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    Angular Expansion Joints

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    Table ofcontents

    General information Angular expansion joints 1 Anchors, pipe supports / guides,

    sleeves 2

    Expansion joint systems 3

    Calculations 5

    Program summary 19

    Pipe supports and guides 21

    Anchors,start-up of plant,operating pressure,prestressing 22

    Pre-stressing diagram 23

    Recommendations 24

    Expansion joint data sheet 25

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    Generalinformation

    1

    Angular expansion joints are suited for thecompensation of both long pipe sections ofdistrict heating systems as well as shortboiler and turbine room pipelines in one or

    more planes. For installations with very lim-ited space one should also check the possi-bility of the installation of tied universal orpressure balanced expansion joints. Con-trary to axial and universal expansion jointsthat are suited to compensate for move-ments independently, angular expansionjoints are only elements of an expansionsystem. A minimum of two and a maximumof three angular expansion joints form astatic defined system. The function depends

    on the ability of the bellows to rotate andthe amount of rotation is stated in the tech-nical data sheets as permissible angularrotation.

    Angular expansion joints are usuallyinstalled with 50% pre-stressing. This isaccomplished by pre-stressing the entireexpansion system after its completion. Thepre-stressing amount can be determinedfrom the pre-stressing graph in the sectionassembly instructions taking into accountthe installation temperature.

    The longer the distance L1 between twoangular expansion joints (Fig. 1) is, thelarger the movement that can be compen-sated for by the expansion system and thesmaller the displacement forces become.The longitudinal reaction forces thatorginate from the inner pressure are trans-mitted through the hinges.

    The center of rotation of the hinges lies onthe same axis as the center of the bellows.(Fig. 1)Gimbal expansion joints utilize a round orsquare gimbal joint to restrain the reactionforces. This results in three dimensionalrotations around the axes x and z (Fig. 2).

    Angular expansionjoints

    Fig. 1

    Fig. 2

    L1

    /2 /2

    Z

    X

    Y

    2

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    Angular expansion joints make no specialdemands on pipe supports or guides incontrast to axial expansion joints. Evenswing hangers can be sufficient.

    Additional supports are unnecessary forshort turbine house pipelines. The weightof the pipe sections between the angularexpansion joints must be supported by sup-ports or hangers which must not hinder themovements of the angular expansion joints.Pipe guides placed before and after eachexpansion system are necessary in longpipelines. Pipe guides which have been fit-ted too tightly may become jammed. Theycould then loosen in short bursts whichcould result in severe additional forces.Hinged expansion joints in a two pin Zexpansion system follow an arc due to their

    angular rotation (Fig. 3).

    The pipeline guides should comply with the

    following requirements:1. Support the weight of the pipeline and

    the expansion joints.2. Guide the expanding pipeline in its longi-

    tudinal axis.3. Provide sufficient clearance [s] to assurethat movements of the pipe that are notcompensated for by expansion joints andthat result from the thermal expansionL and the height of the arc [h] can becompensated for by the continuingpipeline without causing the guide tojam.

    Generalinformation

    2

    Anchors,pipe supports / guides

    S h + L

    s

    L+L+h

    h

    Fig. 3

    Sleeves We recommend the installation of expansi-on joints with sleeves if high-frequencyoscillations or turbulences are to be expec-ted in the medium, or if the medium has ahigh flow velocity.

    The diagram Guidelines for use of sleevesshows the limit curves for steam, gas, andliquids, above which the use of sleeves isabsolutely recommended.

    The sleeves serve to protect the bellowsand reduce its tendency towards oscillationinduced by the flow, and to also reducedeposits and wear.

    50 100 150 200 3000

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    Nominal diameter DN

    Flow

    velocity

    v

    [m/s]

    250

    Liquid

    Steam / gas

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    Generalinformation

    3

    Expansion jointsystems

    The following expansion joint arrangementsare most common in the planning of angu-lar expansion systems:

    Two pin Z-systemfor pipelines of any length under utilizationof a given route.

    Three pin L-systemsuited for the compensation of transferpipelines between two tanks for example.

    Two pin gimbal systemfor the compensation of perpendicularmovements in short pipeline sections.

    Three pin U-systempreferably for the compensation of longpipelines.

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    Generalinformation

    4

    Expansion jointsystems

    Three pin W-systemfor the compensation of longest and short-est pipelines with concurrent movementsfrom two directions.

    Three pin Z-systemfor the compensation of pipelines underutilization of given pipeline routings includ-ing the compensation of the verticalpipeline section.

    Three pin gimbal W-systemfor the compensation of three dimensionalsystems, for example boiler and turbinehouse pipelines.

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    e3 stretche

    d

    positi

    on

    21

    e1

    22

    B1

    B2

    L3

    L2

    L01

    22

    L1

    L02

    B3

    21

    Calculations

    5

    In the following example, the three pin W-system is used to explain the basic proce-dure for the design of expansion systems.First of all, one has to choose a suitable

    expansion system under consideration ofthe given routing and the anticipatedexpansion of the pipeline. Note that bothends of the line must be limited by pipeanchors.For our example, we assume an L-shapedpipe routing of which the thermal expansion1 and 2 from the pipe sections L01 and L02will be optimally compensated for by a sys-tem of three hinged expansion joints in thethree pin W arrangement.

    neutral position(without pre-stressing)

    Initially, one must determine the thermalexpansion 1 and 2 under consideration ofthe maximum temperature difference of thepipeline (refer to Expansion Joints sectionbasic principals).Then, one must calculate the expansionsystem. Two options are available:1.) Choose the geometry of the system (thedistances L1, L2 and L3) and calculate theeffective angular rotation e of eachhinged joint by using the given formulae(see the following pages).Next, from the data sheets, select hingedexpansion joints that are suited for theoperating conditions (DN, PN) and thathave a permissible angular rotation zulthat is equal to or greater than the effectiverotation e.

    2.) Choose suitable hinged expansionjoints and then calculate the required dis-tances L1 and L3.If the operating conditions exceed the nom-inal conditions, one must ensure that thenominal angular rotations as per thedata sheets are converted to permissiblevalues following the rules given in the sec-tion basic principals, nominal conditions.

    In order to get small angles of rotation forthe expansion joints, the distancesbetween the pins of the joints L1 and L3should be as long as reasonably possibleand the distance L2 as short as possible.

    installed positions(50% pre-stressed)

    The calculation formulae for the determin-ation of the angular rotation of three pinsystems are approximates with sufficientaccuracy for practical use. A more accurate

    calculation of the angular rotations be-comes necessary for very straight systemsif the center joint moves too close to thestretched out position when the system ispre-stressed.Consult us in such cases. In order toachieve optimum utilization of the permissi-ble angular rotation zul of hinged expan-sion joints, a 50% pre-stressing of the sys-tem is required (see fig).If pre-stressing is not possible, the angularrotation to one side of the centerline doub-les. This normally requires an angularexpansion joint with a larger nominal angu-

    lar rotation.Anchor and nozzle loads can be determ-ined by using the formulae for the calcula-tion of the displacement forces F and bend-ing moments M.

    operating position

    e zul

    zul = K(tB) KLExpansion systemsgeneral information

    2e1

    e3

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    Calculations

    6

    Two pin Z-system2 Z

    Two pin S-system2 S

    System calculation Required hinge distanceUnder consideration of the permissibleangular rotation [zul] and a 50% pre-stressing, the minimum required distancebetween the hinges L1 is:

    Resulting arc heightAt the maximum effective angular rotation(e) the vertical distance between thehinges is reduced by the dimension h dueto the circular motion of the expansionjoints.

    The height of the arc and the thermal

    expansion of the pipe section L1 must becompensated for by the pipe section (2.5 L1) or a sufficient clearance in the pipeguide must be available.

    L1 =

    [mm]2 sinzul

    Effective angular rotationIf the pin distance L1 ist given, the effectiveangular rotation of the angular expansionjoints (B) is calculated as follows if the sys-tem is pre-stressed at 50%:

    At 100 % and at 0% pre-stressing, theangle of rotation of the angular expansionjoints doubles, but in one direction only. Theeffective angle of rotation [e] must be mul-tiplied by 2 in this case.

    h = L1 (1 cose) [mm]

    = anchor= pipe support / guide

    FX

    L1h

    b B

    aB

    My2

    My1

    2.DN+2

    L0

    2

    pre-stressing gap

    z

    y

    x

    -FX

    2,5.L1

    FX

    L1

    h

    B

    B

    2,5.L1

    2.DN+2

    L0

    2

    pre-stressing gap

    z

    y

    x

    -FX

    e = arcsin( ) [degr.]2 L1

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    Calculations

    7

    Anchor / connectionpoint forces

    Bending moments of angular expansionjointsIn order to calculate the bending momentsand forces, the absolute values of the effec-

    tive angular rotations (without signs) mustbe used in the following equation.

    If the system ist pre-stressed at 50%, themoments and forces have different signs inthe pre-stressed position and operatingposition of the system.Forces at the connection points

    Bending moments at the connection points

    MB = Cr p + C e + Cz p e [Nm]

    Fx =2000 MB [N]

    L1

    My1 = MB + Fx a

    [Nm]1000

    My2 = MB + Fx b

    [Nm]1000

    a, b Center to center distance betweenbellows and connection point [mm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction[Nm/bar]

    Cz Additional moment from rotationand pressure [Nm/(bar degr.)]

    Fx Displacement force in x-direction [N]

    h Height of arc [mm]

    L1 Center to center distance betweenthe bellows [mm]

    My 1, 2 Bending moment at theconnection point [Nm]

    MB Bending moment of theexpansion joint [Nm]

    p Operating pressure [bar]

    e Effective angular rotation of oneexpansion joint [degr.]

    zul Permissible angular rotation ofone expansion joint [degr.]

    Movement of the pipeline [mm]

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    Calculations

    8

    Resulting expansion

    Required hinge distanceUnder consideration of the permissibleangular rotation [zul] and 50% pre-stress-ing, the minimum required distancebetween the hinges L1 is:

    Effective angular rotationIf the pin distance L1 is given, the effectiveangular rotation of the angular expansionjoints (B) is calculated as follows if the sys-

    tem is pre-stressed at 50%:

    At 100% and at 0% pre-stressing, the

    angles of rotation of the angular expansionjoints doubles, but in one direction only. Theeffective angles of rotation [e, ex, ey]must be multiplied by 2 in this case.

    Resulting arc heightAt the maximum effective angular rotation(e) the vertical distance between thehinges is reduced by the dimension h dueto the circular motion of the expansionjoints:

    The height of the arc and the thermal

    expansion of the pipe section L1 must becompensated for by the pipe section (2.5 L1) or a sufficient clearance in the pipeguide must be available.

    = 12 + 22 [mm]

    h = L1 (1-cose) [mm]

    L1 = [mm]

    2 sinzul

    Two pingimbal-system

    2 K

    System calculation

    = anchor= pipe support/guide

    e = arcsin( ) [degr.]2 L1

    ey = arcsin( 1 ) [degr.]2 L1

    ex = arcsin( 2 ) [degr.]2 L1

    L1B

    2,5.L1

    pre-stressinggap

    z

    y

    x

    B

    1 -F

    X

    2.DN

    + 12

    LO1

    a

    b

    Mx1My1

    Mx2My2

    LO2

    2

    Fy

    -Fy

    FX

    pre-st

    ressin

    ggap

    2

    2

    1

    2

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    Calculations

    9

    Anchor / connectionpoint forces

    Bending moments of angular expansionjointsIn order to calculate the bending momentsand forces, the absolute values of the effec-

    tive angular rotations (without signs) areused in the following formulae:

    If the system ist pre-stressed at 50%, themoments and forces have different signs in

    the pre-stressed position and operatingposition of the system.

    Forces at the connection points

    Bending moments at the connection points

    MBy = Cr p + C ey + Cz p ey [Nm]

    MBx = Cr p + C ex + Cz p ex [Nm]

    Fx = 2000 MBy [N]

    L1

    Fy =2000 MBx [N]

    L1

    My1 = MBy + Fx a

    [Nm]1000

    Mx1 = MBx + Fy a

    [Nm]1000

    My2 = MBy + Fx b

    [Nm]1000

    Mx2 = MBx + Fy b

    [Nm]1000

    a, b Center to center distance betweenbellows and connection point [mm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction [Nm/bar]

    Cz Additional moment from rotationand pressure [Nm/(bar degr.)]

    Fx, y Displacement force in x and y-direction [N]

    h Height of arc [mm]

    L1 Center to center distance betweenthe bellows [mm]

    Mx,y1,2 Bending moment at theconnection point [Nm]

    MBx, y Bending moment of theexpansion joint [Nm]

    p Operating pressure [bar]

    ey, x Effective angular rotation of oneexpansion joint [degr.]

    zul Permissible angular rotation ofone expansion joint [degr.]

    1, 2 Movement of the pipeline [mm]

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    Calculations

    10

    Three pin U-system3 U

    System calculation Required hinge distanceIf the permissible angular rotation [zul] ofall three expansion joints is the same andthe system is pre-stressed at 50%, then theminimum distance between the hinges isdetermined as follows L1:

    L1 =

    [mm]2 sinzul.

    Effective angular rotationIf the pin distance L1 is given, the effectiveangular rotation of the angular expansionjoints (B1, B2) is calculated as follows if thesystem is pre-stressed at 50%:

    At 100% and at 0% pre-stressing, the angleof rotation of the angular expansion jointsdoubles, but in one direction only. In thiscase, the effective angular rotation [e]must be multiplied by 2.

    e1 = arcsin ( )[degr.]2 L1

    e2 = e1 [degr.]2

    Bending moments of angular expansionjointsIn order to calculate the bending momentsand forces, the absolute values of the effec-tive angular rotations (without signs) mustbe used in the following equations:

    If the system is pre-stressed at 50%, theforce and the moment will have differentsigns in the pre-stressed position and oper-ating position.

    Forces at the connection points

    Bending moment at the connection points

    MB1 = Cr p + C e1 + Cz p e1 [Nm]

    MB2 = Cr p + C e2 + Cz p e2 [Nm]

    Fx =1000(MB1+ MB2) [N]

    L1

    My2 = MB2 [Nm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction [Nm/bar]

    Cz Additional moment from rotationand pressure [Nm/(bar degr.)]

    Fx Displacement force in x-direction [N]

    L1 Center to center distance betweenbellows [mm]

    My2 Bending moment at the connectionpoint [Nm]

    MB1, 2 Bending moment ot theexpansion joint [Nm]

    p Operating pressure [bar]

    e1, 2 Effective angular rotation perbellows [degr.]

    zul Permissible angular rotation perbellows [degr.]

    Movement of the pipeline [mm]

    = pipe guide

    L2 should be chosen as short as possible.

    +FX

    L2

    B1

    B2

    2.DN+2

    L 0

    2

    pre-stressing gap

    z

    y

    x

    -FXMy2

    B2

    My2

    L1

    = anchor

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    Calculations

    11

    Required hinge distancesIf the permissible angular rotation [zul] ofall three expansion joints is the same andthe system is pre-stressed at 50%, then theminimum distances L1 and L3 between thehinges are determined as follows:

    L1 = 1 (L2 + L3) [mm]2sinzul L3 - 2

    Effective angular rotationIf the pin distances L1 and L3 are given, theeffective angular rotation of the angularexpansion joints (B1, B2, B3) is calculatedas follows if the system is pre-stressed at50%:

    At 100% and at 0% pre-stressing, the angleof rotation of the angular expansion jointsdoubles, but in one direction only. In thiscase, the effective angular rotation (e1,2,3)must be multipled by 2.

    If the result of L1 (or L3) is negative or thedistance is too long, then one mustincrease the distance L3 (or L1) accordinglyor one must choose expansion joints with alarger permissible angular rotation.

    e1 = arcsin( 1 ) [degr.]2 L1

    e2 = (e1 + e3) [degr.]

    e3 = arcsin (1 L2+2 L1) [degr.]2 L1 L3

    when L2 and L3 have been chosen and

    L3 = 1 L2 + 2 L1 [mm]2sinzul L1 - 1

    when L1 and L2 have been chosen.

    L1,3 Center to center distancebetween the bellows [mm]

    e1,2,3 Effective angular rotation perbellows [degr.]

    zul Permissible angular rotationper bellows [degr.]

    1,2 Movement of pipeline [mm]

    Three pin W system3 W

    System calculation

    = anchor= pipe guide

    In general, L1 and L3 should be as long asreasonably possible and L2 should be asshort as possible.

    L2 B1

    B2

    2.DN+ 22

    pre-stressing gap

    z

    y

    xB3

    L1

    22

    2.DN+ 12

    L3

    2

    L02

    12

    1

    L01

    pre-stressing gap

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    Calculations

    12

    Three pin W system3 W

    Anchor andconnection point

    loads

    In installations with short pipe sections forexample, between vessels, turbines andcondensers, that are typical in power sta-tions, the forces and moments of theexpansion system at the connection pointsare of importance.These forces and moments are the result ofthe bending moments of the angular expan-sion joints and the distance between thosejoints and the connection points.In order to proceed with the following calcu-

    lations the coordinates must be determinedunder consideration of the pipeline routing.

    The direction of the reaction forces at theconnection points of the system are deter-mined according to the direction of themovements (system in pre-stressed oroperating position). The common rules ofthe equilibrium of forces should be takeninto account.

    Bending moments of the angular expan-sion jointsIn order to calculate the bending momentsand forces, the absolute values of the effec-tive angular rotations (without signs) mustbe used in the following formulae.

    Forces at the connection points

    Bending moments at the connection pointsMB1 = Cr p + C e1 + Cz p e1 [Nm]

    MB2 = Cr p + C e2 + Cz p e2 [Nm]

    MB3 = Cr p + C e3 + Cz p e3 [Nm]

    Fz = 1000(MB2+ MB3) [N]L3

    M0 = MB2+ Fz L2 [N]

    1000

    Fx =1000(MB1+ M0) [N]

    L1

    My1 = - MB1 - Fx a

    [Nm]1000

    a, b Distance between the center ofthe bellows and the connectionpoint [mm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction [Nm/bar]

    Cz Additional moment from rotationand pressure [Nm/(bar degr.)]

    Fx,z Displacement force in x andz direction [N]

    L1,3 Center to center distance betweenthe bellows [mm]

    My1,2 Bending moments at theconnection points [Nm]

    MB1,2,3Bending moment of theexpansion joints [Nm]

    p Operating pressure [bar]

    e1,2,3 Effective angular rotation perbellows [degr.]

    Signs and directions refer to operating(hot) conditions of the system

    My2 = MB3 + Fz b

    [Nm]1000

    L2

    B1

    +z

    +y

    +x

    B2

    L 1

    B3

    d

    cc

    L3 b

    a

    +FX

    -F Z

    -F X

    +FZ

    -My1

    MB1

    Mo MB2

    MB3

    +My2

    If the system is pre-stressed at 50%, theforce and the moment will have differentsigns in the pre-stressed position andoperating position.

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    Calculations

    13

    The thermal expansion or movement of the

    connection points, for example in turbinenozzles, should be added to the thermalexpansion 1, 2 or 3, of the pipe section

    if both move in the same direction and

    should be subtracted if they move in oppo-site directions.

    Effective angular rotationsIf the pin distances L1 and L3 are given, theeffective angular rotation of the angularexpansion joints (B1, B2, B3) is calculatedas follows if the system is pre-stressed at50 %:

    e1 = arcsin( 1

    ) [degr.]2 L1

    e2x = e3x = arcsin ( 3 ) [degr.]2 L3

    e2 = (e2x2 + e2y2) [degr.]

    e3 = (e3x2

    + e3y2

    ) [degr.]

    e2y = (e1 + e3y) [degr.]

    e3y = arcsin(1 L2+2 L1) [degr.]2 L1 L3

    At 100% and at 0% pre-stressing, the angleof rotation of the angular expansion jointsdoubles, but in one direction only. In thiscase, the effective angular rotation[e1,2,3,x,y] must be multiplied by 2.

    Three pin gimbal Wsystem3 KW

    System calculation

    B1 = One single hinged expansion joint(angular rotation on one plane)One gimbal expansion joint each

    B2 and B3 = (angular rotation on any perpen-dicular plane)

    Choose L1 and L3 as long as reasonably possibleChoose L2 as short as possible

    {

    L3B2

    z

    y

    x

    2

    -FX

    b

    C

    3

    -Fy

    L2 L1

    a

    B1

    B3

    -FZ-My1

    Mz1

    -Mx1

    FXFy

    FZMy2

    -Mz2

    -Mx 2

    1

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    Calculations

    14

    Anchor andconnection point

    loads

    Bending moments of the angular expan-sion jointsIn order to calculate the bending momentsand forces, the absolute values of the effec-

    tive angular rotations (without signs) areused in the following formulae.

    MB1y = Cr p + C e1 + Cz p e1 [Nm]

    MB2y = Cr p + C e2y + Cz p e2y [Nm]

    MB3y = Cr p + C e3y + Cz p e3y [Nm]

    MB2x = Cr p + C e2x + Cz p e2x [Nm]

    MB3x = Cr p + C e3x + Cz p e3x [Nm]

    Forces at the connection points

    Fx =1000(MB2y+ MB3y) [N]

    L3

    Fy =1000(MB2x+ MB3x) [N]

    L3

    M0 = MB2y+ Fx L2 [N]

    1000

    Fz =1000(MB1y+ M0) [N]

    L1

    a,b Distance between the center ofthe bellows and the connectionpoint [mm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction [Nm/bar]

    Cz Additional moment from rotationand pressure = [Nm/(bar degr.)]

    Fx,y,z Displacement force in x, y and z

    direction [N]L1,3 Center to center distance

    between the bellows [mm]

    Mx,y,z,1,2 Bending moments at theconnection points [Nm]

    MBx,y1,2,3Bending moment of theexpansion joints [Nm]

    p Operating pressure [bar]

    ex,y;1,2,3 Effective angular rotation perbellows [degr.]

    zul Permissible angular rotation per

    bellows [degr.]1,2,3 Movement of pipeline [mm]

    Bending moments at the connection points

    My1 = - MB1y - Fz a

    [Nm]1000

    My2 = MB3y + Fx b

    [Nm]1000

    Mx1 = - MB2x - Fy L2 [Nm]

    1000

    Mz1 = Fy L1 + a

    [Nm]1000

    Mz2 = - Fx c

    [Nm]1000

    Mx2 = - MB3x - Fy b + Fz

    c[Nm]

    1000 1000

    If the system is pre-stressed at 50%, theforce and the moment will have differentsigns in the pre-stressed position and oper-ating position.

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    Calculations

    15

    Required hinge distancesIf the permissible angular rotation[zul] of allthree expansion joints is the same and thesystem is pre-stressed at 50%, then theminimum distances L1 and L3 between thehinges are determined as follows:

    L1 =1 (8 L2 + 1+4 L3) [mm]

    8sinzul L3 - 4 2

    L3 =1 (8 L2 + 1) +4 L1 2 [mm]

    8sinzul L1 - 4 1

    Effective angular rotationIf the pin distances L1 and L3 are given, theeffective angular rotation of the angularexpansion joints (B1, B2, B3) is calculatedas follows if the system is pre-stressed at50 %.

    At 100% and at 0% pre-stressing, the angleof rotation of the angular expansion jointsdoubles, but in one direction only. In thiscase, the effective angular rotation [e1,2,3]must be multiplied by 2.

    If the result of L1 (or L3) is negative or thedistance is too long, then one mustincrease the distance L3 (or L1) accordinglyor one must choose expansion joints with a

    larger permissible angular rotation.

    e1 = arcsin( 1 ) [degr.]2 L1

    e2 = (e1 + e3) [degr.]

    e3= arcsin(1(8 L2+1)+4L12)[degr.]8 L1 L3

    when L2 and L3 have been chosen, and

    when L1 and L2 have been chosen.

    Three pin Z-system3 Z

    System calculation

    = anchor

    = pipe guide

    In general L1 and L3 should be as long asreasonably possible while L2 should be asshort as possible.

    FX

    B1

    2.DN+12

    L0

    12

    pre-stressing gap

    z

    y

    x

    -FX

    -F Z

    L2a

    2

    My1

    L1

    L2B2

    L3 b

    1FZB3

    My2

    2.DN+ 1

    2

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    Calculations

    16

    Anchor andconnection point

    loads

    Bending moments of the angular expan-sion jointsIn order to calculate the bending momentsand forces, the absolute values of the effec-

    tive angular rotations (without signs) areused in the following formulae.

    MB1 = Cr p + C e1 + Cz p e1 [Nm]

    MB2 = Cr p + C e2 + Cz p e2 [Nm]

    MB3 = Cr p + C e3 + Cz p e3 [Nm]

    Forces at the connection points

    Fz =1000(MB2+ MB3) [N]

    L3

    Fx =1000(MB1+ MB2) + Fz 2 L2 [N]

    L1

    Bending moments at the connection points

    My1 = MB1 + Fz a

    [Nm]1000

    My2 = MB3 + Fz b

    [Nm]1000

    If the system is pre-stressed at 50%, theforce and the moment will have differentsigns in the pre-stressed position and oper-ating position.

    a,b Distance between the center of thebellows and the connection point[mm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction [Nm/bar]

    Cz Additional moment from rotationand pressure [Nm/(bar degr.)]

    Fx,z Displacement force in x and zdirection [N]

    L1,3 Center to center distance betweenthe bellows [mm]

    My1,2 Bending moments at theconnection points [Nm]

    MB1,2,3Bending moment of theexpansion joints [Nm]

    p Operating pressure [bar]

    e1,2,3 Effective angular rotation perbellows [degr.]

    zul Permissible angular rotation perbellows [degr.]

    1,2 Movement of pipeline [mm]

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    Calculations

    17

    Required hinge distancesIf the permissible angular rotation [zul] of

    all three expansion joints is the same andthe system is pre-stressed at 50%, then theminimum distances L1 and L3 between thehinges are determined as follows:

    L1 = 1 L3 [mm]

    2sinzul L3 - 2

    Effective angular rotationIf the pin distances L1 and L3 are given, the

    effective angular rotation of the angularexpansion joints (B1, B2, B3) is calculatedas follows if the system is pre-stressed at50%:

    At 100% and at 0% pre-stressing, the angleof rotation of the angular expansion jointsdoubles, but in one direction only. In thiscase, the effective angular rotation [e1,2,3]must be multiplied by 2.

    If the result of L1 (or L3) is negative or thedistance is too long, then one mustincrease the distance L3 (or L1) accordinglyor one must choose expansion joints with alarger permissible angular rotation.

    e1 = arcsin( 1 ) [degr.]2 L1

    e2 = (e1 + e3) [degr.]

    e3 = arcsin( 2 ) [degr.]

    2 L3

    when L3 has been chosen, and

    L3 = 2 L1 [mm]

    2sinzul L1 - 1

    when L1 has been chosen.

    Three pin L-system3 L

    System calculation

    = anchor= pipe guide

    In general, L1 and L3 should be as long asreasonably possible while L2 should be asshort as possible.

    FX

    B1

    22

    pre-stressing gap

    z

    y

    x

    -FXFZ

    2

    My1

    L1

    B2

    L3

    1FZ

    B3

    My2

    a

    L02

    b

    12

    pre-stressing gap

    L01

    2.DN+

    12

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    Calculations

    18

    Anchor andconnection point

    loads

    Bending moments of the angular expan-sion jointsIn order to calculate the bending momentsand forces, the absolute values of the effec-

    tive angular rotations (without signs) areused in the following formulae.

    MB1 = Cr p + C e1 + Cz p e1 [Nm]

    MB2 = Cr p + C e2 + Cz p e2 [Nm]

    MB3 = Cr p + C e3 + Cz p e3 [Nm]

    Forces at the connection points

    Fx =1000(MB2+ MB3) [N]

    L3

    Fz =1000(MB1+ MB2) [N]

    L1

    Bending moments at the connection points

    My1 = MB1 + Fx a

    [Nm]1000

    My2 = MB3 + Fx b

    [Nm]1000

    If the system is pre-stressed at 50%, theforce and the moment will have differentsigns in the pre-stressed position and oper-ating position.

    a,b Distance between the center of thebellows and the connection point[mm]

    C Bending spring rate [Nm/degr.]

    Cr Hinge friction [Nm/bar]

    Cz Additional moment from rotationand pressure [Nm/(bar degr.)]

    Fx,z Displacement force in x and zdirection [N]

    L1,3 Center to center distance betweenthe bellows [mm]

    My1,2 Bending moments at theconnection points [Nm]

    MB1,2,3Bending moment of theexpansion joints [Nm]

    p Operating pressure [bar]

    e1,2,3 Effective angular rotation perbellows [degr.]

    zul Permissible angular rotation perbellows [degr.]

    1,2 Movement of pipeline [mm]

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    19

    Single hinged expansion jointwith bellows of stainless steel 1.4541 (up toDN 50 1.4571).On both sides with weld ends of carbon

    steel, external restraints of carbon steel,suited for angular rotation around one axis.Type 7510 (previous: 307/250)DN ..... / PN ... / ang ..... / Bl .....

    Design of restraints varies with manufactur-ing program.

    Single hinged expansion jointwith bellows of stainless steel 1.4541 (up toDN 50 1.4571).On both sides with flanges of carbon steel,external restraints of carbon steel, suitedfor angular rotation around one axis.Type 7520 (previous: 307/251)DN ..... / PN ... / ang ..... / Bl .....

    Design of restraints varies with manufactur-ing program.

    Single hinged expansion jointwith bellows of stainless steel 1.4541, onboth sides with weld ends of carbon steel,external gear-restraints of carbon steel,suited for large angular rotation around oneaxis.Type 7510 BAS (previous: 307/250 Z)DN ..... / PN ... / ang ..... / Bl .....

    On both sides with flanges:Type 7520 BAS

    Angular expansionjoints for angularrotation aroundone axis

    Special design

    Program

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    20

    Program

    Gimbal expansion jointwith bellows of stainless steel 1.4541 (up toDN 50 1.4571).On both sides with weld ends of carbon

    steel, external gimbal restraints of carbonsteel, suited for perpendicular angular rota-tion.Type 7610 (previous: 307/260)DN ..... / PN ... / ang ..... / Bl .....

    Design of restraints varies with manufactur-ing program.

    Gimbal expansion jointswith bellows of stainless steel 1.4541 (up toDN 50 1.4571).On both sides with flanges of carbon steel,external gimbal restraints of carbon steel,suited for perpendicular angular rotation.Type 7620 (previous: 307/261)DN ..... / PN ... / ang ..... / Bl .....

    Design of restraints varies with manufactur-ing program

    (Angular) gimbalexpansion joints

    for perpendicularrotation

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    21

    Installationinstructions

    Angular expansion joints that allow anangular rotation on one plane only (singlehinged expansion joints) must be installedwith a correct orientation respect to the

    direction of the movement that will be com-pensated for. The movement must alwaysact perpendicular to the axis of the hingepins.

    In contrast to axial expansion joints, angu-lar expansion joints are less demandingwith regards to pipe guides and supports.

    They have to support the weight of thepipeline including the insulation and flow,wind and other external loads if applicable,in such a way that they relieve the expan-sion joints from those loads without hinder-ing their movement.

    In short pipe routings such as in compactpower house pipe systems, pipe supportsand guides may not be necessary at all.

    In long pipe lines, a pipe guide should beinstalled on each side of the expansion sys-tem.

    Pipe supports andguides

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    22

    Installationinstructions

    The permissible operating pressure resultsfrom the nominal pressure, taking into

    account the reduction factors according tothe technical data sheets.

    Angular expansion joints in expansion sys-tems are commonly pre-stressed at 50%.The actual temperature of the pipeline atthe time of installation must be taken intoaccount when pre-stressing is applied.

    If the temperature at the time of installationdeviates from the lowest possible tempera-ture, then the amount of pre-stressing mustbe determined according to the followingpre-stressing diagram.

    Start-up of plant

    Operating pressure

    Pre-stressing

    Pipe anchors, supports and guides must befirmly installed prior to filling the system orcommencing the pressure test. The per-missible test pressure must not be exceed-ed.The bellows must be protected againstweld, mortel or plaster splatter, dirt or any

    form of mechanical damage during installa-tion.Steam pipe systems must be installed onan incline and must further be heated at aslow rate to remove condensate that mightcause steam hammers. Sufficient insula-

    tion and the avoidance of water pockets arerecommended. Steam cleaning should beavoided due to the risk of water hammersand unwanted vibration of the bellows.Expansion joints with inner sleeves must beinstalled under consideration of the flowdirection with the fixed end of the sleeve

    facing up-stream. Otherwise, common prin-ciples such as proper water treatment,electrical bridges in copper and galvanizedpipes etc. for the avoidance of corrosiondefects must be adhered to.

    Only one expansion system should beinstalled between two anchors. Theseanchors must withstand the displacementforces of the system that result from the

    bending spring rates of the bellows and thefriction in the hinges, as well as the frictionforces in the pipe supports and guides.

    Pipe guides with excessive friction as aresult of overloading, deposits of dirt or cor-rosion may gall and cause excessive strainin the pipe, its anchors and connections.

    Anchors

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    23

    Installationinstructions

    Pre-stressingdiagram

    Given: Expansion system for a 140 mlong pipeline

    Lowest possible temperature:7 C

    Maximum temperature: +293 C Maximum thermal expansion ac-

    cording to T 300 C = 500 mm.Determine the correct amount of pre-stressing if the expansion system is to bepre-stressed at 50% of the total movement(= 250 mm) and when the actual tempera-ture at the time of installation is +20 C.Answer: The thermal expansion of thepipeline between 7 C and +20 C (T =27 C) is 45 mm. To determine the correctamount of pre-stressing, this amount mustbe deducted from the total amount of pre-stressing, i.e. 250 45 = 205 mm.The diagram provides a quick resolution with-out the need of a mathematical calculation:1. Temperature difference between installa-

    tion temperature (+20 C) and lowesttemperature (7 C) = 27 C.

    2. Total length of pipeline = 140 m.3. Draw a vertical line from point 27 C at

    the top of the diagram downwards to theline that connects the point 0 and thepoint 140 at the right side of the dia-gram.

    4. From this intersection draw a horizontalline to the left side of the diagram. Thenumber 45 [mm] indicates the thermalexpansion of the pipe at installation tem-perature.

    5. Draw a line from point 45 to the point500 in the next diagram to the left andextend this line to the far left diagram.

    The number 205 [mm] indicates theamount of pre-stressing by which theexpansion system must be pre-stressedinto the opposite direction of the expectedthermal growth of the pipeline.

    Example

    0

    50

    100

    150

    125

    75

    25

    175

    200

    225

    250

    275

    600

    550

    500

    450

    400

    350

    300

    250

    200

    150

    100

    50

    0

    80

    90

    70

    100

    60

    40

    30

    20

    10

    0

    80

    90

    70

    100

    60

    50

    40

    30

    20

    0

    10

    110

    120

    130

    140

    150

    160

    10 20 30 40 50

    Temperature difference between installationtemperature and lowest temperature in C

    Lengthofpipeinm

    Total movement capacity of expansion system in mm

    Amount of pre-stressing of the expansion system in mm

    205

    27

    only applicalbe for pipes of St 35 material

    45

    50

    Expansionofpipeatinstallationte

    mperatureinmm

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    24

    Installationinstructions

    Avoid the installation of standard expansionjoints in the immediate proximity of pres-sure reducers, superheated steam con-densers and quick actuated shut-off valves

    as high frequency vibrations might be gen-erated by this equipment. Provide heavywall sleeves for the expansion joints, perfo-rated flow visors in the pipeline or equaliz-ing sections to protect the bellows againstfailures.

    If high frequency vibrations, turbulence orhigh flow velocities are anticipated, we rec-ommend the installation of expansion jointswith inner sleeves (liners).

    For pipeline diameters equal to or largerthan 150 mm, we recommend internalsleeves if the flow velocity exceeds 8 m/sfor a gaseous flow and 3 m/s for liquids.

    Recommendations

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    Expansionjoint data sheet

    25

    Type of expansion joint:

    Nominal diameter DN:

    Design conditionsDesign pressure bar

    Design temperatureo

    C

    Movements

    axial compress.+/ mm

    axial extension +/ mm

    lateral +/ mm

    angular +/ degr.

    Vibrations frequency Hz

    amplitude mm

    Type of vibration

    Number of cycles

    Flow medium

    Flow velocity

    Limitations mechanical properties:

    axial spring rate N/mm

    lateral spring rate N/mm

    angular spring rate Nm/degr.

    axial force Nlateral force N

    angular moment Nm

    pressure thrust N

    Quality tests:

    Hydraulic press. test yes no

    Leak test

    with air yes no

    with helium yes no

    permissible leak rate mbar l/s

    Auxiliary items:Inner sleeve yes no

    External shroud yes no

    Other items (specify)

    Size/End fittings: material:

    Weld ends Fixed flange

    Loose flange

    Other (specify)

    Space:

    maximum length: mm

    maximum diameter: mm

    Additional NDE BL RL BRR RR other items

    X-ray examination %

    dye penetrant examination %

    ultrasonic examination %

    magnetic particle examination %

    BL = bellows longitudinal weld seam RL = pipe longitudinal weld seamBRR = bellows to pipe circumferential weld seam RR = pipe circumferential weld seam

    QA/QC requirements

    Design codeSpecial specifications

    Certification

    Authorized inspection party

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    000

    353

    K.0

    612.6.1

    .en.S

    to.2

    240

    BOA Balg- und Kompensatoren-Technologie GmbH

    Lorenzstrasse 2-6

    D-76297 Stutensee

    Postfach 11 62

    D-76288 Stutensee

    Phone: +49 (0)7244 99-0

    Fax: +49 (0)7244 99-372

    E-Mail: [email protected]

    Internet: www.boagroup.com