Pipelines stress analysis Report Slides

8/4/2019 Pipelines stress analysis Report Slides

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4/21/12

Stresses in pipe lines


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4/21/12Contents Introduction

Steps of piping system design

Stress analysis techniques

Classification of loads

Primary Vs Secondary loads

Static Vs Dynamic loads

Principal stresses

Applied loads which causes normal and shear stresses

Theories of failure

Piping codes

ASME B31.1

ASME B31.3


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4/21/12Contents Pipe Supports

Different types of supports

Piping systems supports designing

Buried pipes design

Soil Mechanics

Rigid Vs flexible pipes

Water systems

Marston load theory


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4/21/12Introduction to piping stressanalysis

Pipes are the most delicate components in any processplant.

It is very important to take note of all potential loads that apiping system would encounter during operation as well asduring other stages in the life cycle of a process plant.

Ignoring any such load while designing, erecting, hydro-testing, start-up shut-down, normal operation, maintenanceetc. can lead to inadequate design and engineering of

a piping system.

Stress analysis and safe design normally requireappreciation of several related concepts.


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4/21/12Steps of piping system design An approximate list of the steps that would be involved is as

follows:

1. Identify potential loads.

2. Relate each one of these loads to the stresses and strains.

3. Decide the worst three dimensional stress state .

4. Get the cumulative effect of all the potential, loads on

the 3-D stress scenario in the piping system underconsideration.

5. Alter piping system design to ensure that the stress

pattern is within failure limits.


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4/21/12Stress analysis techniques The analysis of stresses may be carried to varying degrees

of refinement.

Manual systems allow for the analysis of simple systems.

There are methods like chart solutions (for three-dimensional

routings) and rules of thumb (for number and placement ofsupports) etc. involving long and tedious computations andhigh expense.

All such methods may be classified as follows:

1.Approximate methods dealing only with special piping

configurations of two-three or four-member systems .

The approximate methods falling into this category are

limited in scope of direct application.


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4/21/12Stress analysis techniques

2. Methods restricted to square-corner, single-plane systems

with two fixed ends, but without limit as to the number of

members.

3. Methods adaptable to space configurations with square

corners and two fixed ends.

4. Extensions of the previous methods to provide for

the special properties of curved pipe by indirect means,

usually a virtual length correction factor.


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4/21/12Classification of loads andfailure modesClassification of loads:

A. Primary Loads.

B. Secondary Loads.

Classification of failure modes:

A. sudden failure due to onetime loading(attribute to primary

loading) B. fatigue failure due to cyclic loading(attribute to secondary

loading)


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4/21/12Primary Loads

These are typically steady or sustained types of loads.

Primary loads are usually force driven.

Primary loads are not self-limiting.

Allowable limits of primary stresses are related to ultimatetensile strength.

Design requirements due to primary loads are encompassedin minimum wall thickness requirements (In codes).


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4/21/12Secondary Loads Secondary loads are usually displacement driven.

Secondary loads are self-limiting.

Allowable loads for secondary stresses are based uponfatigue failure modes.

Secondary loads are cyclic in nature (expect settlement).

Secondary application of load never produces sudden failureand sudden failure occurs after a number of applications ofload.


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4/21/12Static vs. Dynamic loads

Static loads are those loads applied on to the piping systemso slowly that the system has time to respond, react and alsoto disturb the load. Hence, the system remains in equilibrium.

The dynamic load changes so quickly with time that thesystem will have no time to distribute the load. Hence the

system develops unbalanced forces.


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4/21/12Types of dynamic loading

1. Random: here the load changes unpredictably with time.

The major loads covered under this type are :-

(a) Wind load.

(b) Earthquake.

2. Harmonic: here the load changes in magnitude and

direction in a sine profile. The major loads

covered under this are:-

(a) Equipment Vibration.

(b) Acoustic Vibration.

3. Pulsation: This type of loading occurs due to flow from

reci rocatin um s, com ressors etc.


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4/21/12Types of stresses acting on apipe

When calculate stresses, we choose a set of orthogonaldirections and define the stresses in this co-ordinate system.

Types of loads according to their direction are axial ,

circumferential (Hoops direction) and radial


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4/21/12Principal stresses The mechanics of solids state that it would also be

orientation which minimizes some other normal stress.

Normal stresses for such orientation (maximum normalstress orientation) are called principal stresses, and aredesignated S1 (maximum), S2 and S3 (minimum).

Solid mechanics also states that the sum of the three normalstresses for all orientation is always the same for any givenexternal load.


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4/21/12Principal stresses In addition to the normal stresses, a grain can be subjected

to shear stresses as well.

The maximum shear stress in a 3-D state of stress can beshown to be

Use of Mohr's circle then allows calculating the two principle

stresses and maximum shear stress as follows:


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4/21/12Applied Loads which causesnormal and Shear Stresses

Axial Load

Internal / External Pressure

Bending Load

Shear Load

Torsional Load


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4/21/12Axial Load A pipe may face an axial force (FL).

It could be tensile or compressive.


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4/21/12Internal / External Pressure A pipe used for transporting fluid would be under internal

pressure load. (Like jacketed pipe core or tubes in a Shell)


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4/21/12Bending Load The bending moment can be related to normal and shear

stresses.

Pipe bending is caused mainly due to two reasons: Uniformweight load and concentrated weight load


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4/21/12Bending Load Stress due to bending moment is not uniform through all the

pipes cross section


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4/21/12Shear Load Shear load causes shear stresses.

Shear load may be of different types. Common load is theshear force (V) acting on the cross-section of the pipe


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4/21/12Torsional Load The shear stress caused due to torsion is maximum at outer

pipe radius & it is given in terms of the torsional moment andpipe dimensions.


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4/21/12Allowable stresses

Allowable stresses as specified in the various codes arebased on the material properties. These can be classified intwo categories

Time Independent stresses

Time dependent stresses


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4/21/12Theories of Failure There are various theories of failure that have been put forth.

These theories differ only in the way the above mentionedfunction is defined.

Important theories in common use are considered here

Maximum Stress Theory (Rankine Theory)

Maximum Shear Theory (Tresca Theory)

Octahedral Shear Theory (Von Mises Theory)


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4/21/12Rankine Theory Maximum Stress Theory (Rankine Theory)

According to this theory, failure occurs when the maximumprinciple stress in a system is greater than the maximum tensileprinciple stress at yield in a specimen subjected to uni-axialtension test.


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4/21/12Maximum Shear Theory(Tresca Theory)

According to this theory, failure occurs when the maximum shearstress in a system max is greater than the maximum shearstress at yield in a specimen subjected to uni-axial tension test.


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4/21/12Octahedral Shear Theory (VonMises Theory)

Octahedral Shear Theory (Von Mises Theory)

According to this theory, failure occurs when the octahedral shearstress in a system is greater than the octahedral shear stress atyield in a specimen subjected to uniaxial tension test.


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4/21/12Design under Secondary Load A pipe designed to withstand primary loads and to avoid

catastrophic failure may fall after a sufficient amount of timedue to secondary cyclic load causing, fatigue failure.

The secondary loads are often cyclic in nature. The numberof cycles to failure is a property of the material ofconstruction just as yield stress is.

This number of cycles to failure is the corresponding material

property important in design under cyclic loads aim atensuring that the failure does not take place within a certainperiod for which the system is to be designed.


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4/21/12Design under Secondary Load Fatigue test is carried out on a specimen subjected to cycles

of uni-axial tensile and compressive loads of certainamplitude. The specimen is subjected to a graduallyincreasing load leading to a maximum tensile load of W, thenthe load is removed gradually till it passes through zero andbecomes gradually a compressive load of W (i.e. a load of

W), then a tensile load of W and so on. Time averaged loadis thus zero.

The cycles to failure are then measured; the experiments are

repeated with different amplitudes of load.


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4/21/12Piping codes The most famous codes for pipe design are the ASME Codes

From the ASMEs various codes the most used are

ASME 31.1 Power piping

ASME 31.3 Process piping

ASME 31.9 Building services piping


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4/21/12ASME code This code was published by ASA ( American standardAssociation ) known as ANSI ( American national standardinstitute ) then its developed to the current ASME code

The code is divided into several documents each isconcerned with particular industry .

Code is consists of:

B31.1 Power Piping

B31.3 Process Piping

B31.4 Pipeline Transportation Systems for Liquid Hydrocarbonsand Other Liquids

B31.5 Refrigeration Piping

B31.8 Gas Transportation and Distribution Piping

B31.9 Building Services Piping

B31.11 Slurry Transportation Piping Systems.


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4/21/12ASME 31.1 Power piping This code relates particularly to piping that would be found in

electrical power plants, commercial and institutional plants,geothermal plants, and central heating and cooling plants.(soits called power piping)

Its used in piping known as boiler external piping as its

considered part of the boiler This code cant be used in industries such as :

component covered by pressure vessel code or ASME boilercode

Structural components . Tanks and instrumentation.

The code specify some useful formulas for determiningeither the design pressure of a particular pipe or the requiredwall thickness of a pipe operating at a certain pressure.


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4/21/12ASME 31.1 Design equations

Where

P = Internal design gage pressure [psi or kPa]The pressure is either given or solved for in the equations.S = Maximum allowable stress values in tension for the materialat the design temperature [psi or kPa]E,F,A = welding efficiency , casting factor and additionalthickness respectively


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4/21/12ASME 31.1 Limits

The code also specify the limits for : sustained and displacement stresses

Where :

Ss = Sustained stress i = Stress Intensification factor.

Sh = Basic allowable stress at the operating temperature

MA = Resultant moment due to primary loads

= ( Mx + My + Mz ) 0.5


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4/21/12ASME 31.1 Limits cont.

Occasional stresses

Where:

So = Occasional stress. K = Occasional load factor

Expansion stresses

Where:

SA = Allowable expansion stress range


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4/21/12ASME 31.1 Flexibilityanalysis To study the system behavior when its temperature changes

from ambient to operating point, so as to arrive at the mosteconomical layout with adequate safety.

The considerations that decide the minimum acceptableflexibility on a piping configuration:

1. The maximum allowable stress range in the system.

2. The limiting values of forces and moments that the pipingsystem is permitted to impose on the equipment to which it is

connected.

3. The displacements within the piping system.

4. The maximum allowable load on the supporting structure.


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4/21/12Methods of Flexibility Analysis There are two methods of flexibility analysis which involve

manual calculations:

1. Check as per clause 119.7.1/319.4.1 of the piping code

K DY/(L-U) 2

1. Guided Cantilever Method

. L= (DE/48f)1/2


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4/21/12ASME 31.1 Testing

Pressure Test: After a pipe system is installed in the field, it isusually pressure tested to ensure that there are no leaks.Once a system is in operation, it is difficult, if not impossible,to repair leaks.

Hydrostatic Testing: It is important to provide high point ventsand low point drains in all piping systems to be hydrotested.The high point vents are to permit the venting of air, which iftrapped during the hydrotest may result in fluctuatingpressure levels during the test period. The drains are to allowthe piping to be emptied of the test medium prior to fillingwith the operating fluid.

pneumatic test: A preliminary pneumatic test is often applied,holding the test pressure at 25 psig to locate leaks prior totesting at the test pressure. The test pressure for pneumatictests is to be at least 1.2 but not more than 1.5 times thedesign pressure.


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4/21/12ASME 31.3 Process piping

The term process piping is generally considered to be the pipingthat one may find in chemical plants, refineries, paper mills, andother manufacturing plants.

The ASME 31.3 code is arranged as 31.1 chapters and paragraphsbut here the paragraph has number 300 instead of 100

Scope

The scope of this code includes all fluids. This scope specificallyexcludes the following:

Piping with an internal design pressure between 0 and 15 psi(105 kPa)

Tubes inside fired heaters

Pressure vessels, heat exchangers, pumps, or compressors.


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4/21/12ASME 31.3 cont.

Design criterionThe difference between ASME 31.1 and 31.3 that 31.1 is focused

more on steel pipe and fittings, while 31.3 pertains more tononmetallic pipe and fittings. The obvious reason is that processpiping deals with more fluids that are corrosive to steel. In manycases, thermoplastics, thermosetting plastics, and resins will be moreappropriate materials for the fluids handled in the purview of theprocess piping code.

Fluid Categories:

D fluids : nonflammable, nontoxic, and not damaging to human tissue.design pressure does not exceed 150 psig (1035 kPa) & design

temperature is between -20F and 366F (-29C and 186C).

M fluids : a single exposure to a very small quantity could lead to seriousirreversible harm

High pressure fluid : higher than allowed in ASME B16.5 PN420

All fluids not listed in the above categories


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Where :tm = Minimum required wall thickness [in or mm].t = Pressure design thickness, as determined byany of the Formulas (3a) through (3b) [in or mm].c = Mechanical, corrosion, or erosion allowances [in or mm]

S = Stress in material at the design temperature [psi or kPa].E = Quality Factor W = Weld Joint Strength Factor.Y = A coefficient used to account for material creep


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4/21/12ASME 31.3 Limits

As ASME 31.1, ASME 31.3 has limits formulas For sustain stresses

Where :

FAX = Axial force due to sustained ( primary ) loading

Mi = In-plane loading moment due to sustained ( primary )

Mo = Out-plane loading moment due to sustained (primary ) loading.

ii , io = in-plane and out plane stress intensificationfactors.

Sh = Basic allowable stress at operating temperature.


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4/21/12ASME 31.3 Limits cont.

For expansion

Where:

SE = Expansion stress range

MT = Range or torsional bending moment due to expansionload

SA = Allowable stress range.


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4/21/12ASME 31.3 cont.

ASME 31.3 specify branching specifications for each fluidcategory defining some parameters and requirements

The run pipe diameter-to-thickness ratio (Dh/Th) < 100

the branch-to-run diameter ratio (Db/Dh) is not greater than 1.0.

If Dh/Th >= 100, the branch diameter Db has to be less than one-half the run diameter Dh.

The angle between the branch and run is at least 45.

Another section of ASME 31.3 is for the welding types foreach fluid category

ASME 31.3 also discussed the pipes that required to besafeguarded ( need more protective measures to minimizethe risk of accidental damage to a piping system)


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4/21/12ASME 31.3 Testing

Leak test: all piping designed in accordance with B31.3 beleak tested according to fluid category the test steps isspecified.

Hydrostatic test: As in ASME 31.1 pneumatic leak test: Due to the possibility of brittle fracture of

nonmetallic piping which may be found in systems under thescope of B31.3 the test requires a pressure relief devicehaving a set pressure of the test pressure plus the smaller of50 psi or 10 percent of the test pressure.

Because chemical piping can involve core complicatedequipment and piping designs, there may be additional

factors to be considered in a pressure test. Because there may be elevated temperatures, the code

includes a provision for establishing a more appropriate testpressure.

ASME 31 9 B ildi i


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4/21/12ASME 31.9 Building servicespiping

The scope of this code envelopes industrial, institutional,commercial, public buildings and multi-unit residences.

there are many similarities between B31.9 and B31.1.

Both codes cover boiler external piping. However, B31.9includes steam boilers up to 15 psig maximum, while B31.1uses 15 psig as a lower limit of its scope. Similarly, B31.9includes water heating units up to 160 psig maximum, whileB31.1 uses 160 psig as its lower limit for hot water.


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Where :

the variables are defined as in ASME B31.1.

tm = Minimum required wall thickness[in. or mm]

P = Internal design gage pressure [psi or kPa]

The pressure is either given or solved for in theequations.

S = Maximum allowable stress values in tension for thematerial

at the design temperature [psi or kPa]

E, A = welding efficiency and additional thickness


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4/21/12Pipe supports

It transmits the load from pipe to structures or pressureequipment .

It bear the dead loading, live loading, wind, snow, andseismic loadings, as well as the loads imposed or caused byvariations in temperatures.

Pipe supports standards

ANSI31.1 &31.3 i.e. Power Piping & Process Piping.

MSSSP 58 Pipe Hangers and Support: Materials, Design &Manufacturers.

MSSSP 69 Pipe Hangers and Supports: Selection &Application.

MSSSP 77 Guidelines for Pipe Supports ContractualRelationships.


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4/21/12Types of supports

There are six main types of supports:1. Rigid or weight supports & hangers.

2. Variable effort supports & hangers.

3. Constant effort supports.

4. Spring loaded sway braces.

5. Dynamic restraints.

6. Snubbers & shock absorbers.

7. Ancillary items

These types of supports can be divided into three main typeswhich are rigid supports, variable effort support and constanteffort support


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Rigid Hangers are normally used at suspension points whereno vertical movement occurs and the only considerations arethe Load at the point of support, line temperature, PipeMaterial of construction, and insulation thickness.

Rigid supports support the Pipe line from the bottom and

usually rest on the floor, pipe rack or structure. Pipe linesubjected to horizontal expansions only may be supported byPipe roller guides and when both X & Z directionmovement takes place pipe lines are supported by pipeshoes with low friction slide bearings beneath them.

Rigid supports


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4/21/12 Variable effort supports also known as variable hangers or

variables are used to support pipe lines subjected tomoderate (approximately up to 50mm) vertical thermalmovements.

Variable effort supports are used to support the weight ofpipe work or equipments along with weight of fluids (gasesare considered weightless) while allowing certain quantum ofmovement with respect to the structure supporting it.

Spring supports may also be used to support lines subject torelative movements occurring typically due to subsidence orearthquakes.

Variable effort supports &hangers


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In a constant effort support the loadremains constant when the pipe movesfrom its cold position to the hot position.Thus irrespective of travel the loadremains constant over the completerange of movement.

When confronted with large verticalmovements typically 150 mm or 250 mm,there is no choice but to select a constanteffort support (CES).

For pipes which are critical to theperformance of the system or so calledcritical piping where no residual stressesare to be transferred to the pipe it is acommon practice to use CESs.

Constant effort supports andhangers


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4/21/12Sway braces They are spring loaded units

mounted on pipe work to limit theswaying or vibration induced byexternal forces by applying anopposing force on the pipe.

Dynamic restraints

A restraint is a device that preventseither the pipe work or the plant towhich the pipe work is connectedbeing damaged due to theoccurrence of Earthquakes, Fluiddisturbances and otherenvironmental influences

It is designed to absorb and transfersudden increases in load from thepipe into the building structure and todeaden any opposing oscillationbetween the pipe and the structure.


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4/21/12Snubbers and shock absorbers A fluid passes through a spring-

loaded valve, the spring beingused to hold the valve open. If thedifferential pressure across thevalve exceeds the effectivepressure exerted by the spring, thevalve will close. This causes the

snubber to become rigid andfurther displacement issubstantially prevented.

Ancillary items

Ancillaries are the hardware thatcomplement supports and allowthe connection of the pipe to thebuilding structure, sometimes assimple as a pipe shoe orcomprised of many items from a

beam clamp through hanger rods,spreader beams and pipe clamps.


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4/21/12Pipe system support designing

Supports specifications These specifications must be taken into consideration by the

designer:

1. The exact hot or operating load required to be supported during theworking condition.

2. Hydrostatic test load.

3. The total travel.

4. The direction of travel either upwards or downwards from the erectedposition.

5. The set pin locking position.

6. The basic model.

7. Requirements of bottom accessory components such as rods, clampsetc.

8. Any hazardous environmental conditions.

9. Any special finish on the body such as galvanizing.


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4/21/12 Supports should be located at near as possible to

concentrated loads as valves, flanges etc. to keep thebending stresses to the minimum.

Location of supports

Th l t i i


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Pipe lines which carry fluids have a tendency to expand withincrease in temperature.

Thermal movement in pipesupports

Thermal movement in pipe


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4/21/12 To avoid the above situation a flexible support is introduced

which will allow the Pipe to move vertically and at the sametime support the load of the pipe to prevent its weight beingtransferred to the nozzle.

Thermal movement in pipesupports


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This is the variation in load or stress imposed on the pipework system when moving from the cold condition to the hotcondition. This is usually expressed as a percentage of thehot load.

As the pipe is suspended or supported directly on a springany thermal movement of pipe line will force the support toexpand or compress causing either a decrease or increase inload.

LV= (Hot Load Cold Load)*100/Hot Load

LV= (Travel * Spring rate)*100/Hot Load

Maximum Load Variation

Steps for selection of


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4/21/12 Determine the required supporting effort & pipe movement

Locate the spring size which accommodates the required Load.

Use tables to choose a type and use trial and error method.

Calculate the cold or hot loads.

Ensure that both the cold load & hot load can be accommodatedin the same type of support .

If the Loads & travel cannot be accommodated, try the next sizeor the next travel range.

Continue this iteration process till the following criteria aremet:

Operating & Preset Load in the same type.

Load variation less than specified LV%.

Smallest possible size selected.

phangers to suit specified

load variation


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4/21/12Buried Pipe Design

Underground conduits have served to improve peoplesstandard of living since the dawn of civilization. . Remnants

of such structures from ancient civilizations have been found

in Europe, Asia, and even the western hemisphere.

Today, underground conduits serve in diverse applications

such as sewer lines, drain lines, water mains, gas lines,

telephone and electrical conduits, culverts, oil lines, coal

slurry lines, subway tunnels, and heat distribution lines.

It is true we must build down before we can build up..

In the early 1900s, Anson Marston developed a method of

calculating the earth load to which a buried conduit is


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4/21/12Soil Mechanics

Various parameters must be considered in the design of a buriedpiping system. soil type, soil density, moisture content, anddepth of the installation are commonly considered. If finiteelement analysis is used, many soil characteristics are requiredas input to the mathematical soil model.

the Unified Soil Classification System (USCS) is most commonlyused in the construction industry.

Soil stiffness (modulus) is an extremely important soil propertyand is the main contributor to the pipe-soil system performance.Experience has shown that a high soil density will ensure high.soil stiffness. Therefore, soil density is usually given specialimportance in piping system design.

Materials used in buried


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4/21/12Materials used in buriedpipes

There are many types of piping materials on the market today

ranging from rigid concrete to flexible thermal plastic. Such

things as inherent strength, stiffness, corrosion resistance,

lightness, flexibility, and ease of joining are some characteristics

that are often given as reasons for using a particular material.

A pipe must have enough strength and/or stiffness to perform its

intended function. It must also be durable enough to last for its

design life.

Piping materials are generally placed in one of two

classifications: rigid or flexible. A flexible pipe has been defined

as one that will deflect at least 2 percent without structural

distress.


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4/21/12Rigid pipes Vs Flexible pipes

For rigid pipes, strength to resist wall stresses due to the combinedeffects of internal pressure and external load is usually critical.

For flexible pipes, stiffness may be important in resisting ringdeflection and possible buckling

For a thermal plastic pipe, such as PVC pipe, strength is measured

in terms of a long-term hydrostatic design hoop stress.


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4/21/12Pipe Hydraulics

The field of study of fluid flow in pipes is often referred to ashydraulics.

Flow in pipes is usually classified as pressure flow for systems

where pipes are flowing full or open-channel flow when pipes

are not flowing full. Water systems are pressure systems and

are considered to be flowing full.

On the other hand, sewer systems, for the most part, are open-

channel systems.

The relatively small concentration of solids is not sufficient, Thus

sewage is accepted to have the same hydraulic flowcharacteristics as water.

For pressure flow, the Hazen-Williams equation is widely

accepted.

S


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4/21/12Water Systems

Water systems are lifelines of communities. They consist of suchitems as valves, fittings, thrust restraints, pumps, reservoirs,and, of course, pipes and other miscellaneous appurtenances

The water system is sometimes divided into two parts: thetransmission lines and the distribution system.

The design of distribution piping system is somewhat similar tothat of transmission lines except that a substantial surgeallowance for possible water hammer is included in the pressuredesign.

The hydraulic analysis of such a system is almost impossible by

hand methods, but is readily accomplished using programmingmethods via digital computers.

B i d Pi D i


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4/21/12Buried Pipe Design

The piping system must be strong enough to withstand inducedstresses, have relatively smooth walls, have a tight joiningsystem, and be somewhat chemically inert with respect to soiland water.

The normal design life for such systems should be 50 yearsminimum. However, 50 years is not long enough. Government

and private agencies cannot afford to replace all the buried pipeinfrastructures on a 50-year basis.100 year is better.

For engineers, economics is always an important consideration;any economic evaluation must include more than just initial cost.Annual maintenance and life of the system must also be

considered.

The question is not whether the pipe will last, but how long itwill perform its designed function.

M t l d th


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4/21/12Marston load theory

a) Rigid pipe

The Marston load theory is based onthe concept of a prism of soil in thetrench that imposes a load on the pipe.

M t l d th


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4/21/12Marston load theory.

a) Rigid pipe Embankment conditions.

Not all pipes are installed in ditches (trenches); therefore, it isnecessary to treat the problem of pipes buried in

embankments.

An embankment is where the top of the pipe is above thenatural ground.

M t l d th


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Embankmentconditions.

Not all pipes areinstalled in ditches(trenches); therefore,

it is necessary to treatthe problem of pipesburied inembankments.

M t l d th


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Tunnel construction.Marstons theory may be used to determine soil loads onpipes that are in tunnels or that are jacked into place throughundisturbed soil. The Marston tunnel load equation is

C is very important in determining the load. Unfortunately,values of the coefficient C have a wide range of variationeven for similar soils.

M t l d th


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b) Flexible pipe

* A flexible pipe derives its soil-load-carrying capacityfrom its flexibility. Under soil load, the pipe tends to deflect,thereby developing passive Soil support at the sides of the

pipe.* The effective strength of the flexible pipe-soil system isremarkably high

M t l d th


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Marston load theory.

For the special case when the side fill and pipe have thesame stiffness.

Pipe stiffness versus soil


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4/21/12Pipe stiffness versus soilcompressibility

Measurements revealed that the load on a flexible pipe issubstantially less than that on a rigid pipe.The magnitude of this difference in loads may be a littleshocking.

Suppose a weight is placed on a spring. We realize thespring will deform, resisting deflection because of its springstiffness.When load versus deflection is plotted, we find that thisrelationship is linear up to the elastic limit of the spring



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4/21/12Pipe stiffness versus soilcompressibility When a load is placed on a flexible pipe, the pipe also

deflects and resists deflection because of its stiffness. It iseven possible to think of soil as being a nonlinear spring thatresists movement or deflection because of its stiffness.



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we can easily visualize the soil deforming and the pipecarrying the majority of the load.If the situation is reversed, placing a flexible spring betweentwo springs(soil), we can picture the pipe deflecting and thesoil is being forced to carry the load to a greater extent.

4/21/12Pipe stiffness versus soil


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Pipe stiffness versus soil compressibilityWhen a flexible pipe is buried in the soil, the pipe and soilthen work as a system in resisting the load.

4/21/12Pipe stiffness versus soil


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The reduction in load imposed on a pipe because of itsflexibility is referred to as arching. However, the overallperformance is not just due to arching, but is also due to thesoil at the sides of the pipe resisting deflection

4/21/12Continue Marston load


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4/21/12theory

Prism loadIt is the weight. of the soil over the pipeAgain, Eq. (2.4) represents a maximum-type loadingcondition, and Eq. (2.10) represents a minimum.

For a flexible pipe, the maximum load is always much toolarge. The mini is the same.The actual load will lie somewhere between these limits.

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Tunnel Loadingsince a flexible pipe develops a large percentage of its load-carrying capacity from passive side support, this supportmust be provided, or the pipe will tend to deflect until thesides of the pipe are being supported by the sides of thetunnel.

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Documents

Pipelines stress analysis Report Slides