which small size branch lines are attached to

larger size main lines. It is called "the tail does not wag the dog" assumption. After the main line is

analysed, the displacement (linear and angular) at the intersection points found in the thermal analysis of the

main line are input as extraneous anchor displacements in the analysis of the branches. The SIFs at the

branch connections must be included in the analysis of both the main line and the branch lines.

This can be done because the stiffness of a piece of pipe is proportional to its moment of inertia, which

increases geometrically with increasing pipe size. For example, an NPS 3 Sch 40 pipe is over 4 times as

stiff as an NPS 2 Sch 40 pipe and an NSP 12 Sch. 40 pipe is almost 100 times stiffer than an NPS 3 Sch 40

pipe. This means that smaller branch lines usually have such a small effect on the larger main lines that they

can be ignored. This will unestimate the displacement stresses in the main line and overestimate thedisplacement stresses in a branch. This technique is not appropriate for sustained stresses.

Another technique to simplify the analysis is to use anchors to break the system into smaller parts. Find a

suitable place to restrain the system, anchor it, and then perform the analysis separately on each part of the

system. This is easier than trying to analyse the entire system at once and is appropriate for both sustained

and displacement stresses. The anchor must be installed when the system is built.


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11.0 SUPPORT SELECTION:

Sustained loadings on a piping system often necessitate the use of supports between anchors. To provide

this support, three types of hangers are generally employed :

a) Rigid Supports:Rigid supports are those which prevent movement in one or more directions. Typical rigid supports are rod

hangers, pipe shoes, longitudinal guides, transverse guide and intermediate anchors.

b) Variable supports (spring hangers )

Variable supports or spring hangers provide a supporting force that changes with thermal deflection. This

type of hanger is used at points where both support and flexibility are required to some degree.

b) Constant support spring hangers:

Constant spring hangers provide a constant supporting force throughout the thermal cycle. This type hanger

does not resist thermal deflection and therefore will not increase either displacement stresses or restraint

reaction loads. This hanger is used where larger thermal displacements are encountered.

11.1 RIGID SUPPORTS:

When modelling rigid pipe supports keep in mind that :

1) Rigid supports usually are not really rigid and cannot be designed to prevent a movement of less than 1/16".

They can have significant inherent flexibility. This can be an important consideration when a support to

prevent movement is needed. It is not practical to reduce the restraint reaction loads on a nozzle by

preventing displacement at the nozzle with a rigid support.

2) Thermal forces may tend to make a pipe lift off its supports. If the thermal forces pushing up on a pipe are

greater than the weight forces holding it down, the pipe will lift off when hot thereby rendering the support

ineffective during that part of the cycle.

3) Sliding type supports can cause friction loads that significantly affect the piping system. Because thermalloads are cyclical, friction loads will be in one direction when the pipe is warming up and in the other

direction when the pipe is cooling down. The coefficient of friction for steel on steel ranges from 0.25 to

0.50. Friction forces are particularly important in bridge piping as the system can have a tendency to snake

because of friction. It is usually good practice to guide and anchor these systems whenever possible to

eliminate the tendency to snake.

11.2 SPRING HANGERS:

Spring hangers are used to reduce stresses and reactions in piping systems. Different methods of analysis for

sizing the hangers are employed depending upon whether stress reduction or reaction reductions is the

primary concern.

11.2.1STRESS REDUCTION:The following method is used to size spring hangers to reduce the stress in a piping system.

1) Run a weight analysis with the points at which the spring hangers are located modelled as rigid in the

vertical or Y-direction. From this analysis the hot loads LH or the loads which the spring hangers are to

support in the hot condition are determined.

2) Run a thermal-plus-pressure analysis with the points at which spring hangers are located, free to deflect -

unrestrained - in the vertical direction. From this analysis the Y deflection (!Y), the deflection range

through which the spring hangers will operate, are determined.

3) Using the hot loads and Y deflections determined in Step 1 & 2, size and select the appropriate hanger using

the method set forth in vendor catalogues.


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In the sizing process, the spring constant K is developed and the cold load calculated by the following

equation.

LC = LH + K !Y (9)

Note :

The cold load is the load to which the spring hanger should be preloaded when delivered and installed. The

cold load must always be included in spring hanger specifications and requisitions.

To check the effect of the selected spring hangers on the stresses in the piping, analyse the system for

sustained and displacement stresses by the following procedure.

1) Run a weight-plus-pressure analysis. Specify the spring constants and cold loads for each point at which aspring hanger is located. Compare the computed stresses with the hot allowable stress Sh.

2) Run a thermal analysis specifying the spring constant for each spring hanger. Compare these stresses withthe allowable stress range SA.

12. REDUCING STRESSES:

To simplify the process for determining the best way to reduce stresses in piping systems, the problem is

broken into two parts. These are : 1) reducing stresses resulting from sustained loads; and 2) reducingstresses due to displacement loads. The two considerations require significantly different approaches and

frequently counteract each other. The general considerations for each are :

TO REDUCE STRESSES DUE TO SUSTAINED LOADS:

- Add supports to relieve stresses caused by weight.- Use thicker wall pipe to reduce stresses caused by pressure.

TO REDUCE STRESSES DUE TO DISPLACEMENT LOADS:

- Replace rigid supports with spring hangers.

- Revise the geometry of the system to increase flexibility.- Add expansion joints.

12.1 REDUCING STRESSES DUE TO SUSTAINED LOADS:

The obvious first step to reduce the stresses is to ascertain its cause. Many times the cause can be identified

by visual inspection of the system. Long spans of pipe, for example, are suspect. In other instances, a

detailed interpretation of the computer analysis is required to identify the best solution - location and type of

restraints for example.

If the stresses are caused by the weight of the system, adding supports is the solution. If pressure is the

cause, the pipe wall thickness must be increased. Occasionally thicker wall pipe is also the best solution to a

weight problem.

12.2 REDUCING STRESSES DUE TO DISPLACEMENT LOADS:

As with sustained loads, the initial step in the correction process is to identify the source of the stress. This

usually requires a detailed interpretation of the computer analysis which should include :

- Checking the input data to assure that the system is modelled exactly as intended.- Inspecting the computed stresses to identify the types of forces and moments causing those stresses.

- Evaluating the nature of the movement of the pipe. The translations and rotations, given for each mode,

often tell the story. In some cases, the pipe moves too much.

- Analysing the reactions on the system restraints. Both the moments and the forces should be checked to

assure that the restraints are not overloaded. These reactions can provide information to help determine the

cause of stresses.


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After the cause of the stresses is understood, the stress reduction process can begin. To reduce displacement

load stresses, flexibility is added to the system. Knowing the cause of the stresses permits adding flexibility

where it will be most effective. The three ways most frequently employed to add flexibility are to :

- Replace rigid supports with spring hangers.

- Add expansion joints and

- Revise the system geometry.

The usual approach to changing the system geometry to increase flexibility is to add expansion loops. An

expansion loop inserted in a straight run adds four elbows to the system. Elbows are much more flexible

then straight pipes. Whenever increased flexibility is required the addition of elbows should be considered.

A couple of elbows inserted at strategic places is frequently the economical solution to a flexibility

problem.

When flexibility is added to a system, the displacement load stresses are decreased but the sustained load

stresses are increased. Therefore these must be checked to see whether they remain within allowable limits.

The analyst must be aware that

- When sustained load stresses are reduced (system stiffness increased) displacement load stresses areincreased.

- When displacement load stresses are reduced (system flexibility increased) sustained load stresses areincreased, and

- Whenever one type of stress is reduced, the other must be checked to see if it is within its allowable value.

13. DESIGNING WITH EXPANSION JOINTS:Expansion joints can solve many problems encountered by the pipe stress analyst. Properly applied,

expansion joints can simplify layouts and are more economical than other solutions to expansion problems.

On the other hand, improper application of expansion joints can result in expensive repairs and

modifications, as well as costly shut-downs. The piping network must be carefully designed when using

expansion joints. There are three types of expansion joints ball type, slip type and bellows or corrugated

type. The ball- type and slip-type joints are seldom used because the packing is difficult to maintain or

because leaks through the packing are intolerable.

13.1 BELLOWS EXPANSION JOINTS:Bellows expansion joints (also known as corrugated expansion joints) are commonly used in piping systems

and are quite versatile. They are best suited for absorbing direct axial movement but can be used to absorb

lateral or angular movement. See Figure 19.


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Bellow expansion joints are essentially rigid in torsion.

By using appropriate hardware and two or more bellows to form an expansion joint, one can construct

universal, hinged, gimbals or pressure balanced joints as illustrated in Figure 20.

Many designers try to avoid the use of expansion joints because of previous un-fortunate experiences. There

are inherent problems which can be minimised with proper selection and application. Characteristics of

bellows expansion joints are :

1. Bellows are made of relatively thin metal. Corrosion can be a real problem because there is little metal

available. The bellows must be fabricated from a material resistant to corrosion attack by the process fluid.

An internal sleeve may be required to protect the bellows from erosion.

The relatively thin metal must be protected from abuse during shipment and construction, as well as after it is

installed. External blows on a bellows can render it useless. External protective covers should be

considered.

2. Bellows are designed to deform plastically. Because the bellows repeatedly yield as they move through

their rated cycle, they can be subject to premature fatigue failures. The normal high state of stress in the

bellows makes them prime candidates for stress corrosion attack. Austenitic stainless steel bellows should

not be specified for steam or water service, for example.

3. Bellows expansion joints can be easily misapplied. Without a thorough understanding of the limitations ofa bellows expansion joint, a designer may make a number of mistakes which lead to failures.

An example is over looking the pressure thrust from an expansion joint. This can result in specifying a joint

whose rated displacement is not sufficient to accommodate the movement of the system. Significant

torsional loads can also cause failure.

13.2. SELECTION AND SPECIFICATION:

The first step in designing with expansions joints is to make sure that the expansion joint is the practical and

economical means for providing flexibility. This is most often the case with large diameter pipe (greaterthan NPS 12) in compact layouts, and when there are low allowable reactions, such as at pump and turbine

nozzles.


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To protect the expansion joint from failure, it must be protected from excessive movement unless the pipe is

properly anchored and guided. The anchors and guides must take the test pressure thrust. The pressure

thrust is defined by :

dp2

TP = % PT (10)

4

The pressure thrust can be considered as two equal and opposite forces acting at each end of the expansion

joint, as illustrated in Figure 21.

Without the guide marked (1) the pipe might be overstressed at anchor A and the expansion joint could be

overextended. Guide (2) & (3) are necessary to prevent excessive lateral displacement and rotation of the

expansion joint. In general, the expansion joint must be free to move in the direction intended and must be

secured against deformation in other directions.

Pressure thrust can be eliminated from the piping system by using gimbals or hinged expansion joints.

If the bellow is near a machine which vibrates, the vibration amplitude and frequency should also be

specified. Occasionally, the limit rods (or tie rods) are subjected to thermal loads in addition to the loads

caused by pressure thrust. These loads must be described in detail to the expansion joint manufacturer.

Additional information is required to specify hinged, gimbals, or pressure-balanced expansion joints.


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14.0 SAMPLE DATA FOR EXPANSION RATE & ALLOWABLE STRESSES

14.1 MATERIAL : ASTM-A53GR.B, A106 GR.B, API 5L GR.B

TEMPERATURE $ E ANSI B31.3 - 1987 Ed

F C ( mm / M ) Kg / Cm2x106 &, Kg / Cm2 &A, Kg / Cm

2

-425 -254 - - - -

-375 -226 - - - -

-325 -198 -2.0 2.110 - -

-300 -184 -1.9 2.102 - -

-250 -157 -1.6 2.088 - -

-200 -129 -1.4 2.074 - -

-150 -101 -1.2 2.057 - -

-100 -73 -1.0 2.039 - -

-50 -46 -0.7 2.017 - -

-20 -29 -0.5 2.005 1406 2110

0 -18 -0.4 1.994 1406 2110

32 0 -0.2 1.980 1406 2110

70 21 0.0 1.962 1406 2110

100 38 0.2 1.959 1406 2110150 66 0.5 1.954 1406 2110

200 93 0.8 1.948 1406 2110

250 121 1.2 1.937 1406 2110

300 149 1.5 1.927 1406 2110

350 177 1.9 1.913 1406 2110

400 204 2.2 1.899 1406 2110

450 232 2.6 1.878 1368 2100

500 260 3.0 1.856 1329 2090

550 288 3.4 1.831 1273 2076

600 316 3.8 1.807 1217 2062

650 343 4.2 1.775 1195 2057

700 371 4.7 1.744 1160 2048750 399 5.1 1.694 914 1986

800 427 5.6 1.645 759 1948

850 454 6.0 1.473 612 1910

900 482 6.5 1.301 457 1872

950 510 6.9 1.192 316 1837

1000 538 7.4 1.083 176 1802

1025 552 7.6 1.041 144 1794

1050 566 7.9 0.999 113 1786

1075 579 8.1 0.957 91 1781

1100 593 8.4 0.914 70 1776

1125 607 8.6 - - -

1150 621 8.8 - - -1175 635 9.0 - - -

1200 649 9.2 - - -

1250 677 9.7 - - -

1300 704 10.2 - - -

1350 732 10.6 - - -

1400 760 11.1 - - -

1450 788 - - - -

1500 816 - - - -

&A = ( 1.25 &c + 0.25 &h ) i. e. Allowable stress range

! = Total thermal expansion (from 70 F / 21 C to indicated temp.)

E = Young's modules ; & = Allowable stress.


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14.2 MATERIAL : ASTM-A335 GR.P11 (SEAMLESS) COMPOSITION : 1.25 Cr. -0.5 Mo


F C ( mm / M ) Kg / Cm2x106 &, Kg / Cm2 &A, Kg / Cm2

-425 -254 - - - -

-375 -226 - - - -

-325 -198 -2.0 2.180 - -

-300 -184 -1.9 2.174 - --250 -157 -1.6 2.163 - -

-200 -129 -1.4 2.151 - -

-150 -101 -1.2 2.145 - -

-100 -73 -1.0 2.138 - -

-50 -46 -0.7 2.128 - -

-20 -29 -0.5 2.121 1406 2110

0 -18 -0.4 2.117 1406 2110

32 0 -0.2 2.111 1406 2110

70 21 0.0 2.102 1406 2110

100 38 0.2 2.096 1406 2110

150 66 0.5 2.085 1361 2098

200 93 0.8 2.074 1315 2087

250 121 1.2 2.056 1290 2080

300 149 1.5 2.039 1266 2075

350 177 1.9 2.025 1248 2070

400 204 2.2 2.011 1231 2066

450 232 2.6 1.990 1220 2063

500 260 3.0 1.969 1210 2060

550 288 3.4 1.948 1192 2056

600 316 3.8 1.927 1174 2051

650 343 4.2 1.899 1139 2043

700 371 4.7 1.870 1097 2032

750 399 5.1 1.839 1069 2025

800 427 5.6 1.807 1055 2022

850 454 6.0 1.765 1020 2013900 482 6.5 1.723 900 1983

950 510 6.9 1.670 774 1951

1000 538 7.4 1.617 549 1895

1025 552 7.6 1.571 468 1875

1050 566 7.9 1.525 387 1855

1075 579 8.1 1.479 334 1841

1100 593 8.4 1.434 281 1828

1125 607 8.6 1.350 229 1815

1150 621 8.8 1.265 176 1802

1175 635 9.0 1.181 130 1790

1200 649 9.2 1.097 84 1778

1250 677 9.7 - - -1300 704 10.2 - - -

1350 732 10.6 - - -

1400 760 11.1 - - -

1450 788 - - - -

1500 816 - - - -

&A = ( 1.25&c + 0.25&h ) i. e. Allowable stress range


E = Young's modules ; & = Allowable stress.


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14.3 MATERIAL : ASTM-A312 TP 304 SEAMLESS) COMPOSITION : 18 Cr. - 8 Ni


F C ( mm / M ) Kg / Cm2x106 &, Kg / Cm2 &A, Kg / Cm2

-425 -254 - - 1406 2110

-375 -226 - - 1406 2110

-325 -198 -3.2 2.138 1406 2110

-300 -184 -3.0 2.131 1406 2110

-250 -157 -2.6 2.117 1406 2110

-200 -129 -2.3 2.103 1406 2110

-150 -101 -1.9 2.085 1406 2110

-100 -73 -1.4 2.067 1406 2110

-50 -46 -1.0 2.044 1406 2110

-20 -29 -0.8 2.031 1406 2110

0 -18 -0.6 2.022 1406 2110

32 0 -0.4 2.006 1406 2110

70 21 0.0 1.989 1406 2110

100 38 0.3 1.980 1406 2110

150 66 0.7 1.964 1406 2110

200 93 1.2 1.948 1406 2110

250 121 1.7 1.927 1406 2110

300 149 2.2 1.905 1406 2110

350 177 2.7 1.888 1360 2098

400 204 3.2 1.871 1315 2086

450 232 3.7 1.853 1272 2076

500 260 4.2 1.835 1230 2065

550 288 4.7 1.810 1191 2055

600 316 5.2 1.786 1153 2046

650 343 5.7 1.765 1139 2042

700 371 6.3 1.744 1125 2039

750 399 6.8 1.720 1097 2032

800 427 7.4 1.695 1069 2025850 454 7.9 1.670 1048 2020

900 482 8.4 1.645 1026 2014

950 510 9.0 1.620 998 2007

1000 538 9.6 1.596 970 2000

1025 552 9.8 1.584 914 1986

1050 566 10.1 1.572 858 1972

1075 579 10.4 1.560 770 1950

1100 593 10.7 1.547 682 1928

1125 607 10.9 1.535 612 1911

1150 621 11.2 1.523 541 1893

1175 635 11.5 1.511 482 1878

1200 649 11.8 1.498 422 18631250 677 12.4 1.477 330 1840

1300 704 13.0 1.456 260 1823

1350 732 13.5 1.406 204 1809

1400 760 14.1 1.357 162 1798

1450 788 14.7 - 127 1789

1500 816 15.4 - 98 1782

&A = ( 1.25&c + 0.25&n ) i. e. Allowable stress range


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