CAESAR II Expansion Joints
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CH AP TER
5
ݸ¿°¬»® ë Û¨°¿²·±² Ö±·²¬ This chapter explains how ÝßÛÍßÎ ×× models various expansion joints.
ײ ̸· ݸ¿°¬»® Simple Bellows with Pressure Thrust ...................................................... 5-2 Tied Bellows - Simple vs. Complex Model............................................. 5-4 Tied Bellows Expansion Joint - Simple Model ....................................... 5-5 Tied Bellows Expansion Joint - Complex Model .................................... 5-7 Universal Expansion Joints - Simple Models .......................................... 5-9 Universal Joint Comp. Tie Rod ............................................................ 5-14 Universal Joint With Lateral Control Stops Comp. Tie Rod Model........ 5-15 Hinged Joint............................................................................................. 5-16 Slotted Hinge Joint - Simple Model ........................................................ 5-18 Slotted Hinge Joint - Comprehensive Model ........................................... 5-19 Slip Joint .................................................................................................. 5-20 Gimbal Joints ........................................................................................... 5-22 Dual Gimbal ............................................................................................ 5-23 Pressure-Balanced Tees and Elbows ....................................................... 5-25
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Í·³°´» Þ»´´±© ©·¬¸ Ю»«®» ̸®«¬ Bellows expansion joints can be modeled with either a zero or a finite length. When finite length bellows are used, either the bending or the transverse stiffness must be left blank. ÝßÛÍßÎ ×× will calculate the exact stiffness coefficient for the term left blank. For finite length expansion joints, the user is recommended to leave the Bending Stiffness field blank, and to enter the lateral stiffness given by the manufacturer into the Transverse Stiffness field on the expansion joint spreadsheet. The lateral stiffness may be computed from the axial stiffness (if not provided) from the equation:
KTR = (3/2) (KAX) (D/L) 2 If the bending stiffness is given, its value should be approximately (within 1%) equal to:
KBEND =(1/2) (KAX) (D2) ( /180) KAX - is the axial stiffness of the expansion joint D - is the effective diameter of the expansion joint L - is the flexible length of the joint. For zero length expansion joints:
KBEND = (1/8) (KAX) (D2) ( /180) When a zero length expansion joint is used, ÝßÛÍßÎ ×× will use either the preceding or the following element to determine the axial direction of the bellows stiffnesses. The preceding element is checked first. Bellows are very fragile under torsional loading. It is recommended that accurate torsional stiffnesses and allowable torsional rotations be obtained from the vendor. Systems using untied bellows should either be of very low pressure or adequately anchored to withstand the possibly large thrust loads developed due to the unrestrained bellows. Bellows and any other miscellaneous weights should be added to flanges on either side of the bellows (or can be added as concentrated forces). This is particularly true when the bellow is part of a hanger sizing weight calculation. A zero or blank Bellows ID results in a zero pressure thrust. The Bellows ID is the diameter used to find the area for pressure thrust calculations. The total thrust load is applied at the From and To ends of the bellows, and is used to open the bellows (providing the pressure is positive). The magnitude of the thrust load is P * A, where P is the pressure in the pipe above atmospheric, and A is the area, found from
A = /4 * (Bellows ID) 2 Many manufacturers specify the effective area of the bellows. The Bellows ID for ÝßÛÍßÎ ×× input may be calculated by using the following equation:
Bellows ID =
4 Effective Area [
In the system shown below, the untied bellows runs between the nodes 8 and 9. The elbow at 11 is anchored to take the thrust load developed in the bellows. The manufacturer's specification for the joint's axial stiffness is 6530 lb./in. with a transverse stiffness of 3250 lb./in. The bending stiffness is left blank, and will be calculated by ÝßÛÍßÎ ×× since the bellows has a finite length. The pump and the baseplate at 5 must be able to withstand the large axial force that may develop due to pressure thrust in the bellows.
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Aeff= 67.5 in2 P= 175 psi Thrust = 67.5(175)=11812 lb. (automatically applied by ÝßÛÍßÎ ××)
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Ì·»¼ Þ»´´±© ó Í·³°´» ªò ݱ³°´»¨ Ó±¼»´ Complex models of expansion joints are much more difficult to build than simple models. Unfortunately there are no hard and fast rules for when to use simple models and when to use complex models. The following guidelines are presented to aid the engineer in making this decision. Complex models are used whenever a failure is being investigated. Complex models are normally used when the pipe diameter and number of convolutions become large. Complex models are used when nuts are only on the outside of the flange, allowing the tie bars to only carry tension. Complex models give good values for the load distribution in the tie bars. Simple models give no indication of the load distribution. In some cases, where the tie bars combine to resist relative bending of the joint ends, one pair of tie-bars can be in compression while the other pair is in tension. This effective redistribution of load in the tie bars will never be observed in a simple model. When this does occur, and if the tie bars are very long, buckling of the rods in the complex model should be investigated (evaluate whether the rods can withstand the compressive forces reported in the output report). The single tied bellows is designed to absorb movement by lateral deflection only. There is no axial deflection or relative bending rotations at the joint ends. Simple models should only be used where the tie bars are either guaranteed to be carrying tension, or have nuts on either side of the flange and so will carry compression if needed. Be sure to enter the lateral instead of the bending spring rate from the manufacturers catalog. See the previous discussion for a simple bellows for more information about bellows stiffnesses. The weights of the bellows and associated hardware should be added to the flange weights on either side of the bellows. This is particularly true if the expansion joint is between a hanger to be sized and an anchor. The expansion joint user should be sure to check the displacement limits for the expansion joint once the protected equipment loads are within the allowables. ÝßÛÍßÎ ×× has a processor called EJMA Expansion Joint Rating accessible through the Analysis option of the Main Menu, which helps the user to compute relative bellows movements for evaluating the bellows distortion. Simple models of single tied bellows are built by entering a large axial stiffness. This axial stiffness simulates the tie bars, preventing relative axial movement of the bellows. Tie rods may also be modeled with a single rigid element along the centerline of the bellows, with zero weight and rotational restraints, prevents the ends of the joint from rotating relative to one another. In reality the tie bars being offset from the centerline prevent this rotation. The complex models are built by running pipe elements whose diameter is equal to the diameter of the tie-bars, and whose wall thickness is equal to half of the tie-bar diameter, between rigid elements that extend normal to the pipe axis and from the centerline and to their intersection with the tie-bar centerline (See the following illustration). Some manufacturers feel that friction at the tie bar ends, plus other effects serve to limit the overall lateral flexibility of this joint. For lack of a better value, a 30% increase in lateral stiffness is sometimes used to compensate for these frictional effects. Field situations such as loose nuts on tie-bars, etc. can be modeled using the complex expansion joint model.
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Ì·»¼ Þ»´´±© Û¨°¿²·±² Ö±·²¬ ó Í·³°´» Ó±¼»´ Compute the lateral stiffness for the bellows. The flexible length of the bellows is not listed in most expansion joint catalogs. The listed lengths include the rigid end pieces such as flanges or pipe ends. Since the transverse stiffness is based on the flexible length, the flexible length must be known. A very simple way of pulling this value from the catalog is to examine the incremental increase in overall length of the joint as additional convolutions are added. With all convolutions the same length, this incremental length can be used to calculate the total flexible length. In this example the total length of a 4 convolution joint is 8 in. and the total length of an 8 convolution joint is 12 in. This means that the extra four convolutions add 4 in., so the length of all twelve convolutions is 12 in. (This also indicates that the rigid end pieces on this joint of 4, 8, or 12 convolutions is 4 in.) Deff=
(4Aeff/ ) 1/2 = 10.0 in.
KTR =
(3/2) (KAX) (Deff/L)2
L
Flexible Convolution Length = 12 in.
=
KTR = =
(3/2) (850) (10.0/12.0)2 885.4 lb./in.
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Zero-weight rigid element (tie rod)
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Build the ÝßÛÍßÎ ×× model of the flexible portion of the expansion joint. Note how the rotational restraints between nodes 29 and 30 keep the two flanges parallel. In the field, the tie bars at four points around the expansion joint will keep the flanges parallel. (The flanges and the tie bars form a parallelogram upon lateral deflection.)
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Ì·»¼ Þ»´´±© Û¨°¿²·±² Ö±·²¬ ó ݱ³°´»¨ Ó±¼»´ In the system shown below the flexible joint is between the nodes 30 and 35. The flanged ends of the joint are modeled as the rigid elements 20 to 30 and 35 to 45. Additional rigid elements, perpendicular to the pipe axis, extend from each flange. The tie bars are 1-in. in diameter. The following nodal layout and input is used to build a comprehensive model of the tied bellows.
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Weightless rigid elements extend from the flange centerline to the outside edge of the flanges where the tie rods are attached. Only 2 of eight element inputs shown.
Tie Rod will usually be at ambient temperature.
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˲·ª»®¿´ Û¨°¿²·±² Ö±·²¬ ó Í·³°´» Ó±¼»´ Please refer to the previous models of bellows expansion joints for specific notes relating to individual bellows designs, and to some comparisons of simple and complex expansion joint input. The tied universal bellows is designed to absorb movement by lateral deflection only. There is no axial deflection or relative bending rotations at the joint ends. Lateral instead of the bending spring rates from the manufacturers catalog should be entered. See the simple bellows discussion for more information about bellows stiffnesses. Manufacturers publish a wide variety of data for universal expansion joints. In most cases the published spring rates are for the universal joint as a whole assembly. When the lateral stiffness is given for the whole assembly the simple or complex models of single bellows can be used. In this case the manufacturer must also provide a cumulative assembly displacement limit so that the piping designer can verify that neither of the bellows are over-extended. Many universal expansion joint assemblies have stops along the tie-bars that are connected to the center spool-piece. These stops are designed to prevent over-extension of the bellows and can be modeled in the complex universal joint model. For the simple universal joint models, the user must check the results to verify that the stops are not engaged. Stops should typically be considered a safety feature, and should not be included as a working part of the design, unless particular attention is paid to the design surrounding the stop components. The expansion joint user should be sure to check the displacement limits for each of the expansion joints once the protected equipment loads are within the allowables. ÝßÛÍßÎ ×× has a program called Expansion Joint Rating - EJMA, which helps the user compute relative bellows movements for evaluating the convolutions strength. This program only works on single bellows, however, and so the user would need to model and then check each bellows in the universal assembly. Some manufacturers feel that friction at the tie bar ends, plus other effects serve to limit the overall lateral flexibility of this joint. For lack of a better value, a 10% increase in overall lateral stiffness is sometimes used to compensate for these frictional effects. The complex models are built by running pipe elements, whose diameter is equal to the diameter of the tie-bars, and whose wall thickness is equal to half of the tie-bar diameter, between rigid elements that extend normal to the pipe axis and from the centerline and to their intersection with the tie-bar centerline. The weights of the bellows and associated hardware should be added to the flange weights on either side of the bellows. This is particularly true if the expansion joint is between a hanger to be sized and an anchor. In-situ field effects like loose nuts on tie-bars, etc., can be modeled using the complex expansion joint model. Descriptions of various universal models display in the following figures. The two models shown also have example inputs given. Simple models should only be used when the user knows that both ends of the tie-bars will be fixed to the flanges, i.e. when there are nuts on both sides of the flange. (The top drawing shows nuts on only one side of the flange at the left end. This configuration should be modeled with a complex joint model unless the user is sure that all tie-bars will remain in tension.) The top model is used when the analyst is provided with global assembly data for the universal, i.e. the assembly lateral stiffness. The second model is used when the analyst is given angular spring rates for each of the two bellows used in the model.
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When provided individual bellows angular stiffness:
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Note: This model does not show the addition of any extra hardware or bellows weights which could affect load distribution and spring hanger design in the area.
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When provided individual bellows angular stiffness:
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Note: The rigid tie bar(s) should be modeled at the ambient temperature
Note: Pressure thrust is contained by double-nutted tie rods. Effective ID and axial restraints can be eliminated.
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Note: This model does not show the addition of any extra hardware or bellows weights, which could affect weight load distribution and spring hanger design in the area.
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˲·ª»®¿´ Ö±·²¬ ó ݱ³°®»¸»²·ª» Ì·» α¼ The comprehensive universal joint model involves defining, as accurately as possible; all tie rods and connections between tie rods and end plates.
The following groups illustrate the method used in constructing the universal expansion joint model shown above. Rigid Elements (Flanges) 15-17 / 31-33 Rigid Elements normal to the pipe axis and between the pipe and tie bar centerlines. At the end where there are nuts on either side of the flange, fixing the tie-bar to the flange: 33-1033 / 33-2033 / 33-3033 Rigid Elements normal to the pipe axis, and between the pipe and tie-bar centerlines. At the end where there are nuts only on the backside of the flange: 15-1015 / 15-2015 / 15-3015 Intermediate lateral tee supports (Rigid) 23-1023 / 23-2023 / 23-3023 25-1025 / 25-2025 / 25-3025 Tie-bars 1033-1034-1035-1036 2033-2034-2035-2036 3033-3034-3035-3036 Restraints with connecting nodes at the tension-only flange end. RESTR NODE = 1036 CNODE = 1015 TYPE = -X , Y , Z RESTR NODE = 2036 CNODE = 2015 TYPE = -X , Y , Z RESTR NODE = 3036 CNODE = 3015 TYPE = -X , Y , Z Restraints with connecting nodes at the intermediate support points. RESTR NODE = 1035 CNODE = 1023 TYPE = Y , Z RESTR NODE = 2035 CNODE = 2023 TYPE = Y , Z RESTR NODE = 3035 CNODE = 3023 TYPE = Y , Z RESTR NODE = 1034 CNODE = 1025 TYPE = Y , Z RESTR NODE = 2034 CNODE = 2025 TYPE = Y , Z RESTR NODE = 3034 CNODE = 3025 TYPE = Y , Z
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˲·ª»®¿´ Ö±·²¬ É·¬¸ Ô¿¬»®¿´ ݱ²¬®±´ ͬ±° ó ݱ³°®»¸»²·ª» Ì·» α¼ Ó±¼»´ Double-acting restraints with connecting nodes and gaps are used to model stop gaps along the tie bars. Stops along the tiebars are installed to restrict lateral motion at each end of the universal joint.
The following groups illustrate the method used in constructing the universal joint with lateral stops shown above. Only the right side tie rod elements are shown below. Standard pipe elements 34-36 / 36-38 Rigid flange elements 30-32 / 40-42 Bellows elements 32-34 / 38-40 Rigid elements from the pipe to the tie-bar centerline (Normal to the pipe axis) 30-1030 / 36-1036 / 42-1042 Tie-bar elements 1003-1002 / 1002-1001 Restraints with connecting nodes RESTR NODE=1001 CNODE = 1042 TYPE = +Y , X , Z RESTR NODE=1002 CNODE = 1036 TYPE = Y w/gap=1.5 , X , Z
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Ø·²¹»¼ Ö±·²¬ The hinged joint is defined using a zero length expansion joint with axial, transverse, and torsional stiffnesses rigid. The bending stiffness is set equal to the bending stiffness of the hinge. Hinge directions are defined using restraints and connecting nodes. The restraint line of action is always normal to the hinge axis. Hinged joints are designed to take pressure thrust. The analyst should make sure that the joint manufacturer is aware of the design loads in the hinges. Some expansion joint manufacturers believe that the hinge friction can provide considerable additional resistance to bending. Certainly as the axial load the hinge is to carry becomes large, this hinge friction effect will increase. Approximations to this increase in bending stiffness can be made by increasing the stiffness of the bellows in proportion to the axial load on the hinge. The expansion joint manufacturer can hopefully provide assistance here. Several typical geometries for hinged expansion joints are shown in the figures below:
In the example that follows, the hinged joint is zero length and is defined between nodes 45 and 46. X is the hinge axis, i.e. all relative rotations are permitted between 45 and 46 about the X axis. 45 and 46 are fixed rotationally relative to each other in the Y axis. (See the second note above.)
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The following figures display the coding of the hinged joint for the model shown on the bottom of the previous page.
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Í´±¬¬»¼ Ø·²¹» Ö±·²¬ ó Í·³°´» Ó±¼»´ The hinged joint is defined using a zero length expansion joint and rigid elements with zero weight to define the interaction of the hinge geometry. Hinge directions are defined using restraints with connecting nodes. The restraint line of action is always normal to the hinge axis.
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Elements from 10 to 15 and from 16 to 20 are weightless 9 in. long rigids.
Note: In this model, the relative rotation at the hinge about the Y axis is assumed to be zero. The slots on either side will provide some limit to this Y rotation. In most applications of this type, the relative Y rotation is zero because the problem is kept planar using guides. A good first pass can be made using the model shown, then if the analysis shows that the RY restraint between nodes 15 and 16 is supporting load, a further refinement to the model can be made.
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Í´±¬¬»¼ Ø·²¹» Ö±·²¬ ó ݱ³°®»¸»²·ª» Ó±¼»´ This model is somewhat different from the previous model because of the need to provide for the non-hinge axis rotation due to the slots on either side of the joint. The schematic below illustrates the extra input required to incorporate this effect.
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Zero weight rigid elements defining the hinge assembly are listed below: 10 10 55 55 15 35 50 30
-
15 35 30 50 20 40 45 25
Normal to pipe axis to centerline of hinge assy. " " " Parallel to pipe axis to centerline of hinge axis. " " "
The finite length bellows must be defined accurately between nodes 10 and 55. This typically means entering the correct flexible length and using the manufacturers axial and lateral spring rates. Remember that manufacturers angular spring rates should not be used in finite length expansion joint models.
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Í´·° Ö±·²¬ Large slip joints are usually difficult to install and difficult to accurately model. Smaller diameter slip joints are telescoping, axial displacement devices that permit considerable axial displacement of the slip joint ends and moderately rigid resistance to pipe bending. Smaller slip joints are usually categorized by having two annular packing glands separated axially along the joint by a dead air space, or by a small bellows sleeve. The following figure shows the cross-section of a typical large slip joint. The stiffnesses between nodes 15 and 25 are a function of the packing stiffness for transverse and rotational relative deformation and of packing stiffness and tightening for axial relative deformation.
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Ò±¬» ïæ Typical delta dimensions are: 5 - 10 The distance from the closest guide or support to the end of the joint. (The same values would also be used for 25 - 30.) 10 - 15 The effective length of the joint if known, or the travel expected plus 4", or a 12" estimate if nothing else is known. Ò±¬» îæ
K1 is the spring stiffness for forces below the yield force, FY.
Ò±¬» íæ K2 is the spring stiffness (for joint compression) for forces greater than FY. The best estimate for this resistance is cumulative friction effects of guides and supports, given by the vendor. K2 =((100)N/(a)
(Approximation)
Where (N) is the nominal pipe diameter in inches, and (a) is the thermal expansion at the operating temperature in inches per 100 ft. Ò±¬» ìæ Fy is the joint friction thrust from the vendor catalog. Typical values are given as 400 lbs times the nominal pipe size.
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Ù·³¾¿´ Ö±·²¬ Gimballed joints are designed to resist pressure thrust. The analyst should make sure that the joint manufacturer is aware of the design loads on the gimbals. The angular-only gimbal can be input as a zero length expansion joint with rigid axial, transverse, and torsional stiffnesses. The bending stiffness is set equal to the rotational stiffness specified in the manufacturer's catalog. Angular and Offset gimbals should probably be thoroughly modeled as shown in the following figures. Angular and Offset gimballed joints are usually installed in large diameter lines where lumped property assumptions for the bellows may not be within reasonable engineering accuracy.
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Rigid elements between nodes 105 and 110 and nodes 111 and 115 each contain half the weight of the hinge mechanism.
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Ü«¿´ Ù·³¾¿´ Dual gimbal joints are two, usually angular-only, gimballed joints in series in the pipeline. Putting two (or three) angularonly gimballed joints together provides for an ability to absorb lateral and possibly axial deformation. A Pipe Flexibility program will never be able to model the axial-only component of the possible deformation because it requires large rotation of the expansion joint componentssomething not considered in such programs. The single angular deformation only gimbal should always be used in series with at least one other gimballed joint. It is only in series that the angular deformation only gimbal provides for any lateral movement. Gimballed joints are designed to take pressure thrust. Analysts should verify that the joint manufacturer is aware of the design loads on the gimbal. Each individual angular-only gimbal joint should be modeled as a zero length expansion joint with rigid axial, transverse, and torsional stiffnesses. The bending stiffness should be equal to the manufacturer's published rotational stiffness term. The minimum required distance L between adjacent single gimballed joints (shown as 8-7 in the following example), is principally a function of the angular and rotational deformation to be absorbed, the diameter, and the number of convolutions per joint. The following figure shows a dual gimbal comprised of two angular-only gimbals. The bending stiffness for each gimballed joint is 490.0 in. lb./deg.
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Note: Both expansion joints use the same stiffness values, so it is only shown once here.
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Ю»«®»óÞ¿´¿²½»¼ Ì»» ¿²¼ Û´¾±© Pressure balanced tees and elbows are used primarily to absorb axial displacements at a change in direction, without any associated pressure thrust. Pressure balanced tees can also be used in universal type configurations to absorb axial and lateral movement.
The example below shows briefly the coding of a pressure-balanced tee in a turbine exhaust line. The bottom side of the tee is blanked off. The tee is a standard unreinforced fabricated tee. The tie bars will only act in tension.
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