C-27 PIPING FLEXIBILITY ANALYSIS

TRAINING MANUAL- PIPING PIPING FLEXIBILITY ANALYSIS Uhde India Limited

DOC No. : 29040-PI-UFR-0027 Rev.

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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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TRAINING MANUAL- PIPING PIPING FLEXIBILITY ANALYSIS Uhde India Limited 1.0


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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.

2.0

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.

PIPING CODES In 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 -320°F, 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 multiunit 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. This design 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 due to thermal effects and movement of the connections at the ends of the pipe.



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3.3 Designing the piping system to prevent its exerting excessive forces and moments on equipment such as pumps and tanks or on other connection and support points. Figure 1 schematically illustrates the flexibility analysis system. It is discussed in detail in Para. 9

Para.4 through 7 provide detailed explanation of the basic considerations involved in piping stress analysis Para.8 explains how to determine which piping systems justify computer modelling Para.9 deals with Piping Flexibility Analysis. Paras.10 through 13 discuss other aspects of evaluating and controlling the stress in piping system. 4.

DEFINITIONS : The following symbols and definitions are used in this document. Aw Cross-sectional area of corroded pipe wall, inch2 C Cold spring factor. D Outside diameter of pipe, inch. dp Pitch diameter of bellows expansion joint, inch. E Casting quality or weld joint factor. Ea Modulus of elasticity at installation temperature, psi. Ej Weld joint factor for welded pipe. Em Modulus of elasticity at design maximum temperature, psi. FA Axial force, lbf. f Stress range reduction factor based on the total number of full temperature cycles (f =1 for 7000 or fewer cycles). h Flexibility characteristic. ii Inplane stress intensification factor. io Outplane stress intensification factor. K Spring constant, lbf / inch. LC Cold load exerted by spring hanger, lbf. LH Hot load exerted by spring hanger, lbf. M Bending moment, ft-lbf. Mi Inplane bending moment, in-lbf.

TRAINING MANUAL- PIPING PIPING FLEXIBILITY ANALYSIS Uhde India Limited Mo Mt P Pr PT R RT +P RW S SA Sb


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Outplane bending moment, in-lbf. Torsional moment, in-lbf. Concentrated force, lbf. Internal pressure, psi. Test pressure, psi. Total reaction forces & moments, lbf or ft-lbf. Variable reaction caused by thermal & pressure effects, lbf, ft-lbf. Weight reaction, lbf or ft-lbf. Basic allowable stress from Appendix A of B31.3, psi. Allowable stress range, psi. Resultant bending stress, psi. 0.5

2

+

2

(i i M i ) (i o M o ) _______________ z Basic allowable stress at minimum metal temperature during the displacement cycle, psi Computed displacement stress range, psi. Basic allowable stress at maximum metal temperature during the displacement cycle, psi. Sum of longitudinal stresses caused by pressure, weight and other sustained loadings, psi. Torsional stress, psi = M t / 2Z Pressure thrust of bellows expansion joint, lbf. Pipewall thickness, inch. Deflection in y-direction, inch. Section modulus of pipe, inch3. =

Sc SE Sh SL St Tp t y Z 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 δ. 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 δ, 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 and restraint 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 = (S b2 + 4S t2)½

(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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BASIC ALLOWABLE STRESSES : The code sets forth the rules for deriving basic allowable stresses for metals in the clause, 302.3.2 - Bases for design stresses. The significant aspect of these rules is that B31.3 permits the use of one third the tensile strength, rather than one fourth the tensile strength as used by Section VIII, Division I, of the ASME Code, using section VIII allowable stresses for piping is unduly conservative. For piping flexibility analysis, longitudinal stresses, i.e. stresses which act in the direction parallel to the centerline of the pipe, are the primary concern. Appendix A Table 1 of the Code tabulates basic allowable stresses.

6.2

ALLOWABLE SUSTAINED STRESS : The allowable stress for sustained loads is the basic allowable stress at the maximum metal temperature, Sh. See Para.5.1

6.3

ALLOWABLE DISPLACEMENT STRESS RANGE : The computed displacement stress range SE in a piping system shall not exceed the allowable displacement stress range. SA calculated by equation No.5. S A = f ( 1.25 S c

+

0.25 S h )

(5 )

When S h is greater than S L, the difference between them may be added to the term 0.25 S h in equation 5. In that case, the allowable stress range is calculated by equation No.6. S A = f [ 1.25 ( S c

+

Sh) - SL ]

(6 )

6.3.1 EXPLANATION FOR STRESS RANGE : Note that an allowable stress range rather than an allowable stress are considered for displacement loads. In addition, the allowable stress range can exceed the yield strength but not the elastic range of the material. (S A can be as large as 1/3-2/3 times the yield strength of the material. The code allows the piping material to yield during its initial cycle provided it afterwards stays within its elastic range. The stress-strain diagram illustrates this concept.

During the initial cycle, the material is strained along the path represented by the line OA and strained beyond yield by as much as 0.1%. When the displacement load is released, the strain relaxes along the line AB. Repeated cycles cause the material to behave elastically, i.e., follow the elastic line represented by the line AB. If the stress range for a piping system is greater than the elastic range of the material (about twice the yield strength), the material would yield repeatedly at each end of the displacement load cycle (line CDEF), causing premature failure.

TRAINING MANUAL- PIPING PIPING FLEXIBILITY ANALYSIS Uhde India Limited 6.3.2


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TYPICAL EXAMPLE OF STRESS RANGE

Let it be assumed that the 90º turn shown above is to absorb 6" of expansion between anchors and that the calculated maximum stress is 24,000 psi. Supposing the material at the particular operating temp. has 18,000 psi yield stress, further thermal expansion will be associated with yielding equal to ∆Y. After this when system is cooled down to ambient conditions it induces stress in opposite direction equivalent to yielding i.e. from 18,000 to 24,000 equal to 6,000 psi.

This -ve cold stress is again limited to cold yield stress Syc (otherwise there will be repetitive hot and cold yielding and pipe will fail). Therefore actual stress range available to us, SR=Syc + Syh



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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 Sh which 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.

6.4

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)

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 Double welded slip-on flange Socket weld flange or fitting, fillet welded joint Lap joint flange Threaded pipe joint or threaded flange

1.0 1.2 1.3 - 2.1 1.6 2.3



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Omission of appropriate SIFs from the input for any piping stress analysis can result in a gross underestimation 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 simplified methods 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 not necessarily 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. The concentrated 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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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 w = 25 lb / ft Z=22.0 inch3 P = 200 psi

30'

Section B 24'

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'

FIGURE 12 A - SECTION A

M=

wLL2 2

25 ( 202 ) = 5000 FT-lb 2 M Sw =

5000 (12 in./ft.) =

Z

= 2727 psi

22

LL



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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 LL are combined into a concentrated load P acting at the end of the shorter 15 feet cantilever leg LS. In this case the analyst considered the effective weight of L L to be one half its actual weight.

P = w (Lv + L L/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 = 22

= 10,125 psi

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

P rD 4t

200 ( 12.75) =

= 3542 psi 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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EXAMPLES :

The following illustrate the application of the guided cantilever method for evaluating flexibility. Example in Figure 15 Header : NPS 6, A53 Gr.B Branches : NPS 2, A53 Gr.B SA = 29.6 ksi TCOLD = 70 º F THOT = 275º F Expansion = 1.61 in/100 ft. SIF at stub-ins (2), (3) & (4) = 3.36 3ED∆ 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 is adequately 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 º F THOT = 550º 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 the analysis 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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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 required The process and mechanical data required for the weight-plus-pressure analysis of a piping system include :

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Appropriate piping drawings or sketches to give the geometry of the system (Isometric). Piping specification to provide wall thickness, materials of construction, types of branch connections, etc. Specific gravity of the fluid in the pipe. Maximum and minimum design temperature and pressure. Insulation specification to obtain insulation density. Ambient temperature. Young's modulus of elasticity 'Ec' at ambient temperature. Young's modulus of elasticity 'Eh' at flex. temperature. Bend radius. Weight of valves, control valves, flanges & other items. Support locations and type. Allowable stress ranges SA, Sh, Sc. End point movements, and type of restraints. Weight of valves and special items. Type of fittings. 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. 2.

All data as listed for weight-plus-pressure analysis. 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 without introducing 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 of the vessel in the thermal analysis.



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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 analysis includes 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+P by the ratio of the modulus of elasticity at design temperature Em to the as-installed modulus Ea, that is RT+P

Em Ea

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

+

RT + P

Em

(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, even when modified by Eq.7. That is, the actual reaction R at anchor C will be greater than the calculated reaction RC when 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 piping materials 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 of a 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 : Em R = 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 with elaborate 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 simplifying assumptions 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 4½ 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 the displacement 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 thermal loads 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. 11.2.1 STRESS 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 a spring 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 with the 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) reducing stresses 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

13.

13.1

When sustained load stresses are reduced (system stiffness increased) displacement load stresses are increased. When displacement load stresses are reduced (system flexibility increased) sustained load stresses are increased, and Whenever one type of stress is reduced, the other must be checked to see if it is within its allowable value. 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. 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 of a 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 (greater than 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 : T P = π PT

dp2

(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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SAMPLE DATA FOR EXPANSION RATE & ALLOWABLE STRESSES

14.1

MATERIAL : ASTM-A53GR.B, A106 GR.B, API 5L GR.B TEMPERATURE ∆ E ˚F ˚C ( mm / M ) Kg / Cm2x106 -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 0 -18 -0.4 1.994 32 0 -0.2 1.980 70 21 0.0 1.962 100 38 0.2 1.959 150 66 0.5 1.954 200 93 0.8 1.948 250 121 1.2 1.937 300 149 1.5 1.927 350 177 1.9 1.913 400 204 2.2 1.899 450 232 2.6 1.878 500 260 3.0 1.856 550 288 3.4 1.831 600 316 3.8 1.807 650 343 4.2 1.775 700 371 4.7 1.744 750 399 5.1 1.694 800 427 5.6 1.645 850 454 6.0 1.473 900 482 6.5 1.301 950 510 6.9 1.192 1000 538 7.4 1.083 1025 552 7.6 1.041 1050 566 7.9 0.999 1075 579 8.1 0.957 1100 593 8.4 0.914 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 σA = ( 1.25 σ c + 0.25 σ h ) i. e. Allowable stress range ∆ = Total thermal expansion (from 70º F / 21º C to indicated temp.) E = Young's modules ; σ = Allowable stress.

ANSI B31.3 - 1987 Ed σ, Kg / Cm2 σA, Kg / Cm2 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1368 2100 1329 2090 1273 2076 1217 2062 1195 2057 1160 2048 914 1986 759 1948 612 1910 457 1872 316 1837 176 1802 144 1794 113 1786 91 1781 70 1776 -


σA

MATERIAL : ASTM-A335 GR.P11 (SEAMLESS) TEMPERATURE ∆ E ˚F ˚C ( mm / M ) Kg / Cm2x106 -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 0 -18 -0.4 2.117 32 0 -0.2 2.111 70 21 0.0 2.102 100 38 0.2 2.096 150 66 0.5 2.085 200 93 0.8 2.074 250 121 1.2 2.056 300 149 1.5 2.039 350 177 1.9 2.025 400 204 2.2 2.011 450 232 2.6 1.990 500 260 3.0 1.969 550 288 3.4 1.948 600 316 3.8 1.927 650 343 4.2 1.899 700 371 4.7 1.870 750 399 5.1 1.839 800 427 5.6 1.807 850 454 6.0 1.765 900 482 6.5 1.723 950 510 6.9 1.670 1000 538 7.4 1.617 1025 552 7.6 1.571 1050 566 7.9 1.525 1075 579 8.1 1.479 1100 593 8.4 1.434 1125 607 8.6 1.350 1150 621 8.8 1.265 1175 635 9.0 1.181 1200 649 9.2 1.097 1250 677 9.7 1300 704 10.2 1350 732 10.6 1400 760 11.1 1450 788 1500 816 = ( 1.25σc + 0.25σ h ) i. e. Allowable stress range

∆

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

E

=

Young's modules ;

σ = Allowable stress.


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COMPOSITION : 1.25 Cr. -0.5 Mo

ANSI B31.3 - 1987 Ed σ, Kg / Cm2 σA, Kg / Cm2 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1361 2098 1315 2087 1290 2080 1266 2075 1248 2070 1231 2066 1220 2063 1210 2060 1192 2056 1174 2051 1139 2043 1097 2032 1069 2025 1055 2022 1020 2013 900 1983 774 1951 549 1895 468 1875 387 1855 334 1841 281 1828 229 1815 176 1802 130 1790 84 1778 -


MATERIAL : ASTM-A312 TP 304 SEAMLESS) TEMPERATURE ∆ E ˚F ˚C ( mm / M ) Kg / Cm2x106 -425 -254 -375 -226 -325 -198 -3.2 2.138 -300 -184 -3.0 2.131 -250 -157 -2.6 2.117 -200 -129 -2.3 2.103 -150 -101 -1.9 2.085 -100 -73 -1.4 2.067 -50 -46 -1.0 2.044 -20 -29 -0.8 2.031 0 -18 -0.6 2.022 32 0 -0.4 2.006 70 21 0.0 1.989 100 38 0.3 1.980 150 66 0.7 1.964 200 93 1.2 1.948 250 121 1.7 1.927 300 149 2.2 1.905 350 177 2.7 1.888 400 204 3.2 1.871 450 232 3.7 1.853 500 260 4.2 1.835 550 288 4.7 1.810 600 316 5.2 1.786 650 343 5.7 1.765 700 371 6.3 1.744 750 399 6.8 1.720 800 427 7.4 1.695 850 454 7.9 1.670 900 482 8.4 1.645 950 510 9.0 1.620 1000 538 9.6 1.596 1025 552 9.8 1.584 1050 566 10.1 1.572 1075 579 10.4 1.560 1100 593 10.7 1.547 1125 607 10.9 1.535 1150 621 11.2 1.523 1175 635 11.5 1.511 1200 649 11.8 1.498 1250 677 12.4 1.477 1300 704 13.0 1.456 1350 732 13.5 1.406 1400 760 14.1 1.357 1450 788 14.7 1500 816 15.4 σA = ( 1.25σ c + 0.25σ n ) i. e. Allowable stress range ∆ = Total thermal expansion (from 70º F / 21º C to indicated temp.) E = Young's modules ; σ = Allowable stress.


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COMPOSITION : 18 Cr. - 8 Ni ANSI B31.3 - 1987 Ed σ, Kg / Cm2 σA, Kg / Cm2 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1406 2110 1360 2098 1315 2086 1272 2076 1230 2065 1191 2055 1153 2046 1139 2042 1125 2039 1097 2032 1069 2025 1048 2020 1026 2014 998 2007 970 2000 914 1986 858 1972 770 1950 682 1928 612 1911 541 1893 482 1878 422 1863 330 1840 260 1823 204 1809 162 1798 127 1789 98 1782

C-27 PIPING FLEXIBILITY ANALYSIS

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