stress analysis concept

8/9/2019 Stress Analysis Concept

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PIPE STRESS ANALYSIS

- CONCEPTS

Satyashish Sahu

Month YearMonth Year


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Date of last change Reference/Name of Presentation/SN 2

PIPE STRESS ANALYSIS -

CONCEPTS

l Analytical procedure to evaluate the stress state at

various points in a piping system.

l Also known as flexibility analysis since it also helps

ascertain the required flexibility in the piping system

l Helps determine displacements and forces / moments on

the hangers, supports, restraints, guides, stops and

anchors in the piping system

- STRESS ANALYSIS -- STRESS ANALYSIS -

What is piping stress analysis


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PIPE STRESS ANALYSIS -

CONCEPTS

l Stress in pipesl Stress categories

l Thermal behavior of pipes

l Stress in piping components

l External load categories

l Piping supportsl Spring hangers

l Constant effort hangers

l Friction

l Piping codes

l ASME B 31.1 - Power piping code


Contents


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Stress in pipes


Fig-1 Biaxial stress state in a pipe

sl= PDO/4t + BM/Z

Where BM = (Mx2+My2)1/2

sh= PDO/2t

t= TM/J

Where TM= Mz


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Stress in pipes


Fig-2 Mohrs circle of the biaxial stress state


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Stress in pipes

l Figure-1 shows the stresses in pipes. The various stresses includedin stress evaluation are:

Pressure Hoop stress

Pressure longitudinal stress

Bending & torsional stress due to weight of pipe, contents and insulation

Bending & torsional stress due to any point loads, wind loads,

earthquake loads, hammer loads

Bending & torsional stress due to restriction of thermal expansion

l It is always assumed (in fact due care is taken to ensure) that plant

piping will consist of at least two perpendicular segments between

anchors. The Axial stresses due to thermal effects and also due to

any other external loading in such a case will be negligible and are

hence neglected in stress calculations. So also is buckling neglected.


Stress in pipes


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Stress categories

l Primary membrane stress This is the stress due to external loading of the pipe like weight,

point load, wind, earthquake

If this exceeds the allowable stress it will cause failure of the pipe

through continuous yielding

l Secondary stress This stress is not caused by any external loading but by such

physical tendencies as thermal expansion

This stress is self-limiting in nature. It relieves itself upon yielding.

It is due to this fundamental difference in behavior between

primary and secondary stress that these two stress categoriesare treated very differently. These stresses are never added up

and have different allowable values


Classification of stress


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Thermal behavior of pipes

l When a pipe is heated up, stresses are caused if the free thermalmovement of the pipe is restricted. Upon reaching the yield point, the

pipe starts yielding and the stresses as well as the thermal loads on

the restraints get relieved. This is called thermal shakedown. When

the pipe is cooled, it comes back to its original position and now the

stresses and restraint loads reappear but with opposite signs.

The difference between the hot stress and the cold stress is called

the stress range.


Thermal shakedown / Stress range


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Thermal behavior of pipes


Fig-3 Stress range

Total

stress range ST= Shy + Scy

where:

Shy = Hot yield strength

Scy = cold yield strength


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Stress in piping components


Stress intensification factors - SIF

l Elbows, branch connections and reducers will have a higher level of

stress when compared to a straight pipe for the same amount of

bending moment.

l The factor by which the stress in the pipe component exceeds that of

the straight pipe is called SIF (stress intensification factor).l SIF of a component depends upon its geometry and is calculated

using empirical formulae available in piping codes.

l For special components like Y-piece where no empirical relations are

available, SIF will have to be determined through a analytical

procedure like FEM.


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Relation between Elbow geometry and SIF

l Elbow / bend radius - Has inverse relation to SIFl Elbow diameter - Has direct relation to SIF

l Elbow thickness - Has inverse relation to SIF

Relation between Branch geometry and SIF

l Header diameter - Has direct relation to header & branch SIFs

l Header thickness - Has inverse relation to header & branch SIFs

l Branch diameter - Has direct relation to branch SIF. Has no bearing

on header SIF

l Branch thickness - Has direct relation to branch SIF. Has no bearing

on header SIF


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Relation between Branch type and SIF

l The various branch types are listed with their SIF in the

increasing order

Welding Tee

Integrally reinforced fitting as per MSS SP 97

Reinforced fabricated Tee

Unreinforced fabricated Tee Increa

sing

SIF


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External load categories


Types of external loading on pipes

l Sustained loading These loads will act on the pipe throughout its operating tenure

and include

Dead loads like weight of pipe, insulation and inline

components

Live loads like weight of contents in the pipe

l Occasional loading

These loads act on the pipe only for certain duration or during

abnormal operating conditions and include

wind Dynamic loads like earthquake, hammer, safety valve thrust


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Piping supports


Types of pipe supports

l Rigid support - An inflexible restraint used primarily to carry thesustained pipe loading. They cannot be used where there is upward

pipe movement.

Rigid hanger

Sliding base support

l Variable effort (spring) support - A flexible spring used to carry the

sustained pipe loading while allowing for upward / downward pipe

movement. The supporting effort varies as the pipe moves up or

down.

l Constant effort support - Used to carry the sustained pipe loading

while allowing for upward / downward pipe movement. The

supporting effort remains constant throughout the upward /downward travel of the pipe.


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Piping supports


Types of pipe supports (cont)

l Thermal Restraint - This is usually a rigid element used to alter /control the thermal growth of the piping system so as to bring theterminal point forces / moments and thermal stresses under limit.

Axial restraint : Movement prevented in pipe axial direction

Transverse / Lateral restraint : Movement prevented in pipe transversedirection

l Guides - Guides are similar to bi-directional restraints but with theprimary purpose of guiding the pipe smoothly into the pipe axial orlateral direction.

Transverse / Lateral guide : Pipe movement guided into the transversedirection

Axial guide : Pipe movement guided into the pipe axial direction

l Anchors - Anchors arrest all the six degrees of freedom of the pipe.

Anchors are sometimes inserted to completely separate twoconnected pipes to enable the analyst to analyse the pipesindependently.


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Spring Hangers


Spring Hanger selection procedure

For spring hanger selection the following steps are required

l Calculation of weight balance load

The load that would act on the spring hanger if it were completely rigid

and the piping system was in static equilibrium under sustained loading

condition

l Calculation of vertical free thermal movement

The thermal growth of the pipe under the influence of temperature I.e the

vertical pipe length x the coeff of thermal expansion

l Selection of appropriate spring constant

An appropriate spring constant from a supplier catalogue based upon theweight balance load and vertical thermal movement such that the load

variation between the cold and hot positions is within 25%.


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Spring Hangers


Hot setting / Cold setting of springs

There are two ways of setting the springs - Hot setting and Cold setting

l Hot setting - The spring is set such that it carries the weight balance

load in the hot position of the pipe

l Cold setting - The spring is set such that it carries the weight balance

load in the cold position of the pipe.

The behavior of the piping system will vary under hot and cold setting

because the spring carries different loads under the two settings.

Fig-4 shows how exactly these two types of spring setting affect the

load carried by the spring.


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Spring Hangers


Fig-4 Hot / Cold setting

Springcagemovement

0%

100%

Cold pos of

pipe

Hot pos of

pipe

Load

Weightba

lance

load

Coldsetting

Hot

setting


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Spring Hangers


Spring hanger terminologies

l Cold load - The load carried by the spring when the pipe is in coldposition

l Hot load - The load carried by the spring when the pipe is in hot

position

l Installation load - The load the spring would carry when the pipe is at

its installation position I.e zero vertical displacement. The installation

load would be equal to the cold load provided the vertical pipe

displacement in the cold condition is zero. But this may not be the

case always.

The spring is pre-compressed to the installation load, locked and

then erected on the pipe.


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Constant effort Hangers


Constant effort hangers

l When pipe vertical movement is high (above 50 mm), it is usually not

possible to select variable effort hangers with load variation within

25%. In such a situation, constant effort hangers are used.

l Constant effort hangers as the name suggests apply a constant effort

on the pipe throughout the complete range of the pipe vertical

movement.

l The effect of the constant effort hanger is similar to that of supporting

the pipe with a chain-pulley-block system


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Friction


Frictional effects of pipe supports

l Friction at sliding surfaces of supports especially in hot pipes

generate significant forces which affect the pipe stresses as well as

the loads on anchors and restraints.

l It is advisable to avoid sliding supports / restraints in hot critical

piping systems - like Main steam, Cold and Hot reheat piping

systems - and use instead the angulating types.

l If sliding supports / restraints are used for critical applications, then

the sliding surfaces should be of rust free materials like stainless

steel / teflon and the appropriate friction coefficient must be includedin the analysis.


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Piping codes


Importance of piping codes in stress analysis

l Piping codes are industry specific. They outline the stress evaluationcriteria and also the design requirements specific to the industry over

which they have their jurisdiction.

l The piping code lies at the heart of any stress analysis. A piping

system necessarily has to be qualified as per the stress criteria

established in the particular piping code.l The stress evaluation criteria - while largely based on the

fundamentals discussed earlier - differ from code to code, the

different criteria necessitated by the specific operating conditions

and requirements of the industry to which the particular code caters

to. The difference in the criteria are in some cases also attributed to

the historical circumstances / different committees that have

established the codes.


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Piping codes


Important ASME piping codes

l Power piping ASME B 31.1l Process piping ASME B 31.3

l Pipeline transportation systems for

liquid hydrocarbons and other liquids ASME B 31.4

l Refrigeration piping and heat transfer

components ASME B 31.5l Gas transmission and distribution piping

systems ASME B 31.8

l Nuclear piping ASME section III

The ASME B 31.1 power piping code forms the basis for pipingdesign and stress analysis of all piping except Boiler internal

piping at ALSTOM.


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ASME B 31.1 - Power piping

code


Allowable stress

l The allowable stress for various ASTM piping materials at varioustemperatures are listed in Appendix-A of the code.

l The allowable stresses are actually reproduced from the ASME

Boiler & pressure vessel code, section II

Basis for allowable stress in ASME section II part D

Min of: R/4, 1.1/4 x Rt, 0.67 E, 0.67 Et, 0.67 Sr, 0.8 Sr min and 1.0 S

R = Specified minimum tensile strength at room temperature.

Rt = Specified minimum tensile strength at the temperature.

E = Yield point (0.2% proof stress at room temp)

Et = Yield point (0.2% proof stress at the temp)

Sr = Average stress at the temp to cause rupture at the end of 100,000 hr.

Sr min = Minimum stress at the temp to cause rupture at the end of 100,000 hr.

S = Average stress at the temp to produce an elongation of 1% (creep) in 100,000 hr.


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code


Other important data

l The thermal expansion data for the various materials are listed in

Table B-1 of Appendix-B of the code.

l The modulus of elasticity data for the ferrous materials are listed in

table C-1 of Appendix-C of the code.

l The formulae for the SIF and flexibility factors for various pipe

components are listed in Table D-1 of Appendix-D of the code.


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code


Comments on allowable stress values of Appendix-A

l The values listed include weld joint efficiency factors whereapplicable. Weld joint efficiencies affect only the hoop direction and

not the longitudinal pipe direction. Since in stress analysis, we are

interested in the longitudinal stresses only, the allowable stress for

stress calculation must be obtained by dividing the values from

appendix-A by the appropriate weld efficiency factor.

l The actual stress may exceed the allowable for occasional short

periods by the following factors:

15% for events duration < 8 hrs at any one time and 800 hrs/year

20% for events duration < 1 hrs at any one time and 80 hrs/year

The allowables may be exceeded due to external occasional loads or

due to pressure-temperature excursions (which would bring down the

allowables).


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code


Comments on allowable stress values of Appendix-A

l The allowable stress in shear can be taken as 80% of the allowables

listed in appendix-A.

l The allowable stress in bearing can be taken as 160% of the

allowables listed in appendix-A.

l The stress in pipe during hydrotest can be considered as high as

90% of yield stress.


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code


Code qualification equations

l Stress due to sustained loads (Clause 104.8.1 of B31.1) SL= (PDO/4Tn) + (0.75iMA/Z) < 1.0ShWhere MA= resultant moment loading on cross section due to all sustained loads

The above relation can be easily derived by considering the stressstate of fig-1 and applying the Maximum shear stress theory.

From maximum shear stress theory, failure would occur when the

max shear stress is > half of allowable stress in tension.

Max shear stress can be calculated from mohr's circle (fig-2) as follows:

2tmax= 2 x radius of mohr's circle

= {(sh-sl)2+ 4t

2}1/2

= {(PDO/4t + BM/Z)2+ 4 (TM/J)

2}

1/2

= {(PDO/4t)2+ (M/Z)

2+ 2 . PDO/4t . BM/Z}

1/2Where M = (Mx

2+My

2+Mz

2)1/2

= PDO/4t + M/Z ( by substituting BM with M; this makes the calculated tmaxsl ightly conservative)

To avoid failure, PDO/4t + M/Z < Sh

Incorporating fitting SIF into the above eqn gives the 31.1 code eqn for sustained stresses

PDO/4t + 0.75iMA/Z < Sh


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code


Code qualification equations (cont)

l Stress due to occasional loads (Clause 104.8.2 of B31.1) (PDO/4Tn) + (0.75iMA/Z) + (0.75iMB/Z) < k.Sh

WhereMB= resultant moment loading on cross section due to all occasional loads

k = stress exceeding factor (1.15 or 1.20 depending on occasional load

duration)

l Thermal expansion stress range (Clause 104.8.3 of B31.1)

SE= iMC / Z < SA+ f (Sh-SL)

Where MC= range of resultant moments on cross section due to thermal expansion

SA= Allowable stress range

= f (1.25 Sc + 0.25 Sh)

Sc= basic material allowable stress (appendix-A) at cold temperature

Sh= basic material allowable stress (appendix-A) at hot temperature

f = stress range reduction factor for cyclic loading (= 1 for general power

plant applications)


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code


Code qualification equations (cont)

l Understanding allowable stress rangeFrom figure-3, Total stress range

ST = Shy + Scy

= 1.5 Sh + 1.5 Sc

Taking only 83.3% so as to have margin,

ST = 1.25 Sh + 1.25 Sc

Thus for thermal expansion, the allowable stress range

SA = 0.25 Sh + 1.25 Sc (deducting 1.Sh for sustained loading)

Incorporating the fatigue factor gives the 31.1 code equation

SA = f .(0.25 Sh + 1.25 Sc)


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code


Important code considerations

l Modulus of elasticity - The code stipulates that the stress must be

evaluated considering the cold modulus of elasticity. However, forces

and moments on anchors and restraints can be evaluated

considering the hot modulus.

l Corrosion allowance and mill tolerance - The stress analysisincluding evaluation of restraint loads is to be done on the nominal

pipe thickness. Corrosion allowance and mill tolerance are not

considered.


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