Pip­ing stress anal­y­sis primer

S. Raghava Chari - Con­sul­tant

Chemical Industry Digest - - What’s In? - S. Raghava Chari

A com­pre­hen­sive dossier on pip­ing stress from the sources of such stresses to its man­age­ment and on pre­vent­ing fail­ures. De­tailed very well through case stud­ies and use­ful do’s and don’ts.

Pip­ing Stress Anal­y­sis (PSA)

Listed be­low are items that con­sti­tute PSA.

1. An an­a­lyt­i­cal pro­ce­dure to cal­cu­late the stresses at var­i­ous points of a pipe­line sys­tem.

2. PSA’s other name is flex­i­bil­ity anal­y­sis, as it de­ter­mines the nec­es­sary pipe­line flex­i­bil­ity for its safe op­er­a­tion

3. PSA as­cer­tains dis­place­ments, forces, and turn­ing mo­ments etc. on pipe­line sup­port­ing items e.g. the hang­ers, sup­ports, re­straints, guides, stops and an­chors for their proper selec­tion

PSA Ben­e­fits

1. PSA en­ables de­sign­ing pipe­line sys­tems lim­it­ing the stresses at var­i­ous points of the pipe­line as per stan­dards spec­i­fied for pipe­line safety, dura­bil­ity. This en­ables un­in­ter­rupted ser­vice.

2. In ad­di­tion, it en­ables lim­it­ing ma­chines and equip­ment e.g. pumps’, com­pres­sors’, and ves­sels’ noz­zle loads be­low API 610 & 617, ANSI, NEMA, or SM23 etc. stan­dards pre­scribed val­ues for safety and dura­bil­ity and re­li­a­bil­ity.

3. It en­ables de­sign­ers to limit ves­sel stresses at pip­ing con­nec­tions within ASME Sec­tion VIII pre­scribed val­ues

4. PSA en­ables de­ter­min­ing pip­ing dis­place­ments and to pro­vide for these to avoid un­duly stressed pipes and joint leaks from skewed flanges – case study 1

5. PSA solves pip­ing dy­namic prob­lems e.g. those aris­ing from me­chan­i­cal and or acous­tic vi­bra­tions, fluid ham­mer, flow pul­sa­tions, tran­sient flows and re­lief valve dis­charges

6. De­ter­min­ing the above op­ti­mizes pipe de­sign i.e. pro­vides safe and re­li­able pipe­line at least costs

Case study-1: Per­sis­tent Flange Leaks on ac­count of pip­ing stress

Fig-1 shows a 25 MW 10,000 RPM steam tur­bine driv­ing the syn­the­sis gas com­pres­sor K-601 of an am­mo­nia plant; it ex­tracts 90% of its 106-bar in­let steam into 40 bars header to drive other tur­bines which start ahead of K-601 and con­denses the bal­ance. In case K-601 is not in op­er­a­tion or trips in ser­vice, 3 Nos. of let­down sta­tions in a - hor­i­zon­tal plane take over au­to­mat­i­cally. Dis­trib­uted Con­trol Sys­tem (DCS) sens­ing tur­bine not run­ning con­di­tion, opens CV1 70% (found by trial) within 2 sec­onds to let­down most of the steam into the 40-bar header to avoid the be­low listed se­ri­ous ill con­se­quences:

1. 106-bar header over­pres­sure, con­se­quent 106-bar steam header re­lief valve blow­ing and con­se­quent likely dis­as­trous plant shut downs

2. Un­af­fected run of the other 40-bar steam tur­bines. DCS finely con­trols 106-bar steam header pres­sure by ma­nip­u­lat­ing CV2 and CV3 in split range mode. Five Nos. of 6” 1500 # RTJ Flanged Re­stric­tion Ori­fices (FRO) down­stream of each let­down CV ab­sorb most of the ΔP and thus pre­vent CVs seats & plugs ero­sion for their long and durable ser­vice.

Huge steam leaks at all the 15 FRO flange joints plagued the plant since com­mis­sion­ing. Re­peated ring gasket changes, tight­en­ing, and hot bolt­ing and on­line leak seal­ing were fu­tile.

The au­thor sub­sti­tuted shop made butt weld end

Re­stric­tion Ori­fice As­sem­blies (ROAs) elim­i­nated 15 flange sets and their leaks. But leaks to a much smaller ex­tent de­vel­oped at the three Nos. CV flanges left un­touched as the process li­cen­sor did not ap­prove weld­ing CVs to the pipelines.

Sev­eral se­ri­ous in­spec­tions led the au­thor to con­clude that the three let­down sta­tions of short pip­ing length op­er­at­ing at 520O C and solidly sup­ported to the ground could not ex­pand freely to ab­sorb the pip­ing ther­mal ex­pan­sion i.e. these lacked pip­ing flex­i­bil­ity.

Listed be­low are some of the im­proved so­lu­tions the au­thor im­ple­mented for eas­i­est pip­ing flex­i­bil­ity:

1. Crew flame cut the sup­port foot plate bolt holes on ei­ther side of the pil­lar welded to the pipe ob­long along pipe lon­gi­tu­di­nal cen­ter­line (fig 1)

2. They in­serted shop made spac­ers (S) pro­trud­ing 1 mm over the sup­port foot plate

3. The nuts se­cur­ing the foot plate to ground bot­tom on the spac­ers; this fea­ture al­lows the pipes to ex­pand / con­tract freely with temp changes along with the sup­ports welded to them. In short this sim­ple mod­i­fi­ca­tion in­tro­duces pip­ing flex­i­bil­ity eas­ily, in­ex­pen­sively and on­line.

Ben­e­fits of the RCA based so­lu­tion

1. The three year long flange leaks van­ished as if magic con­firm­ing the di­ag­no­sis and ef­fec­tive­ness of the so­lu­tion.

2. Had the plant lived with the prob­lem longer, the pip­ing could have cracked, nay even bro­ken due to ex­ces­sive stress and led to an sur­prise un­man­age­able catastrophe

Sources of Pipe­line Stresses

Listed be­low are few of the pipelines stress causes:

1. Line op­er­at­ing/upset pres­sures & tem­per­a­tures

2. Equip­ment con­nec­tion to pipelines

3. Pipe and Equip­ment ma­te­rial of con­struc­tion (MOC)

4. Pipe thick­ness

5. Pipe­line con­fig­u­ra­tion

Ex­am­ples of pipelines mer­it­ing care­ful PSA – man­ual and or com­put­er­ized – are as un­der:

1. Pumps’ e.g. Cen­trifu­gal-API/ANSI, gear, screw, pis­ton and plunger suc­tion and dis­charge pipelines mostly 4 inches and larger; for the pis­ton and plunger pumps con­sid­er­ing pul­sa­tion damp­en­ers may be also nec­es­sary

2. Cen­trifu­gal Com­pres­sor in­let and out­let pip­ing.

3. Lines to and from steam gen­er­a­tors.

4. Higher temp pipelines e.g. steam which ex­pand as the pipe­line temp in­creases and vice versa; de­sign­ers con­sider ex­pan­sion joints in­clud­ing pro­pri­etary ex­pan­sion de­vices.

5. Steam and Gas Tur­bine in­let and out­let pip­ing.

6. Air Cooler and Process Heater in­let and out­let pip­ing (3 inch and larger).

7. Lines be­long­ing to ASME B31.3 cat­e­gory M clas­si­fi­ca­tion

8. Pipelines suf­fer­ing too high cyclic tem­per­a­ture con­di­tions.

9. All jack­eted lines.

10. Pipelines con­nect­ing to ma­chines and equip­ment. Codes / sup­ply­ing ven­dors limit the noz­zle loads for safety and dura­bil­ity. Pipelines de­sign­ers must limit the noz­zle loads be­low pre­scribed loads

11. Dy­namic Loads sub­jected pipelines; few ex­am­ples are: a. e.g. re­lief lines b. lines with large pres­sure drop at con­trol valves, c. lines sub­jected surge pres­sure, slug flow, churn, two phase flow, wa­ter ham­mer, flash­ing, etc.

12. All Fiber­glass, Alu­minum al­loy, re­frac­tory or elas­tomer lined pip­ing.

13. All pip­ing sys­tems con­nected to FRP, plas­tic, glass lined steel or sim­i­lar brit­tle equip­ment

14. Lines sub­jected to non-ther­mal move­ments e.g. dif­fer­en­tial set­tle­ment be­tween struc­tures, struc­ture-equip­ment foun­da­tion etc., process equip­ment growth, header growth, tower growth or other sig­nif­i­cant dis­place­ments, etc.

15. ≥8” Pipelines of op­er­at­ing temp ≥150OC, ≥20” Pipelines of op­er­at­ing temp ≥80OC and all ≥36” Pipelines of any op­er­at­ing temp

16. Spe­cial “cold” sup­ports sup­ported pipelines op­er­at­ing be­low -45OC

17. All plas­tic lined pipelines; de­sign­ers shall give spe­cial at­ten­tion to add enough ad­di­tional sup­ports to limit the ex­ter­nal forces and mo­ments at the flange joints to min­i­mize risks of flange to pipe joint cracks, and leaks from skewed flanges

18. All ≥ 4” pipelines con­nected to safety pres­sure re­liev­ing sys­tems, but ex­clud­ing ther­mal re­liefs

19. Pipelines, which the lead pip­ing en­gi­neer/stress en­gi­neer judges as of in­ad­e­quate flex­i­bil­ity

20. Large tem­per­a­ture gra­di­ents across the pipe­line length that could cause ther­mal bow­ing or pip­ing con­nect­ing high ther­mal growth equip­ment of­ten war­rant de­tailed man­ual and or com­puter anal­y­sis.

Spe­cial Re­quire­ments for thin walled pipelines

Thin wall pipelines are pipes where D/T ≥ 100, where D is pipe OD and T wall thick­ness both in mm. A qual­i­fied and ex­pe­ri­enced stress en­gi­neer shall re­view and cus­tom de­sign thin walled pip­ing as ex­plained be­low:

1. ASME B31.3, 304.3.2 thru 304.3.4 spec­i­fied stub-in con­nec­tions don’t ap­ply to thin wall pip­ing, where the branch di­am­e­ter ≥ ½ main line di­am­e­ter

2. Lines con­nected to non-fer­rous equip­ment

3. Un­der­ground process lines of ≤ 30O C dif­fer­ence be­tween de­sign and am­bi­ent tem­per­a­ture.

4. All ver­ti­cal lines con­nect­ing to ver­ti­cal ves­sels and sup­ported or guided from that ves­sel.

5. All lines ≥4 inch sub­ject to ex­ter­nal pres­sure or vac­uum con­di­tions.

6. All lines sub­ject to vi­bra­tions from high ve­loc­ity process fluid flows, high pres­sure drop, wa­ter ham­mer or mixed phase flow.

7. All lines con­nect­ing to equip­ment of MOC of ther­moset, ther­mo­plas­tic ma­te­ri­als and or glass, re­frac­tory, or elas­tomer lined.

8. All pres­sure con­tain­ing non-metal­lic lines.

9. All flare line head­ers

10. Lines for which an Al­ter­na­tive Leak Test has been spec­i­fied

Pipelines Clas­si­fied ac­cord­ing to Crit­i­cal­ity

Most or­ga­ni­za­tions di­vide their pipelines into 3 groups ac­cord­ing to their crit­i­cal­ity:

1. Crit­i­cal­ity Group 1 (C1) lines. These re­quire thor­ough re­view

2. Mod­er­ately Crit­i­cal or Group 2 (C2) lines

3. Low crit­i­cal lines or (C3) lines

In­for­ma­tion Re­quired for Stress Anal­y­sis

1. Pipe OD & wall thick­ness or nom­i­nal di­am­e­ter, sched­ule num­ber

2. Flow­ing medium tem­per­a­ture

3. Pip­ing Ma­te­rial; this is nec­es­sary to get val­ues of Temp Ex­pan­sion Co­ef­fi­cient, Young’s mod­u­lus of elas­tic­ity, and ma­te­rial den­sity

4. In­su­la­tion thick­ness and in­su­la­tion ma­te­rial; where non given de­sign­ers as­sume stan­dard thick­ness for cal­cium sil­i­cate in­su­la­tion

5. Flow­ing medium spe­cific grav­ity

6. Wind load if any and its di­rec­tion

7. Any an­chor ini­tial trans­la­tion. (For tow­ers, ex­chang­ers, and so on, noz­zle ini­tial trans­la­tion is im­por­tant.)

8. Pip­ing Cor­ro­sion al­lowance for

9. Flange rat­ing, (ANSI B16.5)

10. De­sign­ers usu­ally use stan­dard valve & flange weights; spec­ify where dif­fer­ent weights ap­ply

11. De­sign­ers as­sume long ra­dius el­bows; if oth­er­wise mark on the iso­met­ric el­bow ra­dius;

12. Per­mis­si­ble ma­chin­ery / equip­ment noz­zle loads – get from ven­dors

13. Pre­ferred ex­pan­sion loops, ex­pan­sion joints etc. where re­quired

14. Pre­ferred branch off con­nec­tion; re­in­forced fab­ri­cated tee, etc.

15. Mark avail­able steel cross­ing, bridges etc. along the route

16. Is con­sid­er­ing ad­di­tional load while hy­draulic test­ing nec­es­sary?

Pip­ing Loads

Com­monly con­sid­ered pip­ing loads are: Pri­mary, Sec­ondary, Sus­tained Loads, Oc­ca­sional Loads, Static Pri­mary Load:

These steady or sus­tained types of loads arise from in­ter­nal fluid pres­sure, ex­ter­nal pres­sure, pipe weight, fluid, forces due to re­lief or blow down and pres­sure waves gen­er­ated due to wa­ter/steam ham­mer ef­fects.

Sus­tained Loads: In­ter­nal/Ex­ter­nal Pres­sure - A fluid flow­ing through a pipe ex­erts in­ter­nal pres­sure load. Of­ten a net ex­ter­nal pres­sure ex­ists on the ex­te­rior of Jack­eted pipe cores and Shell & Tube ex-changer tubes etc. In­ter­nal or ex­ter­nal pres­sure stresses the pipe in the ax­ial as well as cir­cum­fer­en­tial (Hoop Stress) di­rec­tions, con­sid­er­ably and in neg­li­gi­bly ra­di­ally. The ax­ial force F on the pipe from in­ter­nal pres­sure equals F=P*π*d^2/4 Where

F Ax­ial force in New­ton on the pipe wall P Pres­sure in the pipe in kPa d Pipe In­ter­nal dia in m

Dead Weight: It is the to­tal of the weights of the pipe, the con­tained fluid, fit­tings, and other pipe com-

po­nents e.g. valves, in­su­la­tion etc. The dead weight loads tend to bend the pipes and the bend­ing mo­ment im­pose nor­mal and shear stresses on the pipe wall. Two prin­ci­pal pipe bend­ing causes are dis­trib­uted (e.g. fluid and pipe self-weight) and con­cen­trated weight loads (e.g. valve weight).

Oc­ca­sional Loads: De­tails of oc­ca­sional loads fol­low:

1. Wind Load: De­sign­ers de­sign out­door pip­ing to with­stand the max­i­mum wind ve­loc­ity ex­pected dur­ing the plant op­er­at­ing life. They model the wind force as uni­form load act­ing upon the pro­jected length of the pipe per­pen­dic­u­lar to the wind di­rec­tion, us­ing the for­mula Fw = Pw*S*A where FW To­tal wind force in New­ton

Pw Equiv­a­lent Wind Pres­sure kPa at var­i­ous lo­ca­tions

S Wind Shape fac­tor – di­men­sion less

A Pipe ex­posed area in m2

2. Seis­mic Load: Seis­mic load, earth­quake engi­neer­ing’s a ba­sic con­cept means con­sid­er­ing and pro­vid­ing for earth­quake-gen­er­ated ag­i­ta­tion to struc­tures. Earth­quake-gen­er­ated ag­i­ta­tions and or grav­ity waves from tsunami stress struc­tures con­tact­ing the ground or ad­ja­cent ground con­tact­ing struc­tures.

3. Wa­ter Ham­mer: Sud­den stop or di­rec­tion change of flu­ids flow in pipes cre­ates a high mag­ni­tude pres­sure surge. This is known as wa­ter ham­mer or more ac­cu­rately fluid ham­mer. A com­mon cause of fluid ham­mer is rapid clos­ing of a valve at the end of a pipe­line. The gen­er­ated pres­sure wave prop­a­gates in the pipe and stresses the pipe enor­mously called hy­draulic shock.

4. Steam ham­mer: Steam ham­mer, the pres­sure surge gen­er­ated by su­per-heated or sat­u­rated steam flow rapid changes in a pipe­line tend to vi­brate the pipes. De­sign­ers cal­cu­late such forces and pro­vide ad­e­quate pip­ing sup­ports.

5. Safety Valve Dis­charge: De­sign­ers pro­vide for the re­ac­tion forces from re­lief valve dis­charges. Though oc­ca­sional loads, these merit se­ri­ous con­sid­er­a­tion. They cal­cu­late it us­ing the pro­vi­sions of ASME B31.1 Ap­pen­dix II.

Sec­ondary Loads:

The pri­mary loads dis­cussed above orig­i­nate from forces im­posed on pipelines, the sec­ondary loads to be dis­cussed from pipe­line dis­place­ment. E.g. when a stor­age tank slightly sinks down due to its and filled fluid weight, so do the tank noz­zle and pipe con­nected to it. Sim­i­larly, a ves­sel grow­ing up­wards due to temp in­crease pulls the con­nected pipe too up­wards. Sim­i­larly pipes con­nected to ma­chin­ery e.g. pumps and com­pres­sors vi­brate fol­low­ing the ma­chin­ery vi­bra­tions.

Dis­place­ment Loads: Be­low de­scribed are the loads im­posed on pipelines due to dis­place­ment:

1. Pipe­line Ther­mal Ex­pan­sion in­duced Load

2. Con­nected Equip­ment Ther­mal Ex­pan­sion caused Load

A pipe get­ting hot­ter on high temp fluid flow or on heat­ing it ex­pands and vice versa. Con­se­quently the sec­ondary loads im­posed are of­ten cyclic but not al­ways. E.g. load due to tank set­tle­ment is one way. But that from ves­sel noz­zle move­ment dur­ing op­er­a­tion is cyclic, be­cause the ves­sel noz­zle re­turns to orig­i­nal el­e­va­tion on plant shut­down and the ves­sel at­tain­ing am­bi­ent temp. It comes back again on restart­ing the plant and the ves­sel at­tain­ing op­er­at­ing temp.

Pip­ing Stresses- Pri­mary, Sec­ondary

1-Pri­mary stress (mem­brane and bend­ing):

– This is the stress re­sult­ing from load­ing the pipe ex­ter­nally e.g. pipe weight, point load e.g. valve, wind and earth­quake etc.

– Pipes sub­jected to the above ex­ceed­ing the al­low­able stress fail through con­tin­u­ous yield­ing even in the ab­sence other stresses

2-Sec­ondary stress

– Sec­ondary stresses arise not from ex­ter­nal load­ing but from phys­i­cal ten­den­cies e.g. pre­vented ther­mal ex­pan­sion

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

Thanks to this fun­da­men­tal in be­hav­ior dif­fer­ence of the two kinds of stresses, de­sign­ers treat these dif­fer­ently, never add these, and use dif­fer­ent al­low­able val­ues for pipe de­signs.

3-Peak stress:

– Peak stresses are cycli­cal stresses in pipes which cause fail­ure of poorly de­signed pipelines by fa­tigue.

Pip­ing Com­po­nent Stress In­ten­si­fi­ca­tion Fac­tors (SIFs). Be­low listed are SIFs:

1. El­bows, branch con­nec­tions and re­duc­ers are stressed more than straight pipes sub­jected to equal

bend­ing mo­ment.

2. The ra­tio of the com­po­nent’s stress to that of the straight pipe­line = SIF (stress in­ten­si­fi­ca­tion fac­tor).

3. A com­po­nent’s SIF de­pends upon its ge­om­e­try; pip­ing codes of­fer em­pir­i­cal for­mu­lae to cal­cu­late SIFs.

4. For com­po­nents not cov­ered by SIF for­mu­las, e.g. Y piece de­ter­mine SIF through an­a­lyt­i­cal pro­ce­dure like Fi­nal El­e­ment Method (FEM).

Re­la­tion be­tween El­bow ge­om­e­try and SIF:

SIF Re­la­tion­ship α 1/R R- El­bow, bend ra­dius α d; d-dia of com­po­nent α 1/t t-el­bow thick­ness α D D-header di­am­e­ter α t; t-header wall thick­ness α d; d-branch dia t- the branch thick­ness does not af­fect header SIF α D D-header dia α 1/T where T is header thick­ness α d; d – branch dia; no ef­fect on header SIF α t; t-branch thick­ness

Re­la­tion be­tween Branch ge­om­e­try and SIF

1. Header di­am­e­ter – Has di­rect re­la­tion to header & branch SIFs

2. Header thick­ness – Has in­verse re­la­tion to header & branch SIFs

3. Branch di­am­e­ter – Has di­rect re­la­tion to branch SIF. Has no bear­ing on header SIF

4. Branch thick­ness – Has di­rect re­la­tion to branch SIF. Has no bear­ing on header SIF Stress in pip­ing com­po­nents

Re­la­tion be­tween Branch types and SIFs. Listed be­low are the var­i­ous branch types’ SIFs:

1. Weld­ing Tee – Least SIF

2. In­te­grally re­in­forced fit­ting as per MSS SP 97

3. Re­in­forced fab­ri­cated Tee

4. Un­re­in­forced fab­ri­cated Tee – Max SIF Fail­ure The­o­ries: Prin­ci­pal Axis Sys­tem knowl­edge sim­pli­fies un­der­stand­ing the com­plex sub­ject of stress anal­y­sis of pip­ing sub­jected to pres­sure, weight and ther­mal ex­pan­sion. Stress by def­i­ni­tion is the ra­tio of Force to Area. To find the stress in the small el­e­ment, say a very small cube of a piece of pipe, draw three mu­tu­ally per­pen­dic­u­lar lines to the cube’s face and in­ter­sect­ing one another (fig 2). The three lines are the three prin­ci­pal axes. One can re­solve each force, act­ing on the cube along each of the axis. Di­vid­ing each force act­ing on the cube face by cube face area yields the prin­ci­pal stress.

The prin­ci­pal stress act­ing along the pipe cen­ter­line (X-axis) has the name of ‘Lon­gi­tu­di­nal Prin­ci­pal Stress (LPS). Hor­i­zon­tal pipe CL has the name of X-axis, Ver­ti­cal CL Y-axis and per­pen­dic­u­lar to the x-y plane Z-axis (fig 2). The forces bend­ing the pipe lon­gi­tu­di­nally, forces act­ing along the pipe cen­ter­line, force due to the pipe fluid pres­sure cause LPS.

Ra­dial prin­ci­pal stress (RPS) acts along ra­dial line from pipe cen­ter to the pipe wall. This is com­pres­sive stress act­ing on pipe wall in case of in­ter­nal pres­sure and ten­sile stress in case of a in­ter­nal vac­uum. Cir­cum­fer­en­tial prin­ci­pal stress, aka Hoop or tan­gen­tial stress, acts along the cir­cum­fer­ence of the pipe. This stress tends to open-up the pipe wall. In­ter­nal pres­sure causes it.

Two or more prin­ci­pal stresses act­ing at a point on a pipe gen­er­ate shear stress. Mag­ni­tudes of var­i­ous stresses are as un­der



CPS Aka hoop stress PD/2T

Fail­ure The­o­ries:

1. The Code presents equa­tions to cal­cu­late Lon­gi­tu­di­nal, Hoop, and Ra­dial pipe stresses and pro­vides stress lim­its for us­ing with the for­mu­las.

2. Ac­cord­ing to the max­i­mum prin­ci­pal stress fail­ure the­ory, on any of the three mu­tu­ally per­pen­dic­u­lar prin­ci­pal stresses ex­ceed the ma­te­rial’s yield strength at its op­er­at­ing tem­per­a­ture the pipe­line would fail

3. Ac­cord­ing to the the max­i­mum shear fail­ure the­ory, on the max­i­mum shear stress (arith­metic av­er­age of largest mi­nus small­est prin­ci­pal stresses) ex­ceeds ½ of the ma­te­rial’s yield strength at its op­er­at­ing tem­per­a­ture the pipe­line would fail

Stress Types:

ASME B31.3 Code pro­vides de­sign guid­ance for pri­mary & sec­ondary stresses. Pri­mary stress con­tin­ues to ex­ist as long as the ap­plied load ex­ists; it does

not di­min­ish with time or as de­for­ma­tion takes place – its ba­sic char­ac­ter­is­tic. In other words it is not self­lim­it­ing. Pro­gress­ing gross de­for­ma­tion to rup­ture is pri­mary stress’s fail­ure mode. Pipe in­ter­nal pres­sure caused cir­cum­fer­en­tial stresses and that from grav­ity caused lon­gi­tu­di­nal bend­ing stresses are pri­mary stress ex­am­ples.

On the other hand, self-lim­it­ing is sec­ondary stress’s ba­sic char­ac­ter­is­tic. It re­sult­ing from cyclic ther­mal ex­pan­sion and con­trac­tion di­min­ishes with time and strain. Its fail­ure mode is small crack lead­ing to leak­age. Sec­ondary stresses are due to.

Pip­ing Sup­ports: Ad­e­quately sup­port­ing pipes is manda­tory to pre­vent:

1. Pip­ing over­stresses

2. Joints leak­ages

3. Over­stressed sup­ports

4. Limit forces from pip­ing to con­nected equip­ment

5. In­ter­fer­ence with ther­mal ex­pan­sion

6. Ex­ces­sive pipe sag (es­pe­cially for pip­ing re­quir­ing drain)

7. Ex­ces­sive heat flow to pre­vent pipe sup­ports’ tem­per­a­tures beyond their lim­its

The ad­di­tional fac­tors given be­low also ap­ply:

1. De­sign­ers en­sure that pipe sup­ports con­trol pip­ing sys­tem weight ef­fects – higher of op­er­at­ing or hy­dro-test loads -, and those from pres­sure, thrust, vi­bra­tion, wind, earth­quake, shock, and ther­mal dis­place­ment.

2. The B31.3 STAN­DARD, MSS SP-58, TA­BLE 326.1 guides se­lect­ing pipe sup­port types and ma­te­ri­als to suit ap­pli­ca­tion needs

3. Se­lect­ing proper MOC for clamps and bolts, for ex­am­ple, is of prime im­por­tance in el­e­vated tem­per­a­ture ser­vice

4. Re­view­ing SP-58 ta­bles re­veals the in­ad­e­quacy of Car­bon Steel as clamp MOC and of the com­mon ASTM A307 fas­ten­ers at temp ≥ 400O C.

5. The SP-58 stan­dard guides us­ing al­loy steel ASTM A240 clamps and ASTM A193-Grade B7 fas­ten­ers

Pipe Sup­port Span, based on de­flec­tion: Pipe­line de­sign­ers of­ten use the equa­tion given be­low to limit mid span pipe de­flec­tion within per­mis­si­ble lim­its: y = (5wL^4+8w L^3) / (384EI) where:


Lm pipe sup­port span ym per­mis­si­ble mid-span de­flec­tion

W N/m uni­formly dis­trib­uted load (pipe + fluid wt) wN Con­cen­trated Load


E MPa Youngs mod­u­lus of elas­tic­ity of pipe ma­te­rial I m^4 pipe mo­ment of in­er­tia; I for pipe = π(D^4-d^4)/64; D-Pipe OD; d-pipe ID; both in m

Pipe Sup­port Span, based on stress: Another method based on per­mis­si­ble stress based sup­port span cal­cu­la­tion us­ing the equa­tion given be­low is also avail­able. The y based sup­port span cal­cu­la­tion is more com­mon:

Max Bend­ing Stress

S = ((0.0624wL^2+0.1248w L)D)/I Where the sym

b c bols and units are as above.

Ther­mal ex­pan­sion: Most ma­te­ri­als ex­pand with in­creas­ing temp and vice versa aka called ther­mal ex­pan­sion. The de­gree of ex­pan­sion di­vided by the change in tem­per­a­ture is called the ma­te­rial’s co­ef­fi­cient of ther­mal ex­pan­sion and gen­er­ally varies with tem­per­a­ture.

Forces and Pip­ing Stress due to ther­mal ex­pan­sion: Con­sider a 20 m long straight CS pipe con­nect­ing ves­sel V1’s Noz­zle to that of V2 (fig 3) of same el­e­va­tion. When 200O C prod­uct flows from V1 to V2, the pipe at­tains that temp and ex­pands by 20*13*10^6*(200-20)=46.8 mm – 13*10^6 = CS ther­mal ex­pan­sion co­ef­fi­cient (ct). In case of very high tem­per­a­tures e.g. su­per­heated steam, the stresses aris­ing from con­strain­ing the much greater pipe ex­pan­sion could dent the ves­sel or if the ves­sel is very strong bow the pipe as the dot­ted lines show and in ex­treme cases break the ves­sel noz­zle or break the pipe with cat­a­strophic con­se­quences

One way of avoid­ing the catastrophe is off set­ting the ves­sels and con­nect­ing these by pipe legs AB and CB pipes at right an­gles (fig 4). This pip­ing con­fig­u­ra­tion ex­pands as shown by the dot­ted line and thanks to the bend, the stresses are con­sid­er­ably less. We may as­sume the longer leg ex­pands as if guided by a

guide near its end and the shorter leg end B lifts as a can­tilever. Pip­ing prac­tice calls this ‘guided can­tilever con­fig­u­ra­tion. De­tails of cal­cu­lat­ing stress of leg AB fol­low:

Min­i­mum Per­pen­dic­u­lar Length: Struc­tural beams strength cal­cu­la­tions the­ory of­fers the 2 for­mu­lae given be­low for de­ter­min­ing the min length of leg AB, for a given length of CB and given temp to limit the pip­ing stress within ac­cept­able lim­its and to de­ter­mine the stresses in the shorter leg of the con­fig­u­ra­tion: L=√(3*10- 6DEy/ S) For­mula 1

S =(3*10- 6DEy/ L2) For­mula 2 Where


Lm Min re­quired AB length for given CB length and vice versa and temp to limit pip­ing stresses within ac­cept­able lim­its

D mm Pipe OD; us­ing nom­i­nal pipe size is OK as

er­ror would be < 5%

E MPa Young’s mod­u­lus of elas­tic­ity for pipe ma­te­rial; Any con­sis­tent unit is OK as E&S ap­pear in nu­mer­a­tor and de­nom­i­na­tor in the equa­tion 1; SA will be in the as­sumed E units in eqn 2 y mm Long leg’s ther­mal ex­pan­sion

S MPa Per­mit­ted pip­ing Stress Value

S MPa Ac­tual Stress value in the given con­figura


tion at op­er­at­ing temp

The two ex­am­ples be­low il­lus­trate these for­mu­lae use:

Prob­lem 1; De­ter­mine the min length L of leg AB (fig 2) to limit the pip­ing stress SA to 1120 kg/cm2 given that CB is 10m long; E=2065000 kg/Cm2; and pipe dia is 6.625”, flow­ing fluid temp temp is 200O C and am­bi­ent 20O C. Pipe MoC is CS of Co­eff of ther­mal ex­pan­sion 13*10^ 6 / o C So­lu­tion:

Step 1; Cal­cu­late the ther­mal ex­pan­sion of leg AB AB’s ther­mal ex­pan­sion 23.4 10*1000*13*10^- 6*( 200-20) mm

L for CB = (3*10^- 6DEy/ s)^0.5 4.7 m


=(3*10^- Ans


*6.625*25.4*2065000*23.4/1120)^0.5 m


Prob­lem 2; in prob­lem 1 the ac­tual lay­out shows that CB is 10 m long. What is the pip­ing stress

S = (3*10- 6DEy/ L2)= (3*10- 6* 2065000*23.4/10^2) 244 kg/ A cm2

Note: The pip­ing stress de­creases as the leg lengths’ dif­fer­ence de­creases

En­sur­ing Ad­e­quate Pip­ing Flex­i­bil­ity: Elab­o­rate com­puter pro­grams e.g. Ceaser are avail­able to check pip­ing flex­i­bil­i­ties. Such pro­grams be­ing ex­pen­sive to buy re­quire gath­er­ing lots of data and feed­ing in to a com­puter.

On the other hand the above de­scribed quick pip­ing flex­i­bil­ity check method pop­u­larly known as the ‘Guided Can­tilever Method’ is very sim­ple to use, least time tak­ing, re­sults in very close to com­put­er­ized pro­gram re­sults. Any sys­tem pass­ing the above method surely passes the elab­o­rate com­puter anal­y­sis too.

Facts to Re­mem­ber while us­ing the quick flex­i­bil­ity check method: Re­mem­ber the facts be­low while ap­ply­ing the quick check method:

Pipe fit­tings have a “stress in­ten­si­fi­ca­tion fac­tor” (SIF), i.e. the ac­tual stress in the pip­efit­ting = SIF*stress in the ad­ja­cent pipe. The net fit­ting stress shall not ex­ceed the per­mis­si­ble stress for ad­e­quate safety of the sys­tem with rea­son­able Safety Fac­tor. Ex­ces­sive fit­ting stresses could cause fa­tigue cracks fail­ures. No doubt, fit­tings have “flex­i­bil­ity fac­tor” (FF), i.e. the el­bow goes out of round un­der stress and con­se­quently re­lieves part of the stress from longer and shorter leg ex­pan­sions. How­ever, the stress re­duc­tion from FF is smaller com­pared to the in­crease from SIF. Hence, de­sign­ers usu­ally ig­nore the re­lief from FFs.

Few SIF & FF facts:

1. Usual SIFs range from 2.0 to 3.0.

2. De­sign­ers limit the stress on pipes and pipe fit­tings to 1.5 times the yield stress of 138 to 207 MPa to avoid fa­tigue fail­ures. Hence, us­ing 69 MPa as per­mit­ted stress for both CS and SS Pip­ing, 2.0 to 3.0 SIF, and ig­nor­ing FFs re­sults in pip­ing of ad­e­quate flex­i­bil­ity at least ma­te­rial use.

More on Pip­ing Flex­i­bil­ity Quick Check Method: Two tricks of the trade viz. 1) fic­ti­tious an­chors and 2) the-tail-does-not-wag-the-dog prin­ci­ples ex­tend the ap­pli­ca­tion of the quick check method to more com­plex pip­ing sys­tems. De­tails fol­low:

Fic­ti­tious An­chors: The crux of ‘fic­ti­tious an­chors (fig 5) prin­ci­ple is that one can an­chor any point or points on a com­pli­cated pip­ing net­work with­out ad­verse pip­ing stress ef­fect. Con­versely im­pos­ing a fixed dis­place­ment or ro­ta­tion also does not ad­versely af­fect the pip­ing sys­tem stress. The net ef­fect of these is that if each sub­sys­tem is ad­e­quately flex­i­ble with ‘fic­ti­tious an­chors’ so is the en­tire sys­tem with an­chors re­moved. Un­for­tu­nately this ax­iom ap­plies to equal dia pipe &

sch legs only. Let us con­sider an ex­am­ple:

Adding the imag­i­nary fic­ti­tious an­chor to the fig 5 de­picted com­plex sys­tems breaks it into 1-a 20x20 m and 2-a 10x10 m sim­ple guided can­tilever sys­tems and en­ables solv­ing as in prob­lems 1&2.

Re­mem­ber the square root re­la­tion­ship be­tween the re­quired length and mag­ni­tude of ther­mal ex­pan­sion. Hence, if the 10x10 leg is ad­e­quately flex­i­ble the 20x20 leg would be lot more flex­i­ble. This is the case even with the imag­i­nary an­chor re­moved. Let us check the fig 5, 10’X10’ sub­sys­tem flex­i­bil­ity:

SS’s Young’s Mod­u­lus of Elas­tic­ity in 201840

(Mega Pas­cal) MPa

10 m leg ther­mal ex­pan­sion = mm 27.2 10*1000*17*10^-6*(180-20)

Pipe Nom­i­nal Size 4” mm mm 101.6 Per­mis­si­ble sec­ondary stress from 10 m leg length ex­pan­sion MPa; as­sume S=70 MPa

L =(3*10^- 6* 201840*27.2*101.6/70)^0.5 m 4.9

Since the short leg is 10 m long i.e. >> than the re­quired min 4.9 the 10X10 sys­tem is ad­e­quately flex­i­ble. Hence, much more is the 20x20 sys­tem and the en­tire sys­tem with the fic­ti­tious an­chor re­moved.

Where to put the fic­ti­tious an­chor: Put the fic­ti­tious an­chor on the longer leg from the lower bend so as to cre­ate an equal legged lower sub­sys­tem.

The Tail Does Not Wag the Dog: Con­sider the fig 5 de­picted pip­ing con­fig­u­ra­tions: Strength of ma­te­ri­als for­mula says that a beam’s re­sis­tance to bend­ing mo­ment is pro­por­tional to sec­tion mod­u­lus aka area mo­ment of in­er­tia (I). I = kr3 where r is the mean

Thin Walled Pipes ra­dius. Hence, ob­vi­ously in a pip­ing sys­tem the larger di­am­e­ter pipe dom­i­nates ther­mal dis­place­ment re­ac­tions of com­plex pip­ing sys­tems lot more than smaller di­am­e­ter pipe. Eg I is ≈ 5*I

6” NPS Sch 40 Pipe 3” NPS Sch 40 Pipe, I-be­ing area mo­ment of In­er­tia, even though the size ra­tio ≈ 2 only. Ob­vi­ously the ther­mal ex­pan­sion ef­fects of the smaller 3” NPS will not in­flu­ence the larger dia pipe, mak­ing the say­ing the “tail” can­not wag “dog” true.

Clearly, the 3” NPS 10mX10m sub­sys­tem would then fail a man­ual check. Hence, the en­tire sys­tem re­quires a com­puter anal­y­sis.

Types of Ex­pan­sion Loops: The above dis­cus­sions tell us that re­strict­ing pip­ing ther­mal ex­pan­sion im­poses heavy loads on the con­nected equip­ment and dam­age these. Hence, al­low­ing pipes to ex­pand freely is nec­es­sary. The ex­pan­sion loops de­scribed be­low serve this re­quire­ment:

1. Full loop (fig 6): This is sim­ply one com­plete turn of the pipe. Pre­ferred prac­tice is fit­ting the steam pipework full loop in the hor­i­zon­tal rather than a ver­ti­cal leg to pre­vent up­stream side con­den­sate ac­cu­mu­la­tion and con­se­quent wa­ter ham­mer prob­lems. Take great care that the down­stream side passes be­low the up­stream side, as fit­ting the wrong way re­sults in con­den­sate ac­cu­mu­la­tion in the bot­tom. In ad­di­tion, en­sure sup­ply of cor­rect handed full loops for fit­ting in con­fined spa­ces. Full loops don’t pro­duce a force re­sist­ing the pipe ex­pan­sion as some other loops do. But in­side fluid pres­sure tends to un­wind the loop and thus stresses the flanges ad­di­tion­ally. Full loops use is nearly ex­tinct now due to large space oc­cu­pied and ex­pan­sion bel­lows easy avail­abil­ity. are now more read­ily avail­able. How­ever, large dia out­door steam pip­ing sys­tems still use these as space is no con­straint and these are cheaper than other types.

2. Horse­shoe or lyre loop (fig 7): Used in few no space con­straint ap­pli­ca­tions. Best fit is in a hor­i­zon­tal pipe­line with the horse­shoe fac­ing up­wards with loop pipe­line in one plane. Pres­sure does not tend to blow the ends of the loop apart, but slightly straighten the loop but not high enough to mis­align the flanges. Fit­ting a valved drain on up­stream en­try is nec­es­sary.

Fab­ri­cated Ex­pan­sion Loop (fig 8): Most plant work­shops can eas­ily fab­ri­cate the fab­ri­cated ex­pan­sion loop by weld­ing short pipe lengths to 1.5 R ra­dius el­bows as in fig 8.

Fab­ri­cated Ex­pan­sion Loop

Sizing: Con­sult Fig 8 and ta­ble 1 for in­for- ma­tion.

Com­monly Used Fab­ri­cated Ex­pan­sion Loops: Figs 9, 10 and 11 show the com­monly used ex­pan­sion loops.

Pipe-way Lay­out Points: Re­mem­ber and ap­ply the fol­low­ing points while pre­par­ing a pipe-way lay­out:

1. be­tween pipes) +in­su­la­tion thick­ness + 25 all in mm

2. If the line spac­ing wastes berthing space at the turns, iden­tify and elim­i­nate the max space wasters Move the an­chors of these lines closer to the cor-

ners. Place one or more loops be­tween these two an­chors & size the loops to fit the avail­able space.

3. Group the lines re­quir­ing big­gest loop near the outer edge with the lines re­quir­ing smaller loops pro­gress­ing to­wards the mid­dle

4. Check the an­chor forces

5. Ide­ally cen­ter ex­pan­sion loops cen­ter to get equal dis­tance be­tween an­chors; where im­prac­ti­cal, try to make each half as close as pos­si­ble. at the cen­ter be­tween an­chors with equal legs on ei­ther side of an­chor. If it isn’t prac­ti­cal, make legs on ei­ther side of an­chor as equal as pos­si­ble.

6. Al­low for ther­mal ex­pan­sion while spac­ing ad­ja­cent loops Use ta­ble 1 data to de­sign ex­pan­sion loops

7. De­cide sup­port length & breadth to ac­com­mo­date pipe ex­pan­sion; e.g. in fig 13 the 37 m por­tion will ex­pand by 37*1000*17*10^- 6*( 260-21) = 150.3 mm. Hence the dis­tance d of left sup­port shall be > 150.3 mm

8. Sup­port the ex­pan­sion loop on a cross beam as shown in fig 15 and never as in fig 14

9. Use ta­ble 1 data to de­cide on ex­pan­sion Loop de­tails

10. Cal­cu­late the spac­ing at the turns. Re­mem­ber pipelines cen­ter to cen­ter dis­tance in a rack = Pipe OD D +0.5S (space be­tween pipe ODs) + 25 all in mm.



Pip­ing is not as sim­ple as it meets the eye. For safety fol­low this ar­ti­cle given guide lines. Check­ing ad­e­quacy of pip­ing flex­i­bil­ity of same size through­out pip­ing as this ar­ti­cle ex­plains is ad­e­quate. When pipe sizes dif­fer, thor­ough com­puter anal­y­sis is nec­es­sary. Do not hastily mod­ify pip­ing. Con­sult a qual­i­fied and ex­pe­ri­enced pip­ing spe­cial­ist.

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