Stress Analysis Concepts

PIPE STRESS ANALYSIS- CONCEPTSSatyashish Sahu

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PIPE STRESS ANALYSIS -CONCEPTS

! Analytical procedure to evaluate the stress state at

various points in a piping system.

! Also known as flexibility analysis since it also helps

ascertain the required flexibility in the piping system

! 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


PIPE STRESS ANALYSIS -CONCEPTS

! Stress in pipes! Stress categories! Failure of pipes! Thermal behavior of pipes! Stress limits! Stress in piping components! External load categories! Piping supports! Spring hangers! Constant effort hangers! Friction! Piping codes! ASME B 31.1 - Power piping code! Linear and non linear supports! Effect of supports on stress


Contents


Stress in pipes


Fig-1 Biaxial stress state in a pipe

l = PDO/4t + BM/ZWhere BM = (Mx2+My2)1/2

h = PDO/2t = TM/JWhere TM= Mz


Stress in pipes


Fig-2 Mohrs circle of the biaxial stress state


Stress in pipes

! 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

! It is always assumed (in fact due care is taken to ensure) that plantpiping will consist of at least two perpendicular segments betweenanchors. The Axial stresses due to thermal effects and also due toany other external loading in such a case will be negligible and arehence neglected in stress calculations. So also is buckling neglected.


Stress in pipes


Stress categories

! Primary stress (membrane and bending) 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

! 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 betweenprimary and secondary stress that these two stress categoriesare treated very differently. These stresses are never added upand have different allowable values


Classification of stress


Stress categories

! Peak stress Peak stresses are cyclical stresses which cause fatigue failure in

pipes


Classification of stress


Failure of pipes

! Plastic deformation leading to bursting - This happens whenever themagnitude of the primary membrane stress exceeds the yieldstrength.

! Plastic instability or incremental collapse - This occurs when thesecondary stress range exceeds twice the yield stress as explainedunder title stress range.

! Fatigue - Low cycle fatigue occurs in piping systems due to cyclicloads (like thermal load cycles, vibrations, etc).This occurs when thecumulative usage factor exceeds 1.0.

! Creep - Creep or elastic instability or elastic follow-up is a timedependent failure phenomenon that occurs in high temperaturepiping - typically above 750 deg F (400 deg C). Creep failure wouldeventually occur if the primary stress in the pipe is above the creepstrength of the material.


Failure mechanism


Thermal behavior of pipes

! When a pipe is heated up, stresses are caused if the free thermalmovement of the pipe is restricted. Upon reaching the yield point, thepipe starts yielding and the stresses as well as the thermal loads onthe restraints get relieved. This is called thermal shakedown. Whenthe pipe is cooled, it comes back to its original position and now thestresses and restraint loads reappear but with opposite signs.

The range between the hot stress and the cold stress is called thestress range.


Thermal shakedown / Stress range


Thermal behavior of pipes


Fig-3 Stress range

Total stress range ST = Shy + Scy

where:Shy = Hot yield strengthScy = cold yield strength

If deformation exceeds case-IIas in case III, there will beplastic instability in subsequentcycles leading eventually toincremental collapse.


Stress Limits


FIG-4 Limit stress-combined tension and bending. (ASME, Criteria. )! Fig shows two curves - one the

limit stress or the failure curveand the other the design limitcurve.

! A conservative design limit of0.66Sy for primary membrane(tensile) and 1.0Sy for combinedbending and membrane stress isused.


Stress Limits


Stress limits for Time dependent deterioration - Fatigue and Creep

! Low cycle Fatigue (load cycles lower than 105)

Stress reduction factor f for the allowable stress range for different

cumulative cycles are available in the piping codes. Ensuring that the

piping is not stressed beyond these levels guarantees that the pipe would

not fail in fatigue for the postulated number of operating cycles.

! Creep

The allowable stress values for various material listed in the piping codes

take into account the creep strength in the high temperature range (above

400 deg C). Limiting the primary stress in the pipe below the allowable

stress value as listed in the piping code would ensure that the creep rate

is no more than 1% per 100,000 hours.


Stress Limits


FIG-5 Stress categories and limits of stress intensity(Source:ASME Section VIII Div-2, Appendix-4)


Stress Limits


FIG-5 Stress categories and limits of stress intensity (Contd)(Source:ASME Section VIII Div-2, Appendix-4)


Stress in piping components


Stress intensification factors - SIF! Elbows, branch connections and reducers will have a higher level of

stress when compared to a straight pipe for the same amount ofbending moment.

! The factor by which the stress in the pipe component exceeds that ofthe straight pipe is called SIF (stress intensification factor).

! SIF of a component depends upon its geometry and is calculatedusing empirical formulae available in piping codes.

! For special components like Y-piece where no empirical relations areavailable, SIF will have to be determined through a analyticalprocedure like FEM.




Relation between Elbow geometry and SIF! Elbow / bend radius - Has inverse relation to SIF! Elbow diameter - Has direct relation to SIF! Elbow thickness - Has inverse relation to SIF

Relation between Branch geometry and SIF

! Header diameter - Has direct relation to header & branch SIFs! Header thickness - Has inverse relation to header & branch SIFs! Branch diameter - Has direct relation to branch SIF. Has no bearing

on header SIF! Branch thickness - Has direct relation to branch SIF. Has no bearing

on header SIF




Relation between Branch type and SIF

! The various branch types are listed with their SIF in theincreasing order Welding Tee

Integrally reinforced fitting as per MSS SP 97

Reinforced fabricated Tee

Unreinforced fabricated Tee

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External load categories


Types of external loading on pipes! Sustained loading

These loads will act on the pipe throughout its operating tenureand include

Dead loads like weight of pipe, insulation and inlinecomponents

Live loads like weight of contents in the pipe

! 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


Piping supports


Types of pipe supports! Rigid support - An inflexible restraint used primarily to carry the

sustained pipe loading. They cannot be used where there is upwardpipe movement. Rigid hanger Sliding base support

! Variable effort (spring) support - A flexible spring used to carry thesustained pipe loading while allowing for upward / downward pipemovement. The supporting effort varies as the pipe moves up ordown.

! Constant effort support - Used to carry the sustained pipe loadingwhile allowing for upward / downward pipe movement. Thesupporting effort remains constant throughout the upward /downward travel of the pipe.


Piping supports


Types of pipe supports (cont)! 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 transverse

direction! Guides - Guides are similar to bi-directional restraints but with the

primary purpose of guiding the pipe smoothly into the pipe axial orlateral direction. Transverse / Lateral guide : Pipe movement guided into the transverse

direction Axial guide : Pipe movement guided into the pipe axial direction

! 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.


Spring Hangers


Spring Hanger selection procedureFor spring hanger selection the following steps are required! Calculation of weight balance load

The load that would act on the spring hanger if it were completely rigidand the piping system was in static equilibrium under sustained loadingcondition

! 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

! Selection of appropriate spring constant An appropriate spring constant from a supplier catalogue based upon the

weight balance load and vertical thermal movement such that the loadvariation between the cold and hot positions is within 25%.


Spring Hangers


Hot setting / Cold setting of springsThere are two ways of setting the springs - Hot setting and Cold setting

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

load in the hot position of the pipe

! 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.


Spring Hangers


Fig-6 Hot / Cold setting

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100%

Cold pos of pipe

Hot pos of pipe

Load

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Coldsetting

Hotsetting


Spring Hangers


Spring hanger terminologies! Cold load - The load carried by the spring when the pipe is in cold

position

! Hot load - The load carried by the spring when the pipe is in hotposition

! Installation load - The load the spring would carry when the pipe is atits installation position I.e zero vertical displacement. The installationload would be equal to the cold load provided the vertical pipedisplacement in the cold condition is zero. But this may not be thecase always.

The spring is pre-compressed to the installation load, locked andthen erected on the pipe.


Constant effort Hangers


Constant effort hangers! When pipe vertical movement is high (above 50 mm), it is usually not

possible to select variable effort hangers with load variation within25%. In such a situation, constant effort hangers are used.

! Constant effort hangers as the name suggests apply a constant efforton the pipe throughout the complete range of the pipe verticalmovement.

! The effect of the constant effort hanger is similar to that of supportingthe pipe with a chain-pulley-block system


Friction


Frictional effects of pipe supports! 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.

! 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.

! 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 included

in the analysis.


Piping codes


Importance of piping codes in stress analysis! Piping codes are industry specific. They outline the stress evaluation

criteria and also the design requirements specific to the industry overwhich they have their jurisdiction.

! The piping code lies at the heart of any stress analysis. A pipingsystem necessarily has to be qualified as per the stress criteriaestablished in the particular piping code.

! The stress evaluation criteria - while largely based on thefundamentals discussed earlier - differ from code to code, thedifferent criteria necessitated by the specific operating conditionsand requirements of the industry to which the particular code catersto. The difference in the criteria are in some cases also attributed tothe historical circumstances / different committees that haveestablished the codes.


Piping codes


Important ASME piping codes! Power piping ASME B 31.1! Process piping ASME B 31.3! Pipeline transportation systems for

liquid hydrocarbons and other liquids ASME B 31.4! Refrigeration piping and heat transfer

components ASME B 31.5! Gas transmission and distribution piping

systems ASME B 31.8! 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 internalpiping at ALSTOM.


ASME B 31.1 - Power pipingcode


Allowable stress! The allowable stress for various ASTM piping materials at various

temperatures are listed in Appendix-A of the code.! The allowable stresses are actually reproduced from the ASME

Boiler & pressure vessel code, section II

Basis for allowable stress in ASME section II part DMin 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.




Other important data! The thermal expansion data for the various materials are listed in

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

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

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

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

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




Comments on allowable stress values of Appendix-A! The values listed include weld joint efficiency factors where

applicable. Weld joint efficiencies affect only the hoop direction andnot the longitudinal pipe direction. Since in stress analysis, we areinterested in the longitudinal stresses only, the allowable stress forstress calculation must be obtained by dividing the values fromappendix-A by the appropriate weld efficiency factor.

! The actual stress may exceed the allowable for occasional shortperiods 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 ordue to pressure-temperature excursions (which would bring down theallowables).




Comments on allowable stress values of Appendix-A! The allowable stress in shear can be taken as 80% of the allowables

listed in appendix-A.

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

allowables listed in appendix-A.

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

90% of yield stress.




Code qualification equations! 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:2max = 2 x radius of mohr's circle = {(h-l)2 + 42}1/2

= {(PDO/4t + BM/Z)2 + 4 (TM/J)2}1/2

= {(PDO/4t)2 + (M/Z)2 + 2 . PDO/4t . BM/Z}1/2 Where M = (Mx2+My2+Mz2)1/2

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

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

Incorporating fitting SIF into the above eqn gives the 31.1 code eqn for sustained stressesPDO/4t + 0.75iMA/Z < Sh




Code qualification equations (cont)! Stress due to occasional loads (Clause 104.8.2 of B31.1)

(PDO/4Tn) + (0.75iMA/Z) + (0.75iMB/Z) < k.ShWhere MB = 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)

! 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)




Code qualification equations (cont)! Understanding allowable stress range

From figure-3, Total stress rangeST = 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 equationSA = f .(0.25 Sh + 1.25 Sc)




Important code considerations! 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.

! Corrosion allowance and mill tolerance - The stress analysis

including evaluation of restraint loads is to be done on the nominal

pipe thickness. Corrosion allowance and mill tolerance are not

considered.


Linear and non linear supports


What are Linear and non linear supports! Linear Supports

These supports do not change their stiffness over the complete range of

pipe displacement in the direction of their application. All bi-directional

restraints without gap and friction and spring hangers fall in this category

! Non linear supports

These supports change their stiffness when the pipe moves from cold to

hot position. All restraints with gap and friction and single directional

restraints fall in this category.


Effect of supports on stress


Pipe supports & stress! When a pipe lifts up in hot condition, the

change in stress from cold to hot position

can be considered as secondary stress

only if the displacement is minor.

! In case of significant displacements, the

stress assumes both - primary and

secondary stress characteristics and

hence must be checked against the

primary & secondary stress allowables

simultaneously.

Coldposition

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Effect of supports on stress


Spring hangers & stress! Similarly in case of spring hangers, when

pipe moves from cold to hot position, the

stress level in the pipe changes due to

change in the supporting effort of the

spring. The change in the stress level

has primary characteristics and hence

should be limited to 25% to ensure a safe

design.

Hotposition

Coldposition

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Stress Analysis Concepts

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