Stress Analysis of Piping1

Stress Analysis Of Hot Wall Flue Gas Piping At FCCU Plant, Reliance

K.L.E. Society’s College Of Engineering and Technology, Belgaum

1

Chapter 1: INTRODUCTION TO STRESS ANALYSIS

Pipes are required for carrying fluids. These fluids can be of various states of

matter. Gaseous fluids ( like LPG ), Liquid Fluids ( like Water ) and Solid or Semi-solid

( like plastic pellets ).

The pipes in Process Industry like in Reliance are used for transferring fluids at

higher temperature and pressure.

The various processes in a Process plant cause the liquids to be pressurized and to

be heated up. Thus the liquids passing through the pipes attain a high pressure and/or a

high temperature.

When a metal is heated it expands. If this metal of pipe is allowed to expand

freely, there is no overstress in the same. But suppose the free movement is restricted by

any means, stress is introduced in the system.

The case becomes more complicated by considering weight of the pipe, the

insulation, weights of the valves, flanges and other fittings and the pressure of the fluids

that is flowing through the piping.

So the task of the Stress Engineer is

1) To select a piping layout with an adequate flexibility between points of anchorage

to absorb its thermal expansion without exceeding allowable material stress levels,

also reacting thrusts & moments at the points of anchorage must be kept below

certain limits.

2) To limit the additional stresses due to the dead weight of the piping by providing

suitable supporting system effective for cold as well as hot conditions.

Piping systems are not self supporting and hence they require pipe supports to

prevent from collapsing. Pipe supports are of different types like Rest, Guides, Linestops,

Hangers, Snubbers, and Struts. Each type of pipe support plays a vital role in supporting

the pipe system. Pipe supports are desirable to reduce the weight, wind and where

possible, expansion and transient effects, so that piping system stress range is not

excessive for the anticipating cycles of operation, us avoiding fatigue failure. Limiting the

line movement at specific locations may be desirable to protect sensitive equipment, to



2

control vibration or to resist external influences such as wind, earthquake, or shock

loadings.

All these objectives are achieved by :-

1) Limiting the sagging of the piping system within allowable limits

( i.e. In Sustain case the max vertical movement should be less than 10mm ).

2) Directing the line movements so as protect sensitive equipments against

overloading ( i.e. nozzle loads are always kept under the allowable nozzle

loading provided by the vendor ).

3) Resisting pipe system to collapse in case of earthquake, wind or shock

loadings.



3

Chapter 2 : PIPE SUPPORTS

Pipe supports[4] are essential features of piping systems as most piping systems

can be described as irregular space frames which usually are not self supporting and

therefore they must be provided with supports to prevent sagging. The loads imposed on

the pipe must, in all cases be transmitted from pipe to the supporting structure. Limiting

the line movement at specific locations may be desirable to protect sensitive equipment,

to control vibration or to resist external influences such as wind, earthquake, or shock

loading.

Support restraints and braces are therefore desirable to reduce weight, wind and

where possible expansion and transient effects, so that the piping system stress range is

not excessive for the anticipated cycles of operation, thus avoiding fatigue failure.

Piping supports are required for the following purpose :-

• To limit the sagging of the piping system within allowable limits (Rest, Hangers)

• To limit or direct line movement at specific locations so as to protect sensitive

equipment against overheads (guides, Linestops, directional restraints)

• To control vibrations (vibration dampers)

• To resist external influences such as wind, earthquake, and shock loading

(Snubbers)

The most common types of supports used to support piping are mentioned below :-

• Gravity support – Rests, Hangers

• Thermal restraints – Guides, anchors, directional restraints

• Special purpose supports – Sway brace, vibration dampers.

• Dynamic restraints against shock, occasional loading – Snubbers.

Supports to reduce friction loadings- PTFE, Slide plates, rollers and Graphite plate.



4

2.1 Rigid supports The main purpose of the rigid supports are to provide supports in one or more

directions. Different types of rigid supports are Rest, Guide and Linestops.

2.1.1 Rest Rest is used to support the pipe from sagging thus

restricting only downward movement of pipe. It allows

motion of pipe in all direction except downward

direction.

Figure 2 - 1

2.1.2 Guide Guide is used to support the pipe from sagging and avoid

pipe deflection in lateral direction thus restricting

downward and lateral movement of pipe. Usually 2 mm

gap is provided between guide and pipe.

Figure 2 - 2

2.1.3 Linestop Linestop is used to support the pipe from sagging and

avoid pipe deflection in axial direction thus restricting

downward and axial movement of pipe. Usually 2 mm gap

is provided between Linestop and pipe.

Figure 2 - 3

A combination of only guide or only Linestop i.e. without any rest can be used

where as even PTFE plates can be used to reduce the friction between rest and the

ground. To restrict motion of pipe in axial as well as in lateral direction both linestop and

guide can be used simultaneously.



5

2.2 Dynamic supports There are different types of dynamic or flexible support. Each has its own

purpose. Dynamic supports support the pipe in vibrations, seismic, winds and even take

loads in working conditions.

2.2.1 Hangers To prevent constraints in the system, thermal

expansion in the piping and the other piping

components must not be hindered. The piping must

therefore be supported in a correspondingly elastic

manner so to compensate slight vertical

displacements in the piping, spring components are

used as supports.

Figure 2 - 4

2.2.2 Sway Braces

Figure 2 - 5

These particular components act both in tension and compression and are used to

stabilize the piping and other plant components and an additional damping effect is

obtained at the same time.



6

2.2.3 Snubbers

Figure 2 - 6

Snubbers are installed to restrict axial or lateral movement of pipe in case of

earthquake. In normal condition snubber does not restrict axial or lateral movement of

pipe.

Operation :-

Control valves- The function of snubber is controlled by the main control valve (B),

axially mounted within the hydraulic piston (A).

During the piston movement ( ≤ 2 mm/s ) the valve is kept open by spring

pressure and hydraulic fluid flows freely from one side of the piston to the other. During

rapid piston movement ( approx. ≥ 2 mm/s ) above the speed limit, the resulting fluid

flow pressure on the valve plate closes the main valve. The flow of hydraulic fluid is

stopped and movement is blocked. The compressibility of the fluid cushion has a

softening effect on the restriction of the piston. This prevents damaging load spikes.

For movement in the compressive direction, the compensating valve (D) closes

almost synchronously with main valve.[4]



7

Chapter 3 : COLD SPRING

Cold spring is the process of offsetting the piping system with displacement loads

( usually accomplished by cutting short or long the pipe runs between anchors ) for the

purpose of reducing the absolute expansion load on the system. However many engineers

avoid cold spring due to the difficulty of maintaining accurate records throughout the

operating life of the unit and whereas the future analysts attempting to make field repairs

or modifications may not necessarily know about cold spring specification. Therefore

instead of cold spring expansion loops are suggested where limitation of space is not the

criteria.[5]

Cold spring is used to do the following :

• Hasten the thermal shakedown of the system in fewer operating cycles.

• Reduce the magnitude of loads on equipment and restraints, since often only a

single application of a large load is sufficient to damage these elements.

Figure 3 - 1

Several things to be considered when using cold spring :

• Cold reactions on equipment nozzles due to cold spring should not exceed

nozzle allowable.

• The expansion stress range should not include the effect of the cold spring.

• The cold spring should be much greater than fabrication tolerances.



8

• It should be noted that credit cannot be taken for cold spring in the stress

calculations, since the expansion stress provisions of the piping codes require the

evaluation of the stress range, which is unaffected by cold spring. The cold spring

merely adjusts the stress mean, but not the range.

Due to the difficulty of properly installing a cold sprung system, most piping

codes recommend that only 2/3 of the specified cold spring be used for the equipment

load calculations.

The cold spring amount is calculated as :

Ci = ½ * L * α * ∆T

where,

Ci = length of cold spring in direction I ( where i is on X,Y, or Z), (m)

L = Total length of pipe subject to expansion in direction i, (m)

α = Mean thermal expansion coefficient of material between ambient and operating

temperature, (m/m/ºC)

∆T = Change in temperature, (ºC)

Note that the ½ in the equation for the cold spring amount is used such that the

mean stress is zero. In some cases it is desirable to have the operating load on the

equipment as close to zero as possible. In this latter case the ½ should be omitted. The

maximum stress magnitude will not change from system without cold spring, but will

now exist in the cold case rather than the hot.

Now in my project line Cold spring has been used near the expander inlet.

Length of expander inlet, L = 26.379 m

Design temperature, T1= 742 ºC

From ASME B31.3 [8],

α = 19.026 * 10-6 m/m º C at 732.222 º C

α = 19.062 * 10-6 m/m º C at 746.111 º C

Using interpolation method we get,

( α - 19.026 * 10-6 ) = (19.062 – 19.026) * 10-6

( 742 – 732.222 ) ( 746.111 – 732.222 )



9

Solving the above eqn. we get,

α =1.9052 * 10-5 m/m ºC at 742 °C

The cold spring amount is calculated as :

Ci = ½ * 26.379 * 1.9052 * 10-5 * ( 742 – 21 )

= 0.1812 m

= 181.2 mm

It is seen that length of the cold spring is 181 mm which says the pipe length

should be shortened by 181 mm to reduce the magnitude of loads on equipment.

Shortening the pipe by 181 mm is not possible so another alternative is to provide

Expansion loop of use of bellows.

Due to congested space and complexity of the line the expansion loop is not

feasible therefore in this line two bellows are used which take care of expansion and cold

spring of 13 mm is used to reduce the load on expander inlet. Thus it is seen from

analysis report that the line is safe in CODE COMPLIANCE having code Highest code

stress 20.1 N/mm².



10

Chapter 4 : STRESSES ON PIPE

When any piping isometric drawing is given for stress analysis the aim of the

stress analysis Engineer is to ensure the safety against failure of the piping system by

verifying the structural integrity against loading conditions, both external and internal

expected to occur during the lifetime of the system in the plant.

Hence the objectives of the stress analysis could be listed as :-

• Ensure that stresses in piping components in the systems are within the allowable

limits.

• Ensure the nozzle loadings are within the allowable limits.

• Ensure that sustain vertical displacement is within 10mm.

• Ensure the safety against the occasional loadings such as Seismic and wind.

• Solve dynamic problems developed due to mechanical vibrations, acoustic

vibration, fluid hammer, pulsation, relief valves etc.

4.1 Causes of pipe stress :- The two common causes of pipe stress are weight and thermal loads which causes

loads on equipment nozzles.

4.1.1 Weight Weight causes the pipe to sag, which puts stress into the piping material

and forces onto equipment nozzle. It includes the weight of pie, weight of the insulation,

weight of valves, instruments etc.

4.1.2 Thermal When temperature of the pipe is higher the size of the pipe increases which

causes the nozzle loads to increase and the nozzle loads are further increased when the

supports restrain the pipe from moving. Thus improperly stress analyzed system will

cause very high loads on connecting equipment nozzles.

The other causes of the pipe stress are the occasional loads caused due to Wind,

earthquakes, dynamic loads due to equipment operation like Reciprocating Compressor,

Pilot safety valve reaction force, Slug flow etc.



11

4.2 Types of stresses to be checked as per CODE :- Stresses and flexibility in the piping systems are checked as per the governing

design codes to achieve minimum requirements for safe operation. The governing code

depends on service of the piping system. Two codes used by commonly used by piping

are:-

1. ASME B 31.1 ( Power Piping Code ).

2. ASME B 31.3 (Petrochemicals and Refinery Piping or Process Piping).

4.2.1 Minimum required load cases for computer analysis are[9] :- 1. Weight only, for support design loads.

2. Operating case, for displacements, equipment and component loads, and support

design.

• Design or maximum operating temperature.

• Expansion and displacement of connected equipment or structures.

• Design pressure

• Wind ( usually in horizontal directions )

• Weight from all sources

• Relative settlement

• Dynamics such as PSV action, slug flow, etc.

3. Expansion case, for Code Compliance

• Design or maximum operating temperature

• Expansion and displacement of connected equipment or structures

4. Sustained case, for Code Compliance

• Design pressure

• Weight from all sources

• Any sustained effects of dynamic loads.



12

4.3 Loads on the piping system The system behavior and failure are dependent on the type of loading imposed.

These are mainly classified as Primary vs. Secondary or Static vs. dynamic or Sustained

vs Occasional.

4.3.1 Primary vs Secondary loads The failure of the piping system may be sudden failure due to one time loading or

fatigue failure due to cyclic loading. The sudden failure is attributed to primary loadings

and the fatigue failure to secondary loading.

Primary loads :-

• Primary loads are usually force driven ( gravity pressure, spring forces, relief

valve, fluid hammer etc. )

• Primary loads are not self-limiting. Once plastic deformation begins it continues

till the failure of the cross section results.

• Allowable limits of primary stresses are related to ultimate tensile strength.

• Primary loads are not cyclic in nature.

• Design requirements due to primary loads are encompassed in minimum wall

thickness requirements.

Secondary loads :-

• Secondary loads are usually displacement driven ( Thermal expansion, Settlement,

Vibration etc. )

• Secondary loads are self-limiting i.e. the loads tends to dissipate as the system

deforms through yielding.

• Allowable loads for secondary stresses are based upon fatigue failure modes.

• Secondary loads are cyclic in nature ( expect settlement ).

• Secondary application of load never produces sudden failure and sudden failure

occurs after a number of applications of load.

4.3.2 Static vs. Dynamic loads Static loads are those loads applied on to the piping system so slowly that the

system has time to respond, react and also to disturb the load. Hence, the system remains

in equilibrium. The examples of such loadings are the thermal expansion, weight etc.



13

The dynamic load changes so quickly with time that the system will have no time

to distribute the load. Hence the system develops unbalanced forces.

The examples of Dynamic loadings are wind load, earthquake, fluid hammer etc.

these can be categorized in to mainly three types:-

4.3.2.1 Random :

In this type of loading the load changes unpredictably with time. The

major loads covered under this type are :-

• Wind load :

In most of the cases analysis is done using static equivalent of dynamic

model. This is achieved by increasing the static loading by a factor to account for the

dynamic effects.

• Earthquake :

Here again the analysis is done using static equivalent of a dynamic

loading model. This is again is approximate.

4.3.2.2 Harmonic :

In harmonic type of profile, the load changes in magnitude and direction in

a sine profile. The major loads covered under this are :-

• Equipment Vibration :

This is mainly caused by the eccentricity of the equipment drive shaft of

the rotating type of equipment connected to the piping.

• Acoustic Vibration :

This is mainly caused by change of fluid flow condition within pipe i.e.

from laminar to turbulent e.g. Flow through orifice. Mostly these vibrations follow

harmonic patterns with predictable frequencies based on flow conditions.

4.3.2.3 Pulsation :

This type of loading occurs due to flow from reciprocating pumps,

compressors etc. if this type of profile the loading starts from zero to some value, remains

there for certain period of time and then comes back to zero. The major types of loads

covered under this are :-



14

• Relief valve outlet :

When the relief valve opens the flow raises from zero to full value over the

opening time of the valve. This causes a jet forces and this remains until the full venting

is achieved to overcome the over pressure situation and then valve closes bringing down

the force over the closing time to valve.

• Fluid hammer :

If the flow of fluid is suddenly stopped due to pump trip or sudden closing

of valve, there will compression of fluid at one side and relaxation at the other side. This

wave propagates causing pulsation flow.

4.3.2.4 Slug flow :

This happens mainly due to multi phase flow. In general when fluid

changes direction in a piping system, it is balanced by net force in the elbow. This force is

equal to change in momentum with respect to time. Normally this force is constant and

can be absorbed through tension in pipe wall, to be passed on to adjacent elbow which

may have equal and opposite load and gets nullified. Hence, these are normally ignored.

However, if density of fluid velocity changes with time similar to slug of liquid in a gas

system, this momentum load will change with time as well leading to dynamic load.

4.3.3 Sustained vs. Occasional loads The loads on the piping system which are steady and developed due to internal

pressure, external pressure, weight etc. affecting the structure design of the piping

component are called the sustained loading. These loadings develop longitudinal, shear or

hoop stresses in the pipe wall. These could be either tensile or compressive in nature.

They can be defined as below.

4.3.3.1 Longitudinal stress :

These are axial stresses acting parallel to the longitudinal axis of the pipe.

This is caused due to internal force acting axially within the pipe and internal pressure of

the pipe.

Longitudinal stress due to Axial force is ,

SL = Fax / Am. …(4.1)

Where,



15

SL = Longitudinal stress.

Fax = Internal axial force

Am = Cross sectional area = (pi/4)* ( do² - di² ) = pi * dm * t

dm = Mean diameter = (do + di )/2

Longitudinal stress due to internal pressure is,

SL = (P * (pi / 4) * di²) / Am

= P * di² / ( 4*dm*t )

This is often conservatively approximated as

SL=P*do / (4*t) …(4.2)

4.3.3.2 Bending stress :

This is another component of the axial stress. Pipe bending is mainly due

to two reasons, uniform loads and concentrated load depending on the type of support at

the ends, the maximum bending moment is given by the bending theory as follows

Figure 4-1

Variation in bending stress through cross section of pipe is as shown. The bending

stress is zero at the neutral axis and varies linearly across the cross section from

maximum compressive to maximum tensile.

SL = Mb * c/I

Where,

Mb = Moment of the beam.

c = distance of point of interest from the neutral axis.

I = Moment of inertia

Z = Section modulus = c/I

The stress is maximum where c is greatest i.e. at the outer radius.

SL=Mb*Ro / I = Mb / Z …(4.3)



16

Now summing up eq. (4.1), (4.2), (4.3) we get,

SL = ( Fax / Am ) + P * do / ( 4*t ) + Mb / Z …(4.4)

4.3.3.3 Hoop stress :

This is caused by the internal pressure and acts in a direction parallel to the

pipe circumstance.

SH = (P * di * l) / ( 2*t*l) = P * di/( 2* t)

Or conservatively SH = P * do/( 2* t) …(4.5)

4.3.3.4 Shear Stress :

Shear stress is caused by torsional loads. Shear stress has the same units as

normal stress (force / area) but represents a stress that acts parallel to the surface (cross

section). This is different from normal stress which acts perpendicular (normal) to the

cross section. Torsion is a force that causes shear stress but this is not the only force that

can cause shear stress. For example, a beam that supports a shear force also has a shear

stress over the section (even without torsion).

Shear stress = MT * c / R

Where,

MT = Internal torsional moment acting on cross section

c = Distance of point of interest from torsional centre of Cross-section

R = Torsional resistance of cross section = 2 I

Maximum Shear stress = MT * Ro / ( 2*I ) = MT / ( 2*Z )

4.4 ALLOWABLE STRESSES Allowable stresses as specified in the various codes are based on he material

properties. Theses can be classified in two categories as below.



17

4.4.1 Time Independent stresses Time independent allowable is based on either yield stress or the ultimate tensile

strength measured in a simple tensile test.

Figure 4-2

The yield stress is the elastic limit and that is the value below which the stresses

are proportional to strain and when the load is removed, there is no permanent distortion.

The tensile strength is the highest load, which the specimen can be subject to without

failure.

The code ANSI / ASME B 31.1 permits smaller of ¼ of the tensile strength or 5/8

of the yield strength. ANSI / ASME B 31.3 uses lower of 1/3 of the tensile strength or 2/3

of the yield strength.

4.4.2 Time dependent stresses The time dependent allowable is related to “Creep rupture strength” at high

temperature. This is best explained for a piping system as follows.

Pipe running between two equipment expands as it gets heated up. The increased

length can be accommodated only by straining the pipe as its ends are not free to move.



18

This straining induces stress in the pipe. However when the line is cooled during

shutdown to ambient temperature the expansion returns to zero, the straining no longer

exists and hence stress also disappears. Every time the plant starts from a stress free

condition i.e. cold condition and soon gets to stressed with maximum at operating

conditions from cold get stressed with stress reaching maximum at operating condition

and then reducing to zero when operating stops and system cools down.

The actual performances of the piping system do not exactly follow the above

path. The piping system can absorb large displacement without returning to exactly to

previous configuration. Relaxation to the sustaining level of material will tend to establish

a condition of stability in few cycles, each cycle lowering the upper limit of hot stress

until a state of equilibrium is reached in which the system is completely relaxed and

capable of maintaining constant level of stress. The stress at which the material is relieved

due to relaxation appears as stress in opposite sign. Thus the system which originally was

stressless could within a few cycles accommodate stress in the cold condition and spring

itself without the application of external load. This phenomenon is called “Self

springing”. This is also called the Elastic shake down. This can be represented as shown

in the sketch below. Here the maximum stress range is set to 2 Sy or more accurately the

sum of hot and the cold yield stresses in order to ensure eventual elastic cycling.

The degree of self springing will depend upon the magnitude of the initial hot

stresses and temperature, so that while hot stresses will gradually decrease with time, the

sum of the hot and cold stress will stay the same. This sum is called the Expansion Stress

range. This concepts lead to the selection of an allowable stress range.

For materials below the creep range the allowable stresses are 62.5% of the yield

stress, so that bending stress at which plastic flow starts at elevated temperature is 1.6 Sh

and by same reasoning 1.6 Sc will be stress at which flow would take place at minimum

temperature. Hence, the sum of this could make the maximum stress the system could be

subjected to without flow occurring in either the hot or cold condition.

Therefore, Smax = 1.6(Sc+Sh)



19

4.5 CODE EQUATIONS 4.5.1 ANSI B 31.1 – Power piping The power piping Code ANSI B 31.1 specifies that the developed stresses due to

the sustained, occasional and expansion stresses be calculated in the following manner.

4.5.1.1 Sustained

Ss = ( 0.75*i*MA / Z ) + ( P*di / 4 t ) ≤ Sh

where,

Ss = Sustained stress.

i = Stress Intensification factor.

MA = Resultant moment due to primary loads

= ( Mx² + My² + Mz² ) 0.5

Sh = Basic allowable stress at the operating temperature

Z = Section modulus.

4.5.1.2 Occasional

So = ( 0.75*i*MA / Z ) + ( 0.75*i*MB / Z ) + ( P*do / 4 t ) ≤ KSh

where,

So = Occasional stress.

MB = Resultant range of moments due to occasional loads

= ( Mx² + My² + Mz² ) 0.5

K = Occasional load factor

= 1.2 for loads occurring less than 1% of the time

= 1.15 for loads occurring less than 10% of the time.

4.5.1.3 Expansion

SE = (i Mc / Z) ≤ SA

Where,

Mc = Resultant range of moments due to Expansion (secondary)

loads

= ( Mx² + My² + Mz² ) 0.5

SA = Allowable expansion stress range



20

4.5.2 ANSI B 31.3 – Process piping

In Petroleum Industry like Reliance uses ANSI B 31.3 for the calculation of

stresses[8] .

4.5.2.1 Sustained

Ss = FAX / AM + ((ii Mi ² + io Mo ²) / Z) + ( P*do / 4 t ) ≤ Sh

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 intensification factors.

Sh = Basic allowable stress at operating temperature.

4.5.2.2 Occasional

The code states that calculate the stresses due to sustained and occasional loads

independently as per the above equation and then add them absolutely. The sum should

not exceed 1.33 Sh.

4.5.2.3 Expansion

SE = (ii Mi ² + io Mo ² + 4 MT ²) 0.5 / Z ≤ SA

where,

SE = Expansion stress range

Mi = Range of inplane bending moment due to expansion (secondary) load

Mo= range of outplane bending moment due to expansion (secondary) load

MT = Range or torsional bending moment due to expansion load

SA = Allowable stress range.

4.6 Limits of stresses set by code ANSI / ASME B 31.3 4.6.1 Limits of Calculated stresses due to Occasional loads ANSI / ASME B 31.3 in clause 302.3.6 specifies that the sum of longitudinal

stresses due to pressure, weight and other sustained loadings and of the stresses due to

produced by occasional loads such as wind or earthquake, may be as much as 1.33 times

the basic allowable stress. Wind and earthquake forces need not be considered as acting

concurrently.



21

When the piping system is tested, it is not necessary to consider other occasional

loads such as wind and earthquake as occurring concurrently with test loads.

4.6.2 Limits of calculated stresses due to Sustained loads ANSI / ASME B 31.3 in clause 302.3.5 specifies that the sum of longitudinal

stresses, SL in any component in a piping system due to pressure, weight and other

sustained loadings shall not exceed the allowable stress at the design temperature. The

thickness of pipe used in calculating the SL shall be the nominal thickness less the

allowable due to corrosion and erosion.

4.6.3 Limits of Displacement stress range ANSI / ASME B 31.3 limits the allowable stress range to 78% of the maximum

stress the system could be subjected to without flow occurring either in hot or cold

condition.

i.e. Smax = 1.6(Sc + Sh)

Sall = 1.6*0.78(Sc + Sh) = 1.25(Sc + Sh)

From the total stress range 1 Sh is allowed for the loading as above. Reduction for

excessive cyclic condition is also applied to the same. Hence, the allowable stress range

SA is calculated by the formula,

SA = f( 1.25 Sc + 0.25 Sh )

When Sh is greater than SL, the difference between them may be added to the term

0.25 Sh, and the allowable stress range SA works out to be

SA = f{ 1.25 (Sc + Sh) - SL }



22

4.7 ACCEPTABILITY CRITERIA FOR FLEXIBILITY The Piping Engineer will have the following set of conditions to define the

minimum acceptable flexibility in a piping configuration.

1. The Expansion stress range calculated shall not exceed the allowable stress

range. i.e. SE / SA ≤ 1.

2. The reaction on the connected equipment should be within the permitted

values.

3. The displacement of the piping should be such that it should not make the

system interfere with the structures and other piping.

4. The loads and moments imparted by the piping on the supporting

structures should be such that it should be such that it should not create

stresses in the members which are beyond the acceptable limits.



23

Chapter 5 : IMPORTANCE OF THE PROJECT LINE

FOR FCCU

Before I discuss about the Analysis of the line let me tell you about the Expander

and the importance of the line for Fluidilized Catalytic Cracking Unit (FCCU) plant. The

line is connected between Expander inlet and 3rd Separator while the bypass line is

connected to orifice chamber. Expander is a part of Power recovery train which generates

electricity 2.5 MW.

5.1 Power recovery train ( PRT ) Each of the two trains (as shown in figure below) of power recovery system has

an Expander (21 MW), Main Air Blower (18 MW), Steam Turbine (13MW), and a Motor

(9MW)/ Generator (3MW) in a line. Two PRT in one FCCU is first of its kind in the

world. The flue gases at a temperature of 714 ºC and a pressure of 2.3 bar drives the

expander generating about 21 MW power from each machine. Gases from both trains

exit into the Flue Gas Coolers. The motor drawing power from grid together with the

turbine using HP steam from the header, drive the train for startup. The quantity of energy

rich flue gases increases when plant gains load. Then the expander and steam turbine

have sufficient power to drive the main air blower and also to generate about 2.5 MW

(motor now in generator mode) to feed power to the grid. The hot gases exiting the

expander at 0.06 bar and 540 ºC go through a flue gas cooler. It generates High Pressure

Steam (42 bar, 380 ºC) and sends it to the header. Expander bypass damper is available to

send the flue gases directly to the Flue Gas Cooler in case of expander problems. Finally

the energy stripped flue gases escape into the atmosphere through the stack.



24

Figure 5-1

Thus Expander 3rd Separator line is very important unit of FCCU. However this

line has to be analyzed again since it had faced some problems during its operation.

Companies like BECHTEL, PATHWAY PIPING SOLUTIIONS, REFINERY

TECHNOLOGY INC. (RTI) are working on the problems of this line and I too have been

given opportunity to do the analysis for the same.



25

Chapter 6 : PROBLEMS FACED BY PROJECT LINE

The line installed is in operation from 1999. It has experienced a number of

problem. Some supports damage was detected during the 2001 shutdown. There have

been instances of spring load requiring revision, some flange leakages and bellow

element corrosion. Also from the maintenance team of the complex thought have been

expressed that if instead of the pressure-balanced bellow there was a maintenance spool at

the inlet of Expander that would been more helpful.

Since this is a rather critical piping all these factors have led to the requirement to

look at the design of this Critical expander inlet line.

6.1 RTI’s Field observation on Expander inlet line:-

1) The existing expander inlet line in the vertical section does not support

properly. The two out of four hinge expansion joints are bottomed down. The

spring support bottomed-out condition would eventually convert the spring

support device into rigid support. These spring supports were designed to

support the vertical section with movement of 32mm up from cold to hot.

2) In addition, the two constant spring support located at the tee were also to

designed to support the vertical section with movement of 94 mm up from

cold to hot, but these constant spring supports are only moving up at

approximate 60 mm.

3) The un-support piping load on the expander inlet line has created a high Axial

forces on the nozzle which will yield higher bending moment at the 3rd stage

separator’s outlet nozzle. The bending moment will eventually yield and

defect the nozzle over the period of operation. In some case, the refractory in

the nozzle would crack and create a hot spot on the nozzle. RTI has

experienced these conditions and recommends that Reliance should check this

nozzle internally as well as externally to insure the reliability of the expander

inlet line.



26

4) RTI notices that the floating support assembly were made by carbon steel

ASTM A516 Gr.7 except 24”Ø trunnions and the reinforcing pads that welded

to the pipe. These floating rings are insulated may reach the piping

temperature ( 714º C / 742º C ) due to heat transfer. Reliance needs to check

the deformation of the floating rings to assure the functioning of this support

assembly. RTI recommends that Reliance redesigns the floating rings

assemble with all material match pipe material ( stainless steel ) to assure the

safety and reliability of the expander inlet line.



27

Chapter 7 : MANUAL CALCULATIONS

Before we move on to the CAESAR results lets check the feasibility of the

software.

7.1 Considering a Cantilever pipe and calculating stresses due to self

weight and weight of water and comparing with CAESAR Output

Given :-

Leg 10-20 Length, L = 3500 mm

O.D. of pipe, Do = 275.05 mm

Thickness of pipe, t = 9.271 mm

Corrosion allowance, C.A = 1.6 mm

Design Temperature T1 = 350 ºC

Material :- A 106 Gr. B

Density of Pipe = 7833.1567 kg/m³.

According to ASME B31.3[8],

Allowable cold stress range at 21 º C = Sc = 137.9 N/mm²

Allowable hot stress range at 350 º C = Sh = 116.4 N/mm²

7.1.1 Solution :- SA = Allowable stress range = f ( 1.25 Sc + 0.25 Sh )

= 1.0 ( 1.25 * 137.9 + 0.25 * 116.4 )

…..( where f = 1.0 for 7000 load cycles )

SA = 201.5 N/mm² …(7.1)



28

W1 = Weight of the pipe

= Density of Pipe material * Volume of pipe * 9.81

= 7833.1567 * { ( pi/4) * (Do² - Di²) } * L * 9.81

= 7833.1567 * { ( pi/4) * (0.27305 ² - 0.25451 ²) } * 3.5 * 9.81

W1= 2066 N …(7.2)

W2 = Weight of water

= Density of water * Volume of water in pipe * 9.81

= 1000 * { ( pi/4) * ( Di²) } * L * 9.81

= 1000 * { ( pi/4) * ( 0.25451 ²) } * 3.5 * 9.81

W2= 1746.8 N …(7.3)

Therefore,

Total weight, W = Weight of pipe (W1) + Weight of water (W2)

= 2066 + 1746.8

W = 3812.8 N …(7.4)

Therefore,

Shear force, Fs = 3812.8 N

Thus, Bending Moment, Mb = Fs * X c.g

= 3812.8 * ( 3.5 / 2 )

Mb = 6672.4 N-m …(7.5)

Considering, t = t actual - Corrosion allowance

= 9.271 – 1.6

t = 7.671 mm

Therefore, Di = Do – 2 * t

= 273.05 – 2 * 7.671

Di = 257.71 mm



29

Now calculating stresses and comparing with CAESAR OUTPUT. Detailed

CAESAR results are given in APPENDIX D.

1) Longitudinal stress or axial stress = ( P Di) / ( 4 * t )

= ( 0.4 * 257.71 ) / ( 4 * 7.671 )

Longitudinal stress or axial stress = 3.35 N/mm² …(7.6)

where as CAESAR output gives axial stress = 3.26 N/mm²

2) Bending stress = Mb / Z

Now,

Section Modulus, Z = {pi* (Do4- Di4)} / (32*Do)

= {pi* (0.273054- 0.2757714)} / (32*0.27305)

= 0.000412677 m³

Z = 412677 mm³ …(7.7)

Therefore from eqn.(7.5) & (7.7),

Bending Stress = (6672.4 * 10³ / 412677 )

Bending Stress = 16.16 N/mm² …(7.8)

where as CAESAR output gives Bending stress = 16.16 N/mm²

3) Hoop stress = ( P Di) / ( 2 * t )

= ( 0.4 * 257.71 ) / ( 2 * 7.671 )

Hoop stress = 6.72 N/mm² …(7.9)

where as CAESAR output gives Hoop stress = 6.72 N/mm²

4) Max 3D stress intensity

= Axial stress + {(Bending stress)² + 4(Torsional stress)² }^0.5

In this case Torsional stress = 0, as there is no Torsional moment acting on the

pipe.

Therefore from eqn.(6) & (7),

Max 3D stress intensity = 3.35 + {(16.16)² + 4(0)² }^0.5

Max 3D stress intensity = 19.51 N/mm² …(7.10)

where as CAESAR output gives Max 3D stress intensity = 19.42 N/mm²



30

Now Calculating Deflection of Pipe at node 20,

We have for Cantilever beam[10],

y = ( w * L4 ) / ( 8 * E * I )

From ASME B 31.3[8],

Modulus of Elasticity, E = 203391 N/mm² at 350 ºC …(7.11)

Moment of inertia, I = { pi* (Do4- Di4)} / 64

= { pi* (273.05 4- 254.51 4)} / 64

I = 66899732.1 mm4 …(7.12)

Weight per meter, w = W / L

= 3812.8 / 3500 = 1.08937 N/mm …(7.13)

Therefore from eqn. (7.11), (7.12) and (7.13),

y = ( 1.08937 * 3500 4 ) / ( 8 * 203391 * 66899732.1 )

y = 1.502 mm ( downward direction ) …(7.14)

where as CAESAR output gives deflection, y = - 1.523 mm i.e. in downward direction.

Thus it is seen that the result obtained by CAESAR and manual calculation

are nearly same.



31

7.1.2 CAESAR OUTPUT

Figure 7-1

Figure 7-2

Figure 7-3



32

7.2 Considering a Cantilever pipe having perpendicular supporting pipe

and calculating expansion stress due to temperature and comparing

with CAESAR Output

Given :-

Leg 10-30 Length, L = 7500 mm

O.D. of pipe, Do = 275.05 mm

Thickness of pipe, t = 9.271 mm

Corrosion allowance, C.A = 1.6 mm

Design Temperature T1 = 350 ºC

Material :- A 106 Gr. B

Density of Pipe = 7833.1567 kg/m³.

According to ASME B31.3,

Allowable cold stress range at 21 º C = Sc = 137.9 N/mm²

Allowable hot stress range at 350 º C = Sh = 116.4 N/mm²

7.2.1 Solution :- SA = Allowable stress range = f ( 1.25 Sc + 0.25 Sh )

= 1.0 ( 1.25 * 137.9 + 0.25 * 116.4 )

…..( where f = 1.0 for 7000 load cycles )

SA = 201.5 N/mm² …(7.15)

Calculation of expansion of leg 10-20,

L1 = 3.5 m

T1 = 350 ºC

T2 = 21 ºC = ambient temperature

Expansion ∆ 10-20 is calculated by formula[8],

∆ = α . ∆T . L

where,

α = Thermal Expansion coefficient m/m º C

∆T = Temperature difference = ( 350-21 ) = 329 º C



33

L = Leg length of 10-20 i.e. 3.5 m

From ASME B31.3[8],

α = 13.194 * 10-6 m/m º C at 343.333 º C

α = 13.284 * 10-6 m/m º C at 357.222 º C

Using interpolation method we get,

( α - 13.194 * 10-6 ) = ( 13.284 – 13.194 ) * 10-6

( 350 – 343.333 ) ( 357.222 – 343.333 )

Solving the above eqn. we get,

α =1.3237 * 10-5 m/m ºC at 350 °C …(7.16)

Now expansion of leg 10-20,

∆10-20 = α . ∆T . L

= 1.3237 * 10-5 * 329 * 3.5 * 1000

∆10-20 = 15.242 mm …(7.17)

As node 10 is anchored, the expansion takes place near node 20 and as leg 10-20

is horizontal and parallel to X axis, the deflection is in X axis.

CAESAR output gives deflection, DX = 15.241 mm i.e. in positive X direction.

Similarly expansion of leg 20-30,

∆20-30 = α . ∆T . L

= 1.3237 * 10-5 * 329 * 4.0 * 1000

∆20-30 = 17.42 mm …(7.18)

As node 30 is supported from below, the expansion takes place near node 20 and

as leg 20-30 is vertical and parallel to Y axis, the deflection is in + Y axis.

CAESAR output gives deflection, DY = 17. 376 mm i.e. in positive Y direction.



34

7.2.2 Calculation of Bending stress by using Guided Cantilever method : This method is intuitively familiar to many piping designers. Its fundamental

concepts are partially used in the sideway analysis of frames. The assumptions under

lying this method can be listed as follows[1] :-

1. The system has only two terminal points; it is composed of straight legs of pipe of

uniform size and thickness with square-corner intersections.

2. All legs are parallel to the coordinate axes.

3. The thermal expansion in a given direction is absorbed only by legs oriented

perpendicular to this direction.

4. The amount of thermal expansion a given leg can absorb is inversely proportional

to its stiffness. Since the legs are of identical cross section, their stiff nesses will

vary accordingly to the inverse value of the cube of their lengths.

5. In accommodating thermal expansion, the legs act as guided cantilevers; that is,

they are subjected to bending under end displacements, but no end rotation is

permitted.

According to assumptions 3 and 4 the individual legs absorb the following portion of

the thermal expansion in X-direction :

δx = ( L³ . ∆x ) / ∑( L³ - Lx³ ) …(7.19)

where,

δx = lateral deflection in the X-direction for the leg under

consideration, mm.

L = length of the leg in question, m.

∆x = overall thermal expansion of system in x-direction, mm.

∑(L³-Lx³) = sum of cubed length of all legs perpendicular to the direction

considered.

Considering leg 10-20,

L = 3.5 m

∆10-20 = 15.242 mm = ∆x

∆20-30 = 17.240 mm = ∆y



35

∑(L³-Lx³) = 4 ³ = 64 m³

∑(L³-Ly³) = 3.5 ³ = 42.875 m³

As the leg 10- 20 is in horizontal X direction therefore its lateral direction will be in Y

direction.

Now as per eqn. (7.19) we have,

δy = ( L³ . ∆y ) / ∑( L³ - Ly³ )

= ( 3.5 ³ * 17.240 ) / ( 3.5 ³ )

δy = 17.24 mm = δm ...(7.20)

where δm is largest of component deflections δx, δy or δz as per eqn. (7.19)

Now calculating,

{ 39.512 * L ( SA ) } / 10 ³

= { 39.512 * 3.5* ( 201.5 ) } / 10 ³ = 1.963 ≈ 2 …(7.21)

From graph 1 and referring the above value we find out δ

Graph 7-4 : Guided Cantilever Chart



36

Therefore, δ = 06 * 25.4 = 15.24 mm = lateral deflection. …(7.22)

Finding correction factor f :-

( L / LA ) = 3.5 / 4.0 = 0.875 …(7.23)

From graph 2 referring CASE I and the above value we find out f.

Graph 7-5 : Correction factor f, Guided Cantilever method



37

Therefore, f = 1.55 = Correction factor. …(7.24)

Now, f * δ = 1.55 * 15.24 = 23.622.

Bending stress[1] is calculated by,

Bending stress, SE = ( SA .δm ) / ( f * δ )

= ( 201.5 * 17.24 ) / ( 23.622 )

Bending stress, SE = 147.06 N/mm² ...(7.25)

According to CAESAR, Bending stress at node 10 = 116.88 N/mm²

7.2.3 Now using different formula for calculating Bending stress[3] :- SE = ( E. D.∆ ) / ( 48 * 6970 * L20-30 ² )

Where,

E = Modulus of elasticity at 350°C, N/mm²

D = Outer Diameter of the pipe, mm

∆ = Maximum deflection, mm

L20-30 = Length of leg 20-30, m

From ASME B 31.3[8],

E = 203391 N/mm² at 350° C

Therefore,

SE = ( 203391 * 273.05 * 15.242 ) / ( 48 * 6970 * 4.0 ² )

SE= 158.10 N/mm² …(7.26)

It is seen that value obtained by eqn. (7.25) is much nearer to CAESAR value.

Therefore considering SE = 147.06 N/mm²



38

7.2.4. Calculation of Bending moment and force :- 7.2.4.1 Mb = SE * Z / 1000

Where,

Mb = Moment of pipe, N-m

Z = Section modulus of pipe, mm³.

= {pi* (Do4- Di4)} / (32 * Do)

= {pi* (0.273054- 0.2757714)} / (32*0.27305)

= 0.000412677 m³

Z = 412677 mm³ ...(7.27)

Therefore from eqn.(7.25) and (7.27),

Mb = 147.06 * 412677 / 1000

Mb = 60688.28 N-m ...(7.28)

Now Force F,

7.2.4.2 F = Mb / L

Where,

F = Force acting on the pipe, N

Mb = Moment of pipe, N-m

L = Length of the pipe on which moment is acting, m

Therefore,

F = 60688.28 / 3.5

F = 17339.51 N ...(7.29)

According to CAESAR,

Shear force acting on node 10 and 20 = 16362 N

Bending moment at node 10 = 57267.3 N-m

Thus it is seen that the answers are close to the CAESAR output and we can

solve simple problems by manual calculation but as the pipe line goes on changing

directions and as the length goes on increasing the more difficult it becomes to solve

the same problem manually. So in such cases only the Deflection of the pipe is

calculated if done manually.



39

7.2.5 CAESAR OUTPUT

Figure 7-6

Figure 7-7

Figure 7-8



40

Chapter 8 : CAESAR ANALYSIS REPORT

As we have seen that answers achieved by CAESAR are near to manual

calculation and are more correct since it uses iterations to solve a given problem whereas

in manual calculation we only consider the leg and its perpendicular leg for calculation of

moments and forces but in reality this is not the case.

In CAESAR first the line is modeled according to isometric drawings given. Care

is taken that no mistakes are done and modeled with all details as far as possible. The

pipeline design temperature, pressure, insulation thickness, fluid density and all

miscellaneous data is achieved from Line Designation Table ( LDT ) and material-

temperature specification. Equipment modeling is done with help of General arrangement

( GA )drawing. Once the line is completely modeled and checked, analysis is done. Load

case are to be considered for Wind case, Seismic case and any special cases like cold

spring, Pressure safety valve ( PSV ) etc.

For the project line the load cases considered for cold spring, operating, sustain,

wind, seismic, expansion cases which are as follows :-

8.1 Abbreviation [5]:- W – Weight of the pipe + Weight of fluid

P1 – Operating pressure

P2 – Design pressure

T1 – Normal operating mode for the unit would be the expander running hot (742 ºC)

and bypass line running cold (21º C). In order to stimulate the maximum thermal

movements on the bypass line, the line has been considered to be hot from Tee,

node 20, to the end of the north horizontal run, node 220.

T2 – Turbine bypass mode. In order to generate the maximum thermal loads, it has been

assumed that the inlet line is hot all the way down to the isolation valve at node 85.

the balance of the line is at cold ambient temperature, 21ºC and the bypass line is at

full line temperature, 742 ºC.

T3 – Temperature case when both Expander line and bypass lines are on and working at

Design temperature.

T4 – Temperature case when both Expander line and bypass lines are on and working at

Operating temperature.



41

D1 – Displacement of Expander when expander inlet line is off.

D2 – Displacement of Expander when only expander inlet line is on.

D3 – Displacement of Expander when expander inlet line and bypass are on and at

design temperature.

D4 – Displacement of Expander when expander inlet line and bypass are on and at

operating temperature.

H – Hanger loads

CS – Cold spring case

WIN1 – Wind blowing in north direction (i.e. –ve X direction)

WIN2 – Wind blowing in south direction (i.e. +ve X direction)

WIN3 – Wind blowing in east direction (i.e. -ve Z direction)

WIN4 – Wind blowing in west direction (i.e. +ve Z direction)

U1 – Seismic in North-south direction

U1 – Seismic in East-west direction

8.2 Wind velocity at particular height is given below :- V ELEV

mm/s mm 52908.98 10000 55069.41 15000 56635.68 20000

59400 30000 62041.28 50000 65915.4 100000 67445.98 150000 69153.74 200000 70820.34 250000 71230.89 300000

Table 8-1



42

8.3 Load cases considered are :-

NO. LOAD CASE STRESS TYPE

L3 W + D1 + T1+ P1 + H + CS Operating




L7 W + PI + H + CS Operating

L8 W + P1 + H Sustained

L9 W + P2 + H Sustained

L10 WIN1 Occasional

L11 WIN2 Occasional

L12 WIN3 Occasional

L13 WIN4 Occasional

L14 U1 Occasional

L15 U2 Occasional

L16 L14 = L8 + L6 Occasional






L22 L20 = L1 – L5 Expansion



L25 L23 = L4 – L5 Expansion Table 8-2



43

8.4 Steps involved in Analysis 8.4.1 Code Compliance

It is ratio of Obtained Stress and Allowable stress which shows failure

when the ratio is more than 100%.

1) Cases L22, L23, L24 and L25 are checked for Code Compliance and should be

within allowable 60%.

2) Cases L16, L17 are summation of sustain case and wind blowing in North and

South direction respectively. They are checked for Code Compliance and should

be within allowable 60%.

3) Cases L18, L19 are summation of sustain case and wind blowing in East and West

direction respectively. They are checked for Code Compliance and should be


4) Cases L20, L21 are summation of sustain and Seismic in North-south and East-

west direction respectively. They are checked for Code Compliance and should be


8.4.2 Displacement

5) Cases L8 and L9 which are sustain case i.e. only weight of pipe, hanger load and

pressure inside are considered. In this case, the vertical displacement ±Y of pipe

must be less than 10 mm.

6) Cases L3 to L7 which are different operating cases at different conditions as

mentioned in abbreviation are checked for horizontal displacements only i.e. X

and Z direction. If the displacements in respective directions are more than 50

mm than they are mentioned in Isometric drawings so that piping layout Engineer

keeps sufficient place for the expansion.

8.4.3. Restraint Summary

Restraint summary gives us forces, moments and displacements for a

particular support.

7) Cases L3 to L9 which are different operating cases and sustain cases respectively

are checked for Restraint summary. Here the nozzle loads are checked which

should not exceed the allowable given by vendor or should not exceed allowable

load provided by respective equipment standards.

When the line passes in all conditions and cases mentioned above then it can be

said that the line is absolutely safe for operation.



44

Chapter 9 : ANALYSIS REPORT OF PRESENT LINE

The CAESAR output for present line is mentioned in Appendix B. Here only the

report is mentioned. I have modeled the line according to present situation and the

analysis is done which has given me the failure points and by correcting them I will make

the line safer to working environment.

9.1 CODE COMPLIANCE 9.1.1 Code Compliance for Wind case The Code Compliance for all wind case is checked and it is found that the Highest

Codestress ratio is 336.4 at node 343 for load case L16. Node 343 is node of Orifice

chamber i.e. at bypass line. As the Line size is Ø66 inch the wind load will be definitely

more.

The Code Compliance ratio can be reduced by providing additional support by

seeing the space available or it can be reduce by increasing number of springs or by

changing the load and spring rates of present springs.

However care has to be taken that while reducing the Codestress ratio the nozzle

loads don’t exceed the allowable loads or increase than initial obtained loads. In some

cases it happens that you will have to comprise between Codestress ratio and Nozzle

loads. However, it is made sure that nozzle loads don’t increase.

9.1.2 Code Compliance for Seismic case The Code Compliance for all seismic case is checked and it is found that the

Highest Codestress ratio is 370.2 at node 343 for load case L20. Node 343 is node of

Orifice chamber i.e. at bypass line. As the Line size is Ø66 inch the seismic load will be

definitely more. Refer Table 9-1, 9-2 for detail.

One thing has to be noted that the Code compliance is failing both in wind and

seismic case at that same point which means that the load of pipe at that point is definitely

more which is due to lesser supports. So number supports will have to be increased near

that location so that load at that point is reduced or if not possible the spring loads have to

be revised so that load carrying capacity of springs are changed.

Any changes done in providing supports or revising the load of spring should be

done under the observation of nozzle loads which means that every time the load of

spring is changed; Restraint summary has to be checked on nozzle node 345 which is

near to node 343.



45

Table 9-1 : Code Compliance for Wind Case



46




47

9.1.3 Code Compliance for Expansion case The Code Compliance for all expansion case is checked and it is found that the

Highest Codestress ratio is 6.1 at node 11535 for load case L24. It is seen that Expansion

stress is very low which is due to use of cold spring and bellows. Refer Table 9-3 for

more detail.

We have seen that expansion of horizontal line itself will be 362 mm in absence of

cold spring and bellows which will be tremendous forces and moments on the expander

nozzle and thus in turn increase the Codestress causing Code compliance failure.

Thus the use of Cold spring of length 13 mm and two bellows the expansion due

to high temperature is easily absorbed.



48

Table 9-3 : Code Compliance for Expansion Case



49

9.2 DISPLACEMENTS 9.2.1 Displacement due to Sustain

In Sustain only Y displacement is checked. It is found that the maximum Y

displacement = - 43.258 mm at node 2804 for both sustain cases i.e. considering Pressure

P1 and Pressure P2 respectively. Node 2804 is on the vertical section of the Expander

inlet line and 3rd Separator. It is clear that the springs at that section are not taking the

total load and thus the line is sagging downwards. Refer Table 9-4, 9-5 for more detail.

Even the RTI has marked error for the springs at the Tee (see point 2 of page 24).

Thus by providing more support at the vertical section the sustain displacement can be

brought under control but the Piping layout Engineer has to be asked for available space

and available column for hanging springs in case if used.

Target will be to reduce the Sustain Y displacement below 10 mm.



50

Table 9-4 : Displacement For Sustain P1 case



51

Table 9-5 : Displacement For Sustain P2 case



52

9.2.2 Displacement due to Expansion In Operating cases X and Z displacement are checked so that the Layout Engineer

makes note of the expansion and leave free space for it. Usually when the displacement is

more than 50 mm then they have to be marked on the isometric drawing.

9.2.2.1 T1 case,

Max. X = -92.381 mm at Node 226 Max. Z = -363.564 mm at Node 55

As the bypass line is off the Max Z direction is seen at node 55 which is on

vertical line of expander which shows the axial displacement of the expander inlet line.

Max X is seen at node 226 which is on the bypass line. Refer Table 9-6, Table 9-7 for

details.

9.2.2.2 T2 case,

Max. X = 191.168 mm at Node 3700 Max. Z = 158.243 mm at Node 20000

As the expander inlet line is off the Max Z direction is seen at node 20000 which

is on the bypass line which shows the axial displacement of the bypass line. Max X is

seen at node 3700 which is on the bypass line and shows the lateral deflection. Refer

Table 9-8, Table 9-9 for details.

9.2.2.3 T3 case,

Max. X = 191.168 mm at Node 3700 Max. Z = -363.482 mm at Node 55

As the bypass line and the expander line both are on and working at design

temperature the Max Z direction is seen at node 55 which is on vertical line of expander

which shows the axial displacement of the expander inlet line. Max X is seen at node

3700 which is on the bypass line. Refer Table 9-10, Table 9-11 for details.

9.2.2.4 T4 case,


Similarly as the bypass line and the expander line both are on and working at

operating temperature the Max Z direction is seen at node 55 which is on vertical line of

expander which shows the axial displacement of the expander inlet line. Max X is seen at

node 3700 which is on the bypass line. Refer Table 9-12, Table 9-13 for details.



53

Table 9-6 : Displacement For Operating T1 case



54




55




56




57




58




59




60




61

9.3 RESTRAINT SUMMARY Nozzle loads are checked in Restraint summary. Load cases L3 to L9 are checked

for restraint summary.

9.3.1 Expander inlet nozzle

Allowable nozzle loads are given below :-

As per vendor the allowable nozzle load for expander inlet is given as :-

FX = 19578.68 N MX = 11524.30 N-m

FY = 15573.95 N MY = 05965.52 N-m

FZ = 07786.98 N MZ = 05965.52 N-m

Obtained nozzle load at NODE 1000 are :-

FX = 2 N MX = 46255 N-m

FY = 41535 N MY = 8983 N-m

FZ = 15356 N MZ = 724 N-m

Seeing the result it is very clear that the Expander inlet line is not very safe. The

analysis has to be done to revise the spring load or may even require more springs,

supports so that the line becomes safer. As each of the above cases are interlinked with

each other final analysis will show whether the nozzle load will come under allowable or

will exceed more.

9.3.2 3rd Stage Separator nozzle

Third Separator allowable nozzle is calculated as below [6]:-

Nozzle size = 66 inch

For pressure class 600 rating, β = 0.8

We have,

Longitudinal Bending Moment ML,

ML = β * 0.13 * D²

= 0.8 * 0.13 * 66 ²

= 453.024 kNm = 453024 N-m



62

Circumferential Bending Moment MC,

MC = β * 0.10 * D²

= 0.8 * 0.10 * 66 ²

= 348.48 kNm = 348480 N-m

Resultant Bending Moment MR,

MR = ( ML ² + MC ² )0.5

= (453024 ² + 348480 ² )0.5

= 571550 N-m

Axial Load or Compressive load FA,

FA = β * 2 * D

= 0.8 * 2 * 66

= 105.6 kN = 105600 N

Now as our nozzle is inclined to Y and Z direction therefore resultant Force and

Moment is checked at NODE 1:-

Obtained MR = ( MY ² + MZ ² )0.5

= (177093 ² + 456483 ² )0.5

= 489724.38 N-m < Allowable MR

For safer side, MR = ( MX ² + MY ² + MZ² )0.5

= ( 175406² + 177093 ² + 456483 ² )0.5


Obtained FA = ( FY ² + FZ ² )0.5

= (189311 ² + 8687 ² )0.5

= 189510.21 N < 80 % of Allowable MR

Thus Axial Force has to be reduced for safer operation. This problem has been

also marked by the RTI in their report (see point (3), page 24). Thus analysis of this has

given a confirmation to their study.



63

9.3.3 Orifice Chamber Inlet nozzle Orifice chamber allowable inlet nozzle or Bypass line Nozzle is calculated as

below [6]:-

Nozzle size = 66 inch

For pressure class 600 rating, β = 0.8

We have,

Longitudinal Bending Moment ML,

ML = β * 0.13 * D²

= 0.8 * 0.13 * 66 ²

= 453.024 kNm = 453024 N-m

Circumferential Bending Moment MC,

MC = β * 0.10 * D²

= 0.8 * 0.10 * 66 ²

= 348.48 kNm = 348480 N-m

Resultant Bending Moment MR,

MR = ( ML ² + MC ² )0.5

= (453024 ² + 348480 ² )0.5

= 571550 N-m

Axial Load or Compressive load FA,

FA = β * 2 * D

= 0.8 * 2 * 66

= 105.6 kN = 105600 N

Bypass line is not scope of my project but I have to consider it since any change in

loads or supports will indirectly or directly affect the Bypass Nozzle.



64

Obtained bypass nozzle loads at NODE 345 :-

Obtained ML = ( MX ² + MZ ² )0.5

= (28110 ² + 1523896 ² )0.5

= 1524155.24 N-m < 240 % of Allowable ML

Obtained MC = MY

= 72486 N-m < Allowable MC

Obtained MR = ( ML ² + MC ² )0.5

= (1524155.24 ² + 72486 ² )0.5

= 1525877.92 N-m < 170% of Allowable MR

Obtained FA = FY

= 226275 N < 115% of Allowable FA

Moment MZ is tremendously high which is caused by Force FX and Force FY.

Thus if any of the force is brought under control the Moment MZ can be controlled. It is

seen that FY is more which is thus cause of higher Moment and Axial force. Force FY

can be brought under control by increasing spring loads or increasing number of springs.

Refer Table 9-14, 9-15 for detail.



65

Table 9-14 : Nozzle load checked for Node 1



66

Table 9-15 : Nozzle load checked for Node 345 and 1000



67

Chapter 10 : ANALYSIS REPORT OF MODIFIED

LINE As seen in the analysis of present line it was found that the line is failing in

sustain, failing in Code Compliance and failing in Nozzle loads too. Taking all this in

mind I have done the analysis of the present line and modified it and have brought results

closure to acceptable value. Caesar output for the Modified line is mentioned in

Appendix C.

10.1 CODE COMPLIANCE 10.1.1 Code Compliance for Wind case The Code Compliance for all wind case is checked and it is found that the Highest

Codestress ratio is 209.1 at node 965 for load case L16. Node 965 is node on Expander

inlet line having line size 3 inch.

The present line is having highest Codestress ratio 336.4 at node 343. The line is

wholly is supported on Hangers so to reduce Codestress the spring loads were revised and

some new springs are installed which has reduce the code Compliance.

Revised Spring loads are :-

Earlier the Code stress was higher on NODE 343, therefore revised spring load of NODE

331 i.e.

NODE PRESENT spring load MODIFIED spring load

331 132255 N 154760 N

2601 74466 N 92000 N

2602 74466 N 92000 N

2651 74471 N 120000 N and spring rate 533 N/mm


7201 57998 N 67000 N

7202 57998 N 67000 N

New springs were designed at NODE 2802, NODE 2803 and later were checked

from LISEGA HANGER TABLE [4] for the possible actual load spring produced by the

company for that particular size. Revised springs are too seen in the catalog and nearest

load mentioned by the vendor is selected. Earlier spring used at NODE 2651 and 2652

were constant spring supports but now they are revised for variable spring supports. Refer

Table 10-1, 10-2 for detail.



68




69

Table 10-2 : Code Compliance for Wind case



70

10.1.2 Code Compliance for Seismic case The Code Compliance for all seismic case is checked and it is found that the

Highest Codestress ratio is 223.7 at node 9700 for load case 20. Node 9700 is near to

expander inlet line.

Present Codestress ratio is 370.2 at node 343 for load case L20. Earlier the Code

compliance was failing both in wind and seismic case at that same point which was due to

that the load of pipe at that point which was due to lesser supports. So when number of

supports were increased and revised the Code Compliance for Seismic case was reduced.

Restraint summary was simultaneously checked for the node 343 and Node 1000

and it was found that the loads on the nozzles were also reduced. Refer Table 10-3, 10-4

for detail.

10.1.3 Code Compliance for Expansion case In Present Analysis the Code Compliance in Expansion case was passing but in

Modified line analysis the Code compliance is again checked since providing new springs

or revising the spring load may obstruct the expansion of pipe which will cause the rise in

Codestress ratio.

Checking Expansion cases in Code Compliance it was found that Highest

Codestress ratio is 6.7 at Node 11535 for load case L24. Earlier the Codestress ratio was

6.1 at 11535. Refer Table 10-5 for detail.



71

Table 10- 3 : Code Compliance for Seismic case



72

Table 10- 4 : Code Compliance for Seismic case



73

Table 10- 5 : Code Compliance for Expansion case



74

10.2 DISPLACEMENTS 10.2.1 Displacement due to Sustain In Sustain only Y displacement is checked. It is found that the maximum Y

displacement = 19.750 mm at node 11584 for both sustain cases i.e. considering Pressure

P1 and Pressure P2 respectively. This is due to Bottom spring near that point and line is

not completely modeled as that line is not in the scope of project. Therefore neglecting

that line we found that,

Max. Y displacement = -5.702 mm at node 220.

In sustain case the Maximum Y displacement should not be more than 10 mm

which is achieved here. It was clear that the springs at that section are not taking the total

load and thus the line is sagging downwards so to by revising the spring loads and

designing new springs at Node 1801, 1802, 2001 and 2002 the displacement was brought

under control. Spring at Node 18 and Node 200 were replaced by above springs.


18 130274 N -

200 130274 N -

1801 - 134500 N

1802 - 134500 N

2001 - 70000 N

2002 - 70000 N

20000 82328 N -

20001 82328 N -

216 - 64180 N





In present line springs are placed at Node 18 and 200 which are on the Tee section

of the line. These two springs were not sufficient to take the load of the vertical section so

instead of 2 springs the modified line is having 4 springs i.e. 1801, 1802, 2001 and 2002.

As the load of the pipe is reduced the two springs at Node 20000 and 20001 were

replaced by single spring at Node 216. As the vertical displacement were reduced the

constant springs at 4001, 4002, 4003 and 4004 are replaced by variable springs.



75

Table 10- 6 : Displacement for Sustain P1 case



76

Table 10- 7 : Displacement for Sustain P2 case



77

10.2.2 Displacement due to Expansion In Operating cases X and Z displacement are checked so that the Layout Engineer

makes note of the expansion and leave free space for it. Usually when the displacement is

more than 50 mm then they have to be marked on the isometric drawing.

10.2.2.1 T1 case,

Max. X = -96.491 mm at Node 220 Max. Z = -364.668 mm at Node 55

As the bypass line is off the Max Z direction is seen at node 55 which is on

vertical line of expander which shows the axial displacement of the expander inlet line.

Max X is seen at node 220 which is on the bypass line. Refer Table 10-8 for detail.

10.2.2.2 T2 case,

Max. X = 148.625 mm at Node 216 Max. Z = 153.926 mm at Node 2804

As the expander inlet line is off the Max Z direction is seen at node 2804 which is

on the bypass line which shows the axial displacement of the bypass line. Max X is seen

at node 216 which is on the bypass line and shows the lateral deflection. Refer Table

10-9, 10-10 for detail.

10.2.2.3 T3 case,

Max. X = 153.937 mm at Node 2804 Max. Z = -364.668mm at Node 55

As the bypass line and the expander line both are on and working at design

temperature the Max Z direction is seen at node 55 which is on vertical line of expander

which shows the axial displacement of the expander inlet line. Max X is seen at node

2804 which is on the bypass line. Refer Table 10-11, 10-12 for detail.

10.2.2.4 T4 case,


Similarly as the bypass line and the expander line both are on and working at

operating temperature the Max Z direction is seen at node 55 which is on vertical line of

expander which shows the axial displacement of the expander inlet line. Max X is seen at

node 2804 which is on the bypass line. Refer Table 10-13, 10-14 for detail.



78

Table 10- 8 : Displacement for Operating T1 case



79




80




81




82




83




84




85

10.3 RESTRAINT SUMMARY Nozzle loads are checked in Restraint summary. Load cases L3 to L9 are checked

for restraint summary.

10.3.1 Expander Inlet nozzle

Allowable nozzle loads are given below :-

As per vendor the allowable nozzle load for expander inlet is given as :-

FX = 19578.68 N MX = 11524.30 N-m

FY = 15573.95 N MY = 5965.52 N-m

FZ = 07786.98 N MZ = 5965.52 N-m

Obtained nozzle load at NODE 1000 are :-

FX = 1 N MX = 46673 N-m

FY = 41536 N MY = 4153 N-m

FZ = 15356 N MZ = 731 N-m

In present line the Moment MY was 8983 N-m which was more than allowable.

Actually this moment has decreased by changes in spring loads near the nozzle. As there

is no space for any new changes I could only change spring loads at Node 9711 and 9712.

10.3.2 3rd Stage Separator nozzle

Third Separator allowable nozzle is calculated as earlier.

Moment is checked at NODE 1:-

Obtained MR = ( MY ² + MZ ² )0.5

= (106640 ² + 56923 ² )0.5

= 120881.42 < Allowable MR

For safer side, MR = ( MX ² + MY ² + MZ² )0.5

= ( 510257² + 106640 ² + 56923 ² )0.5




86

In present analysis the obtained MR = 489724.38 N-m which was more due to

larger value of MZ. MZ in Modified analysis is reduced by reducing forces FX and FY.

Obtained FA = ( FY ² + FZ ² )0.5

= (127128 ² + 7438 ² ) 0.5

= 127345.41 N < 21 % of Allowable MR

Earlier FA was 189510.21 N which was less than 80 % of Allowable MR.

Axial force on the nozzle was reduced by using 4 springs at Node 1801, 1802,

2001 and 2002 instead of only springs at Node 18 and 200.

10.3.3 ORIFICE CHAMBER INLET NOZZLE Orifice chamber allowable inlet nozzle or Bypass line Nozzle is calculated as earlier :-

Obtained bypass nozzle loads at NODE 345 :-

Obtained ML = ( MX ² + MZ ² )0.5

= (23011 ² + 109703 ² )0.5

= 112090.38 N-m < Allowable ML.

Earlier obtained ML = 1524155.24 N-m which less than 240 % of Allowable

ML. In earlier analysis it was seen that MZ was 1523896 N-m which was very high.

Moment MZ was thus reduced by decreasing FX and FY. Spring loads near the node

were revised and new springs were designed at Node 2802 and Node 2803.


2802 - 32000 N and spring rate 267 N/mm

2803 - 32000 N and spring rate 267 N/mm

Obtained MC = MY

= 53304 N-m < Allowable MC

Obtained MR = ( ML ² + MC ² )0.5

= (112090.38 ² + 53304 ² )0.5


Obtained FA = FY

= 60561 N < Allowable FA

Thus the nozzle of Orifice chamber or Bypass line is totally safe.



87

Table 10- 15 : Nozzle load for Node 1



88

Table 10- 16 : Nozzle load for Node 345 and 1000



89

CONCULSION

Usually results obtained by stress analysis may differ from analyst to analyst since

there are number of ways of reducing the loads of pipe. However results obtained by

making least changes is said as the best Analysis since this will reduce the cost of the

manufacturing, will require lesser space and will require lesser maintenance.

Therefore the best analyst always tries to find solution by making least changes. In

my project I was aware of the congestion of space and the problems faced by the line

which guided me to find a solution. As very less ground support is available the whole

analysis was done on the basis of hangers and they were used to reduce the nozzle loads

which made the line safer.

My objectives of the project were :-

1. Finding out the deviations if any

2. Analyzing the deviations.

3. Finding out acceptability level of deviations.

4. Suggest recommendation for improving unit reliability.

My objectives as mentioned above were achieved and I have suggested

rectifications for spring load and few new springs which are based on the Spring

catalogue. Any further improvement in the analysis is possible by rerouting the line which

will have more ground supports and more flexible.



90

BIBLIOGARPHY [1]. The M.W.Kellogg Company “ Design of Piping Systems, ” revised second edition:

John Wiley & Sons, INC. -1967.

[2]. John Mcketta “ Piping design Handbook, ”: Marcel Dekker, INC.- 1992.

[3] “ Quick check on piping flexibility, ” : L.C.Peng, Peng Engineering, Houston, Texas.

[4]. LISEGA “ Standard Supports 2010, ” edition October : Rosebrock Media Service,

Sottrum – 2001.

[5]. CAESAR 2 version 4.5 “ Technical reference manual ” : C.A.E Engineering software

- 2002.

[6]. “Allowable Forces and Moments ”: 3PS_MV001, Bechtel Standard.

[7]. Mohinder L.Nayyar “ Piping Handbook, ”: seventh edition : McGraw – Hill

handbooks.

[8]. ASME B 31.3 “ Petrochemicals and Refinery Piping or Process Piping, ”: 2002

edition

[9]. “ Pipe stress analysis ” : R.V.Balapure, Reliance Engineering Associates Limited,

India.

[10]. S.Ramamurtham, “ Strength of Materials, ” - Dhanpatrai & Sons,Delhi,1990.

Documents

Stress Analysis of Piping1