# Piping stress analysis primer

## S. Raghava Chari - Consultant

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

LPS PD/4T

RPS P

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:

c

Lm pipe support span ym permissible mid-span deflection

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

c

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

A

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

A

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

min

=(3*10^- Ans

6

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

NotetheconsistentuseofKg/cm2forbothforE&S

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.

o

Conclusion

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.