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FLEXIBILITY ANALYSIS
INTRODUCTION
Flexibility Analysis is a subject which is more talked about and
less
understood
Flexibility Analysis is done on the Piping System to study the
behaviour
on the same, when it changes the temperature from ambient /
installed
to operating, so as to arrive at the most economical layout.
There are mainly three sets of conditions which define the
minimum
acceptable flexibility on a piping configuration. They are:
1. The maximum allowable stress range in the system.
2. The limiting values of forces and moments which the system
is
permitted to impose on the equipment to which it is
connected.
3. The maximum allowable stress on the supporting structure.
When piping is connected to strain sensitive equipments, the
flexibility
required to satisfy the acceptable limits of forces and
moments
overrides that required to satisfy the maximum stress range
conditions
and overstressing of supporting structures.
The Piping Engineer ahs the following choices to establish that
the
required flexibility has been provided in the layout.
1. A per clause 319.4.1 of the code ASME B 31.3 which
specifies
that no formal analysis is required in systems which.a) are
duplicates of successfully operating installations or
replacements.
b) Can really be judged adequate by comparison with
previously
analysed systems.
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c) Satisfies the equation (16) specified in clause 319.4.1
2. Analysing the layout by an appropriate method.
3. Carrying out a comprehensive analysis.
Let us consider those aspects in the code which are
mandatoryrequirements for the expansion and flexibility of metallic
piping.
Pipe is erected at ambient temperature and that depends on the
climatic
conditions. 700F (210C) is the figure commonly used for
calculations. The
same piping when in operation is a Petrochemical Plant could
achieve a
temperature in excess of 5000C if it were in a reactor piping
system or it
could be of the order of - 1200C if it were associated with
Ethylene
refrigeration System.Each material has it own coefficient of
thermal expansion. If the pipe is
carbon steel or low alloy steel each 100 ft will expand at the
rate o to 1
or each 1000 F temperature rise. This means that the pipe
running between
two equipments 100 t. apart may well want to expand to 4 inches
more as
it heats up. The increased length can be accommodated only by
straining
the pipe as the ends are not free to move. 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 I no
longer
required and hence stress also disappears.
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Everytime the plants is in operation and in shut-down, the same
cycle occurs. The pipe starts from stress free condition when cold,
getstress imposed which reaches the maximum at operating condition
and reduce to zero when operation stops and system cools down.
But this is not what exactly happens practically. The piping
system can absorb
displacement without returning exactly to previous
configuration. Relaxation to
the sustaining level of material will tend to establish a
condition of stability in few
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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 the opposite temperature state,
with equal
intensity but of opposite sign. Thus the system which originally
was stress less
could within a few cycles accumulate stress in the cold
condition and spring itself
without the application of external load. This phenomenon is
called self
springing;. This can be demonstrated as below :
24000 psi
4 EXP
System Relaxed 6000 psi System Self Springing
To Sustaining Level
Let us assume that the system absorbs 4 expansion between
anchors and the
calculated maximum stress is 24,000 psi. Suppose the material at
the particular
operating temperature can sustain only 18,000 psi or of the
developed stress,
yielding will take place to its sustaining level. On cooling
back to ambient
temperature the system must contract by 4. At of this
contraction, i.e. at 3 the
system will become stress less. Completion of contraction
through remaining 1
will result in a stress of 6000 psi in the opposite direction.
The system which wasstressless at the start will now cold spring.
Hence it is evident that the true
magnitude of the stress either in hot or cold condition cannot
be determined by
calculation because the amount of relaxation is unknown and
cannot be judged
reliably. However service failure are related to cyclic rather
than static conditions
and it is therefore permissible to assume that the system will
operate.
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For this type of application, calculate the vertical force
component of the verticalconnection excluding pressure loading.
Compare with value of 1/5 the pressure loading.
Use the larger of these two numbers for vertical force component
on connections inmaking calculations outlined in (1) and (2)
The force caused by the pressure loading on the vertical
connections is allowed in
addition to the values established in the above up to a maximum
value of vertical force
(lbs.) on the connection (including pressure loading) of 151/2
times the connection area in
square inches.
These values of allowable forces and moments pertain to the
compressor structure only.They do not pertain to the forces and
moments in the connecting piping flanges and
flange bolting which should not exceed the allowable stress as
defined by applicable
codes and explanatory notes.
Forces on inlet connections are to be transferred along with
moments to discharge
connection to analyze the compressor for resultant forces and
moments. But, the transfer
of force will generate additional transfer moments which are
added to the total ofmoments to give resultant moments.
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RECIPROCATING COMPRESSORS
API 618 Reciprocating Compressor for General Refinery Service do
not specify thelimit on the allowable forces and moments in the
code. The vendor shall specify the
forces and moments for each nozzle in the tabular form. However,
the values are as per
API 610 can considered for guidance.
FIRED HEATERS
The limiting values for forces and moments should be laid down
by the manufactures.Restrictions are applied on nozzle rotations
also in this case to take care of the clearnaces
between the tube and refractory lining.
The thumb rule is used is:
Forces = 200 to 300 lb/in nominal bore of nozzle
Moments Equivalent to Sh/4
Nozzle Rotation From 1/20
to 10
SHELL & TUBE TYPE HEAT EXCHANGERS
The designer has to set the limiting values or check the vessel
connections for the nozzle
loading imposed by the connected piping.
The rough guide generally followed is:-
Resultant Maximum Force 200lb/in NB of nozzle
Bending Moment Equivalent to bending stress in standard
schedule
Pipe between 40000 to 5000 lbs/in2
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327
SELECTION OF SPRING SUPPORTS
When vertical displacement occurs as a result of thermal
expansion, it is necessary to
provide spring supports which applies supporting force
throughout the expansion and
contraction cycle of the system.
Spring supports are of two types.
A. Constant Spring
B. Variable Spring
CONSTANT SPRING
Constant spring hangers provide constant supporting force for
piping throughout its full
range of expansion and contraction. This is accomplished by a
helical coil spring working
in conjunction with a bell crank lever in such a way that the
spring force times itsdistance to liver pivot is always equal to
the pipe load times its distance to liver pivot.
CONSTANT SUPPORT
Because of the consistency in supporting effect these are used
for the support of critical
piping systems. Depending upon the structure availability,
headroom, location of pipe
above or below, the type could be selected. The hanger size is
selected from the LoadTravel Table. The travel shown in the table
is the total travel that is the maximum
vertical movement which the hanger will accommodate. The total
travel of pipe to allow
for any discrepancy. Hence the total travel = Actual travel +
Over travel.
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The over travel shall be 20% of calculate Actual travel and in
no case less than 10mm.
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VARIABLE SPRING
Variable spring hangers are used to support are used to support
piping subject to vertical
movement where constant supports are not required.
In this case, the supporting force varies with spring deflection
and spring scale. Thevariation of supporting force is equal to the
product of the amount of vertical expansion
and the spring scale of the hanger. Since the pipe weight is the
same during any
condition, cold or operating, the variation In supporting force
results in additional stresses
in the piping system.
Accepted practice is to limit the amount of supporting force
variation to 25%.
The spring hangers are specified by the series, the type and the
hanger size.
1. How to select series
The selection of the hanger series shall be done to limit the
supporting force within the
allowable range. In choosing between the series VSI, VS2, and
VS3 it must bedetermined that the calculated movement will fall
within the working load range. The
series VS1 has the maximum variation in supporting force and
hence not a competitiveselection but an invention of necessity
where head room is not sufficient to use VS2.
Good engineering sense combined with available space and
reasonable economic
considerations should ultimately determine which series of
variable spring hangers
should be used.
2. How to determine type
The type of variable spring to be used depends upon the physical
characteristics required
by the suspension problem i.e. available head room, pipe to be
supported above thespring or below the spring etc. The type to be
selected from the seven standard typesavailable. (see sketch for
types A through G)
3. How to determine size
For determine the size of the hanger the load deflection table
shall be preferred. In order
to choose the proper hanger size the data required is the actual
load or the working load
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(also called the hot load) and the amount and direction of the
pipe line movement fromcold to hot.
Locate the hot load in the table. To determine the cold load,
read the spring scale up or
down for the amount of expected movement. The chart must be read
opposite from thedirection of pipe movement. The load arrived is
cold load.
If the cold load falls outside the working load range of hanger
selected, relocate the hot
load to the adjacent column and find the cold load. When both
the hot and cold loads are
within the working range of a hanger, the size of the hanger is
the number found at thetop of the column.
Should it be impossible to select a hanger in any series such
that both loads fall within the
working range, consideration should be given for a constant
spring hanger. Once
selected, the percentage load variation shall be checked as
follows.
Travel x Spring Rate x 100
Load variation percentage =
Hot Load
Which should be within 25% as specified in the code.
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The support location is dependent on pipe size, piping
configuration, the location ofheavy valves and specialties and the
structure that is available for the support of the
piping.
The suggested maximum spans between supports normally adopted
are as follows.
Pipe Size NB inch Span in M. (ft.)
1 2(7)
1-1/2 2.75(9)
2 3(10)
3 3.5 (12)
4 4(14)
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Pipe Size
NB inch
Span in
M. (ft.)
6 5(16)
8 5.75(18)
10 6.50(20)
12 7(23)
14 7.5(25)
16 8.25(27)
18 8.25(28)
20 9(30)
24 10(32)
The above spans are worked out on a combined bending and shear
stress of 1500 psi
when the pipe is filled with water and 3 mm deflection is
allowed between supports. Theydo not apply to concentrated loads or
where change in direction occurs between supports.In case of
concentrated loads, the support should be placed as close as
possible. When
change in direction occurs, I is considered a good practice to
keep the span to 75 % of the
tabulated valves.
In the illustrated example the support H1 is placed near to the
equipment
flange A to reduce the load at the equipment to the minimum.
Support H2
is located as per the standard span. Support H3 on the vertical
leg is
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placed above the center of gravity. Calculations would indicate
that the CG
of the vertical lag falls t 16.16 ft above the lower horizontal
run. If the
hanger would then act as pivot and would not resist sway. It
could also be
checked with minimum leg calculation. The support H7 is placed
adjacentto the valve weight concentration. The proximity of support
to the valve is
helpful in keeping the load at the equipment flange B to a
minimum or nil
as required. The support H6 is located as the standard support
span. The
support H5 is located in such a way that the distance between H6
and H5
is not more than of the standard support span. The support H4
is
located clearing the bend and at standard support span distance
from H5.
The methods involved in locating the supports for this problem
are typical
of those employed by the piping engineer. Although the
individual piping
configuration and structure layout will vary in practically
every instance, the
general methods outlined above will apply for any critical
piping system.
The Determination of Thermal Movement
The next step is to calculate the thermal movements at each
location. The method
illustrated here gives satisfactory values. However this
approximation will always give
positive error.
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