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AutoPIPE Modeling Approaches
Modeling Approaches This help has been provided in order to give
users ideas for modeling typical piping arrangements. The steps
shown in
each example should not be taken as the only method available to
create models. In addition, the intent of the
examples is to present ways to create adequate models of
specific piping components for analytical purposes. It is not
the intent of the examples to represent proper design of the
overall piping system. If you have a specific modeling
problem which you feel is not fully explained in this section,
you are urged to contact Bentley Technical Support for
further discussion.
Example Systems This help has been provided in order to aid
users in modeling more complex piping arrangements. The steps shown
in
each Example System should not be taken as the only method
available to create models. In addition, the intent of the
examples is to present ways to create adequate models for
analytical purposes.
Choose from the following topics:
PipeSOIL Interaction: Transition Example
Water Hammer (Time History) Example
Steam Relief (Time History) Example
Harmonic Analysis Example
Anchors Pipes
Bends Reducers
Cuts Rotating Equipment
Flexible Joints Supports
Frames Tees
Hangers Valves
Nozzles Vessels
Anchors Select from the following anchor-related examples:
Rigid Anchor with Thermal Movement
Flexible Anchor
Anchor Releases for Hanger Selection
Rigid Anchor with Thermal Movement An anchor is used at
locations where the piping system ties into a wall, anchor block,
foundation, or a piece of large
equipment. Most large equipment such as pumps, turbines, or
compressors are massive enough to be considered rigid
when compared to the pipe. In most cases, vessels can be
considered to be rigid when local shell flexibility is not of
concern.
An anchor has the ability to restrain all translations and
rotations of the attached pipe or beam element. Forces and
moments from one side of a rigid anchor are not transmitted to
the other side. This property can be used to control the
movement of a pipe attached to sensitive equipment, or to divide
a large piping system into two or more separate,
manageable systems.
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Example An anchor is used to model a pipe attached to a large
pump which is assumed to be rigid. However, it is known that
when the pump reaches an operating temperature (400F), the pipe
connection point will displace as follows due to the
thermal expansion of the pump itself:
Modeling The thermal movement of the pump can be included in the
AutoPIPE system model by specifying displacement offsets
calculated for each of the defined thermal load cases at the
anchor.
1. Build a system from A00 to A04 using an 8 inch, standard
schedule pipe. Define an operating load case (T1) of 400 F. The
global coordinates for the system points are listed below (length
units are feet, and offsets are
measured from the preceding point):
2. These coordinates define the position of the piping system at
ambient temperature (70F).
3. Select Insert/Anchor to open the Anchor dialog:
4. Define a rigid anchor at point A04. Move the cursor down to
the Thermal anchor movements input fields for
Case 1 and specify (imposed displacement) values:
Note that the offset fields for Case 2 and 3 are closed; this is
because only one operating load condition (T1) was
specified on the General Model Options dialog. In general, when
a static analysis is performed, the results for each
thermal load case (T1, T2 & T3) will include the forces
exerted on the piping system due to the thermal anchor
movements specified for each thermal load case respectively.
Other Anchor-related Topics
DX = 0.0 in DY = +1.25 in DZ = +0.45 in
(no rotation of the attachment point)
Anchor Releases For Hanger Selection The intent of a hanger is
to insure that adjacent equipment does not support the weight of
the attached pipe, or any
other vertical loads resulting from the piping system operating
conditions. This is due to the fact that equipment
manufacturers allowable flange, or nozzle, loads are often
minimal. If an undesigned hanger is located near a piece of
equipment (modeled as a rigid anchor), the cold load and spring
rate determined by the hanger selection procedure
(Analyze/Hanger) will be very small when it is intended for the
hanger to support the vertical loads. In this case, it is
necessary to release restraints at the anchor in order to design
the hanger while maintaining the rigidity of the anchor
for all other purposes.
Example
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Modeling The anchor at the end of the pipe run, which represents
the equipment, is released for vertical shear loads. This means
that when a hanger design run is performed, the anchor will not
support a vertical load. Thus, the hanger is sized
correctly (the vertical forces at the pipe-pump connection point
are eliminated) while the pump itself is modeled rigidly.
1. Define the pipe system by repeating Step 1 from Flexible
Anchor - Model 1.
2. Move the crosshairs to point A03.
3. Select Insert/Support to open the Support dialog, then enable
the "Undesigned" option at point A03.
4. Move the crosshairs to point A04.
5. Select Insert/Anchor to open the Anchor dialog.
6. In the Release for hanger selection field, click inside the Y
field to enable the vertical displacement hanger selection release
option.
Note: The "Release for hanger selection" fields should not be
confused with "Trans. stiff" and "Rot stiff." The latter
define DOF releases or stiffnesses which are in effect at all
times, while the former release a DOF for the purpose of
designing hanger springs only.
Other Anchor-related Topics
Flexible Anchor An anchor is used at locations where the piping
system ties into a wall, anchor block, foundation, or a piece of
large
equipment. A flexible anchor can be defined when the flexibility
of the anchored point is known (such as for modeling
equipment), or when a particular type of support is desired
(e.g. roller, hinge, socket, etc.).
Most large equipment such as pumps, turbines, or compressors are
massive enough to be considered rigid when
compared to the pipe. However, if the local flexibility of the
equipment is known, those values may be specified. For the
special case of vessels, it is recommended that the local
(shell) flexibility be modeled using the Nozzle command.
Model 1: Local Flexibility of the Attached Equipment
Model 2: Definition of a Hinge Support
Other Anchor-related Topics
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Model 1: Local Flexibility of the Attached Equipment If the
local flexibility of the equipment attached to a pipe is known, the
stiffness values can be defined.
1. Build a system from A00 to A04 using an 8 inch standard
schedule pipe. The global coordinates for the system points are
listed below (length units are in feet, and offsets are measured
from the preceding point):
2. Select Insert/Anchor to open the Anchor dialog.
3. Define a flexible anchor at point A04; this allows the cursor
to enter the stiffness fields. Specify translational and rotational
stiffnesses as follows:
The stiffness values entered correspond to a global Z
translation flexibility (axial with reference to the pipe), and
a
bending flexibility in the plane perpendicular to the pipe
(global X-Y).
Other Anchor-related Topics
Model 2: Definition of a Hinge Support A flexible anchor is used
to model a hinge support at the base of a beam member (column).
Modeling specific support
types is allowed for both beams and pipes, however, this
approach is probably more useful for beams. In addition, gaps
and friction cannot be specified for anchors modeled as
supports. For the model that follows, it is assumed that a
framing system (which supports piping) has already been
defined.
1. Move the crosshairs to the beam point that is to be anchored.
For this example, the base of the column (FP1).
2. Select Insert/Anchor to open the Anchor dialog.
3. Define a flexible anchor at point FP1; this allows the cursor
to enter the "Trans. stiff." and "Rot. stiff." fields. Accept the
default stiffnesses (Rigid) in all fields except "Rot. stiff Z";
where 0.00 should be entered as shown:
Entering 0 stiffness for the rotational restraint about the Z
axis allows the column base to rotate freely in the X-Y plane,
thus creating a hinge support.
Note: All degree of freedom (DOF) fields are for the global
coordinate system.
The user is reminded to consider the overall effect on the
system stability when defining a zero stiffness (a DOF
release) in any of the "Trans. stiff." or "Rot. stiff"
fields.
Other Anchor-related Topics
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Bends Choose from the following modeling examples:
45 Elbow
180 Elbow
Flanged Elbow
Elbow Wall thickness
Reducing Elbow
Base Supported Elbow
Miter Bends
45 Elbow A 45 elbow is a common piping component. They are used
whenever a full 90 elbow is not appropriate or required.
Example
Modeling A 45 elbow is modeled as half of a 90 elbow. This is
done by specifying the point following the bend (TIP) in such a
manner that the coordinates define a 45 angle.
1. Build a system from A00 to A01. The global coordinates for
the system points are listed below (length units are feet, and
offsets are measured from the preceding point):
2. Select Insert/Run to open the Run Point dialog.
3. Specify the coordinates for A02 as shown. These values define
a 45 angle with respect to the direction of the pipe established
between A00 and A01, such that the distance between A01 and A02 is
6 ft.
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Display of the 45 Bend
180 Elbow A 180 elbow, or U-bend, is a common component in an
expansion loop. Expansion loops are used to relieve thermal
stresses in the piping system.
Example
Modeling A 180 elbow is modeled as two 90 elbows
back-to-back.
1. Build a system from A00 to A01 using a 12 inch standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
2. Select Insert/Bend to open the Bend Point dialog.
3. Since a bend defaults to a long radius (= 1.5 Dnom), locate
A02 three feet away from A01 as shown in the offset fields. This
will result in two back-to-back bends, such that A01 F coincides
with A02 N.
4. Complete the bend by defining a run of pipe to A03. The
global coordinates for the system point are listed below (length
units are feet, and offsets are measured from the preceding
point):
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Display of the 180 Bend
Flanged Elbow Elbow fittings are often connected to the adjacent
pipe sections with flanges. A flange may exist on one or both sides
of
the bend. Flanges are important in a system model since their
weight may have a significant effect on the pipe stresses.
Also, the stress intensification and flexibility factors for a
given bend will decrease if one or both of its ends are
flanged.
Example
Modeling First a plain elbow bend is defined, then pipe flanges
are placed at the near and far tangent points.
1. Build a system from A00 to A02 using a 12 inch, standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
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2. Move the crosshairs to point A01 N.
3. Select Insert/Flange to open the Flange dialog. Specify a
SLIP-ON flange with a pressure rating of 150. The flange weight is
recalled from the component library since a standard pipe flange
was used. Next, select
SO (slip on) as the type of connection.
4. Repeat Step 3. A second flange should also be defined at A01
N. This provides a mating surface for the first flange, allowing
the pipe and the elbow to be bolted together.
5. Move the crosshairs to point A01 F.
6. Repeat Steps 3 so that two flanges are defined at the other
end of the elbow.
7. Press F3 to open the text window shown below, which displays
the data related to point A01 F. The listing includes the flange
data for this point. A similar display also exists for A01 N.
Display of the Flanged Elbow
Note: AutoPIPE assumes a zero thickness for the flange
component. Thus, the thickness of the real flange may
require an additional point so that the inner face of the flange
is at the tangent point of the bend curve.
Reducing Elbow Reducing elbows provide a means for changing the
pipe size when such a change is required at a bend.
Example
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Modeling AutoPIPE does not have a reducing elbow component.
Therefore, the elbow is simply modeled as a section of pipe
with
a diameter that is equal to the mean of the pipe diameters at
each end. Such a representation is reasonably accurate
for calculation of pipe stresses as long as the reduction is not
too drastic.
In this model a 12 inch pipe is connected to an 8 inch pipe by a
reducing elbow. The bend is modeled with a pipe
section that is an average of the connecting pipes. Next, stress
intensification factors (SIF's) are defined at each end in
order to represent the SIF's for an actual reducing elbow. Since
the piping codes do not specify SIF's for reducing
elbows, this information must be provided by the user. Contact
the elbow manufacturer for information on their
recommendation for SIF values.
1. Build a system from A00 to A01 using a 12 inch, standard
schedule pipe named 12STD. The global coordinates for the system
points are listed below (length units are feet, and offsets are
measured from the
preceding point):
2. Select Insert/Bend to open the Bend Point dialog. The bend
radius must be specified in inches, since a standard bend is
calculated by a single pipe size. Specify the new pipe data
identifier ELBOW. After accepting
this dialog, the Pipe dialog (shown in Step 3) will
automatically be displayed since "ELBOW" has not yet been
defined.
3. Define the new pipe. Enter the pipe data as shown in the
figure (nonstandard nominal size: NS) based on the following
averages:
Do = (12.75" + 8.625") 2 = 10.69 in
t = (0.375" + 0.322") 2 = 0.349 in
4. After providing the data for the new pipe and pressing OK,
the Location dialog requests the specific location on the bend
where the pipe change is to take effect. Select Near for the near
tangent.
5. Select Insert/Pipe Properties to open the Pipe Properties
dialog. Enter 8STD as the pipe identifier and define a nominal 8
inch standard schedule pipe.
6. Again, after providing the data for the new pipe and pressing
OK, a Location dialog requests the location on the bend where the
pipe change is to take effect. Enter Far for the far tangent.
7. Finish the bend by defining a run of pipe to A03. The global
coordinates for the system point are listed below (length units are
feet, and offsets are measured from the preceding point):
8. Move the crosshairs to point A02 N.
9. Select Insert/Xtra Data/User SIF and Flexibility to open the
User Flexibility dialog. Enter the SIF to
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be used at the large end of the elbow. As stated previously,
contact the manufacturer for information on the
SIF's recommended for the particular reducing elbow.
10. Move the crosshairs to point A02 F.
11. Repeat Step 9 for the small end of the elbow.
Elbow Wall Thickness The wall thickness of a bend can be
different than the thickness of the connecting pipes. This allows
specific elbow
fittings to be modeled in a continuous piping system.
Example
Two methods for modeling elbow wall thickness are provided
below:
Elbow Wall Thickness (Method 1)
Elbow Wall Thickness (Method 2)
Elbow Wall Thickness: Model 1 An elbow fitting is modeled by
controlling the bend radius, and the pipe wall thickness. In order
to define an elbow with
a different wall thickness than the joining pipes, the pipe size
can be changed for the bend and then reset to the original
pipe size.
1. Build a system from A00 to A01 using a 12 inch standard
schedule pipe named 12STD. The coordinates of the system points
listed below are global (length units are feet, and offsets are
measured from the preceding
point):
2. Select Insert/Bend to open the Bend Point dialog. Input the
tangent intersection point coordinates as shown and specify the new
pipe data identifier ELBOW. After accepting this dialog, the Pipe
dialog (shown in
Step 3) will automatically be displayed since the pipe named
"ELBOW" has not yet been defined.
3. Define the new pipe. Enter a Nominal Pipe Size of 12.00" and
a Schedule of 120. After providing the data for the new pipe, the
Location dialog is automatically displayed as shown in Step 4.
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4. The Location dialog requests the specific location on the
bend where the pipe change is to take effect: at the near or far
point of the elbow. To change the elbow thickness over the entire
bend, select Near for the near
tangent.
5. Select Insert/Pipe Properties to display the Pipe Properties
dialog. From the selection list, specify 12STD as the pipe
identifier. A message is displayed indicating that "Previously
defined pipe date will be
used."
6. Again, the Location dialog requests the specific location on
the bend where the pipe change is to take effect.
This time select Far for the far tangent. This will place the
pipe 12STD in effect for subsequent piping components.
7. Define a run of pipe to A03. The coordinates for the system
point listed below are global (length units are feet, and offsets
are measured from the preceding point):
Display of the Thick Elbow Model
See Also:
Elbow Wall Thickness: Model 2
Elbow Wall Thickness: Model 2 The entire system defined in Model
1 can be built using the same pipe identifier (i.e. 12STD). The
bend can then be
modified using the Modify/Pipe Properties command.
1. Build a system from A00 to A03 using a 12 inch standard
schedule pipe named 12STD. The global coordinates for the system
points are listed below (length units are feet, and offsets are
measured from the
preceding point):
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2. Position the cursor over the outline of the elbow. After
being properly selected, the elbow is highlighted (you can
accomplish this same task by first selecting the near point of the
elbow, A02 N, then pressing and holding
the [Shift] key while selecting the far point, A02 F).
3. Select Modify/Pipe Properties to open the Pipe Properties
dialog.
4. Define the pipe ELBOW. See Step 3 of Model 1 .
Note: AutoPIPE will issue a warning for these models when the
Global Consistency Check is performed. The
messages are provided to alert the user to the sudden change in
pipe properties in the event that those changes
were unintentional (for our models this is not the case).
See Also:
Elbow Wall Thickness: Model 1
Base Supported Elbow A base elbow, or a dummy leg at a bend
point, can be modeled in various ways depending on the location of
the leg
along the bend and the orientation of the leg. The leg can be
placed at either tangent point, or at a point anywhere
along the bend. The leg itself can be modeled as a support or a
structural member welded to the bend.
It should be noted that supporting an elbow in this manner will
greatly effect the flexibility and stress intensification
factors for the elbow. For simplicity, the following models do
not address this aspect of a base supported elbow.
However, an SIF should be applied at the tangent points of the
bend.
Example
Figure 1.2.6
Four methods for modeling base supported elbows are provided
below:
Model 1: Supported at a tangent point (simple vstop support for
fig 1.2.6 a)
Model 2: Supported at a point along the bend (simple vstop
support for fig 1.2.6 b)
Model 3: Alternate method for defining a support at a
midpoint
Model 4: Modeling a "dummy leg" as a structural member (fig
1.2.6 b & c)
Model 5: Modeling a "dummy leg" as a pipe (Recommended fig 1.2.6
b)
Model 1: Supported at a tangent point
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In this model, a V-stop is to be placed at A02 F as shown in
Figure 1.2.6 (A), above. The support acts along the
centerline of the vertical run and does not restrain the
rotation of the elbow.
1. Build a system from A00 to A03. The global coordinates for
the system points are listed below (length units are feet, and
offsets are measured from the preceding point):
2. Move the crosshairs to point A02 F.
3. Select Insert/Support to open the Support dialog. Select
V-stop from the "Support type" selection list.
Display of Model 1
Other Base Supported Elbow Models
Model 2: Supported at a point along the bend In this model, a
V-stop is placed at a point along the bend at A02 as shown in
Figure 1.2.6 (B). It is assumed that a
system exists with a bend defined, and that A02 is the current
point (repeat Steps 1 and 2 from Model 1).
1. Select Modify/Bend or Modify/Point to open the Bend Point
dialog. Modify the bend to include a midpoint (A02 M) halfway
between A02 N and A02 F.
2. Move the crosshairs to point A02 M.
3. Select Insert/Support to open the Support dialog. Define a
V-stop at this point.
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Display of Model 2
Other Base Supported Elbow Models
Model 3: Alternate method for defining a support at a midpoint A
midpoint may be added to an existing bend without using the
Modify/Point or Modify/Bend command sequence.
This is particularly useful for defining supports at bend points
that have been defined without a midpoint.
1. Build a pipe run from A00 to A03 (see Model 1 , Step 1).
2. Move the crosshairs to A02 (the TIP).
3. Select Insert/Support . Since A02 is not a physical point on
the piping run, a support cannot be placed there. Thus, the
Location dialog is displayed requesting the specific location on
the bend where the support
should be placed. Select Mid from the "Location around the bend"
selection list.
4. Since the midpoint was not specified when the bend point was
created, the location of this point along the bend is requested in
the "Enter percentage along the bend" field. Accept the default
(50) and press OK. Once
the percentage along the bend is accepted, the Support dialog is
automatically displayed. Define a V-stop
support.
Other Base Supported Elbow Models
Model 4: Modeling a "dummy leg" as a structural member In this
model, a beam member is used to model the dummy leg as shown in
Figure 1.2.6 (C). The leg can be placed
either at a tangent point or at a point along the bend. In order
to represent a fully welded moment connection, by
taking into account the rotation of the bend, the dummy leg will
be placed at the midpoint. It is assumed that a system
exists with a bend midpoint defined, and that A02 M is the
current point (see Model 2 , Steps 1 and 2).
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1. Select Insert/Beam to open the Beam dialog:
2. Define the dummy leg as a beam member from A02 M to a new
point named BASE. Specify 2 (two) feet for the length of the leg
from Point I by entering -2.0 in the "DY" field. Enter W as the
"Table Name," W8X24 as the
cross "Section ID," and A36 as the "Material ID." Note that the
Beta angle is 90.
Note: A pipe or any other structural shape can be used to model
the leg.
3. Make "BASE" the current point.
4. Select Insert/Anchor to open the Anchor dialog.
5. Define an anchor at the base of the dummy leg. An anchor can
also be defined at "BASE" without moving to it. While in the Anchor
dialog, enter BASE in the "Point Name" field. This now becomes the
new current point
and the anchor will be placed at this point.
Display of Model 4
Other Base Supported Elbow Models
Model 5: Modeling a "dummy leg" as a pipe In this recommended
model, a short rigid beam member is used to connect a pipe segment
to the bend, to model the
dummy leg as shown in Figure 1.2.6 (B). This model can be used
to capture the radial thermal expansion of the bend
and any thermal growth of the trunnion. It is assumed that a
system exists with a bend midpoint defined, and that A02
M is the current point (see Model 2 , Steps 1 and 2).
1. Select Insert/Beam to open the Beam dialog:
2. Define the dummy leg as a beam member from A02 M to a new
point named B00. Specify a small length of
the leg from Point I by entering DX = 0.01, DY = -0.01' field.
Select "Table Name" - Rigid.
3. Make B00 the current point.
4. Select Insert/Segment to start a new pipe segment from B00
and enter pipe identifier name = Pipe1 (same properties as the
trunnion e.g. 6" standard schedule pipe.
5. Note the coordinates of B00 (using view/point properties, F3)
then click on the bend tip point A02 and also note its coordinates.
Subtract the two sets of coordinates to give the offsets from B00
to A02 i.e. DX =
0.2829', DY = -0.2829' using pipe identifier = Pipe1.
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6. Make B00 (segment B) the current point, Insert/Run (B00 to
B01) and enter offsets from step 5.
7. Insert/Run ( B01 to B02) and enter offsets to the base of the
trunnion e.g DY = -2'.
8. Make B02 the current point, and select Insert/Support to open
the support dialog and select V-stop (using default above gap = 100
and below gap = 0).
9. Click on the pipe between B00 and B01 to select this pipe
(highlighted Red) then select Insert/Rigid Options Over Range with
Include Weight = No, Include Thermal Expansion = Yes (shown as
purple). [This takes account of the radial expansion of the outer
wall surface of the bend assuming temperature is applied from B00
to B01].
Note:
1. If there is temperature e.g. if insulated or connected to a
high temperature line, on the dummy leg B01 to
B02 then apply temperature over this range typically less than
the main pressure pipe due to the heat
conduction along the non-insulated dummy leg.
2. Remember to remove any pressure from segment B since it is a
non-pressure component.
3. The coordinates of Bend tip point A02 and B01 should be the
same.
Display of Model 5
A close up of this trunnion connection to the bend midpoint can
be seen below with pipe = transparent under
View/Transparency.
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Other Base Supported Elbow Models
Miter Bends Miter bends are typically used where space
limitations do not allow the use of elbows, or when using a miter
bend is
more economical than an elbow. Miter bends are most often found
in pressure vessels, steel water piping, and drain
lines.
Miter bends are classified as either closely or widely spaced.
Evenly spaced miter bends, whether close or wide, are
defined by the following parameters:
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The miter is considered to be closely spaced if S < Sb.
Conversely, the miter is widely spaced if S Sb. Where:
Sb = Ra (1 + tan )
The effective miter radius (Re) is:
if closely spaced Re = Rb
if widely spaced Re = 0.5 Ra (1 + cot )
Close miter bends may have from 1 to 9 cuts. A 90 bend modeled
with one cut has a miter angle of 45, a two cut
miter angle is 22.5, a three cut miter angle is 15, and a four
cut miter angle (shown in the figure above) is 11.25.
AutoPIPE allows a closely spaced miter bend to be input on one
&rsquoBend Point dialog regardless of the number of
cuts (the miter cuts are calculated automatically). However, if
the miter is widely spaced, a series of one cut (single
miter) bend points must be input by the user.
Note: The user is responsible for predetermining whether the
miter bend is closely or widely spaced. The current
version of AutoPIPE does not trap an incorrectly specified miter
bend.
Two methods for modeling miter bends are provided below:
Model 1: 3 Cuts - Closely Spaced
Model 2: 3 Cuts - Widely Spaced
Model 1: 3 Cuts - Closely Spaced
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Since S < Sb, the miter is closely spaced. Therefore, the
miter bend can be defined as a single bend point and AutoPIPE
will automatically calculate each miter point (these are
transparent to the user).
1. Build a system from A00 to A01 using a 12 inch standard
schedule pipe named 12STD. The global coordinates for the system
points are listed below (length units are feet, and offsets are
measured from the
preceding point):
2. Select Insert/Bend to open the Bend Point dialog. Define Bend
point A02 with a Short radius, Close (miter) bend with 3 cuts.
Then, input the tangent intersection point coordinates as
shown.
3. Define a run of pipe to A03. The global coordinates for the
system point are listed below (length units are feet, and offsets
are measured from the preceding point):
AutoPIPE displays the miter bend information in the Point Data
Listing sub-report (see SYSNAME.RPT; select the Edit/List
command).
Click here to view the miter data for Model 1.
See Also:
Model 2: 3 Cuts - Widely Spaced
Nom. pipe size 12 in, Std. Sch.
Do 12.75 in
t 0.375 in
Bend type = Short radius, 3 cut miter
90.0
N 3
90.0 (2 3) = 15.0
Rb 1.0 12" = 12.0 in
Ra (12.75" - 0.375") 2 = 6.19 in
Sb 6.19" (1.0 + 0.2679) = 7.85 in
S 2.0 12.0" 0.2679 = 6.43 in < Sb
Model 2: 3 Cuts - Widely Spaced
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Let's define the same bend as in Model 1, except this time using
a long radius (this will result in a wide miter bend).
The changed parameters are:
Bend type: long radius
Rb: 1.5 12" = 18.0 in
S: 2.0 18.0" 0.2679 = 9.65 in > Sb
Since S > Sb, the miter is widely spaced. Therefore, the
miter bend must be defined as a series of single bend points.
1. Determine the effective miter radius Re. This value will be
entered in the "Bend radius" field when defining each miter tangent
intersection point (TIP).
Re = 0.5 6.19" (1 + cot 15) = 14.64 in
2. Determine the coordinates for each of the miter cuts. Since
each cut must be defined as an individual bend, the coordinates
will locate the tangent intersection points TP1, TP2 and TP3.
In order to establish the coordinates for each miter cut TIP it
is necessary to define a reference axis from which
the point offsets can be related. This reference axis shall be
along the centerline of the pipe coming into the
bend to the overall TIP (refer to the Figure above).
a. The first miter cut (TP1) is always located on the reference
axis at a distance of "0.5 S" from the near tangent point (of the
overall bend). Thus, TP1 is located by offsets are measured from
point A01 (see
Model 1 for coordinates):
b. The coordinates for all subsequent miter cuts (regardless of
the total number of cuts in the miter bend) are given by the
following two equations (where, i = miter cut number):
Thus, the coordinates for the second miter cut TP2 (i = 2)
measured from the first miter cut
TP1 are:
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The coordinates for the third miter cut TP3 (i = 3) measured
from the second miter cut TP2
are:
Note: If the bend angle () does not equal 90 or the reference
axis does not coincide with a global axis, a transformation of
coordinate systems must be performed in order to calculate the
correct offset values.
The user should be very careful when calculating coordinate
offsets.
c. Calculate the offset from the last miter cut TP3 to the next
(run) point RUNP on the piping system (the coordinates of RUNP are
the same as A03 in Model 1 ).
4. Define the pipe and system points up to, and including point
A01 by repeating Step 1 from Model 1.
5. Select Insert/Bend to open the Bend Point dialog. Define a
bend point A02 as Wide (miter) bend with a bend radius (Re) of
14.64 inches. Then, input the tangent intersection point
coordinates as shown. Notice that
the Cuts field is closed as wide miters are always a single
cut.
6. Repeat Step 5 for each of the remaining miter cut TIPs (TP2
and TP3). Use the offset values calculated in Step 2 for each bend
TIP.
7. Define a run of pipe to A05, use the offset values calculated
in Step 3. The global coordinates for the points in the completed
system are listed below (length units are feet, and offsets are
measured from the preceding
point):
AutoPIPE displays the miter bend information in the Point Data
Listing sub-report (See SYSNAME.RPT, select the
View/Point Properties [F3] command).
Click here to view the miter data for Model 2.
See Also:
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Model 1: 3 Cuts - Closely Spaced
Cuts: Cold Spring A cold spring is used to reduce thermal forces
on vessels, pumps, and other types of equipment connected to a
piping
system. The force reduction is achieved by fabricating the pipe
slightly shorter than the required dimension and then
pulling it into place during erection (at the ambient
temperature). This creates a state of internal pre-stress which
is
opposed to the stress that results from the (high) temperatures
encountered under operating conditions.
When a cut-short is specified at a point, AutoPIPE applies the
cut to the section of pipe preceding the current point.
Thus, a cut cannot be defined at the first point in the pipe
system. In addition, a cut cannot be specified at a bend.
Example System
Two methods for modeling cold spring cuts are provided
below:
Model 1: Cut-Short (high operating temperature)
Model 2: Cut-Long (low operating temperature)
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Model 1: Cut-Short (high operating temperature) In order to
counter the anticipated thermal stresses, both legs are to be
fabricated 0.27" shorter than the 10'-0" leg
length. First, the system is modeled with the established
dimensions. Then, a cut-short is specified for each pipe leg.
The user has the option to analyze the system with or without
the cold spring effect. If included in the analysis,
the cold spring is applied to the load case in which the cut
short was defined.
1. Build a system from A00 to A03 using an 8 inch, standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
2. Move the crosshairs to point A01.
3. Select Insert/Xtra Data/Cut Short to open the Cut Short
dialog: Specify a cut of 0.27 in the GR load case. A positive value
defines a shortening in the horizontal leg of the system which
causes a pretension
load.
4. Add a cut-short in the vertical leg by repeating Step 3 for
point A03.
5. Select Analyze/Static to open the Static Load Cases dialog.
To include the effects of the cold spring, enable the Cut-short
analysis option.
For proper evaluation of the results, a user combination should
be defined which includes both the GR and T1 load
cases. This combination represents the total effect of the
cut-short pre-stress (defined in GR) and the stress relief
induced by the operating temperature (T1).
See Also:
Model 2: Cut-Long (low operating temperature)
Model 2: Cut-Long (low operating temperature) For this model, we
will use the same example system, but this time the operating
temperature is -150F.
In order to counter the anticipated thermal stresses, both legs
are to be fabricated 0.145" longer than the 10'-0" leg
length.
1. Build the system described in Step 1 of Model 1, in this
section.
2. Move the crosshairs to point A01.
3. Select Insert/Xtra Data/Cut Short to open the Cut Short
dialog. Specify a cut of -0.145 inches in the GR load case. The
negative value defines a lengthening in the horizontal leg of the
system which causes a pre-
compression load.
4. Add a cut-long in the vertical leg by repeating Step 3 for
point A03.
5. Repeat Step 5 from Model 1 in order to include the effects of
the cold spring in the analysis.
As stated for Model 1, a user combination should be defined
which includes both the GR and T1 load cases. This
combination represents the total effect of the cut-long
pre-stress (defined in GR) and the stress relief induced by the
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operating temperature (T1).
Note: The user should be aware that the ASME codes do not allow
the inclusion of the cold spring effect when cyclic
loading is a factor on the system. Refer to the specific code
for details regarding this matter.
The models presented have each used a 100% cold spring. The user
should be aware that this was done for
simplicity, and is not a standard practice in piping design.
See Also:
Model 1: Cut-Short (high operating temperature)
Flexible Joints Choose from the following flexible joint
modeling examples:
Single Bellows Expansion Joint
Tied Bellows Expansion Joint
Tied Universal Expansion Joint
Hinged Expansion Joint
Gimbal Expansion Joint
Slip Joint
Ball and Socket Joint
Pressure Balanced Expansion Joints
Single Bellows Expansion Joint A single bellows expansion joint
is used to absorb the axial and lateral movement (caused by thermal
expansion or
contraction) of the pipe section in which it is installed. It is
not capable of absorbing pressure thrust, which must be
restrained by the piping system itself.
Example
Modeling The primary axial growth of the piping system, due to
thermal expansion, is absorbed by the single bellows acting in
compression. Since the bellows cannot absorb pressure thrust the
bend near the expansion joint is anchored to support
this load.
1. Build a system from A00 to A02 using an 8 inch, standard
schedule pipe. The global coordinates for these
points are listed below (length units are feet, and offsets are
measured from the preceding point):
2. Select Insert/Flexible Joint to open the Flexible Joint
dialog.
3. Define a flexible joint to point A03. Enter a length of 1.0
foot i.e. DX = 1.00, DY = 0.00, DZ = 0.00
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Define Axial stiffness = 1000 lb/in, Y-bending stiffness = 10000
ft-lb/deg, Z-bending stiffness = 10000 ft-lb/deg, All
other stiffness values = Rigid(the default), and the component
weight (user supplied) = 53 lb. Also, a pressure thrust
area of 50.03sq. in should be specified. The area shown assumes
that the bellows has an internal sleeve (based on Di =
7.981").
A = pi (7.981 in)2 4 = 50.03 in2
4. Define the remainder of the piping system. The global
coordinates for these points are listed below (length
units are feet, and offsets are measured from the preceding
point):
5.
5. Move the crosshairs to point A04 N.
6. Select Insert/Support to open the Support dialog. Specify an
Inclined, rigid support acting in the Global X
direction. The (directional) support restrains the pressure
thrust developed in the bellows due to the internal
operating pressure of the pipe.
Display of a system that uses a single bellows to control
thermal expansion
It should be noted that the flexible joint has been placed in
the long leg of the piping system. This orientation enables
the joint to absorb the large (relatively speaking) thermal
expansion axially. In addition, it can be seen that the small
axial expansion in the leg between A04 and A05 is absorbed by
the joint in bending. The designer should always try to
minimize bending loads acting on a single bellows expansion
joint.
Tied Universal Expansion Joint A universal expansion joint
contains two bellows joined by a common connector. It is used for
the purpose of absorbing
any combination of axial movement, lateral deflection, and
angular rotation. Universal joints are usually furnished with
tie rods whose function is to distribute the movement between
the two bellows, and absorb pressure thrust. A common
application of a tied universal joint is its use in a Z bend. In
this case, the joint assembly absorbs the axial expansion of
the long legs as lateral deflection, and the tie rods are
adjusted to prevent axial expansion in the short leg due to
pressure effects.
Example
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Modeling The tie rods in a universal expansion joint can be
modeled using either of two methods in AutoPIPE. The simple
approach is to use a single two-point (tie/link) support, which
represents the total stiffness of the tie rods, to connect
each end of the flexible joint (refer to the approach used for
Model 1 of the Tied Bellows Expansion Joint
Example ). This method neglects bending effects at the joint due
to the actual orientation of the rods.
The second method (modeled below) places the tie rods in their
actual position, in relation to the pipe and bellows. The
end plates are modeled as rigid beams, and the tie rods are
modeled as Tie/link supports with gaps set (rods only resist
tension loads). As will be shown, the gap settings specified
have an important effect on the manner in which the tied
bellows is modeled.
1. Build a system from A00 to A09 using an 8 inch, standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
Note: Points A04 and A06 have been skipped intentionally.
2. Move the crosshairs to point A01.
3. Select Insert/Support to open the Support dialog. Define a
Rigid planar guide by specifying a large (10 inch) gap down and gap
up. This allows the upper section of pipe to move only in the X-Y
plane.
4. Move the crosshairs to point A08. Define another planar guide
at this point (repeat Step 3). Again, specify large values in the
gap down and gap up directions in order to limit movement of the
lower section of pipe to
the Y-Z plane.
5. Move the crosshairs to point A03.
6. Select Insert/Flexible Joint to open the Flexible Joint
dialog.
7. Define a flexible joint to point A04. Enter a length of 1.0
foot i.e. DX = 0.00, DY = -1.00, DZ = 0.00
Axial stiffness = 1000 lb/in, Y-bending stiffness = 10000
ft-lb/deg, Z-bending stiffness = 10000 ft-lb/deg, All other
stiffness values = Rigid (the default), and a component weight
of 53 lb. Also, a pressure thrust area of 50.03 sq.in should be
specified. The area entered assumes that the bellows has an
internal sleeve (based on Di = 7.981").
A = pi (7.981") 4 = 50.03 in
8. Move the crosshairs to point A05. Define a second flex joint
from A05 to A06 (repeat Steps 6 and 7). Again, the point at the far
end of the joint is defined by the point name (A06), and length (1
ft) specified.
9. Move the crosshairs back to point A03. We will now begin to
define the tie rod assembly for the universal joint.
10. Select Insert/Beam to open the Beam dialog.
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11. Define a rigid beam (M1) from A03 to the point TB1. TB1 is
located 6 inches away from A03, in the +X direction.
12. Define the remainder of the rigid beams. Add three more
beams connecting A03 to TB2 through TB4. Then, add four more beams
connecting A06 to TB5 through TB8. The beam point offset
coordinates are as shown
in the table below (DX, DY and DZ lengths are relative to the
point referenced in the "From Point I" field).
13. Select Insert/Support to open the Support dialog.
14. Specify a Tie/link from TB1 to TB5 in order to simulate the
effect of a 0.5" diameter rod. Enter a spring rate of 152171 which
is equal to the axial stiffness (ka) of the rod (Refer to the Note
for Step 4, Model 2, in Section
1.4.2 for additional details on the purpose of the gap setting
values.):
E = 27,900,000 psi L = 36.0 in A = pi (0.50") 4 = 0.1963 in
ka = 27,900,000 psi 0.1963 in 36.0 in = 152,170.9 lb/in
15. Move the crosshairs to point TB2, then repeat Step 14 (place
a tie/link between TB2 and TB6). Continue defining the tie rods in
this manner (there should be ties between TB3 and TB7, and between
TB4 and TB8).
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Hinged Expansion Joint A hinged expansion joint contains one
bellows and is designed to permit angular rotation in one plane
only by the use of
a pair of pins through hinge plates attached to the expansion
joint ends. The hinges and hinge pins must be designed to
restrain pressure thrust and any extraneous forces, where
applicable. Hinged joints should be used in sets of two or
three to function properly.
Example
Modeling A set of hinged joints are commonly used to absorb the
axial (lateral) growth in a planar Z-bend piping system. Each
individual joint in this system is restricted to pure angular
rotation by its hinges. However, each pair of joints, separated
by a section of pipe, will act in unison to absorb lateral
deflection in much the same manner as a universal expansion
joint in a single plane application. For a given angular
rotation of the individual hinges, the amount of lateral
deflection which a pair of hinges can absorb is directly
proportional to the distance between the hinge pins. Thus, in
order to utilize the joints most efficiently, this distance
should be made as large as possible.
1. Build a system from A00 to A09 using an 8 inch, standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
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Note: Points A04 and A06 have been skipped intentionally.
2. Move the crosshairs to point A01.
3. Select Insert/Support to open the Support dialog. Define a
Rigid planar guide by specifying a large (10 inch) "Gap down" and
"Gap up." This allows the upper section of pipe to move only in the
X-Y plane.
4. Move the crosshairs to point A08. Define another planar guide
at this point (repeat Step 3). Again, specify large values in the
"Gap down" and "Gap up" directions in order to limit movement of
the lower section of
pipe to the X-Y plane.
5. Move the crosshairs to point A03.
6. Select Insert/Flexible Joint to open the Flexible Joint
dialog. Define a flexible joint to point A04. Enter a length of 1.0
feet i.e. DX = 0.00, DY = -1.00, DZ = 0.00. Specify a zero (0)
Y-bending stiffness and all
other stiffnesses = Rigid , with the component weight of 53 lb.
Also, a pressure thrust area of 50.03 sq.in should
be specified. The area entered assumes that the bellows has an
internal sleeve (based on Di = 7.981").
A = pi (7.981") 4 = 50.03 in
7. Move the crosshairs to point A05. Define a second flex joint
from A05 to A06 (repeat Step 6). Again, the point at the far end of
the joint is defined by the point name (A06), and length (1 ft)
specified.
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Display of Planar "Z-Bend" Model
Gimbal Expansion Joint A gimbal expansion joint is designed to
permit angular rotation in any plane by the use of two pairs of
hinges affixed to
a common floating gimbal ring. The gimbal ring, hinges, and pins
must be designed to restrain pressure thrust and any
extraneous forces, where applicable. Gimbal expansion joints
should be used in sets of two or three to function
properly.
Example
Modeling A set of gimbal joints are commonly used to absorb the
axial (lateral) growth in a multiplane Z-bend piping system.
Each individual joint in this system is restricted to pure
angular rotation by its hinges. However, each pair of gimbals,
separated by a section of pipe, will act in unison to absorb
lateral deflection in much the same manner as a universal
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expansion joint. For a given angular rotation of the individual
gimbal, the amount of lateral deflection which a pair of
gimbals can absorb is directly proportional to the distance
between the gimbals. Thus, in order to utilize the joints most
efficiently, this distance should be made as large as
possible.
1. Build a system from A00 to A09 using an 8 inch, standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
Note: Points A04 and A06 have been skipped intentionally.
2. Move the crosshairs to point A01.
3. Select Insert/Support to open the Support dialog. Define a
rigid planar guide by specifying a large (10 inch) gap down and gap
up. This allows the upper section of pipe to move only in the X-Y
plane.
4. Move the crosshairs to point A08. Define another planar guide
at this point (repeat Step 3). Again, specify large values in the
gap down and gap up directions in order to limit movement of the
lower section of pipe to
the Y-Z plane.
5. Move the crosshairs to point A03.
6. Select Insert/Flexible Joint to open the Flexible Joint
dialog. Define a flexible joint to point A04. Enter a length of 1.0
feet i.e. DX = 0.00, DY = -1.00, DZ = 0.00. Specify 0 Y and
Z-bending stiffnesses, and all
other stiffnesses = Rigid , with a component weight of 53 lb.
Also, a pressure thrust area of 50.03 sq.in should be specified.
The area entered assumes that the bellows has an internal sleeve
(based on Di = 7.981").
A = pi (7.981") 4 = 50.03 in
7. Move the crosshairs to point A05. Define a second flexible
joint from A05 to A06 (repeat Step 6). Again, the point at the far
end of the joint is defined by the point name (A06), and length (1
ft) specified.
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Display of Multiplane "Z-Bend" Model
Slip Joint A slip joint allows axial expansion of a pipe section
by permitting the adjacent pipes to move through a telescoping
action. Slip joints have the great advantage of being capable of
absorbing relatively large amounts of axial expansion in
a single device and doing so in the most direct way possible.
The slip joint can also accommodate torsional motion.
However, even small bending loads can cause binding or galling,
severely reducing the capacity and effectiveness of the
joint. It should be noted that slip joints are susceptible to
lateral buckling (or squirming) due to the internal pipe
pressure. Therefore, suitable guiding must be provided to assure
that buckling is prevented, and that the male and
female components remain concentric at all times.
Example
Modeling The axial thermal growth of a straight run of pipe is
absorbed by a slip joint. A single action slip joint is placed at
the
end of the long pipe section, near the attached equipment (or
anchor). Then, several guides are provided to assure that
the pipe movement is in the axial direction only.
1. Build a system from A00 to A07 using a 4 inch, standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
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Note: Point A06 has been skipped intentionally.
2. Move the crosshairs to point A05.
3. Select Insert/Flexible Joint to open the Flexible Joint
dialog. Define a flexible joint to point A06. Enter a length of 1.0
foot i.e. DX = 1.00, DY = 0.00, DZ = 0.00. Specify a small value
e.g. 0.1 axial, 0.1 torsional
stiffnesses and all other stiffnesses = Rigid with and a
component weight of 15 lb. Also, a pressure thrust area of 12.73
sq.in should be specified. The area entered assumes that the slip
joint has an internal sleeve (based
on Di = 4.026").
A = pi (4.026") 4 = 12.73 in
Display of System Model
Note: When two slip joints are placed adjacent to each other in
a piping system, the pipe between the two slip joints
is supported primarily by friction. Since AutoPIPE does not
consider friction in the flexible joint component, the Axial
and Torsional stiffnesses should be specified as small values (
0.1 ft lb and 0.1 ft lb/deg) instead of zero in order to
prevent an unstable system error.
Ball and Socket Joint A ball and socket joint allows free
rotation (in any direction) of the connected pipes, but does not
permit translational
movements. Since translation is fixed, pressure loads are
transmitted through the joint, and axial movement cannot be
absorbed. Instead, the joint must be oriented so that movements
are absorbed laterally. Thus, it can be seen that ball
and socket joints provide an alternative to other types of
expansion joints when used in pairs, or in threes. It should be
noted that actual ball and socket joints are limited in their
range of angular rotation. They should be placed in the
piping system so that these limits are not exceeded.
Example
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Modeling A common application for a system of ball joints is a
multiplane Z-bend. This model illustrates an arrangement of
three
ball joints as an alternative to a universal, or gimbal
expansion joint for absorbing thermal expansion laterally.
1. Build a system from A00 to A09 using a 6 inch standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
Note: Points A02, A05 and A07 have been skipped
intentionally.
2. Move the crosshairs to point A01.
3. Select Insert/Flexible Joint to open the Flexible Joint
dialog. Define a flexible joint to point A02. Enter a length of
0.75 feet i.e.DX = 0.75, DY = 0.00, DZ = 0.00. Specify 0.1
ft-lb/deg for torsional, Y-bending and Z-
bending stiffnesses, and a component weight of 30 lb. Also, a
pressure thrust area of 28.89 sq.in should be specified. The area
entered assumes that the ball joint has an internal sleeve (based
on Di = 6.065").
A = pi (6.065") 4 = 28.89 in
4. Move the crosshairs to point A04. Define a second flexible
joint from A04 to A05 (repeat Step 3). Again, the point at the far
end of the joint is defined by the point name (A05), and length
(0.75 ft) specified.
5. Move the crosshairs to point A06. Define a third flexible
joint from A06 to A07 (repeat Step 3). However, a zero torsional
stiffness cannot be used since this will result in free rotation of
the pipe between A05 and A06
about the longitudinal (local x) axis. In order to prevent an
unstable system error, enter a value of
0.1 ft lb/deg.
Note: The 0.1 ft lb/deg torsional stiffness could have been
defined at A05 instead of A06 to prevent
instability.
In this model, the ball joints in the vertical pipe leg absorb
the axial expansion of the (long) horizontal legs. The axial
expansion of the centerspool, in the vertical leg, is absorbed
by the ball joint in the upper horizontal leg. If the
centerspool expansion is small enough to be absorbed by the
flexibility of the horizontal pipe sections, the flexible joint
between A01 and A02 could be omitted.
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Display of Multiplane "Z-Bend" Model
Tied Bellows Expansion Joint Tie rods are devices, usually in
the form of rods or bars, attached to the expansion joint assembly,
whose primary
function is to continuously restrain the full bellows pressure
thrust during normal operation while permitting only lateral
deflection. It should be noted that when tie rods are furnished
on expansion joints subject to external axial movement,
they will only restrain the pressure thrust in the event of an
anchor failure. During normal operation, the adjacent
equipment would be subject to the pressure thrust forces.
Example
Two methods for modeling tied bellows expansion joints are
provided below:
Model 1: Tie rods modeled as a single two-point support
Model 2: Tie rod assembly modeled as beams and two-point
supports
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Model 1: Tie rods modeled as a single two-point support This
approach produces a simplified model of a tied bellows as bending
effects at the expansion joint, due to the actual
orientation of the rods, are neglected. A (Tie/link) support
with gaps is used to model tie rods that act in tension only.
The pressure thrust acting on the bellows is restrained by the
tie rods and thus no external support is required.
1. Build a system from A00 to A07 using an 8 inch standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
Note: Point A05 has been skipped intentionally.
2. Move the crosshairs to point A01.
3. Select Insert/Support to open the Support dialog. Define a
rigid planar guide by specifying a left and right gap of 10 inches.
This allows the pipe to move, due to thermal expansion, in the
plane of the pipe.
4. Move the crosshairs to point A04.
5. Select Insert/Flexible Joint to open the Flexible Joint
dialog.
6. Define a flexible joint to point A05. Enter a length of 1.5
feet i.e. DX = 0.00, DY = 0.00, DZ = 1.50. Specify axial stiffness
= 100 lb/in, Y-shear and Z-shear stiffness (i.e. lateral )= 100
lb/in and torsional & bending
stiffnesses = Rigid, and the component weight of 53 lb. Also, a
pressure thrust area of 50.03 sq.in must be
specified. The area entered assumes that the bellows has an
internal sleeve (based on Di = 7.981").
A = pi (7.981") 4 = 50.03 in
7. Move the crosshairs to point A03.
8. Select Insert/Support to open the Support dialog:
9. Specify a Tie/link from A03 to A06 in order to simulate the
effect of four 0.5" diameter rods (positioned symmetrically between
A04 and A05). Enter a spring rate of 730420 equal to the axial
stiffness (ka) of the four
rods combined:
E = 27,900,000 psi L = 30.0 in A = pi (0.50") 4 = 0.1963 in
ka = 4 (27,900,000 psi 0.1963 in ) 30.0 in = 730,420.3 lb/in
A large forward gap and no backward gap has been specified in
order to model the rods for tension loads only (refer to
the discussion of Tie/Link Supports for details on the forward
and backward directions). When a static analysis is
performed, the "Gaps/Friction/Soil" must be enabled in order to
include the tension only behavior of the tie rods.
Note: Alternatively all stiffnesses (Note: torsion = 1E9 or
Rigid) can be defined for the flexible joint i.e. non-zero and
a
tie-link, rigid X-rotation and rigid Y-rotation connecting from
A03 to A06 which maintains both ends of the tied
bellows will rotate the same i.e remain parallel.
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Display of Model 1
See Also:
Model 2: Tie rod assembly modeled as beams and two-point
supports
Model 2: Tie rod assembly modeled as beams and two-point
supports This is a more accurate model of the tied bellows since
bending effects at the expansion joint are being considered:
the
actual orientation of the rods is specified. The tie rods
themselves cannot restrain bending loads, but their combined
interaction does effect the bending behavior of the joint. The
end plates are modeled as rigid beams, and the tie rods
are modeled as Tie/link supports with gaps set (rods can only
resist tension loads). As will be shown, the gap settings
specified have an important effect on the manner in which the
tied bellows is modeled.
1. Define the pipe system; repeat Steps 1 - 7 from Model 1.
2. Select Insert/Beam to open the Beam dialog. Define a Rigid
beam (M1) from A03 to the point TB1. TB1 is located 6 inches above
A03.
3. Define the remainder of the rigid beams as shown. Add three
more beams connecting A03 to TB2 through TB4. Then, add four more
beams connecting A06 to TB5 through TB8. The beam point offset
coordinates are
as shown in the table below (DX, DY and DZ lengths are relative
to the point referenced in the "From Point I"
field).
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Note: End plate beams could probably have been defined at points
A04 and A05 instead of points A03
and A06 without any significant loss of accuracy.
4. Select Insert/Support to open the Support dialog. Specify a
Tie/link from TB1 to TB5 in order to simulate the effect of a 0.5"
diameter rod. Enter a spring rate of 182605 which is equal to the
axial stiffness (ka) of the
rod:
E = 27,900,000 psi L = 30.0 in A = pi (0.50") 4 = 0.1963 in
ka = 27,900,000 psi 0.1963 in 30.0 in = 182,605.1 lb/in
Note: A large forward gap and no backward gap has been specified
in order to model the rod for
tension loads only. It should be noted that the gap settings can
be used to model limit, or control,
rods by specifying meaningful gap values. For example, defining
a backward gap would model a limit
rod, with the gap value being the amount of axial expansion
allowed (such as the bellows design limit)
before the rods restrain the joint. When a static analysis is
performed, the "Gaps/Friction/Soil" option
must be enabled in order to include the tension only behavior of
the tie rods.
5. Move the crosshairs to point TB2, then repeat Step 4 (place a
tie/link between TB2 and TB6). Continue defining the tie rods in
this manner (there should be ties between TB3 and TB7, and between
TB4 and TB8).
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Single Line Display of ties linking beam members
See Also:
Model 1: Tie rods modeled as a single two-point support
Pressure Balanced Expansion Joints A pressure balanced expansion
joint is designed to absorb axial movement and/or lateral
deflection while restraining the
pressure thrust by means of tie rods interconnecting the flow
bellows with an opposed bellows also subjected to
operating pressure. This type of expansion joint is normally
used where a change of direction occurs in a run of piping
(e.g., at a bend or a tee). A tee may be used in place of the
elbow where flow considerations allow its use.
The major advantage of the pressure-balanced design is its
ability to absorb externally induced axial movement without
imposing pressure loading on the system. Therefore, it is often
used to relieve loads acting on equipment such as
pumps, compressors, and turbines. However, in order for the
expansion joint to function properly, the pressure thrust
restrained by the tie rods must exceed the axial movement
forces.
When large amounts of lateral movement are required, or when the
lateral force must be held to a minimum, a
pressure balanced universal expansion joint is used. In this
case, the flow end of the expansion joint contains two
bellows separated by a common connector (centerspool). The
lateral movement is absorbed by the flow bellows in the
same manner as a tied universal expansion joint.
Two methods for modeling pressure balanced expansion joints are
provided below:
Model 1: Pressure Balanced Elbow
Model 2: Pressure Balanced Tee
Model 1: Pressure Balanced Elbow
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1. Build a system from A00 to A05 using an 8 inch standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
Note: Point A03 has been skipped intentionally.
2. Move the crosshairs to point A02.
3. Select Insert/Flexible Joint to open the Flexible Joint
dialog.
4. Define a flexible joint to point A03. Enter a length of 0.50
feet i.e. DX = 0.50, DY = 0.00, DZ = 0.00.
Define Axial stiffness = 1000 lb/in, Y-bending stiffness = 10000
ft-lb/deg, Z-bending stiffness = 10000 ft-lb/deg, all
other stiffness values = Rigid(the default) with a component
weight of 53 lb. Also, a pressure thrust area of 50.03 sq.in should
be specified. The area entered assumes that the bellows has an
internal sleeve (based on Di = 7.981").
A = pi (7.981") 4 = 50.03 in
5. Select Insert/Segment to begin a new segment: Accept the new
segment name default (B). Enter A03 as the first point. Since A03
already exists, the Tee dialog is automatically displayed once the
current dialog
is accepted.
6. Accept the default type of tee (Welding). All this step does
is assign a stress intensification factor (SIF) at the joint. The
SIF for the default tee type is 1.0. This is an acceptable value
since we are not really modeling a
tee connection.
7. Select Insert/Run to open the Run Point dialog. Define point
B01. Locate this point 1.33 feet from A03 (in the +X
direction).
8. Define a second flexible joint from B01 to B02 (repeat Steps
3 and 4). Again, the point at the far end of the joint is defined
by the point name (B02), and length (0.50 ft) specified.
9. Move the crosshairs back to point A02 to begin defining the
tie rod assembly for the pressure-balanced elbow.
10. Select Insert/Beam to open the Beam dialog. Define a Rigid
beam (M1) from A02 to the point TB1. TB1 is located 6 inches away
from A02, in the +Y direction.
11. Define the remainder of the rigid beams. Add three more
beams connecting A02 to TB2 through TB4. Then, add four more beams
connecting B02 to TB5 through TB8. The beam point offset
coordinates are as shown
in the table below (DX, DY and DZ lengths are relative to the
point referenced in the "From Point I" field).
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12. Move the crosshairs to point TB1.
13. Select Insert/Support to open the Support dialog. Specify a
Tie/Link from TB1 to TB5 in order to simulate the effect of a 0.5"
diameter rod. Enter a spring rate which is equal to the axial
stiffness (ka) of the rod
(195648):
E = 27,900,000 psi L = 28.0 in A = pi (0.50") 4 = 0.1963 in
ka = 27,900,000 psi 0.1963 in 28.0 in = 195,648.3 lb/in
Note: A large forward gap and no backward gap has been specified
in order to model the rod for
tension loads only. It should be noted that the gap settings can
be used to model limit, or control,
rods by specifying meaningful gap values. For example, defining
a backward gap would model a limit
rod, with the gap value being the amount of axial expansion
allowed (such as the bellows design limit)
before the rods restrain the joint. When a static analysis is
performed, the "Gaps/Friction/Soil" option
must be enabled in order to include the tension only behavior of
the tie rods.
14. Move the crosshairs to point TB2, then repeat Step 13 (place
a tie/link between TB2 and TB6). Continue defining the tie rods in
this manner (there should be ties between TB3 and TB7, and between
TB4 and TB8).
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Display of the Pressure Balanced Elbow Model
See Also:
Model 2: Pressure Balanced Tee
Model 2: Pressure Balanced Tee
1. Build a system from A00 to A05 using an 8 inch standard
schedule pipe. The global coordinates for the system points are
listed below (length units are feet, and offsets are measured from
the preceding point):
Note: Point A03 has been skipped intentionally.
2. Move the crosshairs to point A04.
3. Select Insert/Segment to open the Segment dialog. Accept the
new segment name default (B), and enter A04 as the first point.
Since A04 already exists, the Tee dialog is automatically displayed
after closing
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this dialog.
4. Accept the default Type of tee (Welding). This step assigns a
stress intensification factor (SIF) at the joint. The SIF for the
default tee type is 1.0.
5. Complete the tee by defining a run of pipe to B01. The global
coordinates for this point are listed below (length units are feet,
and offsets are measured from the preceding point):
6. Move the crosshairs to point A02.
7. Select Insert/Flexible Joint to open the Flexible Joint
dialog.
8. Define a flexible joint to point A03. Enter a length of 0.50
feet i.e. DX = 0.50, DY = 0.00, DZ = 0.00.
Define Axial stiffness = 1000 lb/in, Y-bending stiffness = 10000
ft-lb/deg, Z-bending stiffness = 10000 ft-lb/deg, all
other stiffness values = Rigid(the default) with a component
weight of 53 lb. Also, a pressure thrust area of 50.03 sq.in should
be specified. The area entered assumes that the bellows has an
internal sleeve (based on Di = 7.981").
A = pi (7.981") 4 = 50.03 in
9. Move the crosshairs to point A05. Define a second flex joint
from A05 to A06 (repeat Steps 7 and 8). Again, the point at the far
end of the joint is defined by the point name (A06), and length
(0.50 ft) specified.
10. Move the crosshairs back to point A02, then select
Insert/Beam to open the Beam dialog. Define a rigid beam (M1) from
A02 to the point TB1. TB1 is located 6 inches away from A02, in the
+Y direction.
11. Define the remainder of the rigid beams. Add three more
beams connecting A02 to TB2 through TB4. Then, add four more beams
connecting A06 to TB5 through TB8. The beam point offset
coordinates are as shown
in the table below (DX, DY and DZ lengths are relative to the
point referenced in the "From Point I" field).
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12. Move the crosshairs to point TB1, then select Insert/Support
to open the Support dialog. Specify a Tie/link from TB1 to TB5 in
order to simulate the effect of a 0.5" diameter rod. Enter a spring
rate which is
equal to the axial stiffness (ka) of the rod (228256.00):
E = 27,900,000 psi L = 24.0 in A = pi (0.50")2 4 = 0.1963 in2 ka
= 27,900,000 psi 0.1963 in2 24.0 in = 228,256.3 lb/in
Note: A large forward gap and no backward gap has been specified
in order to model the rod for
tension loads only. It should be noted that the gap settings can
be used to model limit, or control,
rods by specifying meaningful gap values. For example, defining
a backward gap would model a limit
rod, with the gap value being the amount of axial expansion
allowed (such as the bellows design limit)
before the rods restrain the joint. When a static analysis is
performed, the "Gaps/Friction/Soil" option
must be enabled in order to include the tension only behavior of
the tie rods.
13. Move the crosshairs to point TB2, then repeat Step 12 (place
a tie/link between TB2 and TB6). Continue defining the tie rods in
this manner (there should be ties between TB3 and TB7, and between
TB4 and TB8).
Display of the Pressure Balanced Tee
See Also:
Model 1: Pressure Balanced Elbow
Frames: Pipe Rack Modeling Examples Frame structures are
commonly used to support piping systems. In most cases, the
structure is assumed to be much
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stiffer than the piping itself and can be modeled simply as a
rigid support. However, AutoPIPE also allows a supporting
frame structure, such as a pipe rack, to be included in the
system model.
Example The following models depict a system of parallel pipe
runs (shown in the figure) which are supported by a pipe rack
structure. The pipe-frame connection type varies with each
model. The piping system is usually defined first as this
simplifies the modeling of the frame that supports the
pipes.
Three methods for modeling pipe racks are provided below:
Pipe Rack (Method 1)
Pipe Rack (Method 2)
Pipe Rack (Method 3)
Pipe Rack (Method 1) Each piping point is connected to a
corresponding beam point using a two-point support.
1. Build segments A (12" standard pipe) and B (6" standard
pipe), which are to be supported by a pipe rack in each model. The
global coordinates of the system points are listed below (length
units are feet, and offsets
are measured from the preceding point):
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Note: Save the system as defined at this point. Each of the
three models that follow use this piping
system for the demonstration of pipe-beam connection types.
2. Select Insert/Beam to open the Beam dialog. Define beam M1 as
the first frame leg (a column) from point 1 to point 2. The maximum
pipe diameter and beam depth have been taken into account for
the
calculation of the coordinates for point 2 (also 3, 4 and
5).
3. Define the remainder of the frame. Add a beam between each
beam point listed below (e.g. beam M2 spans from point 2 to 3, M3
spans from 3 to 4, etc.). Length units are feet.
Note: Note that in Step 2, point 2 was defined as an offset from
point 1. By using point 2 as the I
point for beam M2, its coordinates are recalled. Thus, only
point 3 needs to be defined (again as an
offset from point 2). This is a convenient method for defining
beam points.
Another convenient way to define beam points is to enter a
piping point (e.g. A02) which has similar
coordinates as Point I. Then, change the point name (e.g. to 3).
Finally, modify the Y coordinate in
order to position the point as required.
4. Make 1 the current point.
Note: The crosshairs do not have to be located at point 1 in
order to define an anchor (see
Step 5). Entering 1 in the "Point Name" field on the Anchor
dialog will automatically move the
crosshairs.
5. Select Insert/Anchor to open the Anchor dialog. Define a
rigid anchor at point 1. (An anchor may be defined at point 1
without moving to it. While in the Anchor dialog, enter 1 in the
"Point Name" field. This
now becomes the new current point and the anchor is placed at
this point.)
6. Move the crosshairs to Point 6 and insert a second anchor at
that location (repeat Step 5).
7. Make A02 the current point.
8. Connect the piping system to the structural frame with a
two-point support. Select Insert/Support to open the Support
dialog. Select a Tie/link support type, then enter 3 in the
"Connected to" field. A support has
been used to connect A02 to point 3.
Note: In this case a large backward gap has been specified (the
forward direction of the support is
defined as from the pipe to the beam) in order to model the
ability of the pipe to rise off of the support.
In addition, a coefficient of friction has been specified, thus
friction force effects due to the downward
force of the pipe on the support are modeled. In order to
include (nonlinear) support gap and friction
effects in an analysis, enable the "Gaps/Friction/Soil" option
located on the Static Load Cases dialog.
9. Repeat Step 8 for B02 (add a tie/link support between B02 and
point 4).
Two point V-stops or Guides could also have been used in place
of the tie/links specified in Model 1. V-
Beam
Point
Global Coordinate
X Y Z
1 0 0 0
2 0 11 0
3 5 11 0
4 7 11 0
5 12 11 0
6 12 0 0
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stops are commonly used in situations similar to this model
since the direction sense of the gaps is less
confusing than for ties.
Display of Model 1
Other methods for modeling pipe racks
Pipe Rack (Method 2) A pre-defined directional support at each
piping point can be connected to a single beam point. This model
takes
advantage of the fact that a V-stop always restricts the
movement of a point in the vertical direction irrespective of
the
location of the Connected to point. This simplifies the modeling
of the frame itself as definition of all connection points
are not necessary. However, all of the support reactions are
transferred to the one beam point rather than their actual
locations (directly beneath each piping point).
1. Define the pipe system and the first leg of the pipe rack by
repeating Steps 1 and 2 from Model 1 .
2. Define the remainder of the frame. Add a beam between each
beam point listed below (e.g. beam M2 spans from point 2 to 3, M3
spans from 3 to 4, etc.). Length units are feet.
3. Define an anchor at beam points 1 and 5.
4. Make A02 the current point.
5. Connect pipe segment A to the structural frame with a V-stop.
Select Insert/Support to open the Support dialog. Note that point 3
has been entered in the "Connected to" field. Also, a large gap
above pipe
has been specified to allow the pipe to lift off of the
support.
Beam
Point
Global Coordinate
X Y Z
1 0 0 0
2 0 11 0
3 6 11 0
4 12 11 0
5 12 0 0
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6. Connect pipe segment B to point 3 on the structural frame
with a V-stop by repeating Step 5 for B02.
Display of Model 2
Other methods for modeling pipe racks
Pipe Rack (Method 3) Each piping point is connected directly to
a corresponding beam point. This model represents a rigid
connection
between the pipe and beam member.
1. Define the pipe system by repeating Step 1 from Model 1.
2. Select Insert/Beam to open the Beam dialog. Define beam M1 as
the first frame leg (a column) from point 1 to point 2.
3. Define the remainder of the frame. Add a beam between each
point listed below (e.g. beam M2 spans from point 2 to A02, M3
spans from A02 to B02, etc.). Length units are feet.
Beam
Point
Global Coordinate
X Y Z
1 0 0 0
2 0 12 0
A02 5 12 0
B02 7 12 0
3 12 12 0
4 12 0 0
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4. Define an anchor at 1 and 4 by repeating Steps 4 and 5 from
Model 1 for each of these beam points.
Display of Model 3
Other methods for modeling pipe racks
Hangers Select from the following modeling examples:
Variable and Constant Force Hangers
Two-Point Hanger
Imposed Hanger Displacements
Multiple Hanger Arrangements
Variable and Constant Force Hangers A hanger is a device which
is used to suspend a section of pipe. The hanger is designed to
support the weight of the
piping system, and any vertical loads imposed on the hanger due
to the thermal displacement of the supported piping
point.
In AutoPIPE, spring and constant force hangers may be specified
as designed or undesigned. Typically, a hanger which
is present in an existing piping system is designed (where the
spring rate and the cold load, or pre-load, are known). If
the hanger is specified as undesigned, AutoPIPE will determine
the cold and hot loads, the spring rate, and then make a
selection from the specified hanger manufacturer's table when a
hanger run is performed. This is particularly useful if a
new hanger is to be added to a system.
Example
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Modeling Both a designed and an undesigned hanger will be
defined in this model, and then a hanger run will be performed.
Create a model with two operating load conditions and specify
the ambient temperature as 70F. It should be noted that
the hanger run will not alter a user-designed hanger. In other
words, AutoPIPE only selects springs for those hanger
supports which have been specified as undesigned by the user, or
those which were previously AutoPIPE-designed.
1. Build a system from A00 to A04 using an 8 inch standard
schedule pipe. Define T1 as 400F and T2 as 800F. The global
coordinat