Equipment Component and Compliance Corrugated Metal, w/ Asbestos or corrugated metal, jacketed with: soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 2.50 2.75 3.00 3.25 3.50 2900. 3700. 4500. 5500. 6500. 2.75 3.00 3.25 3.50 3.75 3700. 4500. 5500. 6500. 7600. 3.25 3.50 3.75 3.50 3.75 3.75 5500. 6500. 7600. 8000. 9000. 9000. 3.25 3.50 3.75 3.75 4.25 5500. 6500. 7600. 9000. 10100. 4.00 4.75 5.50 6.00 6.50 8800. 13000. 18000. 21800. 26000. Corrugated Metal: soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys Flat metal, jacketed asbestos filled soft aluminum soft copper or brass iron or soft steel Monel 4%-6% chrome Stainless steels and nickel alloys Grooved Metal soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys Solid flat metal soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 800 CAESAR II User's Guide Equipment Component and Compliance Gasket Seating Stress Specifies the initial seating stress required for the gasket being used. This entry is required only if ASME stress calculations are to be performed. The following table, extracted from Sect VIII Div. 1 gives gasket factors for some common types of gaskets. Gasket Materials and Contact Facings Notes Table 2-5.1 Gasket Material Self-energizing types (O rings, metallic elastomer, and other self-sealing types) Gasket Factor Seating Stress m y (^06) 0. 0. Elastomers without fabric or a high percent of asbestos fiber: Below 75A Shore Durometer .50 75A or higher Shore Durometer 1.00 0. 200. Asbestos with Suitable Binder 1/8" thick 1/16" thick 1/32" thick 2.00 2.75 3.50 600. 3700. 6500. Elastomers with cotton fabric 1.25 400. Elastomers with Asbestos fabric 3 ply 2.25 2 ply 2.50 1 ply 2.75 2200. 2900. 3700. Vegetable fiber 1.75 1100. 2.50 3.00 10000. 10000. Spiral-wound, asbestos filled: Carbon Stainless, Monel, Nickel alloys CAESAR II User's Guide 801 Equipment Component and Compliance Corrugated Metal, w/ Asbestos or corrugated metal, jacketed with: soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 2.50 2.75 3.00 3.25 3.50 2900. 3700. 4500. 5500. 6500. 2.75 3.00 3.25 3.50 3.75 3700. 4500. 5500. 6500. 7600. 3.25 3.50 3.75 3.50 3.75 3.75 5500. 6500. 7600. 8000. 9000. 9000. 3.25 3.50 3.75 3.75 4.25 5500. 6500. 7600. 9000. 10100. 4.00 4.75 5.50 6.00 6.50 8800. 13000. 18000. 21800. 26000. Corrugated Metal: soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys Flat metal, jacketed asbestos filled soft aluminum soft copper or brass iron or soft steel Monel 4%-6% chrome Stainless steels and nickel alloys Grooved Metal soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys Solid flat metal soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 802 CAESAR II User's Guide Equipment Component and Compliance Nubbin Width or Ring Specifies the nubbin width, if applicable. This value is required only for facing sketches 1c, 1d, 2 and 6 (FLANGE) equivalents 3, 4, 5, and 9). For sketch 9, this is not a nubbin width but the contact width of the metallic ring. Facing Sketch Specifies the facing sketch number according to the following correlations, according to Table 2-5-2 of the ASME code. Facing Sketch CAESAR II Equivalent Description 1a 1 flat finish faces 1b 2 serrated finish faces 1c 3 raised nubbin-flat finish 1d 4 raised nubbin-serrated finish 2 5 1/64 inch nubbin 3 6 1/64 inch nubbin both sides 4 7 large serrations, one side 5 8 large serrations, both sides 6 9 metallic O-ring type gasket This value is required for calculating the contact gasket width and the effective gasket diameter, G. Facing Column Specifies the facing column number according to the following correlations: Gasket Material Self-energizing types (O rings, metallic elastomer, and other self-sealing types) Facing Column 2 Elastomers without fabric or a high percent of asbestos fiber: Below 75A Shore Durometer 75A or higher Shore Durometer CAESAR II User's Guide 2 2 803 Equipment Component and Compliance Asbestos with Suitable Binder 1/8" thick 1/16" thick 1/32" thick 2 2 2 Elastomers with cotton fabric 2 Elastomers with Asbestos fabric 3 ply 2 ply 1 ply 2 2 2 Vegetable fiber 2 Spiral-wound, asbestos filled: Carbon Stainless, Monel, Nickel alloys 2 2 Corrugated Metal, w/ Asbestos or corrugated metal, jacketed with: soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 2 2 2 2 3.50 Corrugated Metal: soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 2 2 2 2 2 Flat metal, jacketed asbestos filled soft aluminum soft copper or brass iron or soft steel Monel 4%-6% chrome Stainless steels and nickel alloys 2 2 2 2 2 2 Grooved Metal soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome Stainless steels and nickel alloys 804 2 2 2 2 2 CAESAR II User's Guide Equipment Component and Compliance Solid flat metal soft aluminum soft copper or brass iron or soft steel Monel or 4%-6% chrome 2 2 2 2 Stainless steels and nickel alloys 2 Material Data Tab The following options are used to define material and stress-related data. Topics Flange Material .............................................................................. 805 Bolt Material ................................................................................... 805 Design Temperature ...................................................................... 805 Flange Allowable @ Design Temperature..................................... 806 Flange Allowable @ Ambient Temperature................................... 806 Flange Modulus of Elasticity @ Design ......................................... 806 Flange Modulus of Elasticity @ Ambient ....................................... 806 Bolt Allowable @ Design Temperature ......................................... 807 Bolt Allowable @ Ambient Temperature ....................................... 807 Flange Allowable @ Stress Multiplier ............................................ 807 Bolt Allowable Stress Multiplier ..................................................... 808 Flange Material Displays the material database for flanges, taken from ASME Section VIII, Division 1. Bolt Material Displays the material database for bolting, taken from ASME Section VIII, Division 1. Design Temperature Specifies the flange design temperature. This value is required for ASME stress calculations, and for ANSI B16.5/API rating table look-ups. The design temperature is not used in the flexibility model of the flange. CAESAR II User's Guide 805 Equipment Component and Compliance Flange Allowable @ Design Temperature Specifies the allowable stress for the flange material at the design temperature. This value is required only if an ASME stress analysis of the flange is to be performed. This value is available in the ASME Sect. VIII Div. 1 material database delivered with the software. You can access the database by typing a material name in the Flange Material box or by clicking Browse and selecting a material in the Material Selection list. After it is in the database, fill in the spaces for database entry where the defaults are not correct. Press F1 when the material inputs are satisfactory. The material selection can be changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when the cursor is on the appropriate material. When you select the material in this way, it becomes the default for the next material database entry. Flange Allowable @ Ambient Temperature Specifies the allowable stress for the flange material at the ambient temperature. This value is only required if an ASME stress analysis of the flange is to be performed. This value is available in the ASME Sect. VIII Div. 1 material database delivered with the software. You can access the database by typing a material name in the Flange Material box or by clicking Browse and selecting a material in the Material Selection list. After it is in the database, fill in the spaces for database entry where the defaults are not correct. Press F1 when the material inputs are satisfactory. The material selection can be changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when the cursor is on the appropriate material. When you select the material in this way, it becomes the default for the next material database entry. Flange Modulus of Elasticity @ Design Defines the value of the modulus of elasticity to be used for the determination of the Flange Rigidity Factor "J", for the DESIGN case defined in Appendix S of the A93 addendum. Flange Modulus of Elasticity @ Ambient Defines the value of the modulus of elasticity to be used for the determination of the Flange Rigidity Factor "J", for the SEATING case defined in Appendix S of the A93 addendum. 806 CAESAR II User's Guide Equipment Component and Compliance Bolt Allowable @ Design Temperature Indicates the allowable stress for the bolt material at the design temperature. This value is only required if an ASME stress analysis of the flange is to be performed. This value is available in the ASME Sect. VIII Div. 1 material database delivered with the software. You can access the database by typing a material name in the Flange Material box or by clicking Browse and selecting a material in the Material Selection list. After it is in the database, fill in the spaces for database entry where the defaults are not correct. Press F1 when the material inputs are satisfactory. The material selection can be changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when the cursor is on the appropriate material. When you select the material in this way, it becomes the default for the next material database entry. Bolt Allowable @ Ambient Temperature Specify the allowable stress for the bolt material at the ambient temperature. This value is only required if an ASME stress analysis of the flange is to be performed. This value is available in the ASME Sect. VIII Div. 1 material database delivered with the software. You can access the database by typing a material name in the Flange Material box or by clicking Browse and selecting a material in the Material Selection list. After it is in the database, fill in the spaces for database entry where the defaults are not correct. Press F1 when the material inputs are satisfactory. The material selection can be changed after pressing F1 by moving the cursor around the tab fields and pressing Enter when the cursor is on the appropriate material. When you select the material in this way, it becomes the default for the next material database entry. Flange Allowable @ Stress Multiplier Applies the increased allowable (1.5) for the radial and tangential operating ASME flange allowables. This increase is implied in B31.1 Appendix II Section 4.2.3 when it states that the longitudinal hub, tangential and radial stress allowables are equal to the yield stress at design temperature, which is essentially 1.5(S). Prior to the 1992 edition of the ASME NC code, NC paragraph 3658.1(d) also stated that the tangential and radial stress allowables could be increased by 50%. The 1992 edition of NC eliminated this increase on these allowables. CAESAR II User's Guide 807 Equipment Component and Compliance Bolt Allowable Stress Multiplier Designates a factor by which to increase the operating bolt allowables. Section VIII Division 2, Article 4-141 of the ASME Boiler and Pressure Vessel Code allows for operating loads on bolts to equal two times the standard table allowables. In some cases, this increase can be by as much as three times the table allowables. Loads Tab The following options are used to describe the imposed loads. Topics Design Pressure ............................................................................ 808 Axial Force ..................................................................................... 808 Bending Moment ........................................................................... 808 Disable Leakage Calculations ....................................................... 808 Disable Stress Calculations ........................................................... 809 Disable ANSI B16.5 Check ............................................................ 809 Design Pressure Indicates the internal line pressure (lbs./sq.in.) in gage. This pressure is used in the flexibility model of the flange in the ASME stress calculations and is the B16.5/API rating. Axial Force Defines the externally applied axial force applied to the flange joint by the attached piping. The software does not include the effect of shear forces in the flexibility model. Bending Moment Specifies the external moment applied to the flange joint by the attached piping. If you have two bending moments, SRSS them and enter the result here. Disable Leakage Calculations Turns off the leakage calculations performed by CAESAR II. Use this option if you want a flange report, which only contains ASME Section VIII, Division 1, Appendix 2 results. 808 CAESAR II User's Guide Equipment Component and Compliance Disable Stress Calculations Turns off the flange stress calculations performed by CAESAR II. Use this option if you want a flange report, which only contains leakage calculations and omits ASME Section VIII, Division 1, Appendix 2 results. Disable ANSI B16.5 Check Turns off the report for the ANSI B16.5 Equivalent Pressure check. This check compares the equivalent pressure to the MAWP (as listed in ANSI B16.5) for the flange class and material. The ANSI MAWP does not consider bolting or gasket properties, and it is not a good indicator of the leakage characteristics of the flange. Flange Rating This is an optional input. It has been a common practice in the industry to use the ANSI B16.5 and API 605 temperature/pressure rating tables as a gauge for leakage. Because these rating tables are based on allowable stresses and are not intended for leakage prediction, the leakage predictions that resulted are a function of the allowable stress for the flange material, not the flexibility, or modulus of elasticity, of the flange. To give you a comparison to the old practice, the minimum and maximum rating table values from ANSI and API are stored and are used to print minimum and maximum leakage safety factors that are predicted from this method. An example of the output that you get upon entering the flange rating is shown below: EQUIVALENT PRESSURE MODEL ————————-Equivalent Pressure (lb./sq.in.) 1639.85 ANSI/API Min Equivalent Pressure Allowed 1080.00 ANSI/API Max Equivalent Pressure Allowed 1815.00 According to the older method, this shows that leakage occurred if a carbon steel flange is used, and leakage does not occur if an alloy flange is used. Both flanges have essentially the same flexibility tendency to leak. The following input parameters are used only for the ASME Section VIII Division 1 stress calculations: Flange Type Flange Outside Diameter Design Temperature Small End Hub Thickness Large End Hub Thickness Hub Length Flange Allowables Bolt Allowables Gasket Seating Stress Optional Allowable Multipliers Flange Face & Gasket Dimensions CAESAR II User's Guide 809 Equipment Component and Compliance Specify the Flange Type (on page 793) on the Flange (see "Flange Tab" on page 793) tab. To acquire material allowables from the Section VIII, Division 1 material library, use the Flange Material (on page 805) list on the Material Data (see "Material Data Tab" on page 805) tab. An input listing for a typical flange analysis is shown below: CA E S A R I I MISCELLANEOUS REPORT ECHO Flange Inside Diameter [B](in.) 30.560 Flange Thickness [t](in.) 4.060 Flange Rating (Optional) 300.000 Bolt Circle Diameter (in.) 38.500 Number of Bolts 32.000 Bolt Diameter (in.) 1.500 Bolt Initial Tightening Stress(lb./sq.in.) Effective Gasket Diameter [G] (in.) 33.888 Uncompressed Gasket Thickness (in.) 0.063 Basic Gasket Width [b0] (in.) 0.375 Leak Pressure Ratio [m] 2.750 Effective Gasket Modulus(b./sq.in.) 300,000.000 Externally Applied Moment (optional)(in.lb.) 24,000.000 Externally Applied Force (optional)(lb.) 1,000.000 Pressure [P](lb./sq.in.) 400.000 The following inputs are required only if you wish to perform stress calcs as per Sect VIII Div. 1 Flange Type (1-8, see ?-Help or Alt-P to plot) 1.000 Flange Outside Diameter [A](in.) 41.500 Design Temperature°F 650.000 Small End Hub Thickness [g0](in.) 1.690 Large End Hub Thickness [g1](in.) 3.440 Hub Length [h](in.) 6.620 Flange Allowable @Design Temperature(lb./sq.in.) 17,500.000 Flange Allowable @Ambient Temperature(lb./sq.in.) 17,500.000 Flange Modulus of Elasticity @Design(lb./sq.in.) 0.279E+08 Flange Modulus of Elasticity @Ambient(lb./sq.in.) 0.279E+08 Bolt Allowable @Design Temperature(lb./sq.in.) 25,000.000 Bolt Allowable @Ambient Temperature(lb./sq.in.) 25,000.000 Gasket Seating Stress [y](lb./sq.in.) 3,700.000 Flange Allowable Stress Multiplier 1.000 Bolt Allowable Stress Multiplier (VIII Div 2 41411.000 Disable Leakage Calculations (Y/N) N Flange Face OD or Lapjt Cnt OD(in.) 34.500 Flange Face ID or Lapjt Cnt ID(in.) 33.000 Gasket Outer Diameter (in.) 36.000 Gasket Inner Diameter (in.) 33.000 Nubbin Width (in.) Facing Sketch 1.000 Facing Column 2.000 Disable Leakage Calculations (Y/N) N 810 CAESAR II User's Guide Equipment Component and Compliance Pipeline Remaining Strength Calculations (B31G) Analysis > B31G evaluates corroded pipelines to determine when specific pipe segments must be replaced. The original B31G document is conservative. CAESAR II performs additional calculations to modify the original criteria. This additional work can be found in project report PR-3805, by Battelle, Inc. The details of the original B31G criteria, as well as the modified methods, are discussed in detail in this report. CAESAR II determines the following values according to the original B31G criteria and four modified methods. The values are The hoop stress to cause failure The maximum allowed operating pressure The maximum allowed flaw length The four modified methods vary in the manner in which the corroded area is estimated. The methods are: .85dL - Approximates the corroded area as 0.85 times the maximum pit depth times the flaw length. Exact - Determines the corroded area numerically using the trapezoid method. Equivalent - Determines the corroded area by multiplying the average pit depth by the flaw length. Additionally, an equivalent flaw length (flaw length * average pit depth / maximum pit depth) is used in the computation of the Folias factor. Effective - Uses a numerical trapezoid summation; however, various sub-lengths of the total flaw length are used to arrive at a worst case condition. If the sub-length that produces the worst case coincides with the total length, the Exact and Effective methods yield the same result. To begin, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. CAESAR II User's Guide 811 Equipment Component and Compliance The software opens the Pipeline Remaining Strength Calculations (B31G) window. The window consists of two input tabs--Data (see "Data Tab" on page 813) and Measurements (see "Measurements Tab" on page 815). 812 CAESAR II User's Guide Equipment Component and Compliance After the data is entered, click Run Analysis report is shown below: to begin the computations. A typical output For additional information or backup on these computations, an intermediate computation file is generated. For more information on the analysis methods used by this command, see the B31G document or the Battelle project report PR-3-805. CAESAR II User's Guide 813 Equipment Component and Compliance Data Tab Most of the data required by this processor is acquired through actual field measurements. Topics Pipe Nominal Diameter .................................................................. 814 Pipe Wall Thickness ...................................................................... 814 Design Pressure ............................................................................ 814 Material Yield Strength .................................................................. 814 Material Specified Minimum Yield ................................................. 814 Flaw Length ................................................................................... 814 Measurement Increment ................................................................ 815 Factor of Safety (FS) ..................................................................... 815 Design Factor (S) .......................................................................... 815 Pipe Nominal Diameter Specifies the pipe diameter. Pipe Wall Thickness Specifies the un-corroded pipe wall thickness. Design Pressure Specifies the design pressure. This value is the maximum pressure reported in the output section, although the maximum allowed pressure may be less than the input design pressure. Material Yield Strength Defines the material yield strength. If this value is unknown, enter the specified minimum yield strength in this cell. Material Specified Minimum Yield Defines the minimum yield strength. Flaw Length Indicates the length of flaw or anomaly. This value is a measured quantity, usually taken in a straight line. 814 CAESAR II User's Guide Equipment Component and Compliance Measurement Increment Specify the measurement increment in this cell. This value defines how often along the flaw length depth or thickness measurements are made. The number of measurements should be calculated by ( flaw length / measurement increment )+1 Factor of Safety (FS) Defines the factor of safety. For those pipelines in which the maximum operating stress level does not exceed 72% of the specified minimum yield strength, the safety factor is 100/72 = 1.39. The safety factor cannot be less than 1.0. Design Factor (S) Specifies the design factor from the applicable piping code. Measurements Tab You can enter a maximum of twenty pit measurements on the Measurements input screen. CAESAR II User's Guide 815 Equipment Component and Compliance First, you must define the measurements. Select Pits if the measurements are in pit depths. Select Thicknesses if the measurements are remaining wall thicknesses. Pit depths are required for the computations. If remaining thicknesses are specified, the pit depths are computed from wall thickness - remaining thickness. In the individual cells, enter the measurement obtained along the flaw length. The values are based on the selection of Pits or Thicknesses. Expansion Joint Rating Analysis > Expansion Joint Rating computes a limit for the total displacement per corrugation of an expansion joint. According to EJMA (Expansion Joint Manufacturers Association), the maximum permitted amount of axial movement per corrugation is defined as erated where ex + ey + eq < erated The terms in the above equation are defined as: ex = The axial displacement per corrugation resulting from imposed axial movements. ey = The axial displacement per corrugation resulting from imposed lateral deflections. eq = The axial displacement per corrugation resulting from imposed angular rotation, that is, bending. erated = The maximum permitted amount of axial movement per corrugation. You can find this value in the expansion joint manufacturer’s catalog. In addition, EJMA states, “Also, [as an expansion joint is rotated or deflected laterally] it should be noted that one side of the bellows attains a larger projected area than the opposite side. Under the action of the applied pressure, unbalanced forces are set up which tend to distort the expansion joint further. In order to control the effects of these two factors a second limit is established by the manufacturer upon the amount of angular rotation and/or lateral deflection which may be imposed upon the expansion joint. This limit may be less than the rated movement. Therefore, in the selection of an expansion joint, care must be exercised to avoid exceeding either of these manufacturer’s limits.” This module is intended to assist you in satisfying these limitations. This module computes the terms defined in the above equation and the movement of the joint ends relative to each other. These relative movements are reported in both the local joint coordinate system and the global coordinate system. To begin, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. 816 CAESAR II User's Guide Equipment Component and Compliance The software opens the EJMA Expansion Joint window. The window consists of three input screens--Geometry (on page 820), Displacements and Rotations (on page 821), and Allowables (on page 821). After the necessary data is entered, click Run Analysis to begin the computations. After processing completes, a report displaying both the input echo and the output calculations are shown on a new tab called Output. CAESAR II User's Guide 817 Equipment Component and Compliance The units used for the coordinate and displacement values are the length units defined in the active units file. Rotations are in units of degrees. C A E S A R II MISCELLANEOUS REPORT ECHO EJMA EXPANSION JOINT RATING Node Number for “FROM” end 120.000 Node Number for “TO” end 125.000 Number of Convolutions 4.000 Flexible Joint Length (in.)4.447 Effective Diameter(in.)4.996 X Coordinate of “from” end (in.).000 Y Coordinate of “from” end (in.).000 Z Coordinate of “from” end (in.).000 X Coordinate of “to” end (in.)4.447 X Displacement of “from” end (in.).300 Y Displacement of “from” end (in.).250 Z Displacement of “from” end (in.).000 X Rotation of “from” end (deg).000 Y Rotation of “from” end (deg)1.222 Z Rotation of “from” end (deg).030 X Displacement of “to” end (in.)-.100 Y Displacement of “to” end (in.).120 Z Displacement of “to” end (in.).000 818 CAESAR II User's Guide Equipment Component and Compliance X Rotation of “to” end (deg).000 Y Rotation of “to” end (deg)-.020 Z Rotation of “to” end (deg).890 OUTPUT: AXIAL DISPLACEMENTS PER CONVOLUTION Axial Displacement.100 Axial Displacement due to Lateral .133 Axial Displacement due to Rotation.016 Axial Displacement TOTAL.250 RELATIVE MOVEMENTS OF END “i” WITH RESPECT TO END “j” (Local Joint Coordinate System) Relative Axial Displacement, “x”.401 Relative Lateral Displacement, “y”.158 Relative Bending, “theta” (deg)1.511 Relative Torsion (deg) .019 RELATIVE MOVEMENTS OF END “i” WITH RESPECT TO END “j” (Global Piping Coordinate System) Relative X Displacement-.399 Relative Y Displacement-.132 Relative Z Displacement.095 Relative Rotation about X (deg).000 Relative Rotation about Y (deg)-1.242 Relative Rotation about Z (deg).860 In the previous output, the axial displacement total in the report is the total axial displacement per corrugation due to axial, lateral, and rotational displacement of the expansion joint ends. This is the value that is compared to the rated axial displacement per corrugation. If e (total) is greater than the rated axial displacement per corrugation, then there is the possibility of premature bellows failure. Be sure that the displacement rating from the manufacturer is on a per corrugation basis. If it is not, multiply the axial displacement total by the number of corrugations and compare this value to the manufacturer’s allowable axial displacement. Most manufacturers allowed rating is for some set number of cycles (often 10,000). If the actual number of cycles is less, then the allowed movement can often be greater. Similarly, if the actual number of cycles is greater than 10,000, then the allowed movement can be smaller. In special situations, contact the manufacturers because many factors can affect allowed bellows movement. The y in the report is the total relative lateral displacement of one end of the bellows with respect to the other, and theta is the total relative angular rotation of one end of the bellows with respect to the other. CAESAR II does not include x in the denominator for the lateral displacement calculations as outlined in EJMA. CAESAR II User's Guide 819 Equipment Component and Compliance Geometry Topics Node Number for "From" End ........................................................ 820 Node Number for "To" End ............................................................ 820 Number of Convolutions ................................................................ 820 Flexible Joint Length ...................................................................... 820 Effective Diameter ......................................................................... 820 Z Axis Up ....................................................................................... 821 Coordinates ................................................................................... 821 Node Number for "From" End Identifies the node number that represents the From end of the expansion joint. This value is used for labeling purposes. Node Number for "To" End Identifies the node number that represents the To end of the expansion joint. This value is used for labeling purposes. Number of Convolutions Defines the number of convolutions in the expansion joint. Flexible Joint Length Specifies the flexible length of the bellows. Effective Diameter Specifies the diameter of the circle whose area is equal to the effective area of the expansion joint. The effective ID can be estimated using the following equation: 1.13 * sqrt (Effective Area) You can find the effective area of the joint in the manufacturer's catalog. 820 CAESAR II User's Guide Equipment Component and Compliance Z Axis Up Indicates that the z-axis is upward in your CAESAR II input file. Coordinates Defines the spatial coordinate at the appropriate end of the expansion joint Displacements and Rotations Defines the displacements and rotations at the appropriate end of the expansion joint. These values typically come from the displacement report of a CAESAR II run. Allowables Specifies the allowed expansion joint movement (translation or rotation) on a per convolution basis and for the entire bellows. Enter values using the following units of measure: Axial inches Lateral inches Bending inches or degrees Torsional inches or degrees You can acquire this data using the vendor catalog. Structural Steel Checks - AISC Analyze > AISC performs AISC code check on structural steel elements. Compliance is evaluated according to the AISC (American Institute of Steel Construction) code. This code check uses the forces and moments at the ends of the structural members, computes stresses, and allowables, and determines a unity check value. If the unity check value is less than 1.0, the member is acceptable for the given loading conditions. CAESAR II performs the AISC unity check according to either the 1977 or the 1989 edition of the AISC code. Member properties are obtained from the AISC database and used to compute the actual and allowable stress values for the axial and bending terms comprising the unity check equations. The database must be either AISC77.BIN or AISC89.BIN and is set using Tools > Configuration/Setup. For more information, see Configuration and Environment (on page 45). There are a few differences between the 1977 and 1989 AISC Code Revisions that affect unity check computation. The most noticeable difference is that the 1989 code provides a method for computing the unity check on single angles. This procedure, which was not addressed in the 1977 code, can be found in a special code section following the commentary. The steps necessary to compute the unity check for single angles can be followed by reviewing the message file (generated upon request). CAESAR II User's Guide 821 Equipment Component and Compliance The other differences between these two code revisions deal with members in compression. Several constants for Qs have been altered, and a new factor k c” has been added. “kc” is a compression element restraint coefficient defined in the 1989 edition of the code. Because of these code differences, CAESAR II stores the name of the active database in the input file for the AISC module when the data file is first created. Attempting to switch databases or compute unity checks on angles using the 1977 code generates error messages and processing terminates. You are urged to consult the applicable AISC Manuals when using this command. To begin the unity check calculations, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. The software displays the AISC window, which consists of two input screens:Global Input (on page 824) and Local Member Data (see "Local Member Data Tab" on page 826). 822 CAESAR II User's Guide Equipment Component and Compliance Output Reports You can direct the output reports to the screen or to a printer. The output report begins with a one page summary describing the current global data and units, as shown below. The remaining pages in the output report show the data for the individual members. The last column of the report contains the most important data (namely the unity check value) and the governing AISC equation. A sample member output reports are shown below. The report is applicable to jobs where sidesway is allowed. CAESAR II User's Guide 823 Equipment Component and Compliance Global Input The following options are used to enter data that applies to all members being evaluated. Topics Structural Code .............................................................................. 824 Allowable Stress Increase Factor .................................................. 824 Stress Reduction Factors Cmy and Cmz ...................................... 824 Young’s Modulus ........................................................................... 825 Material Yield Strength .................................................................. 825 Bending Coefficient ....................................................................... 825 Form Factor Qa ............................................................................. 825 Allow Sidesway .............................................................................. 825 Resize Members Whose Unity Check Value Is . . . ....................... 825 Minimum Desired Unity Check ...................................................... 826 Maximum Desired Unity Check ..................................................... 826 Structural Code Identifies the code and year, typically matching the database in use. Slight variations in the computations depend on which code year is selected. Single angles can only be checked if AISC 1989 is selected. Allowable Stress Increase Factor Designates the multiplication factor applied to the computed values of the axial and bending allowable stresses. Typically, this value is 1.0. However, in extreme events, such as earthquakes and 100-year storms, the AISC code permits the allowable stresses to be increased by a factor. Usually, a 1/3 increase is applied to the computed allowables, making the allowable stress increase factor equal to 1.33. For more details see the AISC code, section 1.5.6. Stress Reduction Factors Cmy and Cmz Specifies the interaction formula coefficients (Cmy and Cmz) for the strong and weak axis of the elements (in-plane and out-of-plane). Values include the following: 0.85 for compression members in frames subject to joint translation (sidesway). For restrained compression members in frames braced against sidesway and not subject to transverse loading between supports in the plane of bending: 0.6 - 0.4(M1/M2) but not less than 0.4, where (M1/M2) is the ratio of the smaller to larger moments at the ends, of that portion of the member un-braced in the plane of bending under consideration. 824 CAESAR II User's Guide Equipment Component and Compliance For compression members in frames braced against joint translation in the plane of loading and subject to transverse loading between supports, the value of Cmy can be determined by rational analysis. Alternatively, the following values are suggested per the AISC code: 0.85 for members whose ends are restrained against rotation in the plane of bending. 1.0 for members whose ends are unrestrained against rotation in the plane of bending. Young’s Modulus Specifies the slope of the linear portion of the stress-strain diagram. For structural steel this value is usually 29,000,000 psi. Material Yield Strength Defines the minimum yield stress of the steel being used. The term yield stress denotes the minimum yield point (for those steels that have a yield point) or the minimum yield strength (for those that do not have a yield point). Bending Coefficient Specifies the bending coefficient (Cb). Use 1.0 in computing the value of Fby and Fbz for use in Formula 1.6-1a or when the bending moment at any point in an unbraced length is larger than the moment at either end of the same length. Otherwise, Cb shall be: Cb = 1.75 + 1.05(M1/M2) + 0.3(M1/M2)2 but not more than 2.3, where (M1/M2) is the ratio of the smaller to larger moments at the ends. Form Factor Qa Defines the allowable axial stress reduction factor equal to the effective area divided by the actual area. Consult the latest edition of the AISC code for the current computation methods for the effective area. Allow Sidesway Controls the ability of a frame or structure to experience sidesway (joint translation). This affects the computation of several of the coefficients used in the unity check equations. Additionally, for frames braced against sidesway, moments at each end of the member are required. Sidesway is allowed. Resize Members Whose Unity Check Value Is . . . Determines whether the AISC module attempts to resize specific members as a result of the unity check computations. This option is most often used for an initial pass at optimization. Selecting this option requires that you specify a minimum unity check and a maximum unity check. If the computed unity check falls outside this range, the module resizes the member appropriately. The final member size is shown in the output report. CAESAR II User's Guide 825 Equipment Component and Compliance A resized member overwrites the initial input member size in the input file (input and output share a common file). If member resizing occurs, check the final member size to ensure the following: 1. The selected member is commonly available. 2. The selected member is optimal in its group. 3. The selected member does not violate fabrication requirements for flange or web size. Minimum Desired Unity Check Defines the minimum acceptable unity check allowed. Accepted values are between 0.0 and 1.0. Members whose computed unity check value is less than this minimum are resized to a smaller shape. The Minimum Desired Unity Check value must be less than the Maximum Desired Unity Check value. The recommended value for the minimum desired unity check is 0.7, which allows lightly loaded members to be reduced in size. Maximum Desired Unity Check Defines the maximum acceptable unity check allowed. Accepted values are between 0.0 and 1.0. Members whose computed unity check value is greater than this maximum are resized to a larger shape. The Maximum Desired Unity Check value must be greater than the Minimum Desired Unity Check value. The recommended value for the maximum desired unity check is 0.9, which leaves a margin for loading inaccuracies. Local Member Data Tab The following options are used to enter local member data for each member being evaluated. Topics Member Start Node ....................................................................... 827 Member End Node ........................................................................ 827 Member Type................................................................................. 827 In-And Out-Of-Plane Fixity Coefficients Ky And Kz....................... 827 Unsupported Axial Length ............................................................. 828 Unsupported Length (In-Plane Bending) ....................................... 828 Unsupported Length (Out-Of-Plane Bending) ............................... 828 Double Angle Spacing ................................................................... 828 Young's Modulus ........................................................................... 828 Material Yield Strength .................................................................. 828 Axial Member Force ...................................................................... 828 In-Plane Bending Moment ............................................................. 829 Out-of-Plane Bending Moment ...................................................... 829 In-Plane “Small” Bending Moment ................................................ 829 In-Plane “Large” Bending Moment ................................................ 829 Out-of-Plane “Small” Bending Moment ......................................... 829 Out-of-Plane “Large” Bending Moment ......................................... 829 826 CAESAR II User's Guide Equipment Component and Compliance Member Start Node Identifies the start node, or “i” end, of a structural element. This option is required. Enter an integer value between 1 and 32,000. Member End Node Identifies the member end node, or the “j” end, of a structural element. This option is required. Enter an integer value between 1 and 32,000. Member Type Specifies the AISC shape label found in the AISC manual. The shape label is used to acquire the member geometric properties from the database. For properties to be obtained, the label you enter must match exactly the label in the database. Because many of the angle labels can be found in the single angles, the double angles (long legs back to back), and the double angles (short legs back to back), require an angle type to tell them apart. Enter a D double angles with equal legs, and double angles with long legs back to back. Enter a B for double angles with short legs back to back. In-And Out-Of-Plane Fixity Coefficients Ky And Kz Specifies the coefficients used to compute the strong and weak axis slenderness ratios. Recommended values are listed in the following table: End Conditions Theoretical K Recommended Design K fixed-fixed 0.5 0.65 fixed-pinned 0.7 0.8 fixed-sliding 1.0 1.2 pinned-pinned 1.0 1.0 fixed-free 2.0 2.1 pinned-sliding 2.0 2.0 CAESAR II User's Guide 827 Equipment Component and Compliance Unsupported Axial Length Defines the length used to determine the buckling strength of the member. Typically, this is the total length of the member. Unsupported Length (In-Plane Bending) Defines the length of the member between braces or supports which prevent bending about the strong axis of the member. Unsupported Length (Out-Of-Plane Bending) Defines the length of the member between braces or supports which prevent bending about the weak axis of the member. Double Angle Spacing Indicates the gap or space separating the adjacent legs. The spacing, as defined in the AISC manual, must be 0.0, .375, or .75-inches. Young's Modulus Specifies the slope of the linear portion of the stress-strain diagram. For structural steel this value is usually 29,000,000 psi. This value of Young’s modulus overrides the Young's Modulus (see "Young’s Modulus" on page 825) value specified on the Global Input tab. Material Yield Strength Defines the minimum yield stress of the steel being used. The term yield stress denotes the minimum yield point (for those steels that have a yield point) or the minimum yield strength (for those that do not have a yield point). This value of the material yield strength overrides the Material Yield Strength (on page 825) value specified on the Global Input tab. Axial Member Force Specifies the force (tension or compression) that acts along the axis of the member. The sign of the number is not significant because a worst case load condition is assumed, that is, all positive loads. 828 CAESAR II User's Guide Equipment Component and Compliance In-Plane Bending Moment Specifies the maximum bending moment in the member (when sidesway is permitted) that will cause bending about the strong axis Y-Y of the member. The sign of the number is not significant because a worst case load condition of all positive loads is assumed Out-of-Plane Bending Moment Specifies the maximum bending moment in the member (when sidesway is permitted) that will cause bending about the weak axis Z-Z of the member. The sign of the number is not significant because a worst case load condition of all positive loads is assumed In-Plane “Small” Bending Moment Specifies the end moments for structures braced against sidesway. This value is the smaller of the two in-plane bending moments that cause bending about the strong axis Y-Y of the member. In-Plane “Large” Bending Moment Specifies the end moments for structures braced against sidesway. This value is the larger of the two in-plane bending moments which cause bending about the strong axis Y-Y of the member. Out-of-Plane “Small” Bending Moment Specifies the end moments for structures braced against sidesway. This value is the smaller of the two out-of-plane bending moments that cause bending about the weak axis Z-Z of the member. Out-of-Plane “Large” Bending Moment Specifies the end moments for structures braced against sidesway. This value is the larger of the two out-of-plane bending moments that cause bending about the weak axis Z-Z of the member. NEMA SM23 (Steam Turbines) Analysis > NEMA SM23 evaluates piping loads on steam turbine nozzles. There are two types of force/moment allowables computed during a NEMA run: Individual nozzle allowables. Cumulative equipment allowables. Each individual suction, discharge, and extraction nozzle must satisfy the equation: 3F + M < 500De CAESAR II User's Guide 829 Equipment Component and Compliance Where: F = resultant force on the particular nozzle. M = resultant moment on the particular nozzle. De = effective nominal pipe size of the connection. A typical discharge nozzle calculation is shown below For cumulative equipment allowables, NEMA SM23 states that "the combined resultants of the forces and moments of the inlet, extraction, and exhaust connections resolved at the centerline of the exhaust connection", be within a certain multiple of Dc, where Dc is the diameter of an opening whose area is equal to the sum of the areas of all of the individual equipment connections. A typical turbine cumulative (summation) equipment calculation is shown below: 830 CAESAR II User's Guide Equipment Component and Compliance SFX, SFY, and SFZ are the respective components of the forces from all connections resolved at the discharge nozzle. FC(RSLT) is the result of these forces. SMX, SMY and SMZ are the respective components of the moments from all connections resolved at the discharge nozzle. Dc is the diameter of the equivalent opening as discussed above. The software opens the NEMA SM23 window. Aside from the description, there is only one input tab for the NEMA turbine. The Nema Input tab enables iterative addiction of an arbitrary number of nozzles to the model. To add a nozzle, click Add Nozzle. NEMA Turbine Example Consider a turbine where node 35 represents the inlet nozzle and node 50 represents the outlet nozzle. The output from a CAESAR II analysis of this piping system includes the forces and moments acting on the pipe elements that attach to the turbine: NODE FX FY FZ MX MY MZ 30 -108 -49 -93 73 188 603 35 108 67 93 162 -47 -481 50 -192 7 -11 369 -522 39 55 192 -63 11 78 117 -56 To find the forces acting on the turbine at points 35 and 50, reverse the sign of the forces that act on the piping: LOADS ON TURBINE @ 35 -108 -67 -93 -162 47 481 LOADS ON TURBINE @ 50 192 -7 11 -369 522 -39 Output Reports The first page of the output is the input echo. The second page, as well as some of the remaining pages, display the individual nozzle calculations. The last page displays the summation calculations. The example below shows a sample input echo report. CAESAR II User's Guide 831 Equipment Component and Compliance The actual number of output pages varies and depends on the number of nozzles defined in the input. 832 CAESAR II User's Guide Equipment Component and Compliance The NEMA output report for the above turbine example shows that the turbine passed. The highest summation load is only 56% of the allowable. If the turbine had failed, **FAILED** would have displayed, in red, under the STATUS column opposite to the load combination that was excessive. The following two examples show sample NEMA output nozzle calculations and NEMA output summation calculations, respectively. CAESAR II User's Guide 833 Equipment Component and Compliance NEMA Input Data Tab The following options are used to enter input data used to evaluate piping loads for steam turbine nozzles. Topics Z-Axis Vertical................................................................................ 834 Cos X & Y ...................................................................................... 834 Nozzle Number .............................................................................. 834 Nozzle Type ................................................................................... 835 Nozzle Diameter ............................................................................ 835 DX .................................................................................................. 835 DY .................................................................................................. 835 DZ .................................................................................................. 836 Global Force FX ............................................................................ 836 Global Force FY ............................................................................ 836 Global Force FZ ............................................................................. 836 Global Moment MX ........................................................................ 836 Global Moment MY ........................................................................ 836 Global Moment MZ ........................................................................ 836 Select Load Jobs and Load Case ................................................. 837 Z-Axis Vertical Controls the plane in which the Z-axis lies. By default, CAESAR II assumes the Y-axis is vertical with the X- and Z-axes in the horizontal plane. If you select this option, the software places the Z-axis in the vertical plane, and the X- and Y-axes are in the horizontal plane. Cos X & Y Specifies the direction cosines (X, Z) for the equipment shaft centerline. For example, if shaft CL is along the Z-axis, the direction cosines are as follows: cosine X = 0.0 cosine Z = 1.0 Nozzle Number Identifies the node number that describes the nozzle flange connection. Enter a positive number only. 834 CAESAR II User's Guide Equipment Component and Compliance Nozzle Type Identifies the nozzle type. This is used only for informational purposes in the output report. Nozzle Diameter Specifies the nozzle pipe nominal diameter. DX Specifies the X-distance from the force/moment resolution point to the nozzle. NEMA SM 23 is ambiguous about the point of resolution of the combined forces and moments. The resolution points are interpreted to be the following two points: 1. The face of the flange at the exhaust nozzle connection. 2. The intersection point of the exhaust nozzle centerline and the equipment shaft centerline. In order to resolve the forces and moments at the current nozzle connection, enter the Xdistance from the current nozzle to each connection. Distance from the exhaust to the exhaust nozzle is 0.0. In order to resolve the forces and moments at the intersection point of the exhaust nozzle and the shaft centerlines, enter the X-distance from the intersection point to each connection. DY Specifies the Y-distance from the force/moment resolution point to the nozzle. NEMA SM 23 is ambiguous about the point of resolution of the combined forces and moments. The resolution points are interpreted to be the following two points: 1. The face of the flange at the exhaust nozzle connection. 2. The intersection point of the exhaust nozzle centerline and the equipment shaft centerline. In order to resolve the forces and moments at the current nozzle connection, enter the Ydistance from the current nozzle to each connection. Distance from the exhaust to the exhaust nozzle is 0.0. In order to resolve the forces and moments at the intersection point of the exhaust nozzle and the shaft centerlines, enter the Y-distance from the intersection point to each connection. CAESAR II User's Guide 835 Equipment Component and Compliance DZ Specifies the Z-distance from the force/moment resolution point to the nozzle. NEMA SM 23 is ambiguous about the point of resolution of the combined forces and moments. The resolution points are interpreted to be the following two points: 1. The face of the flange at the exhaust nozzle connection. 2. The intersection point of the exhaust nozzle centerline and the equipment shaft centerline. In order to resolve the forces and moments at the current nozzle connection, enter the Zdistance from the current nozzle to each connection. Distance from the exhaust to the exhaust nozzle is 0.0. In order to resolve the forces and moments at the intersection point of the exhaust nozzle and the shaft centerlines, enter the Z-distance from the intersection point to each connection. Global Force FX Specifies the X-component of the force that the piping system exerts on the nozzle. Global Force FY Specifies the Y-component of the force that the piping system exerts on the nozzle. Global Force FZ Specifies the Z-component of the force that the piping system exerts on the nozzle. Global Moment MX Specifies the X-component of the moment that the piping system exerts on the nozzle. Global Moment MY Specifies the Y-component of the force that the piping system exerts on the nozzle. Global Moment MZ Specifies the Z-component of the force that the piping system exerts on the nozzle. 836 CAESAR II User's Guide Equipment Component and Compliance Select Load Jobs and Load Case Opens up a dialog box that you can use to navigate to the appropriate loads job or load case. API 610 (Centrifugal Pumps) Analyze > API 610 evaluates piping loads on centrifugal pumps. In October 2004, API released the 10th edition of API 610 for centrifugal pumps for general refinery service. The API 610 load satisfaction criteria are outlined below: If clause F.1.2 is satisfied, then the pump is acceptable. Clause F.1.2a states that the individual component nozzle loads must fall below two times the allowables listed in the Nozzle Loadings table (Table 4) shown below: Further, F.1.2 b) and c) must also be satisfied. Clause F.1.2b states that the resultant applied forces and moments acting on each pump nozzle flange shall satisfy the equations F.1 and F.2 of the code. Referring to the API 610 report, you can determine whether F.1.2b is satisfied by comparing the Force/Moment to two. If either resultant exceeds two, the nozzle status is reported as ** FAILED **. The F.1.2c requirements give equations translating the applied component forces and moments to the center of the pump. The requirements of these equations, and whether they have satisfied API 610, are shown on the bottom of the report. CAESAR II User's Guide 837 Equipment Component and Compliance To begin an analysis of piping loads on centrifugal pumps, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. . All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. The software displays the API 610 window, which consists of three data input tabs: Input Data (see "Input Data Tab" on page 843), Suction Nozzle (see "Suction Nozzle Tab" on page 846), and Discharge Nozzle (see "Discharge Nozzle Tab" on page 847). 838 CAESAR II User's Guide Equipment Component and Compliance The following example is taken from the API 610 code and shows the review of an overhung end-suction process pump in English units. The three CAESAR II input tabs are shown. CAESAR II User's Guide 839 Equipment Component and Compliance 840 CAESAR II User's Guide Equipment Component and Compliance An example of the processing output is shown below: CAESAR II User's Guide 841 Equipment Component and Compliance API 610 Discharge Nozzle 842 CAESAR II User's Guide Equipment Component and Compliance Input Data Tab The following options are used to enter input data used to evaluate piping loads on centrifugal pumps. Topics Vertical In-Line Pumps .................................................................. 844 Centerline Direction Cosine X ....................................................... 844 Centerline Direction Cosine Z........................................................ 844 Basepoint Node Number ............................................................... 845 Suction Nozzle Node Number ....................................................... 845 Suction Nozzle Nominal Diameter ................................................. 845 Suction Nozzle Type ...................................................................... 845 Discharge....................................................................................... 845 Discharge Nozzle Nominal Diameter ............................................ 845 Discharge Nozzle Type ................................................................. 845 Factor for Table 4 Allowables ........................................................ 846 CAESAR II User's Guide 843 Equipment Component and Compliance Vertical In-Line Pumps Indicates that the pump is the vertical in-line type supported only by the attached piping. API states that for the vertical in-line pump, you can use 2.0 times the loads from Table 4. However, even if the pump fails the 2.0 Table 2 criteria, it may still pass. If the principal stress on the nozzle is less than 6,000 psi, then that nozzle passes. If the principal stress on either nozzle is greater than 6,000 psi, the overall status is reported as **FAILED** In API 610 there is an example problem which illustrates the way stresses are computed on these in-line pump nozzles. The two basic equations for determining stress are Stresses (s) = Force / Area + Moment / Section Modulus Shear Stresses (t) = Force / Area + Torque * distance / J Where J is the polar moment of inertia. In the second equation, both terms of the equation are always added together. On the other hand, the Force/Area term in the first equation depends on the sign of the force (tension or compression) that you enter in the force and moment spreadsheet. The sign of the force is determined by Centerline Direction Cosine X (on page 844). For vertical in-line pumps, enter the value in the direction extending from the discharge to the suction nozzle. The distances that are usually entered for pedestal mounted pumps can be left blank because they are not used. Centerline Direction Cosine X Indicates one of the following, depending on whether Vertical In-Line Pumps is selected. Vertical In-Line Pumps - Specifies the direction cosines (X,Z) for the nozzles. The positive direction is from discharge to the suction nozzle. For example, if the nozzles are in the Xaxis, the direction cosines are: cosine X=1.0 cosine Z=0.0 Horizontal Pumps - Specifies the direction cosines (X,Z) for the pump centerline. For example, if the pump is along the Z-axis, the direction cosines are: cosine X=0.0 cosine Z=1.0 Centerline Direction Cosine Z Indicates one of the following, depending on whether Vertical In-Line Pumps is selected. Vertical In-Line Pumps - Specifies the direction cosines (X,Z) for the nozzles. The positive direction is from discharge to the suction nozzle. For example, if the nozzles are in the Xaxis, the direction cosines are: cosine X=1.0 cosine Z=0.0 Horizontal Pumps - Specifies the direction cosines (X,Z) for the pump centerline. For example, if the pump is along the Z-axis, the direction cosines are: cosine X=0.0 cosine Z=1.0 844 CAESAR II User's Guide Equipment Component and Compliance Basepoint Node Number Identifies the node number that describes the intersection of the axis of the shaft and the centerline of the pedestals. Enter only a positive value. This node does not have to appear in any of the piping models but is used by API 610 as a point of reference on the pump about which to sum moments. In the 8th Ed. of the Standard, the base point refers to the center of the pump. The center of the pump is defined by the intersection of the pump shaft centerline and a vertical plane passing midway between the four pedestals. Suction Nozzle Node Number Identifies the node number that describes the suction nozzle flange connection. Enter only a positive number. Suction Nozzle Nominal Diameter Defines the suction nozzle pipe nominal diameter. Suction Nozzle Type Specifies the location of the suction nozzle. Select Top, Side, or End. Each position has different allowables. For pumps with centerline along Y-axis (vertical), select Side. Discharge Identifies the node number that describes the discharge nozzle flange connection. Enter only a positive number. Discharge Nozzle Nominal Diameter Defines the discharge nozzle pipe nominal diameter. Discharge Nozzle Type Specifies the location of the discharge nozzle. Select Top, Side, or End. Each position has different allowables. For pumps with centerline along Y-axis (vertical), select Side. CAESAR II User's Guide 845 Equipment Component and Compliance Factor for Table 4 Allowables Defines the factor by which all Table 4 allowables are multiplied. This value is between 1.0 and 2.0. Values less than 1.0 are replaced by a default factor of 1.0, while values larger than 2.0 are replaced by a default factor of 2.0. If left blank, a default value of 1.0 is used. Typically, a value of 1.0 is used when evaluating individual nozzle loads. When checking vertical in-line pumps, this value can be equal to 2.0. The value of 2.0 is also valid when suction and discharge nozzle loads are evaluated together as defined in Appendix F of the API 610 Standard. Suction Nozzle Tab The following options are used to enter input data for suction nozzles. Topics DX .................................................................................................. 846 DY .................................................................................................. 846 DZ .................................................................................................. 847 Forces on Nozzle ........................................................................... 847 Moments on Nozzle ....................................................................... 847 DX Specifies the distance between the suction nozzle and base point along the X-axis. Enter a positive value if the suction nozzle X-coordinate is greater than that of the base point, that is, if the suction nozzle is farther out on the positive X-axis. When analyzing vertical in-line pumps, the X-, Y-, and Z-distances (DX, DY, and DZ) are not used. The API 610 10th Edition defines the base point as the center of the pump. The center of the pump is defined as the intersection of the pump shaft centerline and a vertical plane passing through the center of the two pedestals. DY Specifies the distance between the suction nozzle and base point along the Y-axis. Enter a positive value if the suction nozzle Y-coordinate is greater than that of the base point, that is, if the suction nozzle is farther out on the positive Y-axis. 846 When analyzing vertical in-line pumps, the X, Y, and Z distances (DX, DY, and DZ) are not used. The API 610 10th Edition defines the base point as the center of the pump. The center of the pump is defined as the intersection of the pump shaft centerline and a vertical plane passing through the center of the two pedestals. CAESAR II User's Guide Equipment Component and Compliance DZ Specifies the distance between the suction nozzle and base point along the Z-axis. Enter a positive value if the suction nozzle Z-coordinate is greater than that of the base point, that is, if the suction nozzle is farther out on the positive Z-axis. When analyzing vertical in-line pumps, the X, Y, and Z distances (DX, DY, and DZ) are not used. The API 610 10th Edition defines the base point as the center of the pump. The center of the pump is defined as the intersection of the pump shaft centerline and a vertical plane passing through the center of the two pedestals. Forces on Nozzle Identifies the X-, Y-, or Z-component of the force that the piping system exerts on the suction nozzle. Enter the forces in their global orientation. For vertical in-line pumps, the orientation of the nozzle centerline is used to determine if the nozzle is in tension or compression. Positive direction is from discharge to suction nozzle. Moments on Nozzle Identifies the X-, Y-, or Z-component of the moment that the piping system exerts on the suction nozzle. Discharge Nozzle Tab The following options are used to enter input data used for discharge nozzles. Topics DX .................................................................................................. 848 DY .................................................................................................. 848 DZ .................................................................................................. 848 Forces on Nozzle ........................................................................... 849 Moments on Nozzle ....................................................................... 849 CAESAR II User's Guide 847 Equipment Component and Compliance DX Specifies the distance between the discharge nozzle and base point along the X-axis. Enter a positive value if the discharge nozzle X-coordinate is greater than that of the base point, that is, if the discharge nozzle is farther out on the positive X-axis. When analyzing vertical in-line pumps, the X-, Y-, and Z- distances (DX, DY, and DZ) are not used. The API 610 10th Edition defines the base point as the center of the pump. The center of the pump is defined as the intersection of the pump shaft centerline and a vertical plane passing through the center of the two pedestals. DY Specifies the distance between the discharge nozzle and base point along the Y-axis. Enter a positive value if the discharge nozzle Y-coordinate is greater than that of the base point, that is, if the discharge nozzle is farther out on the positive Y-axis. When analyzing vertical in-line pumps, the X-, Y-, and Z-distances (DX, DY, and DZ) are not used. The API 610 10th Edition defines the base point as the center of the pump. The center of the pump is defined as the intersection of the pump shaft centerline and a vertical plane passing through the center of the two pedestals. DZ Specifies the distance between the discharge nozzle and base point along the Z-axis. Enter a positive value if the discharge nozzle Z-coordinate is greater than that of the base point, that is, if the discharge nozzle is farther out on the positive Z-axis. 848 When analyzing vertical in-line pumps, the X-, Y-, and Z-distances (DX, DY, and DZ) are not used. The API 610 10th Edition defines the base point as the center of the pump. The center of the pump is defined as the intersection of the pump shaft centerline and a vertical plane passing through the center of the two pedestals. CAESAR II User's Guide Equipment Component and Compliance Forces on Nozzle Identifies the X-, Y-, or Z-component of the force that the piping system exerts on the discharge nozzle. Enter the forces in their global orientation. For vertical in-line pumps, the orientation of the nozzle centerline is used to determine if the nozzle is in tension or compression. Positive direction is from discharge to suction nozzle. Moments on Nozzle Identifies the X-, Y-, or Z-component of the moment that the piping system exerts on the discharge nozzle. API 617 (Centrifugal Compressors) Analysis > API 617 evaluates piping loads on compressors. The requirements of this standard are similar to those of NEMA SM-23 (1991). The allowable load values for API-617 are approximately 85% higher than the NEMA allowables. To begin, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. The software opens the API 617 window, which consists of the following five input tabs: API 617 Input (see "API 617 Input Tab" on page 850) Suction Nozzle (see "Suction Nozzle Tab" on page 852) Discharge Nozzle (see "Discharge Nozzle Tab" on page 853) Extraction Nozzle #1 (see "Extraction Nozzle #1 Tab" on page 854) CAESAR II User's Guide 849 Equipment Component and Compliance API Extraction Nozzle #2 (see "Extraction Nozzle #2 Tab" on page 856) 617 Input Tab Topics Node Number ................................................................................ 851 Nominal Diameter .......................................................................... 851 Node Number ................................................................................ 851 Nominal Diameter .......................................................................... 851 Node Number ................................................................................ 851 Nominal Diameter .......................................................................... 851 Node Number ................................................................................ 851 Nominal Diameter .......................................................................... 851 Equipment Centerline .................................................................... 851 Factor for Allowables ..................................................................... 852 850 CAESAR II User's Guide Equipment Component and Compliance Node Number Indicates the node number that describes the suction nozzle flange connection. Enter a positive number. Nominal Diameter Specifies the suction nozzle pipe nominal diameter. Node Number Indicates the node number that describes the extraction nozzle #1 flange connection. Enter a positive number. Nominal Diameter Specifies the extraction nozzle #1 pipe nominal diameter. Node Number Indicates the node number that describes the discharge nozzle flange connection. Enter a positive number. Nominal Diameter Specifies the discharge nozzle pipe nominal diameter. Node Number Indicates the node number that describes the extraction nozzle #2 flange connection. Enter a positive number. Nominal Diameter Specifies the extraction nozzle #2 pipe nominal diameter. Equipment Centerline Indicates the direction cosines (X,Z) for the equipment shaft centerline. For example, if shaft CL is along the Z-axis, the direction cosines are: cosine X = 0.0 cosine Z = 1.0 CAESAR II User's Guide 851 Equipment Component and Compliance Factor for Allowables Designates the multiplication factor by which all allowables are multiplied, if necessary API 617 does not recommend the use of a multiplier. The code specifically states what the allowables are. Suction Nozzle Tab The following options are used to enter input data for suction nozzles. Topics X Distance to Suction .................................................................... 852 Y Distance to Suction .................................................................... 852 Z Distance to Suction .................................................................... 852 X Force Acting on Suction Nozzle ................................................. 852 Y Force Acting on Suction Nozzle ................................................. 853 Z Force Acting on Suction Nozzle ................................................. 853 X Moment Acting on Suction Nozzle ............................................. 853 Y Moment Acting on suction Nozzle .............................................. 853 Z Moment Acting on Suction Nozzle ............................................. 853 X Distance to Suction Specifies the X-distance from the largest suction/discharge nozzle to the suction nozzle. Y Distance to Suction Specifies the Y-distance from the largest suction/discharge nozzle to the suction nozzle. Z Distance to Suction Specifies the Z-distance from the largest suction/discharge nozzle to the suction nozzle. X Force Acting on Suction Nozzle Specifies the X-component of the force that the piping system exerts on the suction nozzle. 852 CAESAR II User's Guide Equipment Component and Compliance Y Force Acting on Suction Nozzle Specifies the Y-component of the force that the piping system exerts on the suction nozzle. Z Force Acting on Suction Nozzle Specifies the Z-component of the force that the piping system exerts on the suction nozzle. X Moment Acting on Suction Nozzle Specifies the X-component of the moment that the piping system exerts on the suction nozzle. Y Moment Acting on suction Nozzle Specifies the Y-component of the moment that the piping system exerts on the suction nozzle. Z Moment Acting on Suction Nozzle Specifies the Z-component of the moment that the piping system exerts on the suction nozzle. Discharge Nozzle Tab The following options are used to enter input data for discharge nozzles. Topics X Distance to Discharge ................................................................ 853 Y Distance to Discharge ................................................................ 854 Z Distance to Discharge ................................................................ 854 X Force Acting on Discharge Nozzle ............................................. 854 Y Force Acting on Discharge Nozzle ............................................. 854 Z Force Acting on Discharge Nozzle ............................................. 854 X Moment Acting on Discharge Nozzle ......................................... 854 Y Moment Acting on Discharge Nozzle ......................................... 854 Z Force Acting on Discharge Nozzle ............................................. 854 X Distance to Discharge Specifies the X-distance from the largest suction/discharge nozzle to the discharge nozzle. CAESAR II User's Guide 853 Equipment Component and Compliance Y Distance to Discharge Specifies the Y-distance from the largest suction/discharge nozzle to the discharge nozzle. Z Distance to Discharge Specifies the Z-distance from the largest suction/discharge nozzle to the discharge nozzle. X Force Acting on Discharge Nozzle Specifies the X-component of the force that the piping system exerts on the discharge nozzle. Y Force Acting on Discharge Nozzle Specifies the Y-component of the force that the piping system exerts on the discharge nozzle. Z Force Acting on Discharge Nozzle Specifies the Z-component of the force that the piping system exerts on the discharge nozzle. X Moment Acting on Discharge Nozzle Specifies the X-component of the moment that the piping system exerts on the discharge nozzle. Y Moment Acting on Discharge Nozzle Specifies the Y-component of the moment that the piping system exerts on the discharge nozzle. Z Force Acting on Discharge Nozzle Specifies the Z-component of the force that the piping system exerts on the discharge nozzle. 854 CAESAR II User's Guide Equipment Component and Compliance Extraction Nozzle #1 Tab The following options are used to enter input data for the extraction nozzle #1. Topics X Distance to Extraction Nozzle #1 ............................................... 855 Y Distance to Extraction Nozzle #1 ............................................... 855 Z Distance to Extraction Nozzle #1 ............................................... 855 X Force Acting on the Extraction Nozzle ....................................... 855 Y Force Acting on the Extraction Nozzle ....................................... 855 Z Force Acting on the Extraction Nozzle ....................................... 855 X Moment Acting on the Extraction Nozzle ................................... 855 Y Moment Acting on the Extraction Nozzle ................................... 856 Z Moment Acting on the Extraction Nozzle ................................... 856 X Distance to Extraction Nozzle #1 Specifies the X-distance from the largest suction/discharge nozzle to the extraction nozzle #1. Y Distance to Extraction Nozzle #1 Specifies the Y-distance from the largest suction/discharge nozzle to the extraction nozzle #1. Z Distance to Extraction Nozzle #1 Specifies the Z-distance from the largest suction/discharge nozzle to the extraction nozzle #1. X Force Acting on the Extraction Nozzle Specifies the X-component of the force that the piping system exerts on the extraction nozzle #1. Y Force Acting on the Extraction Nozzle Specifies the Y-component of the force that the piping system exerts on the extraction nozzle #1. Z Force Acting on the Extraction Nozzle Specifies the Z-component of the force that the piping system exerts on the extraction nozzle #1. X Moment Acting on the Extraction Nozzle Specifies the X-component of the moment that the piping system exerts on the extraction nozzle #1. CAESAR II User's Guide 855 Equipment Component and Compliance Y Moment Acting on the Extraction Nozzle Specifies the Y-component of the moment that the piping system exerts on the extraction nozzle #1. Z Moment Acting on the Extraction Nozzle Specifies the Z-component of the moment that the piping system exerts on the extraction nozzle #1. Extraction Nozzle #2 Tab The following options are used to enter input data for the extraction nozzle #2. Topics X Distance to Extraction Nozzle #2 ............................................... 856 Y Distance to Extraction Nozzle #2 ............................................... 856 Z Distance to Extraction Nozzle #2 ............................................... 856 X Force Acting on the Extraction Nozzle ....................................... 856 Y Moment Acting on Extraction Nozzle ......................................... 857 Z Force Acting on the Extraction Nozzle ....................................... 857 X Moment Acting on the Extraction Nozzle ................................... 857 Y Moment Acting on the Extraction Nozzle ................................... 857 Z Moment Acting on the Extraction Nozzle ................................... 857 X Distance to Extraction Nozzle #2 Specifies the X-distance from the largest suction/discharge nozzle to the extraction nozzle #2. Y Distance to Extraction Nozzle #2 Specifies the Y-distance from the largest suction/discharge nozzle to the extraction nozzle #2. Z Distance to Extraction Nozzle #2 Specifies the Z-distance from the largest suction/discharge nozzle to the extraction nozzle #2. X Force Acting on the Extraction Nozzle Specifies the X-component of the force that the piping system exerts on the extraction nozzle #1. 856 CAESAR II User's Guide Equipment Component and Compliance Y Moment Acting on Extraction Nozzle Specifies the Y-component of the moment that the piping system exerts on |the extraction nozzle #2. Z Force Acting on the Extraction Nozzle Specifies the Z-component of the force that the piping system exerts on the extraction nozzle #1. X Moment Acting on the Extraction Nozzle Specifies the X-component of the moment that the piping system exerts on the extraction nozzle #1. Y Moment Acting on the Extraction Nozzle Specifies the Y-component of the moment that the piping system exerts on the extraction nozzle #1. Z Moment Acting on the Extraction Nozzle Specifies the Z-component of the moment that the piping system exerts on the extraction nozzle #1. CAESAR II User's Guide 857 Equipment Component and Compliance API 661 (Air Cooled Heat Exchangers) Analysis > API 661 evaluates piping loads on air-cooled heat exchangers. These calculations cover the allowed loads on the vertical, co-linear nozzles (item 9 in the figure below) found on most single or multi-bundled air cooled heat exchangers. The following figures from API 661 illustrate the type of open exchanger body analyzed by this standard. The two requirements must be met for API 661compliance: 5.1.11.1 - Each nozzle in the corroded condition must be capable of withstanding the moments and forces defined in Heat Exchangers figure. 5.1.11.2 - The sum of the forces and moments on each fixed header, that is, each individual bundle, must be less than 1,500 lb. transverse to the bundle, 2,500 lb. axial to the bundle, and 3,000 pound axial on the nozzle centerline. The allowed moments are 3,000, 2,000, and 4,000 ft.-lb., respectively. This recognizes that the application of these moments and forces will cause movement and that this movement will tend to reduce the actual loads. To begin, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. 858 CAESAR II User's Guide Equipment Component and Compliance The software opens the API 661 window, which consists of the following three screens for input of project-specific data: Input Data (see "Input Data Tab" on page 860), Inlet Nozzle (see "Inlet Nozzle Tab" on page 862), and Outlet Nozzle (see "Outlet Nozzle Tab" on page 863). CAESAR II User's Guide 859 Equipment Component and Compliance A typical API 661 report is shown below: 860 CAESAR II User's Guide Equipment Component and Compliance Input Data Tab The following options are used to enter input data used to evaluate piping loads on aircooled heat exchangers. Topics Inlet Nozzle Node Number ............................................................ 861 Inlet Nozzle Nominal Diameter ...................................................... 861 Outlet Nozzle Node Number.......................................................... 861 Outlet Nozzle Nominal Diameter ................................................... 861 Table 4 Force and Moment Multiplier ............................................ 861 Resultant Force and Moment Multiplier ......................................... 861 Tube Bundle Direction ................................................................... 862 Inlet Nozzle Node Number Indicates the inlet nozzle node number that is the connecting point between piping and the exchanger. This entry is optional. If defined, enter a positive number. Inlet Nozzle Nominal Diameter Specifies the nominal diameter of the exchanger inlet connection. Outlet Nozzle Node Number Indicates the outlet nozzle node number that is the connecting point between piping and the exchanger. This entry is optional. If defined, enter a positive number. Outlet Nozzle Nominal Diameter Specifies the nominal diameter of the exchanger outlet connection. Table 4 Force and Moment Multiplier Defines the Table 4 (Figure 6) Force and Moment multiplier. This is the value upon which the passed or failed status is based. If you leave this option blank, the software uses a default value of 1.0. Resultant Force and Moment Multiplier Indicates the resultant force and moment multiplier. The computed force and moment ratios are compared to this value. If you leave this option blank, the software uses a default value of 1.0. CAESAR II User's Guide 861 Equipment Component and Compliance Tube Bundle Direction Specifies the CAESAR II global tube direction. If the X-direction is defined, the force and moment allowables for the X- and Z-directions are flipped. The same applies to the Resultant Force and Moment Multiplier allowables. Inlet Nozzle Tab The following options are used to enter input data for the inlet nozzle. Topics Y Distance from Nozzle Face to Header Center ........................... 862 X Force Applied to Inlet Nozzle ..................................................... 862 Y Force Applied to Inlet Nozzle ..................................................... 862 Z Force Applied to Inlet Nozzle ..................................................... 862 X Moment Applied to Inlet Nozzle ................................................. 863 Y Moment Applied to Inlet Nozzle ................................................. 863 Z Moment Applied to Inlet Nozzle ................................................. 863 Y Distance from Nozzle Face to Header Center Designates the Y-dimension of the suction nozzle to the header center. This dimension must be positive. Refer to Figure 5 in API 661. In the figure, the number 6 arrowhead points to the approximate center of the header location. X Force Applied to Inlet Nozzle Specifies the X-force that the piping system exerts on the inlet nozzle. Y Force Applied to Inlet Nozzle Specifies the Y-force that the piping system exerts on the inlet nozzle. This component can be considered a radial load. Z Force Applied to Inlet Nozzle Specifies the Z-force that the piping system exerts on the inlet nozzle. 862 CAESAR II User's Guide Equipment Component and Compliance X Moment Applied to Inlet Nozzle Specifies the X-moment that the piping system exerts on the inlet nozzle. Y Moment Applied to Inlet Nozzle Specifies the Y-moment that the piping system exerts on the inlet nozzle. Z Moment Applied to Inlet Nozzle Specifies the Z-moment that the piping system exerts on the Inlet nozzle. Outlet Nozzle Tab The following options are used to enter input data for the outlet nozzle. Topics Y Distance From Header Center to Nozzle Face .......................... 863 X Force Applied to Outlet Nozzle .................................................. 863 Y Force Applied to Outlet Nozzle .................................................. 863 Z Force Applied to Outlet Nozzle .................................................. 864 X Moment Applied to Outlet Nozzle .............................................. 864 Y Moment Applied to Outlet Nozzle .............................................. 864 Z Moment Applied to Suction Nozzle ............................................ 864 Y Distance From Header Center to Nozzle Face Indicates the Y-dimension of the header center to the discharge nozzle. Refer to Figure 5 in API 661. In this figure, the number 6 arrowhead points to the approximate center of the header location. X Force Applied to Outlet Nozzle Indicates the X-force which the piping system exerts on the outlet nozzle. Y Force Applied to Outlet Nozzle Specifies the Y-force that the piping system exerts on the outlet nozzle. This can be considered a radial load. CAESAR II User's Guide 863 Equipment Component and Compliance Z Force Applied to Outlet Nozzle Specifies the Z-force that the piping system exerts on the outlet nozzle. X Moment Applied to Outlet Nozzle Specifies the X-moment that the piping system exerts on the outlet nozzle. Y Moment Applied to Outlet Nozzle Specifies the Y-moment which the piping system exerts on the outlet nozzle. Z Moment Applied to Suction Nozzle Specifies the Z-moment which the piping system exerts on the outlet nozzle. Heat Exchange Institute Analysis > HEI Standard evaluates the allowable loads on shell type heat exchanger nozzles. To begin, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. 864 CAESAR II User's Guide Equipment Component and Compliance The software opens the HEI STD window, in which you can enter the necessary input data. The following example shows sample input for the HEI module: Because the pressure is greater than zero, a pressure thrust force is computed and combined with the radial force. Section 3.14 of the HEI bulletin discusses the computational methods used to compute these allowable loads. The method employed by HEI is a simplification of the WRC 107 method, where the allowable loads have been linearized to show the relationship between the maximum permitted radial force and the maximum permitted moment vector. If this relationship is plotted (using the moments as the abscissa and the forces as the ordinate), a straight line can be drawn between the maximum permitted force and the maximum permitted moment vector, forming a triangle with the axes. For any set of applied forces and moments, the nozzle passes if the location of these loads falls inside the triangle. Conversely, the nozzle fails if the location of the loads falls outside the triangle. Because the pressure is greater than zero, a pressure thrust force is computed and combined with the radial force modified to include both the plot of the allowables and the location of the current load set on this plot. The HEI bulletin states that the effect of internal pressure has been included in the combined stresses; however, the effect of the pressure on the nozzle thrust has not. This requires combination with the other radial loads. CAESAR II automatically computes the pressure thrust and adds it to the radial force if Add Pressure Thrust is selected on the HEI Nozzle (on page 866) tab. CAESAR II User's Guide 865 Equipment Component and Compliance HEI Nozzle The following options are used to enter input data for shell type heat exchanger nozzles. Topics Design Pressure ............................................................................ 866 Nozzle Outside Diameter ............................................................... 866 Shell Outside Diameter .................................................................. 866 Shell Thickness ............................................................................. 866 Material Yield Strength .................................................................. 866 Material Allowable Stress .............................................................. 867 Maximum Radial Force .................................................................. 867 Maximum Longitudinal Moment..................................................... 867 Add Pressure Thrust Force ........................................................... 867 Design Pressure Sets the design pressure under which the vessel is operating. Enter a non-negative value. Nozzle Outside Diameter Sets the design pressure under which the vessel is operating. Enter a non-negative value. Shell Outside Diameter Indicates the outside diameter of the pressure vessel. Shell Thickness Defines the shell wall thickness. This software does not take any corrosion allowance into consideration. Material Yield Strength Specifies the yield strength (Sy) of the shell material at the operating temperature. Refer to ASME Section VIII Division 1 for this information. Enter a positive value. The yield strength is greater than the allowable stress. 866 CAESAR II User's Guide Equipment Component and Compliance Material Allowable Stress Indicates the allowable stress of the shell material at the operating temperature, according to ASME Section VIII Division 1. Enter a positive value. Maximum Radial Force Defines the shell wall thickness. This software does not take any corrosion allowance into consideration. Maximum Longitudinal Moment Specifies the moment about the transverse axis of the vessel which the piping exerts on the nozzle. Enter a non-negative value. Add Pressure Thrust Force Controls whether the thrust force generated by the internal pressure is included or ignored. Select this option to include the pressure thrust force. To ignore this force,do not select this option. All versions prior to CAESAR II 3.21a always included the pressure thrust force in analysis. API 560 (Fired Heaters for General Refinery Services) Analysis > API 560 evaluates piping loads on fired heaters. To begin, specify a new job name in the New Job Name Specification dialog box or click Browse to navigate to an existing job file. All CAESAR II analyses require a job name for identification purposes. After you have created, or opened, a job, you can enter input data on the Global Input and Local Member tabs and Output menus to define, analyze, and review your data. CAESAR II User's Guide 867 Equipment Component and Compliance The software opens the API 560 window. The window consists of one input tab on which you can enter data for the tube nominal diameter and the forces and moments acting on the tube. When you run the analysis, CAESAR II compares the input forces and moments to the allowables as published in API 560. An example of the equipment report output is shown below. T 868 CAESAR II User's Guide Equipment Component and Compliance API 560 Input Data Tab The following options are used to enter input data for the tube nominal diameter and the forces and moments acting on the tube. Topics Tube Node Number ....................................................................... 869 Tube Nominal Diameter ................................................................. 869 Tube Axial Force ........................................................................... 869 Tube Horizontal Shear Force ........................................................ 869 Tube Vertical Shear Force ............................................................. 869 Tube Torsional Moment ................................................................. 870 Tube Horizontal Moment ............................................................... 870 Tube Vertical Moment ................................................................... 870 Tube Node Number Identifies the node number for the tube that is being analyzed. Because there are many tubes in a fired heater, analyze the most highly loaded tubes. Tube Nominal Diameter Indicates the nominal diameter of the tube. Tube Axial Force Specifies the axial force acting on the tube at the tube/header junction. If the tube direction is X, then enter the FX value from the appropriate load case. Tube Horizontal Shear Force Specifies the horizontal force acting on the tube at the tube/header junction. If the tube direction is X, then enter the FZ value from the appropriate load case. Tube Vertical Shear Force Specifies the vertical force acting on the tube at the tube/header junction. If the tube direction is X, then enter the FY value from the appropriate load case. CAESAR II User's Guide 869 Equipment Component and Compliance Tube Torsional Moment Indicates the torsional moment acting on the tube at the tube/header junction. If the tube direction is X, then enter the MX value from the appropriate load case. Tube Horizontal Moment Indicates the horizontal moment acting on the tube at the tube/header junction. If the tube direction is X, then enter the MZ value from the appropriate load case. Tube Vertical Moment Indicates the vertical moment acting on the tube at the tube/header junction. If the tube direction is X, then enter the MY value from the appropriate load case. 870 CAESAR II User's Guide S ECTION 1 4 Technical Discussions In This Section Rigid Element Application .............................................................. 871 In-Line Flange Evaluation .............................................................. 873 Cold Spring .................................................................................... 874 Expansion Joints ........................................................................... 876 Hanger Sizing Algorithm ................................................................ 878 Class 1 Branch Flexibilities ............................................................ 883 Modeling Friction Effects ............................................................... 885 Nonlinear Code Compliance.......................................................... 886 Sustained Stresses and Nonlinear Restraints ............................... 887 Static Seismic Inertial Loads ......................................................... 890 Wind Loads .................................................................................... 891 Hydrodynamic (Wave and Current) Loading ................................. 893 Evaluating Vessel Stresses ........................................................... 906 Inclusion of Missing Mass Correction ............................................ 910 Fatigue Analysis Using CAESAR II ............................................... 916 Pipe Stress Analysis of FRP Piping .............................................. 929 Code Compliance Considerations ................................................. 951 Local Coordinates .......................................................................... 991 Rigid Element Application A piping element that is stiffer or heavier than pipe of the same size (for example, a flanged valve) can be modeled as a rigid element in CAESAR II. CAESAR II sets the stiffness of a rigid element based on the inside diameter defined for the pipe but with a wall thickness set to ten times the entered value. Note that long “rigid” elements may bend. Rigid elements in CAESAR II are rigid relative to the pipe around it. For example, if a 6-inch line ties into a 72-inch heat exchanger and rigid elements are used to model the heat exchanger, those exchanger elements are better represented by 72 inch pipe rather than 6 inch pipe. Rigid Weight Specifies a value for the weight of the rigid element. The rigid material weight is the weight of the rigid excluding insulation, refractory, cladding, or fluid. If left blank, then the weight of the rigid defaults to 0. A rigid element with zero weight is often used as a construction element, used to move a centerline load to the shell wall, or used to model the effective stiffness and thermal growth of a piece of equipment. If left blank or 0, then the software does not add the additional weight due either to insulation, refractory, cladding, or fluid. CAESAR II User's Guide 871 Technical Discussions Fluid Weight in Rigid Elements The fluid weight in a rigid element is assumed to be equal to the fluid weight in an equivalent straight pipe of similar length and inside diameter. Insulation Weight on Rigid Elements The insulation weight for the rigid is assumed to be equal to 1.75 times the insulation for an equivalent length of straight pipe of the entered outside diameter. Total Weight on Rigid Elements The total weight for rigid elements where the entered weight is zero will be zero. The total weight for rigid elements where the entered weight is not zero is calculated as follows: Weight = W u + W f + W r +1.75(W i+W c) Where: W u = User-defined rigid weight (the Thermal Expansion/Pipe Weight report will show user-defined weight divided by entered length) W f = Calculated fluid weight for equivalent straight pipe (this is reduced by refractory lining) W r = Calculated refractory weight for equivalent straight pipe W i = Calculated insulation cladding weight for equivalent straight pipe W c = Calculated cladding weight for equivalent straight pipe CAESAR II does not calculate stress on rigid elements. Forces and moments are not normally printed for rigid elements however, you can select the appropriate check box found in Environment>Special Execution Parameters from the Piping Input spreadsheet to print these loads. Modeling using Rigids Zero-weight rigid elements are useful where modeling non-pipe components where thermal growth or load transfer is important. Use zero-weight rigids to model piping hardware such as expansion joint tie rods, base plates, and trunnions. You can also use these dummy rigids to provide connectivity between the centerline of an element and the outside edge of the element. The most common example of this is when you need to add a dummy rigid that runs from the node at the centerline of the vessel to the outside wall where you want to connect the nozzle. You can also model equipment using a series of rigid elements, joining nozzles to a body and perhaps to a support point. This approach will properly distribute thermal strain through the component based on this geometry and the entered element temperatures. For more information on the use of these construction rigids, see the CAESAR II Applications Guide in various sections as appropriate to a particular modeling technique. 872 CAESAR II User's Guide Technical Discussions In-Line Flange Evaluation Allows you to choose the method to use for evaluating flanges under load: The Kellogg Equivalent Pressure Method The ASME NC-365.8 Calculation for B16.5 Flanged Joints Kellogg Equivalent Pressure Method Converts piping axial forces and bending moments into an equivalent pressure on the flange. After the conversion is complete, the software adds this equivalent pressure to the pressure defined in the load case. It then compares this sum to the allowable pressure rating for the flange at the appropriate temperature. (The pressure-temperature table is defined in the model input and the temperature is specified in the Load Case Options.) The formula for the total equivalent pressure displays below: Peq = 16M/()G3 + 4F/ ()G2 + PD Where: Peq = total equivalent pressure (for checking against flange rating) M = calculated bending moment on flange G = diameter of effective gasket reaction F = absolute value of the calculated axial force on flange PD = pressure specified in the load case (for example, P1 for W+T1+P1) The allowable pressure rating will be multiplied by the occasional load factor specified in the Load Case Options. ASME NC-3658.3 Calculation Method for B16.5 Flanged Joints with High Strength Bolting Restricted to joints using flanges, bolting, and gaskets as specified in ANSI B16.5 that use bolting materials having an S value at 100°F (38°C) greater than or equal to 20,000 psi (138 MPa). CAESAR II uses the analysis method for Service Level A as stated in NC-3658.3(a)(2): Mfs ≤ 3125(Sy/36,000)CAb or Mfd ≤ 6250(Sy/36,000)CAb Where: Mfs = Bending or torsional moment, whichever is greater, acting on the flange, and due to weight, thermal expansion, sustained anchor movements, relief valve steady state thrust, and other sustained mechanical loads. CAESAR II considers any moments developed during a non-Occasional Load Case to be Mfs. Mfd = Bending or torsional moment, whichever is greater, acting on the flange, as defined for Mfs and but also including any dynamic loadings. CAESAR II considers any moments CAESAR II User's Guide 873 Technical Discussions developed during an Occasional Load Case to be Mfd, effectively the doubling flange capacity for Occasional loadings. Sy = Yield strength of flange material at design temperature. CAESAR II allows evaluation to be done using as many as 10 different temperatures; Sy/36,000; where Sy, is given in psi, cannot be greater than 36,000 psi C = Bolt circle diameter Ab = Total cross sectional area of bolts PD = Design pressure CAESAR II calculates an Equivalent Stress S in the flange and compares it to Sy (or 2*Sy for occasional load cases), in the following manner: S = 36,000* Mfs / (CAb * 3125) ≤ Min(Sy, 36000) (non-Occ) S = 36,000 * Mfd / (CAb * 3125) ≤ 2.0 * Min(Sy, 36000) (Occ) For systems of units that do not express stress in psi, the software converts the 36,000 values in the above equations to the appropriate set of units. You can do flange evaluations in Static Analysis only. Cold Spring Cold spring is a method where you introduce pipe strain in the installed state to modify the resulting strain in the operating state. Adding this preload is commonly used to adjust (reduce) equipment load in the operating state. A cut short describes an intentional gap in the pipe assembly requiring an initial tensile load to close the final joint. A cut long describes an intentional overlap in the pipe assembly requiring an initial compressive load to close the final joint. This initial gap or overlap is modeled as a cut short material or a cut long material, respectively. CAESAR II reduces the cut short to zero length and doubles the cut long in any load case that includes the “CS” load in the load case definition. This initial cold pull is difficult to implement with any accuracy and, being used in systems that operate in the creep range, their long term effect is difficult to control or even predict. Due to the difficulty of properly installing a cold spring system, most piping codes recommend that you only use two-thirds of the specified cold spring for equipment load calculations. You can calculate the cold spring element length (ignoring equipment growth) by using the following equation: Ci = xLi dT Where: Ci = length of cold spring in direction i; where i is X, Y, or Z (inches) Li = total length of pipe subject to expansion in direction i (inches) = mean thermal expansion coefficient of material between ambient and operating temperature (in/in/°F) dT = change in temperature (°F) x = percent cold spring When x = 0%, there is no cold spring and there will be no reduction in the thermal strain found in the operating load. When x = 100%, the operating load will have no thermal strain as all the expected pipe strain will be realized in the installed state of the piping system. If x = 50%, the 874 CAESAR II User's Guide Technical Discussions pipe strain will be shared equally by both the installed load and operating load. This percent cold spring (x) is not the same term as the two-thirds allowance mentioned above. No credit can be taken for cold spring in the stress calculations, because the expansion stress provisions of the piping codes require the evaluation of the stress range, which is unaffected by cold spring, except perhaps in the presence of non-linear boundary conditions, as discussed below. The cold spring adjusts installed and operating loads and the stress mean, but not the stress range used in most expansion stress calculations. Cold Spring Considerations You must consider several factors when using cold spring: Verify that the cold reactions on equipment nozzles due to cold spring do not exceed nozzle allowables. Verify that the expansion stress range does not include the effect of the cold spring. Verify that the cold spring value/tolerance is much greater than fabrication tolerances. For elevated temperature cases, where cold spring is used to reduce operating equipment load, using the hot modulus of analysis may also have a significant effect on the load magnitude. Modeling cold springs 1. Specify the cold gaps or overlaps as elements defined as cut short or cut long materials, respectively. 2. Make the lengths of the cold spring elements only ⅔ of their actual lengths to implement the code recommendations. 3. Reset the material property on the element following the cold spring element. 4. Analyze the cold spring system by running the following load cases: Load Case 1 (OPE) W+T1+P1+CS includes all of the design cold spring Load Case 2 (OPE) W+P1+CS includes all of the design cold spring but not the temperature. Load Case 3 (SUS) W+P1 standard sustained case for code stress check Load Case4 (EXP) L1-L2 expansion case for code stress check. Both the sustained loads and the operating loads must fall within the manufacturer’s allowables for a specific piece of equipment. 5. Verify that using cold spring in the ambient state does not overload a piece of rotating equipment as the unit starts. Material numbers 18 and 19 are used to signal CAESAR II that the element in the spreadsheet represents a length of pipe that is to be cut short or long during fabrication. CAESAR II User's Guide 875 Technical Discussions Other Applications for Cold Spring While often used to reduce the magnitude of loads on equipment and restraints (see below), you can also use cold spring to accelerate the thermal shakedown of the system in fewer operating cycles. Expansion Joints Checking the expansion joint box on the element enables definition of an expansion joint for that element. Expansion joints can be modeled as a single element across the flexible length of the joint or as a zero length element at the midpoint of the expansion joint. Expansion joints elements have a zero length if the Delta fields on the Pipe Element spreadsheet are left blank or zero. When an expansion joint has a defined length, CAESAR II builds the expansion joint as a beam element using the element length with the entered expansion joint stiffnesses. Four stiffness values define the expansion joint: 876 Axial Transverse Torsion Bending CAESAR II User's Guide Technical Discussions Examples of the Stiffnesses Define Finite Length Joints For expansion joints where flexible length is defined, the bending stiffness is defined by the entered, flexible, length and the transverse stiffness of the joint. Some expansion joint catalogs list what would be called bending flexibility rather than the required bending stiffness used in CAESAR II. This bending flexibility is adequate for an expansion joint modeled by two rigid elements that are pinned at the joint midpoint (a zero length expansion joint) but it is the wrong value for a flexible beam element. To address this ambiguity, CAESAR II calculates and applies a bending stiffness based on the entered expansion joint length and transverse stiffness. We suggest that you only enter the bending term from manufacturers' catalogs when using the zero-length expansion joint model or for rubber joint which do not follow beam bending definitions. Typically, expansion joint manufacturers do not supply torsional stiffness data. If the manufacturer does not supply the data, enter a large torsional stiffness value, and verify that the resulting load on the bellows is not excessive. When the piping system is tight, and the diameter large, the magnitude of the large torsional stiffness can significantly affect the magnitude of the torsion carried by the joints. For example, a stiffness of 100,000 in.lb./deg. and 1E12 in.lb./deg. can produce considerably different torsional load results. Conservatively speaking, the tendency is to use the larger stiffness except that the torsional stiffness value is probably closer to the 100,000 in.lb./deg. In instances where a large torsional stiffness value is important, you can get a stiffness estimate from the manufacturer, or use the equation below to derive an estimate. Use this equation to conservatively estimate torsional loads on the bellows and surrounding equipment. Where = 3.14159 Re = Expansion joint effective radius t = Bellows thickness CAESAR II User's Guide 877 Technical Discussions E = Elastic Modulus = Poisson’s Ratio L = Flexible bellows length When the expansion joint has a zero length, none of the expansion joint stiffnesses are related. You must be sure that you enter a value in all of the Stiffness fields. Calculate the Pressure Thrust CAESAR II calculates the pressure thrust on the expansion joint if you type a value for the bellows Effective ID on the Expansion Joint auxiliary dialog box. If there is no Effective ID, the mathematical model for pressure thrust applies a force equal to the pressure multiplied by the effective area of the bellows at the two nodes that define the expansion joint. The force can open the bellows if the pressure is positive, and close the bellows if the pressure is negative. You should note that this model does not correctly locate pressure load components in the vicinity of the expansion joint. In most cases, the misapplied load does not affect the solution. There are two components of the pressure thrust to apply in practice rather than the one component applied in the model. The first component is equal to the pressure times the inside area of the pipe and acts at the first change in direction of the pipe on either side of the expansion joint. This load will tend to put the pipe wall between the change in direction and the expansion joint in tension. The second component is equal to the pressure times the difference between the bellows effective area and inside pipe area. This load acts at the end of the expansion joint and tends to open the bellows up putting the pipe between the expansion joint and the change in direction in compression. In the mathematical model, the full component of the pressure thrust force is placed on the ends of the bellows instead of having a portion shifted out on either side of the expansion joint. Effective ID The pressure area used to set the pressure thrust force on an expansion joint is provided by the expansion joint manufacturer either as an effective area or effective inside diameter (ID). If the pressure thrust load is to be included in the analysis, the Effective ID must be provided in the expansion joint model definition. Any load case that includes a pressure term (for example, …+P1…) will include a thrust force on either end of the expansion joint based on this effective ID. Hanger Sizing Algorithm At locations that you define, CAESAR II will select a rigid, variable or constant effort support using the automated procedure defined here. Attention here is focused on selecting a variable (spring) support from a manufacturer’s catalog. Be sure to review and verify all supports sized by CAESAR II. 878 CAESAR II User's Guide Technical Discussions Spring Design Requirements A rigid rod is selected if the vertical thermal growth at the location is less than the value entered as “Rigid Support Displacement Criteria” and a constant support is selected if the vertical thermal growth at the location is greater than the value entered as “Max. Allowed Travel Limit”. Otherwise, CAESAR II selects the smallest single spring that satisfies all design requirements provided in the hanger design data. The spring design requirements are: 1. Both the operating (typically hot) and the installed (typically cold) loads must be within the allowed working range of the spring. 2. The absolute value of the change in the load (the product of the travel and the selected spring rate) divided by the design load must be less than the specified "Allowable Load Variation" value. The default variation is 25%. MSS SP-69 defines load variation as the ratio of the change in load and the operating load. CAESAR II, in using the design load, will use the theoretical cold load (discussed below), instead of the operating load, if the user selects "Cold Load" design. 3. If you specify "Available Space", then this space must be greater than the basic height of the spring selected. Positive values are compared with hanger height and negative values are compared with spring can height. If the software cannot find a single spring that satisfies the design requirements, it searches for two identical springs that will each carry half the load. If the software cannot find any springs that satisfies the design requirements, it recommends a constant effort support for the location. Restrained Weight Case If you need to design a hanger, the first analysis case that you must run is the restrained weight case. This case usually includes weight, pressure, and concentrated loads. Hanger hot loads are calculated in the restrained weight case. Run the restrained weight case 1. Place rigid Y-restraints at each hanger location. 2. Determine any anchors you want to designate as freed. 3. Verify the freed anchors are properly released. Loads on the Y-restraints at hangers, calculated from the restrained weight case, are designated as the hanger hot design loads. CAESAR II User's Guide 879 Technical Discussions Pre-Selection Load Case 2 – Setting Hanger Deflection through the Operating Case After the restrained weight case, you must run an operating analysis. The operating case must always be the second load case in the set of defined analysis cases. You can define the operating load cases for hanger design any way you see fit. CAESAR II recommends the load cases it thinks you should run whenever it detects the first attempt to analyze a particular system. You can accept or reject the recommendations. If you define your own hanger design load cases, you must understand exactly what is done in the "restrained weight" and operating passes of the hanger design algorithm. Run an operating case 1. Remove the Y-restraints. 2. Insert the hot loads calculated from the hanger locations in the restrained weight analysis. 3. Change any freed anchors from the restrained weight analysis to fixed. The vertical displacement of the operating case at each hanger location defines the travel of that particular hanger. If there are single directional restraints or gaps in the system and a changed status in the operating case, then the hanger loads are redistributed. When CAESAR II detects a nonlinear status change, it reruns the restrained weight case with the restraints left as they were at the end of the operating case. To determine the updated travel, you must calculate the new restraint loads and run another operating case. Post-Selection Load Case (Optional) – Setting the Actual Installed (Cold) Load If you need to calculate the actual hanger installed loads, the third analysis level combination case must define the weight configuration that exists in the field when a spring is installed. Typically, this case includes weight without fluid contents and other live loads. The theoretical cold, or installed load, is the load on the spring when the "unbalanced" installed load is applied and the pipe is not allowed to displace vertically (the load will be "balanced" when the pipe is in the operating or design position). The actual installed load may differ from the theoretical installed load by (K)(d), where (K) is the spring stiffness and (d) is the displacement of the pipe in the installed condition. Calculate the actual installed load 880 1. Install the hangers. 2. Apply the theoretical cold load and all other loads (for example, empty weight) that will be present when the springs are set. 3. Calculate the position of all springs (d). 4. Set the actual installed spring load based on this installed position (installed load = Theoretical Cold Load - (K)(d)). CAESAR II User's Guide Technical Discussions Create Spring Load Cases Up to three load cases are needed for spring sizing: "Restrained" Weight (required) Operating (required) Installed Weight (optional) After the Hanger Algorithm runs the hanger load cases, it selects the hangers. The program inserts the newly-selected springs into the piping system and includes them and their preload (the Theoretical Cold Load) in the analysis of all remaining load cases. Hanger installed loads are concentrated forces and are only included in subsequent load cases that contain the hanger preload force set (+H). You can specify any number of user-defined load cases after setting up the required spring load cases. Spring hanger design does not affect the ability of CAESAR II to check code compliance. In load cases recommended by CAESAR II, the normal code compliance cases always follow the set of load cases required for hanger design. Multiple operating case spring hanger design implies that hanger loads and travels from more than one operating case are included in the spring hanger selection algorithm. Each spring in a multiple operating case hanger design has a Multiple Load Case Design option. This design option tells CAESAR II how multiple loads and travels for a single hanger are combined to get a single design load and travel. The set-up of the analysis cases is slightly different for multiple operating case hanger design in that now there is more than one operating case. You can use the Hanger Design Control dialog to specify the actual number of operating cases. The load cases that you analyze for multiple load case hanger design operating cases are: Restrained Weight (this does not change) Operating case #1 Operating case #9 Installed Weight (if requested) CAESAR II User's Guide 881 Technical Discussions Constant Effort Support Enables you to specify the support load for a constant effort hanger and define the hanger location. This value is also included in all hanger design runs and all analysis cases following the hanger cases that include the hanger preload force set in their formulation. Including the Spring Hanger Stiffness in the Design Algorithm The operating cases for hanger travel are normally analyzed with no stiffness included at the hanger locations. This is why these cases are traditionally referred to as "free thermal" cases. However, when the piping system is very flexible, or the selected springs are very stiff, the actual resulting spring loads in the installed condition can vary significantly from the theoretically calculated results. With such a load change, perhaps this shorter, more accurate spring deflection may allow a smaller spring selection. In that case, CAESAR II enables you to include, using an iterative process, the stiffness of the selected springs in the operating cases for hanger travel. You can activate this trait for all new models through the Configure\Setup by setting the option to Include Travel to As Designed. You can also activate this option for individual models on the Load Case Options Tab (Static Analysis Dialog Box) (on page 537) tab by changing the Hanger Stiffness option to As Designed. Selecting this option could lead to convergence problems. If you use this option, be sure to check the hanger load in the cold case in the field so that it matches the reported hanger Cold Load. You must always include the hanger preload force set H (the Theoretical Cold Load) in subsequent load cases. Applying thermal and displacement effects to the live loaded system should make an installed hanger move to the hot, or balanced, load in this operating case. Other Notes on Hanger Sizing At times, CAESAR II indicates that certain hanger locations carry no load and selects “zero load” constant effort supports at these locations. Typically, zero load constant effort supports indicate poor hanger locations. It is important to not simply ignore these selections as and other hangers selected in the vicinity of these “zero load” hangers have improper operating loads assigned. Relocate or remove these “zero load” selections. Unless you specifically designate your hanger design load cases with a KEEP status, they display in the output reports as NOT ACTIVE. 882 CAESAR II User's Guide Technical Discussions Class 1 Branch Flexibilities This analytical option was added to CAESAR II for the following reasons: Automatic local flexibilities at intersections help you bound the true solution. Because the computer time to do an analysis is less expensive, more frequently you can run several solutions of the same model using slightly different input techniques to determine the effect of the modeling difference on the results. This gives you a degree of confidence in the numbers you get. For example, structural steel supporting structures can be modeled to see the effect of their stiffnesses, nozzle flexibilities can be added at vessel connections to see how these features redistribute load throughout the model, friction is added to watch its effect on displacements and equipment loads, and with CAESAR II you can include Class 1 intersection flexibilities. The characteristic that makes this option convenient to use is that you can enable or disable the Class 1 flexibilities using a single option in the setup file. No other modification to the input required. In WRC 329, there are a number of suggestions made to improve the stress calculations at intersections. These suggestions are fairly substantial and are given in order of importance. The most important item, as felt by E. Rodabaugh, in improving the stress calculations at intersections is given, in part, as follows: "In piping system analyses, it may be assumed that the flexibility is represented by a rigid joint at the branch-to-run centerlines juncture. However, you should be aware that this assumption can be inaccurate and should consider the use of a more appropriate flexibility representation." Use of the Class 1 Branch Flexibility feature may be summarized as follows: Include the Class 1 Branch Flex option in the setup file. Where reduced branch geometry requirements are satisfied, CAESAR II constructs a rigid offset from the centerline of the header pipe to its surface, and then adds the local flexibility of the header pipe, between the end of the offset, at the header, and the start of the branch. Stresses computed for the branch are for the point at its connection with the header. Where reduced branch geometry requirements are not satisfied, CAESAR II constructs a rigid offset from the centerline of the header pipe to its surface. The branch piping starts at the end of this rigid offset. There is NO local flexibility due to the header added. (It is deemed to be insignificant.) Stresses computed for the branch are for the point at its connection with the header. The reduced branch geometry requirements that CAESAR II checks are d/D 0.5 and D/T 100.0 Where: d = Diameter of Branch D = Diameter of Header T = Wall thickness of Header If you use the Class 1 branch flexibilities, intersection models in the analysis become stiffer when the reduced geometry requirements do not apply, and become more flexible when the reduced geometry requirements do apply. Stiffer intersections typically carry more loads and thus have higher stresses lowering the stress in other parts of the system that have been CAESAR II User's Guide 883 Technical Discussions unloaded. More flexible intersections typically carry less load and thus have lower stresses. This causes higher stresses in other parts of the system that have "picked up" the extra load. The branch flexibility rules used in CAESAR II are taken from ASME III, Subsection NB, (Class 1), 1992 Edition, Issued December 31, 1992, from Code Sections NB-3686.4 and NB-3686.5. When the reduced branch rules apply, use the following equations for the local stiffnesses: TRANSLATIONAL: AXIAL = RIGID CIRCUMFERENTIAL = RIGID LONGITUDINAL = RIGID ROTATIONAL: AXIAL = RIGID CIRCUMFERENTIAL = (kx)d/EI LONGITUDINAL = (kz)d/EI Where: RIGID = 1.0E12 lb./in. or 1.0E12 in.lb./deg. d = Branch Diameter E = Young’s Modulus I = Cross Section Moment of Inertia D = Header Diameter T = Header Thickness Tb = Branch Fitting Thickness kx = 0.1(D/T)1.5[(T/t)(d/D)]0.5(Tb/T) 0.2(D/T)[(T/t)(d/D)]0.5(Tb/T) kz = For more information, see WRC 329 Section 4.9 Flexibility Factors. A brief quote from this section follows: "The significance of "k" depends upon the specifics of the piping system. Qualitatively, if "k" is small compared to the length of the piping system, including the effect of elbows and their kfactors, then the inclusion of "k" for branch connections will have only minor effects on the calculated moments. Conversely, if "k" is large compared to the piping system length, then the inclusion of "k" for branch connections will have major effects. The largest effect will be to greatly reduce the magnitude of the calculated moments acting on the branch connection. To illustrate the potential significance of "k’s" for branch connections, we use the equation [above] to calculate "k" for a branch connection with D=30 in., d=12.75 in., and T=t=0.375 in.: k = 0.1(80)1.5(0.425)0.5 * (1.0) = 46.6 This compares to the more typical rigid-joint interpretation that k=1, rather than k=46.6 !" Further discussion in section 4.9 illustrates additional problems that can arise by overestimating the stiffness at branch connections. Problems arise by believing "mistakenly" that the stress at the intersection is too high. Further reference should be made to this section in WRC 329. 884 CAESAR II User's Guide Technical Discussions Branch automatic flexibility generation can be used where the user has only defined the branch element in the model, that is has left the header piping out of the analysis. In this case there will be no "offset" equal to one-half of the header diameter applied to the branch end. A "partial intersection" is one where either the header pipe is not modeled, is modeled with a single element, or is part of a geometric intersection where the header pipes are not colinear. In the case where there is no header pipe going to the intersection, there will be no modification to the model for the class 1 branch flexibilities. When at least a single header pipe is recognized, the local flexibility directions are defined by the branch alone and in accordance with the CAESAR II defaults for circumferential and longitudinal directions for the branch and header. You must build full intersection models at all times, not only when employing the class 1 branch flexibility. In most cases, building full intersection models eliminates problems caused by the assumptions necessary when a partial intersection is described. In the equations in NB-3686.5 for tn, the thickness of the branch pipe is used in all cases. When branches are skewed with respect to the header pipe, and where the two header pipes are colinear, the local Class 1 flexibilities are still taken to be the longitudinal and circumferential directions that are tangent to the header surface at its intersection with the branch. Class 1 branch flexibilities can be formed at both ends of a single pipe element. The offsets necessary to form the class 1 intersections are automatically generated by CAESAR II. There is no extra input required by you to have CAESAR II build these intersections. If there are already user-defined offsets at an intersection end, the computed offset to get from the header centerline to its surface along the centerline of the branch is added to the already entered user offset. Automatic offsets are generated providing that the distance from the header centerline to the header surface along the branch centerline is less than or equal to 98% of the total pipe straight length. When an element with a bend designation is part of an intersection model, the offset and flexibility calculations are not performed. Modeling Friction Effects There are two methods to solving friction problems: Insert a force at the node which must be overcome for motion to occur. Insert a stiffness which applies an increasing force up to the value of Mu * Normal Force. CAESAR II uses the stiffness method. If there is motion at the node under evaluation then the friction force is equal to Mu * Normal force. However, because there is a non-rigid stiffness placed at that location to resist the initial motion; the node could experience some displacement. The force at the node is the product of the displacement and the stiffness. If the resultant force is less than the maximum friction force (Mu * Normal Force) the node is assumed to be not sliding. As a result, you might see displacements at nodes that have not achieved the "sliding" friction force in the output report. The maximum value of the force at the node is the friction force (Mu * Normal force). After the system reaches this value, the reaction at the node stops increasing. This constant force value is then applied to the global load vector during the next iteration to determine the nodal displacements. The example below explains what happens in a "friction" problem. CAESAR II User's Guide 885 Technical Discussions 1. The default friction stiffness is 1,000,000 lb./in. To solve convergence problems, consider decreasing this value. 2. Until the calculated load at the node equals (Mu * Normal force), the restraint load is the product of the displacement multiplied by the friction stiffness. 3. Should the calculated load exceed the maximum value of the friction force, the friction force stops increasing because a constant effort force opposite the sliding direction is inserted in the model in place of the friction stiffness. If you increase the friction stiffness in the setup file, the displacements at the node may decrease slightly. Usually, this causes a re-distribution of the loads throughout the system that could have an adverse effect on the solution convergence. If problems arise during the solution of a job with friction at supports, reducing the friction stiffness typically improves convergence. You must do several runs with varying values of the friction stiffness to ensure the behavior of the system is consistent. For more information on this subject, see "Inclusion of a Support Friction into a Computerized Solution of a Self-Compensating Pipeline" by J. Sobieszczanski, published in the Transactions of the ASME, Journal of Engineering for Industry, August 1972. A summary of the major points of this paper is below. Summary of J. Sobieszczanski’s ASME Paper For dry friction, the friction force magnitude is a step function of displacement. This discontinuity means the problem as intrinsically nonlinear and eliminates the possibility of using the superposition principle. The friction loading on the pipe can be represented by an ordinary differential equation of the fourth order with a variable coefficient that is a nonlinear function of both dependent and independent variables. No solution in closed form is known for an equation of this type. The solution has to be sought by means of numerical integration to be carried out specifically for a particular pipeline configuration. Dry friction can be idealized by a fictitious elastic foundation, discretized to a set of elastic spring supports. A well-known property of an elastic system with dry friction constraints is that it may attain several static equilibrium positions within limits determined by the friction forces. The whole problem then has clearly not a deterministic, but a stochastic character. Nonlinear Code Compliance You can adhere to nonlinear piping code compliance requirements by doing the following: 1. Performing an operating and sustained analysis of the system and including with each case the effect of nonlinear restraints. 2. Subtracting the sustained case displacements from the operating case displacements to find the displacement range. 3. Calculating the expansion stresses from the displacement range solved for in step 2. CAESAR II uses this method for calculating the expansion stress range. In addition, CAESAR II scans your input and recommends load cases and combinations for performing the operating, 886 CAESAR II User's Guide Technical Discussions sustained, and expansion stress calculations. This recommendation is useful when performing spring hanger analysis of a multiple operating case system. Sustained Stresses and Nonlinear Restraints The proper computation of sustained stresses has been an issue since the late 1970s when computerized pipe stress analysis programs first attempted to address the problem of nonlinear restraints. The existing piping codes offered little guidance on the subject, because their criteria were developed during the era when all analyses were simplified to behave in a strictly linear fashion. The problem arises because the codes require that a piping system be analyzed separately for sustained loadings; you must determine which stresses are caused by which loadings. Sustained loads are force loadings that are assumed not to change, while expansion loadings are displacement loadings that vary with the system operating conditions. Determination of the sustained loads is the simple part — most everybody agrees that those forces consist of weight, pressure, and spring preloads. These forces remain relatively constant as the piping system goes through its thermal growth. However, confusion occurs when the status of nonlinear restraints change (pipes lift off of supports, gaps close, and so forth) as the pipe goes from installed to operating state. In this case, you must determine which boundary conditions to use when evaluating the applied forces. Or in other words, what portion of the stress in the operating case is caused by weight loads, and what portion is caused by expansion effects? There is no corresponding confusion on the question of calculating expansion stresses, because the codes are explicit in their instructions that the expansion stress range is the difference between the operating and cold stress positions, both of which are known. The obvious answer to this question by the developers of some pipe stress programs was that the sustained stress calculation should be done using the operating, or hot boundary condition. This compounded the problem in that the laws of superposition no longer held. In other words, the results of sustained (W+P) and thermal (T) cases, when added together, did not equal the results of the operating (W+P+T) case. One pioneering program, DYNAFLEX, attempted to resolve this by introducing the concept of the "thermal component of weight" an oxymoron, in our opinion. Other programs, notably those which came from the mainframe/linear analysis world, had to approximate the behavior of these non-linear restraints. Their approach to the problem is to run an operating case, obtain the restraint status, and modify the model according to these results. All subsequent load cases analyzed use this restraint configuration. The fact that the laws of static superposition did not hold was hopefully not noticed by the user. CAESAR II, on the other hand, represents technology developed expressly for operation on the personal computer, and therefore incorporates directly the effects of non-linear restraints. This is done by considering each load case independently. The restraint configuration is determined for each load case by the program as it runs, based upon the actual loads that are considered present. Some users have asserted that there are actually two sustained load cases. In fact, there has been a B31.3 code interpretation that indicates that the sustained stress may also be checked with the operating restraint configuration. Calculating the sustained stresses using the operating restraint status raises several other issues; what modulus of elasticity should be used, and which sustained stresses should be used for occasional cases. It is our assertion that there is only one sustained case (otherwise, it is not "sustained") there can be, however, multiple sustained stress distributions. The two most obvious are those associated with the cold (installed) and hot (operating) configurations; however, there are also numerous inbetween, as the piping system load steps from cold to hot. Whether the "true" sustained load case occurs during the installed or operating case is a matter of the frame of CAESAR II User's Guide 887 Technical Discussions reference. If an engineer first sees a system in its cold condition, and watches it expand to its operating condition, it appears that the first case (because weight and pressure — primary loads — are present) is the sustained case, and the changes he viewed are thermal effects (due to heat up) — secondary loads due to displacements. If a second engineer first sees the same system in the operating case and watches it cool down to the cold case, he may believe that the first case he saw (the operating case) is the sustained case, and changes experienced from hot to cold are the thermal expansion effects (the thermal stress ranges are the same in both cases). Consider the further implications of cryogenic systems where changes from installed to operating are the same as those experienced by hot systems when going from operating to installed. After elastic shakedown has occurred, the question becomes clouded even further due to the presence of thermally induced pre-stresses in the pipe during both the cold and hot conditions. We feel either the operating or installed case (or some other one in-between) could justifiably be selected for analysis as the sustained case, as long as the program is consistent. We have selected the installed case (less the effect of cold spring) as our reference sustained case, because thermal effects can be completely omitted from the solution (as intended by the code). This best represents the support configuration when the sustained loads are initially applied. If the pipe lifts off of a support when going from installed to operating, we view this as a thermal effect which is — consistent with the piping codes’ view of thermal effects as the variation of stress distribution as the piping system goes from cold to hot, and is explicitly corroborated by one code, an earlier edition of the French petrochemical code, which states that weight stress distributions due to thermal growth of the pipe should be considered as expansion stresses). For example, we feel that a change in a rigid support load from 2,000 lbs to zero should be treated no differently than would be a variable spring load changing from 6,000 lbs to 4,000 lbs (or another rigid support load going 2,000 lbs to 1 lb). In the former case, if the pipe became "overstressed", it would yield, and sag back to the support, relieving the stress. This process is identical to the way that all other expansion stresses are relieved in a piping system. We are confident that our interpretation is correct. However, we understand that our users may not always agree with us — that is why CAESAR II provides the greatest ability to custom tailor the analysis to your individual specifications. If you want, you can analyze a "hot sustained" case by adding two load cases to those normally recommended by CAESAR II. This is done by assuming that the pipe expands first, and then the sustained loads are applied (this is of course an idealized concept, but the stresses can only be segregated by segregating the applied loads, so the sustained loads can only be applied either before, or after, the expansion loads). Following are the default load cases, as well as those required for a "hot sustained." Default New L1: W+P1+T1(OPE) L1: W+P1+T1(OPE) L2: W+P1(SUS) L2: W+P1(SUS) L3: L1-L2(EXP) L3: T1(EXP) L4: L1-L2(EXP) L5: L1-L3(SUS) In the new load case list, the second case still represents the cold sustained, while the fourth case represents the expansion case (note that L1-L2, or W+P1+T1-W-P1, equals T1, with non-linear effects taken into account). The third case represents the thermal growth of the "weightless," non-pressurized pipe, against the non-linear restraints. 888 CAESAR II User's Guide Technical Discussions The fifth case (L1-L3, or W+P1+T1-T1, equals W+P1) represents the application of weight and pressure to that expanded case, or the "hot sustained" case. Note that when the piping system is analyzed as above, the actual effects of the non-linear restraints are considered (they are not arbitrarily removed from the model), and the laws of superposition still hold. An alternative school of thought believes that a "hot sustained" is only valid if: (1) the sustained, primary loads are applied, (2) all springs are showing their Hot Load settings, and (3) any supports that lift off (or otherwise become non-active) have been removed from the model. An analysis such as this is achievable by setting the "Keep/Discard" status of the Restrained Weight case (the first hanger design load case) to "Keep", thus permitting the results of that case to be viewable as for any other load case. The Restrained Weight case automatically removes restraints that become non-active during the designated operating case, and apply the Hot Load at each of the hanger locations. Notes on Occasional Load Cases Several piping codes require that you add the stresses from occasional loads (such as wind or earthquake) to the sustained stresses (due to weight, pressure, and other constant loads) before comparing them to their allowables. You can recreate this combination in CAESAR II using the following load cases: CASE # 1 W+P+H (SUS): Sustained stresses 2 WIND (OCC): Wind load set 3 U1 (OCC): Uniform g load set for earthquake 4 L1+L2 (OCC): Code stresses for wind 5 L1+L3 (OCC): Code stresses for earthquake* * Scalar Summation Method required If you must model nonlinear effects in the system, the load case combinations are not so straight forward. Friction, one-direction restraints, and double-acting restraints with gaps are the nonlinear items which complicate modeling. For this example, we will use wind loading on a long vertical run of pipe with a guide. Assume there is a 1-inch gap between the pipe and guide. Under normal operation, the pipe moves ¾-inch towards the stop leaving a gap of 1-¾-inch on either side of the pipe and a ¼-inch gap on the other side. If you analyze the wind loads alone, the pipe is allowed to move 1-inch from its center point in the guide to the guide stop. Because occasional loads are usually analyzed with the system in operation, the pipe may be limited to a ¼-inch motion as the gap is closed in one direction, and 1-¾-inch if the gap is closed in the opposite direction. With nonlinear effects modeled in the system, the occasional deflections (and stresses) are influenced by the operating position of the piping. The following list of CAESAR II load cases takes this point into consideration. The load cases displayed below are only for wind acting in one direction, that is, +X. Depending on the system, the most critical loads could occur in any direction +/-X, +/-Z, or skewed in XZ. The intention of the load case construction is to find the effect of the occasional load on the piping system in the operating condition. The stress due to the moment change from the operating to the operating plus wind case is added to the stress from the sustained case. CAESAR II User's Guide 889 Technical Discussions CASE # 1 W+T1+P1 (OPE): Operation analysis 2 W+P1 (SUS): Sustained stresses 3 W+T1+P1+WIN D1 (OPE): Operating analysis with wind 4 L1-L2 (EXP): Expansion stresses (Algebraic summation) 5 L3-L1 (OCC): Net deflection of wind(Algebraic summation) 6 L2+L5 (OCC): Code stresses for wind (Scalar summation) Case 5 computes the isolated wind effect on the piping system in the operating condition. Case 6 adds the stresses from Case 5 to the sustained stresses from Case 2. Static Seismic Inertial Loads Static earthquake loads are applied in a manner very similar to static wind loads. The static loading magnitude is considered to be in direct proportion to the weight of the element. Express earthquake load magnitudes in terms of the gravitational acceleration constant g. If you model an earthquake with a 0.5-g load in the X direction, then half of the systems weight is turned into a uniform load and applied in the X direction. You create earthquake static load cases the same way you create wind occasional load cases. Use the same load case, nonlinearity, and directional sensitivity logic. In some cases, the client specifies the magnitude of the earthquake loading in g's and the direction(s). In other cases, analysis is left to the discretion of the analyst. It is not unusual to see only X-Y or Z-Y components of an earthquake. It is also not uncommon to see X, Y, and Z simultaneous components. Dynamic (response spectrum) evaluation of earthquake loads are discussed later in this section, in the dynamic analysis and output sections, and in the screen reference section. The ASCE #7 method for determining earthquake coefficients is described below. After you calculate the earthquake coefficients, enter the g-factors as uniform loads on the piping spreadsheet. Calculate the horizontal seismic design force using equation 13.3-1 from ASCE 7 (10): Fp = [(0.4 ap SDS W p) / (Rp / Ip)] (1 + 2 z / h) But since W p is "component operating weight", Fp/W p = calculated (horizontal) acceleration, aH, so; aH = [(0.4 ap SDS) / ( Rp / Ip )] (1 + 2 z / h), additionally; aH 1.6 SDS Ip and: 890 CAESAR II User's Guide Technical Discussions aH 0.3 SDS Ip Where: ap = Component amplification factor, from Table 13.6-1 = 2.5 for "Piping" SDS = Design elastic response acceleration at short period (0.2 sec), from Section 11.4.4 Rp = Component response modification factor, from Table 13.6-1 = 12.0 for "Piping in accordance with ASME B31... with joints made by welding or brazing"; values range as low as 3.0 for other joints and for less ductile materials. Ip = Component importance factor, from Section 13.1.3 = 1.5 for life-safety components, components containing hazardous material, or components that are required for continuous operation; 1.0 for all others z = Height in structure at point of attachment h = Average roof height of structure Wind Loads You can define your own wind pressure profile or wind speed profile, or you can access wind load data from the following wind codes: ASCE7 2005 IBC 2006 AS/NZ 1170:2002 IS 875 Brazil NBR 6123 Mexico 1993 BS6399-97 NBC 2005 China GB 50009 UBC EN 1991-1-4:2005 Generate Wind Loads By defining a wind shape factor in the model input, CAESAR II allows you to define up to four wind vectors in the Load Case Editor. Multiply the pipe exposed area by the equivalent wind pressure and the pipe shape factor. CAESAR II includes insulation thickness in the cladding. You must also consider the angle to the wind with your calculations. Determine the Equivalent Wind Pressure There are three ways to determine the equivalent wind pressure: Selecting a regional wind specification (by building code) Use the Pressure versus Elevation Table Entry method Use the Velocity versus Elevation Table Entry method CAESAR II User's Guide 891 Technical Discussions Calculate the Total Wind Force on the Element Calculate the total wind force on the element by using the following equation: F= PeqSA Where: F = the total wind force on the element Apply the wind force in the three global directions as a function of the element direction cosines. Peq = the equivalent wind pressure (dynamic pressure) Calculate Peq for each end of the element and then take the average. The average applies uniformly over the whole length of the element. S = the pipe element wind shape factor A = the pipe element exposed area as shown in the figure to the right. If you enter velocity versus elevation table data, then the program converts the velocity to a dynamic pressure using the following equation: P = 1/2 V2 Where V is the wind velocity and is the air density. Enter the Wind Shape Factor on the piping spreadsheet. For cylindrical elements, a value between 0.5 and 0.7 is used. A value of 0.65 is typical. The wind shape factor as entered is distributive. This means that the shape factor entered on a spreadsheet is carried forward and applies for all following elements until zeroed or changed. There is no need to enter the same shape factor on each piping spreadsheet. Zero or disable the wind shape factor if the piping system runs inside of a building or similarly protective structure. Enter wind load parameters on the Wind Loads (see "Wind Loads Tab (Static Analysis Dialog Box)" on page 543) tab of the Static Load Case Builder. You can enter up to four different wind loads per analysis. These typically might be setup to model wind loads in the +X, -X, +Z, and -Z directions. 892 CAESAR II User's Guide Technical Discussions Elevation It is important to set the proper elevation of the piping system (height above ground) when running a wind analysis. When a wind shape factor is specified in the input, CAESAR II prompts you for the elevation (and horizontal coordinates) of this first node. By default, CAESAR II assigns the "From" node of the first element an elevation of 0.0. You can also use the procedure below to set the reference wind elevation of the piping system. Set the true elevation 1. Click EDIT > GLOBAL. A dialog appears. 2. Enter the global coordinates of the first node in the system. 3. Repeat step 2 for each (if any) disconnected section until you are finished. You can specify and save the coordinates for up to 100 node points from the model. Hydrodynamic (Wave and Current) Loading Ocean waves are generated by wind and propagate out of the generating area. Ocean wave generation is dependent on the wind speed, the duration of the wind, the water depth, and the distance over which the wind blows the fetch length. There are several two dimensional wave theories, but the three most widely used are the Airy (linear) wave theory, Stokes 5th Order wave theory, and Dean's Stream Function wave theory. The latter two theories are non-linear wave theories and provide a better description of the near surface effects of the wave. Of course, wave motion is a three dimensional action but it can be adequately represented by two dimensions. One dimension is the direction the wave travels, and the other dimension is vertical through the water column. Two dimensional waves are not found in the marine environment, but are somewhat easy to define and determine properties for. In actuality, waves undergo spreading, in the third dimension. To understand this concept think about a stone dropped in a pond. As the wave spreads, the diameter of the circle increases. In addition to wave spreading, a real sea state includes waves of various periods, heights, and lengths. To address these actual conditions you must use a sea spectrum that includes a spreading function. Airy (linear) wave theory assumes the free surface is symmetric about the mean water level. Additionally, water particle motion is in a closed circular orbit, the diameter of which decays with depth. You should take the term circular loosely because, the orbit varies from circular to elliptical based on whether the wave is in shallow or deep water. Additionally, for shallow water waves, the wave height to depth ratio (H/D) is limited to 0.78 to avoid breaking. None of the wave theories address breaking waves. CAESAR II User's Guide 893 Technical Discussions The figure below shows a typical wave and associated hydrodynamic parameters. SWL - The still water level. L - The wave length or horizontal distance between successive crests or troughs. H - The wave height or vertical distance between the crest and trough. D - The water depth or vertical distance from the bottom to the still water level. - The surface elevation measured from the still water level. Ocean Wave Particulars The Airy Wave Theory Implementation (on page 897) theory provides a good first approximation to the water particle behavior. The nonlinear theories provide a better description of particle motion, over a wider range depths and wave heights. Stokes 5tH Wave theory is based on a power series. This wave theory does not apply the symmetric free surface restriction. Additionally, the particle paths are no longer closed orbits, which mean there is a gradual drift of the fluid particles, that is, a mass transport. Stokes 5tH Order Wave theory however, does not adequately address steeper waves over a complete range of depths. Dean’s Stream Function wave theory attempts to address this deficiency. This wave theory employs an iterative numerical technique to solve the stream function equation. The stream function describes not only the geometry of a two dimensional flow, but also the components of the velocity vector at any point, and the flow rate between any two streamlines. 894 CAESAR II User's Guide Technical Discussions The most suitable wave theory is dependent on the wave height, the wave period, and the water depth. Based on these parameters, the applicable wave theory can be determined from the figure below (from API-RP2A, American Petroleum Institute - Recommended Practice 2A). Applicable Wave Theory Determination The limiting wave steepness for most deep water waves is usually determined by the Miche Limit: H / L = 0.142 tanh( kd ) Where: H is the wave height L is the wave length k is the wave number (2)/L d is the water depth CAESAR II User's Guide 895 Technical Discussions Pseudo-Static Hydrodynamic Loading You can model individual pipe elements that experience loading due to hydrodynamic effects. Fluid effects can impose a substantial load on the piping elements in a manner similar to, but more complex than wind loading. Use wave theories and profiles to compute the water particle velocities and accelerations at the node points. Then use, Morrison’s equation, F = ½ * * Cd * D * U * |U| + /4 * * Cm * D2* A to compute the force on the element. Where: - is the fluid density Cd- is the drag coefficient D - is the pipe diameter U - is the particle velocity Cm - is the inertial coefficient A - is the particle acceleration The particle velocities and accelerations are vector quantities that include the effects of any applied waves or currents. In addition to the force imposed by Morrison’s equation, piping elements are also subjected to a lift force and a buoyancy force. The lift force is defined as the force acting normal to the plane formed by the velocity vector and the axis of the element. The lift force is defined as: Fl = ½ * * Cl * D * U2 Where: - is the fluid density Cl - is the lift coefficient D - is the pipe diameter U is the particle velocity The buoyancy force acts upward and is equal to the weight of the fluid volume displaced by the element. A piping system can be described by using the standard finite element equation: [K] {x} = {f} Where: [K] - is the global stiffness matrix for the entire system {x} - is the displacement / rotation vector to solve for {f} - is global load vector 896 CAESAR II User's Guide Technical Discussions Calculate pseudo-static hydrodynamic loading 1. Place the element loads generated by the hydrodynamic effects in their proper locations in {f}, similar to weight, pressure, and temperature. 2. Perform a standard finite element solution on the system of equations to finalize [K] and {f}. 3. Use the resulting displacement vector {x} to compute element forces. 4. Use the computed element forces to compute the element stresses. Except for the buoyancy force, all other hydrodynamic forces acting on the element are a function of the particle velocities and accelerations. Airy Wave Theory Implementation Airy Wave theory is also known as Linear Wave theory due to the assumption that the wave profile is symmetric about the mean water level. Standard Airy Wave theory allows for the computation of the water particle velocities and accelerations between the mean surface elevation and the bottom. The Modified Airy Wave theory allows for the consideration of the actual free surface elevation in the computation of the particle data. CAESAR II includes both the standard and modified forms of the Airy wave theory. To apply the Airy Wave theory, you must enter several descriptive parameters about the wave. The software uses these parameters along with the Newton-Raphston iteration to determine the wave length. Each wave has its own unique wave length that the program determines solving the dispersion relation, shown below: L = (gT2 / 2) * tanh(2D / L) Where: g - is the acceleration of gravity T - is the wave period D - is the mean water depth L - is the wave length to solve for After determining the wave length (L), you can determine any other wave parameters you want. The parameters determined and used by CAESAR II are: the horizontal and vertical particle velocities (UX and UY), the horizontal and vertical particle acceleration (AX and AY), and the surface elevation above (or below) the mean water level (ETA). For more information on the equations for these parameters, refer to any text which discusses ocean wave theories. STOKES 5th Order Wave Theory Implementation The Stokes Wave is a 5th order gravity non-linear wave. CAESAR II uses the solution technique described in a paper published in 1960 by Skjelbreia and Hendrickson of the National Engineering Science Company. The standard formulation as well as a modified formulation, to the free surface, is available in CAESAR II Stokes 5th Order Wave Theory. The solution follows a procedure very similar to that used in the Airy Wave Theory Implementation (on page 897). You can determine the characteristic parameters of the wave by using Newton-Raphston iteration, after finding the water particle values of interest. CAESAR II User's Guide 897 Technical Discussions The Newton-Raphston iteration procedure solves two non-linear equations for constants beta and lambda. After you determine these values, you can compute the other constants. After computing all of the constants, use CAESAR II to compute: the horizontal and vertical particle velocities (UX and UY), the horizontal and vertical particle acceleration (AX and AY), and the surface elevation above the mean water level (ETA). Stream Function Wave Theory Implementation The solution to Dean's Stream Function Wave Theory used by CAESAR II is described in the text by Sarpkaya and Issacson. As previously mentioned, this is a numerical technique to solve the stream function. The solution subsequently obtained, provides the horizontal and vertical particle velocities (UX and UY), the horizontal and vertical particle acceleration (AX and AY), and the surface elevation above the mean water level (ETA). Ocean Currents In addition to the forces imposed by ocean waves, piping elements can also be subjected to forces imposed by ocean currents. There are three different ocean current models in CAESAR II: linear current, piece-wise, and power law profile. The linear current profile assumes that the current velocity through the water column varies linearly from the specified surface velocity (at the surface) to zero (at the bottom). The piece-wise linear profile employs linear interpolation between specific user-defined depth/velocity points. The power law profile decays the surface velocity to the 1/7 power. While waves produce unsteady flow where the particle velocities and accelerations at a point constantly change, currents produce a steady, non-varying flow. Technical Notes on CAESAR II Hydrodynamic Loading The input parameters necessary to define the fluid loading are described in detail in the next section. The basic parameters describe the wave height and period, and the current velocity. The most difficult to obtain, and also the most important parameters, are the drag, inertia, and lift coefficients: Cd, Cm, and Cl. Based on the recommendations of API RP2A and DNV (Det Norske Veritas), values for Cd range from 0.6 to 1.2, values for Cm range from 1.5 to 2.0. Values for Cl show a wide range of scatter, but the approximate mean value is 0.7. The inertia coefficient Cm is equal to one plus the added mass coefficient Ca. This added mass value accounts for the mass of the fluid assumed to be entrained with the piping element. In actuality, these coefficients are a function of the fluid particle velocity, which varies over the water column. In general practice, two dimensionless parameters are computed that are used to obtain the Cd, Cm, and Cl values from published charts. The first dimensionless parameter is the Keulegan-Carpenter Number, K. K is defined as: K = Um * T / D Where: Um = Maximum Fluid Particle Velocity T = Wave Period D = Characteristic Diameter of the Element 898 CAESAR II User's Guide Technical Discussions The second dimensionless parameter is the Reynolds number, Re. Re is defined as Re = U m * D / Where: Um = Maximum Fluid Particle Velocity D = Characteristic Diameter of the Element = Kinematic Viscosity of the Fluid 1.26e-5 ft2/sec for Sea Water After you calculate K and Re use the charts to obtain Cd, Cm, and Cl. For more information, see Mechanics of Wave Forces on Offshore Structures by T. Sarpkaya. Figures 3.21, 3.22, and 3.25 are example charts, which display below. CAESAR II User's Guide 899 Technical Discussions In order to determine these coefficients, the fluid particle velocity (at the location of interest) must be determined. The appropriate wave theory is solved, and these particle velocities are readily obtained. Of the wave theories discussed, the modified Airy and Stokes 5th theories include a modification of the depth-decay function. The standard theories use a depth-decay function equal to cosh(kz) / sinh(kd), Where: k - is the wave number, 2 /L L - is the wave length d - is the water depth z - is the elevation in the water column where the data is to be determined 900 CAESAR II User's Guide Technical Discussions The modified theories include an additional term in the numerator of this depth-decay function. The modified depth-decay function is equal to cosh(d) / sinh(kd), Where: - is equal to z / (d + h) The term d represents the effective height of the point at which the particle velocity and acceleration are to be computed. The use of this term keeps the effective height below the still water level. This means that the velocity and acceleration computed are convergent for actual heights above the still water level. As previously stated, the drag, inertia, and lift coefficients are a function of the fluid velocity and the diameter of the element in question. Note that the fluid particle velocities vary with both depth and position in the wave train (as determined by the applied wave theory). Therefore, these coefficients are in fact not constants. However, from a practical engineering point of view, varying these coefficients as a function of location in the Fluid field is usually not implemented. This practice can be justified when one considers the inaccuracies involved in specifying the instantaneous wave height and period. According to Sarpkaya, these values are insufficient to accurately predict wave forces, a consideration of the previous fluid particle history is necessary. In light of these uncertainties, constant values for C d, Cm, and Cl are recommended by API and many other references. The effects of marine growth must also be considered. Marine growth has the following effects on the system loading: the increased pipe diameters increase the hydrodynamic loading; the increased roughness causes an increase in Cd, and therefore the hydrodynamic loading; the increase in mass and added mass cause reduced natural frequencies and increase the dynamic amplification factor; it causes an increase in the structural weight; and possibly causes hydrodynamic instabilities, such as vortex shedding. Finally, Morrison’s force equation is based the "small body" assumption. The term "small" refers to the "diameter to wave length" ratio. If this ratio exceeds 0.2, the inertial force is no longer in phase with the acceleration of the fluid particles and diffraction effects must be considered. In such cases, the fluid loading as typically implemented by CAESAR II is no longer applicable. Additional discussions on hydrodynamic loads and wave theories can be found in the references at the end of this article. Input: Specifying Hydrodynamic Parameters in CAESAR II The hydrodynamic load analysis requires the specification of several measurable parameters that quantify the physical aspects of the environmental phenomenon in question. You can enter four different wave loads here. Use the Editing Load Case buttons to move up or down between the Wave Load Input Spreadsheets. CAESAR II User's Guide 901 Technical Discussions The necessary hydrodynamic parameters are discussed in the following paragraphs and a CAESAR II hydrodynamic loading dialog is shown in the figure below. 902 CAESAR II User's Guide Technical Discussions Current Data Profile Type — Defines the interpolation method you want CAESAR II to use to determine the current velocity as a function of depth. Available options for this entry are: Power Law Profile — Determines the current velocity at depth D according to the equation: Vd = Vs * [di / D]p Where: Vd - is the velocity at depth di Vs - is the specified velocity at the surface D - is the water depth p - is the power, set to 1/7 Piece-wise Linear Profile — Performs a linear interpolation of a velocity verse depth table that you must provide, to determine the current velocity at depth di. The table should start at the surface (a depth of zero) and progress in increasing depth to the sea bed. Linear Profile — Performs a linear interpolation to determine the current velocity at depth di. However, this method assumes the current velocity varies linearly from the specified surface velocity to zero at the sea bed. Current Speed — Defines the current speed at the surface. The units for this entry are (length/time) as defined by the active units file at the time of input. This value should always be a positive entry. Current Direction Cosines — Defines the direction of fluid transport due tothe current. These fields are unit-less and follow the standard software global axis convention. Wave Data Wave Theory Indicator — Specifies which wave theory to use to compute the water particle velocities and accelerations. The wave theories available are: Standard Airy Wave — This is also known as linear wave theory. Discussion of this theory can be found in the previously mentioned references. Modified Airy Wave — This is a modification of the standard Airy theory which includes the free surface effects due to the wave. The modification consists of determining a depth scaling factor equal to the depth divided by the depth plus the surface elevation. Note that this scale factor varies as a function of the location in the wave train. Standard Stokes 5th Wave — This is a 5th order wave theory, also discussed in the previously mentioned references. Modified Stokes 5th Wave — This is a modification of the standard Stokes 5th theory. The modification is the same as applied to the Airy theory. Stream Function Wave — This isDean’s Stream Function theory, also discussed in the previously mentioned references. Modified Stream Function Wave — This is Dean’s Stream Function theory, modified to directly consider current in the wave solution. CAESAR II User's Guide 903 Technical Discussions Stream Function Order — When the Stream Function theory is activated, the solution order must be defined. Typical values for the stream function order range from 3 to 13, and must be an odd value (see API-RP2A figure). Water Depth — Defines the vertical distance (in units of length) from the still water level the surface to the sea bed. Wave Height — Defines the height of the incident wave. The height is the vertical distance in units of length from the wave crest to the wave trough. Wave Period — Defines the time span (in seconds) for two successive wave crests to pass a fixed point. Wave Kinematic Factor — Because the two dimensional wave theories do not account for spreading, a reduction factor is often used for the horizontal particle velocity and acceleration. Wave kinematic measurements support values in the range of 0.85 to 0.95. Refer to the applicable offshore codes before using this item. Wave Direction Cosines — Define the direction of wave travel. These fields are unit-less and follow the standard software global axis convention. Wave Phase Angle — Defines the position of the wave relative to the starting node of the piping system. The phase angle is a measure (in degrees) of position in the wave train, where 0 is the wave crest, 180 is the wave trough, and 360 is the following crest. Because the wave propagates over the piping structure, each point in the structure experiences all possible wave phase angles. One analysis technique specifies the wave phase at the system origin, and then the phase at each node point in the model is deter\-mined. From these exact phase locations, the water particle data is computed from the wave theory. Alternatively, a conservative engineering approach is to use the same phase angle usually zero for all points in the model. This technique produces higher loads; however, the extra conservatism is warranted when given the unknowns in specifying environmental data. Seawater Data Free Surface Elevation — Defines the height of the free surface from the global system origin. If the system origin is at the free surface, this entry should be specified as zero. If the system origin is at the sea bottom, this entry is equal to the water depth. By default, the first node in a CAESAR II model is at an elevation of zero. You can change the elevation by pressing [Alt-+G]. Kinematic Viscosity — Defines the kinematic viscosity of water. This value is used to determine the Reynolds number, which is subsequently used to determine the hydrodynamic coefficients Cd, Cm, and Cl. Typical values of kinematic viscosity for sea water display below. Temp Deg (F) n(ft2/sec) Temp (C) n(m2/sec) 60 1.26e-5 15.556 1.17058e-6 50 1.46e-5 10.000 1.35639e-6 40 1.55e-5 4.444 1.44000e-6 30 2.00e-5 -1.111 1.85807e-6 Fluid Weight Density - Defines the weight density of the fluid. For sea water, this value is approximately .037037 pounds per cubic inch (.001025 kg/cm3, 1.0256SG). 904 CAESAR II User's Guide Technical Discussions Piping Element Data Element Exposure — In implementing hydrodynamic loading in a software program, you must be able to indicate that elements are either exposed to the fluid or not exposed to the fluid. In CAESAR II, this is accomplished by a set of options, which indicate that the particular element is exposed to hydrodynamic loads, wind loads, or not exposed. This specification carries forward for all subsequent elements until changed. Hydrodynamic Coefficients — Piping elements that are subjected to hydrodynamic loading must have drag (Cd), inertia (Cm), and a lift (Cl) coefficient defined. The specification of these items is optional. Alternatively, you can specify these values as constants to be applied to all subsequent exposed elements, regardless of depth or phase position in the wave. Alternatively, You can leave these values blank, which causes CAESAR II to interpolate their values from the charts previously discussed. Marine Growth — Defines the amount of marine growth on the piping elements. This value is used to increase the diameter of the piping elements. The units for this field are the units of the current diameter. The diameter used in the computation of the hydrodynamic forces is equal to the pipe diameter plus twice the marine growth entry. References 1. Mechanics of Wave Forces On Offshore Structures, Turgut Sarpkaya and Michael Isaacson, Van Nostrand Reinhold Co., 1982, ISBN 0-442-25402-4. 2. Handbook of Ocean and Underwater Engineering, Myers, Holm, and McAllister, McGraw-Hill Book Co., 1969, ISBN 07-044245 -2. 3. Fifth Order Gravity Wave Theory, Lars Skjelbreia and James Hendrickson, National Engineering Science Co., Pasadena, California, 1960. 4. Planning and Design of Fixed Offshore Platforms, McClelland and Reifel, Van Nostrand Reinhold Co., 1986, ISBN 0-442-25223-4. 5. Intercomparison of Near-Bottom Kinematics by Several Wave Theories and Field and Laboratory Data, R. G. Dean and M. Perlin, Coastal Engineering, #9 (1986), p399-437. 6. A Finite Amplitude Wave on a Linear Shear Current, R. A. Dalrymple, Journal of Geophysical Research, Vol 79, No 30, 1974. 7. Application of Stream Function Wave Theory to Offshore Design Problems, R. G. Dean, OTC #1613, 1972. 8. Stream Function Representation of Nonlinear Ocean Waves, R. G. Dean, Journal of Geophysical Research, Vol 70, No 18, 1965. 9. American Petroleum Institute - Recommended Practice 2A (API-RP2A), American Petroleum Institute, July 1993. 10. Improved Algorithm for Stream Function Wave Theory, Min-Chih Huang, Journal of Waterway, Port, Coastal, and Ocean Engineering, January 1989. 11. Stream Function Wave Theory with Profile Constraints, Min-Chih Huang, Journal of Waterway, Port, Coastal, and Ocean Engineering, January/February 1993. CAESAR II User's Guide 905 Technical Discussions Evaluating Vessel Stresses ASME Section VIII Division 2 — CAESAR II applies rules prior to the 2007 Edition — provides a procedure to analyze the local stresses in vessels and nozzles. For this example, we will only discuss the nozzle analysis approach. Always refer to the applicable design code if any of the limits described in this section are approached, or if any unusual material, weld, or stress situation exists, or there are non-linear concerns such as the operation of material within creep range. The first step is to determine if the elastic approach is satisfactory. To summarize, Section AD-160 states that if the model meets all of the following conditions, then a fatigue analysis is not required: 1. The expected design number of full-range pressure cycles does not exceed the number of allowed cycles corresponding to a Sa value of 3Sm (4Sm for non-integral attachments) on the material fatigue curve. Sm is the allowable stress intensity for the material at the operating temperature. 2. The expected design range of pressure cycles other than startup or shutdown must be less than ⅓ (¼ for non-integral attachments) the design pressure times (Sa/Sm), where Sa is the value from the material fatigue curve for the specified number of significant pressure fluctuations. 3. The vessel does not experience localized high stress due to heating. 4. The full range of stress intensities due to mechanical loads including piping reactions does not exceed Sa, from the fatigue curve, for the expected number of load fluctuations. After deciding if an elastic analysis is satisfactory, you must determine whether to take either a simplified or a comprehensive approach to do the vessel stress analysis. For more information on the simplified or the comprehensive approach, see ASME Section VIII Division 2-Elastic Nozzle Simplified Analysis (see "ASME Section VIII Division 2-Elastic Nozzle Simplified Analysis pre-2007" on page 910) or ASME Section VIII Division 2-Elastic Nozzle Comprehensive Analysis (see "ASME Section VIII Division 2-Elastic Nozzle Comprehensive Analysis (pre2007)" on page 906). For more information on Section VIII Division 2 requirements, refer to the latest version of the ASME code. ASME Section VIII Division 2-Elastic Nozzle Comprehensive Analysis (pre-2007) To address the local allowable stress problem, you should have the endurance curve for the material of construction and complete design pressure/temperature loading information. Carefully consult the code before performing the local stress analysis if: any elastic limit is approached there is anything unusual in the nozzle/vessel connection design The material Sm table and the endurance curve for carbon steels used in this section are for illustration purposes. You should only use values taken directly from the code in your design. 906 CAESAR II User's Guide Technical Discussions There are three criteria you must satisfy before considering stresses in the vessel wall due to nozzle loads within the allowables. The three criteria are summarized as: Pm < kSmh Pm + Pl + Pb< 1.5kSmh Pm + Pl + Pb + Q < 3Smavg Where Pm, Pl, Pb, and Q are the general primary membrane stress, the local primary membrane stress, the local primary bending stress, and the total secondary stresses (membrane plus bending), respectively; and k, Smh, and Smavg are the occasional stress factor, the hot material allowable stress intensity, and the average material stress intensity (S mh + Smc) / 2. The stress classification defined by the Section VIII Division 2 code in the vicinity of nozzles, classifies the bending stress terms caused by any external load moments or internal pressure in the vessel wall near a nozzle or other opening, as secondary stress Q, regardless of whether they were caused by sustained or expansion loads. This definition causes P b to disappear and leads to a more detailed classification: Pl - Local primary membrane stress, which may include the following: Pm - General primary membrane stress (primarily due to internal pressure) Membrane stress due to internal pressure Local membrane stress due to applied sustained forces and moments Q - Secondary stresses, which may include the following: Bending stress due to internal pressure Bending stress due to applied sustained loads Membrane stress due to applied expansion loads Bending stress due to applied expansion loads Each of the stress terms defined in the above classifications contains three parts: two stress components in normal directions and one shear stress component. To combine these stresses, the following rules apply: 1. Compute the normal and shear components for each of the three stress types, that is, Pm, Pl, and Q. 2. Compute the stress intensity due to the Pm and compare it against kSmh. 3. Add the individual normal and shear stress components due to Pm resultant stress intensity and compare its value against 1.5kS mh. 4. Add the individual normal and shear stress components due to P m, Pl, and Q, compute the resultant stress intensity, and compare its value to against 3S mavg. 5. Determine if there is an occasional load as well as a sustained load, these types can be repeated using a value of 1.2 for k. CAESAR II User's Guide and Pl; compute the 907 Technical Discussions These criteria can be readily found from Figure 4-130.1 of Appendix 4 of ASME Section VIII, Division 2 2004 and the surrounding text. Note that the primary bending stress term, Pb, is not applicable to the shell stress evaluation, and therefore disappears from the Section VIII, Division 2 requirements. Using the same analogy, write the peak stress limit as: Pl + Pb + Q + F < Sa The preceding equation need not be satisfied, provided the elastic limit criteria of AD-160 is met based on the statement explicitly given in Section 5-100, which is cited below: "If the specified operation of the vessel meets all of the conditions of AD-160, no analysis for cyclic operation is required and it can be assumed that the peak stress limit discussed in 4135 has been satisfied by compliance with the applicable requirements for materials, design, fabrication, testing and inspection of this division." Elastic Analyses of Shells near Nozzles Using WRC 107 Check vessel stresses in shells using WRC 107 1. Check the geometric limitation to see whether WRC 107 is applicable. 2. If yes, determine whether the elastic approach as outlined in Section VIII Division 2 AD160 is applicable. 3. Compute the sustained, expansion, and occasional loads in the vessel shell due to the applied nozzle loads. 4. Consider the local restraint configuration to determine whether some or all the axial pressure thrust load P * Ain should be added to the sustained and occasional loads. If you choose, the program can automatically calculate the thrust load and add it to the applied loads. 5. Calculate the pressure stresses, Pm, on the vessel shell wall in both the longitudinal and circumferential hoop directions for both sustained and occasional load cases. Notice that two different pressure terms are required in carrying out the pressure stress calculations. P is the design pressure of the system (sustained), while P var is the difference between the peak pressure and the design pressure of the system, which is used to qualify the vessel membrane stress under the occasional load case. If you enter the pressure value, the software automatically calculates the P m stresses. 6. The processor will calculate the Pl, and Q stresses as defined earlier. If needed, you can simultaneously compute the local stresses due to sustained, expansion, and occasional loads. 7. Obtain the various stress components by combining the stress intensities computed from applying the sustained, expansion, and occasional loads, if applicable. 8. Then use stress intensities to carry out the stress summations. If needed, use the results to determine the acceptability of the local stresses in the vessel shell. Notice how CAESAR II provides the WRC 107 Stress Summation module in line with the stress calculation routines. 908 CAESAR II User's Guide Technical Discussions The equations used in CAESAR II to qualify the various stress components can be summarized as follows: Pm(SUS) < Smh Pm(SUS + OCC) < 1.2Smh Pm(SUS) + Pl(SUS) < 1.5Smh Pm(SUS + OCC) + Pl(SUS + OCC) < 1.5(1.2)Smh Pm(SUS + OCC) + Pl(SUS + OCC) + Q(SUS + EXP + OCC) < 1.5(S mc + Smh) Description of Alternate Simplified ASME Section VIII Division 2 Elastic Nozzle Analysis pre-2007 The most difficult problem associated with the comprehensive ASME Section VIII Division 2 nozzle/vessel analysis involves the pressure calculation. Hoop and longitudinal pressure hand calculations are not considered reliable, and axial pressure loading on the junction is often miscalculated or omitted. Another issue with the comprehensive calculation is the amount of time it takes to organize and manipulate the stress data. For these reasons, an alternate simplified approach was developed using three checks. The first check, Pm due to pressure, must be 1.0 Smh. To eliminate the concern for pressure, both the loading pressure term on the left side of the inequality and the allowable pressure term on the right side of the inequality cancel out. This assumes that the area of reinforcement around the nozzle satisfies the pressure requirements. Also, let Pm equal the maximum value. The second check, Pm + Pl + Pb, must be 1.5 Smh. Subtract the stress due to pressure, Pm, from both sides of the inequality and assuming Pm equals Smh. This reduces the check to: Pl + Pb 0.5 Smh (due to external sustained forces without pressure). The third check, Pm + Pl + Q, is the root of the application controversy. There are three schools of thought: Pm+Pl+Q is an operating loading condition, and as such, includes the loads due to pressure and weight. Pm+Pl+Q is the range of loads or the expansion loading condition, and as such, excludes the effects of sustained, or primary loads. Also, exclude the primary sustained loads like weight and pressure. Pm+Pl+Q is the range of loads and excludes the primary load weight, but includes the varying pressure load at least in those thermal load cases where the systemgoes from a startup ambient temperature and pressure condition to operating condition. To simplify the calculation, assume that Pm, due to pressure, is included on both sides of the Pm+Pl+Pb+Q < 3Sm inequality. Also, assume that the area reinforcement requirements are exactly satisfied. Again, let Pm = Sm and subtract this term from the expansion allowable (P m + Pl + Q < 3Sm) to provide a simplified allowable limit. The expansion, operating, or both loads from the CAESAR II Restraint report (see "Restraints" on page 569) must satisfy the computed stress requirement: Pl + Pb + Q (operating or expansion excluding pressure) < 2S m. CAESAR II User's Guide 909 Technical Discussions To summarize: 1. Ensure proper nozzle reinforcement for pressure and assume pressure stresses are at their maximum. 2. Compare primary stresses without pressure to ½Smh. 3. Compare stresses due to the sum of primary and secondary loads to 2Sm(avg); where Sm(avg) is the average of the hot and cold allowable stress intensities S mh and Smc. ASME Section VIII Division 2-Elastic Nozzle Simplified Analysis pre-2007 1. Perform a CAESAR II analysis of the piping loads on the vessel/nozzle junction. Use WRC 297 flexibilities to compute loads more accurately, but less conservatively or do two analyses, one with flexibilities and one without. From this analysis you should have sustained, operating, and expansion loads on the vessel/nozzle junction. 2. Find Smh and Smc from the Sect. VIII allowable stress tables. Smh is the vessel material hot allowable, and Smc is the vessel material cold allowable. 3. Run WRC 107 with the sustained loads on the vessel/nozzle junction from CAESAR II, and verify that the computed stress intensities are < 0.5 S mh. This operation helps in conservatively considering bending stresses from internal pressure and sustained moments and also lets you categorize the stresses and moment as a primary classification. If the operation fails, review the stresses in more detail. 4. Run WRC 107 with the operating loads on the vessel/nozzle junction from CAESAR II, and verify that the computed stress intensities are < S mh + Smc. 5. Run WRC 107 with the expansion loads on the vessel/nozzle junction from CAESAR II, and verify that the computed stress intensities are < Smh + Smc. Should any of the checks described fail, then perform the more comprehensive analysis of the junction described earlier. For more information, see ASME Section VIII Division 2 - Elastic Analysis of Nozzle Comprehensive Analysis (see "ASME Section VIII Division 2-Elastic Nozzle Comprehensive Analysis (pre-2007)" on page 906). Inclusion of Missing Mass Correction The response of a system under a dynamic load is often determined by superposition of modal results, with CAESAR II specifically providing the Spectral Analysis method for use. One of the advantages of modal analysis is that usually only a limited number of modes are excited and need be included in the analysis. The drawback to this method is that although displacements may be obtained with good accuracy using only a few of the lowest frequency modes, the force, reaction, and stress results may require extraction of far more modes, possibly far into the rigid range, before acceptable accuracy is attained. The Missing Mass option offers the ability to include a correction which represents the quasi-static contribution of the higher order modes not explicitly extracted for the modal/dynamic response, thus providing greater accuracy with reduced calculation time. 910 CAESAR II User's Guide Technical Discussions The dynamic response of a linear multi-degree-of-freedom system is described by the following equation: Ma(t) + Cv(t) + Kx(t) = F(t) Where: M = n x n mass matrix of system C = n x n damping matrix of system K = n x n stiffness matrix of system a(t) = n x 1, time-dependent acceleration vector v(t) = n x 1, time-dependent velocity vector x(t) = n x 1, time-dependent displacement vector F(t) = n x 1, time-dependent applied force vector Assuming harmonic motion and neglecting damping, the free vibration eigenvalue problem for this system is K - M2 = 0 Where: = n x n mode shape matrix 2 = n x n matrix where each diagonal entry is the angular frequency squared of the corresponding mode The modal matrix can be normalized such that T M = I (where I is the n x n identity matrix) and T = 2. Partition the modal matrix into two sub-matrices: = [e r ] Where: e = mode shapes extracted for dynamic analysis (that is., lowest frequency modes) r = residual (non-extracted) mode shapes (corresponding to rigid response, or the "missing mass" contribution) The extracted mode shapes are orthogonal to the residual mode shapes, or: eT x r = 0 The displacement components can be expressed as linear combinations of the mode shapes: x = Y = e Ye + r Yr = xe + xr Where: x = Total System Displacements x e = System Displacements Due to Extracted Modes x r = System Displacements Due to Residual Modes Y = Generalized Modal Coordinates Ye = partition of Y Matrix Corresponding to Extracted Modes CAESAR II User's Guide 911 Technical Discussions Yr = Partition of Y Matrix Corresponding to Residual Modes The dynamic load vector can be expressed in similar terms: F = K Y = K e Ye + Kr Yr = Fe + Fr Where: F = Total System Load Vector Fe = Load Vector Due to Extracted Modes Fr = Load Vector Due to Residual Modes Y = Generalized Modal Coordinates Ye = Partition of Y Matrix Corresponding to Extracted Modes Yr = Partition of Y Matrix Corresponding to Residual Modes Normally, modal superposition analyses completely neglect the rigid response the displacement Xr caused by the load Fr. This response, of the non-extracted modes, can be obtained from the system displacement under a static loading Fr. Based upon the relation\-ships stated above, you can estimate Fr as follows: F = K e Ye + K r Yr Multiplying both sides byeT and considering that eT r = 0: eT F = eT K e Ye + eT K r Yr = eT K e Ye Substituting e2 for eT K e and solving for Ye: eT F = e2 Ye Ye = eT e-2 F The residual force can now be stated as Fr = F - K e Ye = F - eT K e e-2 F As seen earlier T M2 = I 2 = T K Substituting eT Me e2 for eT K e: Fr = F - eT M e e2 e-2 F = F - eT Me F Therefore, CAESAR II calculates the residual response (and includes it as the missing mass contribution) according to the following procedure: 1. The missing mass load is calculated for each individual shock load as: F r = F - eT M e F 912 The load vector F represents the product of: the force set vector and the rigid DLF for force spectrum loading; the product of the mass matrix, ZPA, and directional vector for non-ISM seismic loads; and the product of the mass matrix, ZPA, and displacement matrix (under unit ISM support displacement) for seismic anchor movement loads. CAESAR II User's Guide Technical Discussions Note that the missing mass load will vary, depending upon the number of modes extracted by the user and the cutoff frequency selected (or more specifically, the DLF or acceleration corresponding to the cutoff frequency). "Rigid," for the purposes of determining the rigid DLF, or the ZPA, may be designated by the user, through a setup parameter, to be either the DLF/acceleration associated with the frequency of the last extracted mode, or the true spectral DLF/ ZPA that corresponding to the largest entered frequency of the input spectrum. 2. The missing mass load is applied to the structure as a static load. The static structural response is then combined (according to the user-specified combination method) with the dynamically amplified modal responses as if it was a modal response. Actually this static response is the algebraic sum of the responses of all non-extracted modes— representing in-phase response, as would be expected from rigid modes. 3. The Missing Mass Data report is compiled for all shock cases, whether missing mass is to be included or not. The percent of mass active is calculated according to: % Active Mass = 1 - ( Fr[i] / F [i]) summed over i = 1 to n, where n is the number of modes included The maximum possible percent that is theoretically possible for this value is of course 100%; however numerical inaccuracies may occasionally cause the value to be slightly higher. If the missing mass correction factor is included, the percent of mass included in the correction is shown in the report as well. CAESAR II User's Guide 913 Technical Discussions Because the CAESAR II procedure assumes that the missing mass correction represents the contribution of rigid modes, and that the ZPA is based upon the spectral ordinate value at the frequency of the last extracted mode, we recommend that you extract modes up to, but not far beyond, a recognized "rigid" frequency. Choosing a cutoff frequency below the spectrum’s resonant peak [point (1) below] provides a non-conservative result, because resonant responses may be missed. Using a cutoff frequency higher than the peak (2), but still in the resonant range, will yield conservative results, because the ZPA/rigid DLF will be overestimated. Extracting a large number of rigid modes for calculation of the dynamic response may be conservative (4), because all available modal combination methods (SRSS, GROUP, ABS, and so forth) give conservative results versus the algebraic combination method which gives a more realistic representation of the net response of the rigid modes. Based upon the response spectrum shown below, an appropriate cutoff point for the modal extraction would be about 33 Hz (3). 914 CAESAR II User's Guide Technical Discussions Maximum Stress Versus Extracted Loads CAESAR II provides two options for combining the missing mass correction with modal dynamic results SRSS and Absolute. The Absolute Combination method provides the more conservative result and is based upon the assumption that dynamic amplification is going to occur simultaneously with the maximum ground acceleration or force load. Literature (References 1, 2) states that the modal and the rigid portions of the response to typical dynamic loads are actually statistically independent, so that the SRSS Combination method is a more accurate representation of reality. Because the SRSS Combination method is most closely aligned to reality, CAESAR II defaults to this missing mass combination method. References 1. A. K. Gupta, Response Spectrum Method in Seismic Analysis and Design of Structures, CRC Press, 1990 2. K. M. Vashi, "Computation of Seismic Response from Higher Frequency Modes," ASME 80-C2/PVP-50, 1980 3. O. E. Hansteen and K. Bell, "On the Accuracy of Mode Superposition Analysis in Structural Dynamics," Earthquake Engineering and Structural Dynamics, Volume 7, John Wiley & Sons, Ltd., 1979 CAESAR II User's Guide 915 Technical Discussions Fatigue Analysis Using CAESAR II For most piping codes supported by CAESAR II, performing a fatigue analysis is an extension to, rather than an explicit part of, the code requirements. However, it is an explicit part of the IGE/TD/12 Pipework Stress Analysis for Gas Industry Plant code. Fatigue Basics Piping and vessels have been known to suffer from sudden failure following years of successful service. Research done during the 1940s and 1950s, primarily advanced by A. R. C. Markl’s "Piping Flexibility Analysis," published in 1955, provided an explanation for this phenomenon, as well as design criteria aimed at avoiding failures of this type. The explanation was that materials were failing due to fatigue, a process leading to the propagation of cracks, and subsequent fracture, following repeated cyclic loading. Steels and other metals are made up of organized patterns of molecules, known as crystal structures. However, these patterns are not maintained throughout the steel producing an ideal homogeneous material, but are found in microscopic isolated island-like areas called grains. Inside each grain a pattern of molecules is preserved. From one grain boundary to the next the molecular pattern is the same, but the orientations differ. As a result, grain boundaries are high energy borders. Plastic deformation begins within a grain that is subject to both a high stress and oriented such that the stress causes a slippage between adjacent layers in the same pattern. The incremental slippages, called dislocations, cause local coldworking. On the first application of the stress, dislocations can move through many of the grains that are in the local area of high stress. As the stress is repeated, more dislocations move through their respective grains. Dislocation movement is impeded by the grain boundaries. After multiple stress applications, the dislocations tend to accumulate at grain boundaries. Eventually they become so dense that the grains "lock up" causing a loss of ductility and thus preventing further dislocation movement. Subsequent applications of the stress cause the grain to tear, forming cracks. Repeated stress applications cause the cracks to grow. Unless abated, the cracks propagate with additional stress applications until sufficient cross sectional strength is lost to cause a catastrophic failure of the material. 916 CAESAR II User's Guide Technical Discussions You can estimate the fatigue capacity of a material through the application of cyclic tensile/compressive displacement loads with a uniaxial test machine. A plot of the cyclic stress capacity of a material is called a fatigue or endurance curve. These curves are generated through multiple cyclic tests at different stress levels. The number of cycles to failure usually increases as the applied cyclic stress decreases, often until a threshold stress, known as the endurance limit, is reached below which no fatigue failure occurs, regardless of the number of applied cycles. An endurance curve for carbon and low alloy steels, taken from the ASME Section VIII Division 2 Pressure Vessel Code displays below: Fatigue Analysis of Piping Systems IGE/TD/12 does present specific requirements for true fatigue evaluation of systems subject to a cyclic loading threshold. Furthermore, ASME Section III, Subsection NB and ASME Section VIII Division 2 provide guidelines by which fatigue evaluation rules can be applied to piping and other pressure retaining equipment. These procedures have been adapted, where possible, to the methodology used by CAESAR II. Perform fatigue analysis 1. From the Allowable auxiliary dialog box, enter fatigue data or import it in from a text file. You can also define your own fatigue curves as discussed later in this section. By doing this, you assign the fatigue curve data to the piping material. To help with your fatigue analysis, CAESAR II provides a number of commonly used curves. CAESAR II User's Guide 917 Technical Discussions 2. From either the Static or Dynamic Load Case Builders you must define, for every fatigue load case, the number of anticipated cycles. Also we have added a new FAT stress type. 3. Unless explicitly defined in the applicable code, CAESAR II calculates the fatigue stress the same way it calculates the stress intensity. IGE/TD/12 is the only piping code supported by CAESAR II that has explicit instructions for calculating fatigue stresses. For more information on IGE/TD/12, refer to IGE/TD/12 (on page 987). 4. Allowable fatigue stresses are interpolated logarithmically from the fatigue curve based upon the number of cycles designated for the load case. For static load cases, the calculated stress is assumed to be a peak-to-peak cyclic value (for example, thermal expansion, settlement, pressure, and so forth), so the allowable stress is extracted directly from the fatigue curve. For harmonic and dynamic load cases, the calculated stress is assumed to be a zero-to-peak cyclic value (for example, vibration, earth\-quake, and so forth), so the extracted allowable is divided by two prior to use in the comparison. 5. The flip side of calculating the allowable fatigue stress for the designated number of cycles is the calculation of the allowable number of cycles for the calculated stress level. You can do this by logarithmically interpolating the "Cycles" axis of the fatigue curve based upon the calculated stress value. Because static stresses are assumed to be peak-to-peak cyclic values, the allowable number of cycles is interpolated directly from the fatigue curve. Because harmonic and dynamic stresses are assumed to be zero-to-peak cyclic values, the allow\-able number of cycles is interpolated using twice the calculated stress value. 6. CAESAR II provides two reports for viewing the results of load cases for the FAT stress type. The first of these is the standard Stress report that shows the calculated fatigue stress and fatigue allowable at each node. You can generate individual stress reports for each load case to show whether any of the individual load cases in isolation fail the system However, in those instances where there is more than one cyclic load case potentially contributing to a fatigue failure, the Cumulative Usage report is appropriate. To generate this report select all the FAT load cases that contribute to the overall system degradation. The Cumulative Usage report lists for each node point the usage ratio actual cycle divided by allowable cycles, and then sums these to obtain the total cumulative usage. A total greater than 1.0 indicates a potential fatigue failure. Static Analysis Fatigue Example Consider a sample job that potentially has several different cyclic load variations: Operating cycle from ambient 70°F to 500°F, 12,000 cycles anticipated Shut down external temperature variation from ambient 70°F to -20°F, 200 cycles anticipated Pressurization to 1800 psig, 12,000 cycles anticipated Pressure fluctuations of +/- 30 psi from the 1800 psig, 200,000 cycles anticipated To do a proper fatigue analysis, you must group the load pairs that represent the worst-case combination of stress ranges between extreme states. These load variations can be laid out in graphical form. The figure below shows a sketch of the various operating ranges this system 918 CAESAR II User's Guide Technical Discussions experiences. Each horizontal line represents an operating range. At the each end of each horizontal line, the temperatures and pressures defining the range are noted. At the center of each horizontal line, the number of cycles for each range is defined. Using this sketch of the operating ranges, the four fatigue load cases can be determined. Case 1: Cover the absolute extreme, from -20°F and 0 psi to 500°F and 1830 psi. This occurs 200 times. As a result of this case, the cycles for the ranges defined must be reduced by 200. The first range (-20, 0 to 70, 0) is reduced to zero, and has no contribution to additional load cases. The second range (70, 0 to 500, 1800) is reduced to 11,800 cycles. The third and fourth ranges are similarly reduced to 199,800 cycles. These same steps can be used to arrive at cases 2 through 4, reducing the number of considered cycles at each step. This procedure is summarized in the table below. Segment -20, 0 to 70, 0 70, 0 to 500, 1800 500, 1700 to 500, 1800 500, 1800 to 500, 1830 Initial 200 12,000 200,000 200,000 After 1 0 11,800 200,000 199,800 After 2 0 0 200,000 188,000 After 3 0 0 12,000 0 After 4 0 0 0 0 Case This table is then used to set the load cases as cycles between the following load values: Between -20°F, 0 psig and 500°F, 1830 psig (200 cycles) Between 70°F, 0 psig and 500°F, 1830 psig (11,800 cycles) Between 500°F, 1770 psig and 500°F, 1830 psig (188,000 cycles) Between 500°F, 1770 psig and 500°F, 1800 psig (12,000 cycles) CAESAR II User's Guide 919 Technical Discussions These temperatures and pressures are entered as operating conditions accordingly: Next enter the fatigue curve data for the material. This is done by clicking Fatigue Curves to activate the Material Fatigue Curve dialog box. This dialog box can be used to enter the fatigue curve for the materials. For IGE/ TD/12, you only need to enter five sets of fatigue curves for fatigue classes D, E, F, G, and W. 920 1. Enter up to eight Cycle versus Stress data points to define the curve. Interpolations are made logarithmically. 2. Enter Cycle/Stress pairs in ascending cycle order. CAESAR II User's Guide Technical Discussions 3. Enter stress values as the allowable stress range, rather than the allowable Stress Amplitude. You can enter fatigue curve data from a text file, by clicking Read from file. This displays a list of all \CAESAR\SYSTEM\*.FAT files. The following fatigue curve files are delivered with CAESAR II. You can also construct additional fatigue curve files. For more information on fatigue curve files, see Appendix A below: 5-110-1A.FAT ASME Section VIII Division 2 Figure 5-110.1, UTS < 80 ksi 5-110-1B.FAT ASME Section VIII Division 2 Figure 5-110.1, UTS = 115-130 ksi 5-110-2A.FAT ASME Section VIII Division 2 Figure 5-110.2, Curve A 5-110-2B.FAT ASME Section VIII Division 2 Figure 5-110.2, Curve B 5-110-2C.FAT ASME Section VIII Division 2 Figure 5-110.2, Curve C CAESAR II User's Guide 921 Technical Discussions In this case for A106B low carbon steel operating at 500°F, 5-110-1A.FAT is the appropriate selection. This populates the fatigue curve data boxes in the dialog box: Error check the job, and set up your load cases. The static load case builder offers a new stress type, FAT (fatigue). Selecting this stress type does the following: 922 1. Enables you to define the number of cycles for the load case. Dragging the FAT stress type into the load case or clicking the Load Cycles button opens the Load Cycles field. 2. Calculates the stress range as per the Fatigue Stress method of the applicable code. This is the stress intensity for all codes except IGE/TD/12. 3. Compares the calculated stress range to the full value extracted from the fatigue curve. Indicates that the load case may be included in the Cumulative Usage report. CAESAR II User's Guide Technical Discussions The last four load cases represent the load set pairs defined earlier. After you run the job the presence of a FAT stress type adds the Cumulative Usage report to the list of available reports. CAESAR II User's Guide 923 Technical Discussions You can check the fatigue stress range against the fatigue curve allowable for each load case by selecting it along with the Stresses report. A review of each load case confirms that all stress levels passed. 924 CAESAR II User's Guide Technical Discussions However, this is not a true evaluation of the situation because it is not a case of either-or. The piping system is subjected to all of these load cases throughout its expected design life, not just one of them. Therefore, we must also review the Cumulative Usage (see "Cumulative Usage Report" on page 579) report, which shows the total effect of all fatigue load cases, or any user-selected combination, on the design life of the system. This report lists for each load case the expected number of cycles, the allowable number of cycles (based upon the calculated stress), and the Usage Ratio (actual cycles divided by allowable cycles). The Usage Ratios are then summed for all selected load cases. If this sum exceeds 1.0, the system has exceeded its fatigue capabilities. In this case, it is apparent that with the maximum cumulative usage ratio of 0.87 at node 115, this system is not predicted to fail due to fatigue: Fatigue Capabilities in Dynamic Analysis Fatigue analysis capability is also available for harmonic and dynamic analyses. Harmonic load cases are entered as they always have been. They can be designated as being stress type FAT by entering the number of expected load cycles on the harmonic input dialog box: CAESAR II User's Guide 925 Technical Discussions This produces the same types of reports as are available for the static analysis. They can be processed as discussed earlier. The only difference between the harmonic and static fatigue analyses is that for harmonic jobs the calculated stresses are assumed to be zero-to-peak calculations so that they are compared to only half of the stress value extracted from the fatigue curve. Likewise, when creating the Cumulative Usage report, the number of allowable cycles is based upon twice the calculated stress. For other dynamic applications (response spectrum and time history), the stress type can be identified as fatigue by selecting the stress type from the drop list for the Load Case or Static/Dynamic Combination, and by entering the number of expected cycles in the provided field. Note that as with the harmonic analyses, the calculated stresses are assumed to be zero-topeak calculations so that they are compared to only half of the stress value extracted from the fatigue curve. Likewise, when creating the Cumulative Usage report, the number of allowable cycles is based upon twice the calculated stress. Creating the .FAT Files The .FAT file is a text file, containing the data points necessary to describe the fatigue curve for the material, for both butt welded and fillet welded fittings. A sample FAT file is shown below. * ASME SECTION VIII DIVISION 2 FATIGUE CURVE * FIGURE 5-110.1 * DESIGN FATIGUE CURVES FOR CARBON, LOW ALLOY, SERIES 4XX, * HIGH ALLOY AND HIGH TENSILE STEELS FOR TEMPERATURES NOT * EXCEEDING 700 F * FOR UTS 80 KSI * 0.5000000 - STRESS MULTIPLIER (PSI); ALSO CONVERTS AMPLITUDE TO FULL RANGE * 10 580000.0 100 205000.0 1000 83000.0 10000 38000.0 926 CAESAR II User's Guide Technical Discussions 100000 500000 1000000 0 * 20000.0 13500.0 12500.0 0.0 You can create this text file by using any text editor. Lines beginning with an * are treated as comment lines. It is good practice to use comment lines so that the data can be tied to a specific material curve. The first data line in the file the stress multiplier. This value is used to adjust the data values from "zero to peak" to "peak to peak" or to convert the stress levels to psi. The entered values are divided by this number. For example, if the stress values in the file represent the stress amplitude, in psi, rather than a range, this "stress multiplier" should be 0.5. Following the stress multiplier is the Fatigue Curve Data table. This table consists of eight lines, of two columns. The first column is the Cycle column, and the second is the Stress column. For each value in the cycle column, a corresponding stress value from the material fatigue curve is listed in the stress column. Fatigue curves intended for use with IGE/TD/12 are built slightly different. The first data line contains three values: the stress multiplier, a modulus of elasticity correction, and a modulus of elasticity multiplier (the correction factor is divided by this to convert to psi). After the files are read in, the modulus of elasticity correction is inserted into the appropriate field on the Fatigue Curve dialog. IGE/TD/12 fatigue files also include five sequential fatigue curves, Fatigue Class D, E, F, G, and W, rather than one. You can use optional comment lines to separate the tables. The comments help with the readability of the data file. You can best determine the format of the IGE/TD/12 fatigue files by reviewing the contents of the TD12ST.FAT file. In all tables, the number of cycles increases as you work down the table. If you do not have enough data to use all eight lines, fill the unused lines with zeroes. Calculation of Fatigue Stresses For IGE/TD/12 the computation of fatigue stresses is detailed in Section 5.4.4 of that code. This section of the code states: "The principal stress in any plane can be calculated for any set of conditions from the following formula:" Where: Sh = Hoop stress Sa = Axial stress Sq = Shear stress "This should be used for establishing the range of stress, due regard being paid to the direction and sign." For all other piping codes in CAESAR II, the fatigue stress is computed as the stress intensity, as follows: 3D Maximum Shear Stress Intensity (Default) SI = Maximum of: S1OT - S3OT S1OB - S3OB CAESAR II User's Guide 927 Technical Discussions Max(S1IT,RPS) - Min(S3IT,RPS) Max(S1IB,RPS) - Min(S3IB,RPS) Where: S1OT=Maximum Principal Stress, Outside Top = (SLOT+HPSO)/2.0+(((SLOT-HPSO)/2.0)2+TSO2)1/2 S3OT=Minimum Principal Stress, Outside Top =(SLOT+HPSO)/2.0-(((SLOT-HPSO)/2.0)2+TSO2) 1/2 S1IT=Maximum Principal Stress, Inside Top =(SLIT+HPSI)/2.0+(((SLIT-HPSI)/2.0)2+TSI2) 1/2 S3IT=Minimum Principal Stress, Inside Top =(SLIT+HPSI)/2.0-(((SLIT-HPSI)/2.0)2+TSI2) 1/2 S1OB=Maximum Principal Stress, Outside Top =(SLOB+HPSO)/2.0+ (((SLOB-HPSO)/2.0)2+TSO2) 1/2 S3OB=Minimum Principal Stress, Outside Bottom =(SLOB+HPSO)/2.0- (((SLOB-HPSO)/2.0)2+TSO2) 1/2 S1IB=Maximum Principal Stress, Inside Bottom =(SLIB+HPSI)/2.0+ (((SLIB-HPSI)/2.0)2+TSI2) 1/2 S3IB=Minimum Principal Stress, Inside Bottom =(SLIB+HPSI)/2.0- (((SLIB-HPSI)/2.0)2+TSI2) 1/2 RPS=Radial Pressure Stress, Inside HPSI=Hoop Pressure Stress (Inside, from Lame's Equation) HPSO=Hoop Pressure Stress (Outside, from Lame's Equation) SLOT=Longitudinal Stress, Outside Top SLIT=Longitudinal Stress, Inside Top SLOB=Longitudinal Stress, Outside Bottom SLIB=Longitudinal Stress, Inside Bottom TSI=Torsional Stress, Inside 928 CAESAR II User's Guide Technical Discussions TSO=Torsional Stress, Outside Pipe Stress Analysis of FRP Piping Underlying Theory The behavior of steel and other homogeneous materials has been long understood, permitting their widespread use as construction materials. The development of the piping and pressure vessel codes (Reference 1) in the early part of this century led to the confidence in their use in piping applications. The work of Markl and others in the 1940’s and 1950’s was responsible for the formalization of today’s pipe stress methods, leading to an ensuing diversification of piping codes on an industry by industry basis. The advent of the digital computer, and with it the appearance of the first pipe stress analysis software (Reference 2), further increased the confidence with which steel pipe could be used in critical applications. The 1980’s saw the wide spread proliferation of the microcomputer, with associated pipe stress analysis software, which in conjunction with training, technical support, and available literature, has brought stress analysis capability to almost all engineers. In short, an accumulated experience of close to 100 years, in conjunction with ever improving technology has led to the utmost confidence on the part of today’s engineers when specifying, designing, and analyzing steel, or other metallic, pipe. For fiberglass reinforced plastic (FRP) and other composite piping materials, the situation is not the same. Fiberglass reinforced plastic was developed only as recently as the 1950’s, and did not come into wide spread use until a decade later (Reference 3). There is not a large base of stress analysis experience, although not from a lack of commitment on the part of FRP vendors. Most vendors conduct extensive stress testing on their components, including hydrostatic and cyclic pressure, uni-axial tensile and compressive, bending, and combined loading tests. The problem is due to the traditional difficulty associated with, and lack of understanding of, stress analysis of heterogeneous materials. First, the behavior and failure modes of these materials are highly complex and not fully understood, leading to inexact analytical methods and a general lack of agreement on the best course of action to follow. This lack of agreement has slowed the simplification and standardization of the analytical methods into universally recognized codes BS 7159 Code Design and Construction of Glass Reinforced Plastics Piping (GRP) Systems for Individual Plants or Sites and UKOOA Specification and Recommended Practice for the Use of GRP Piping Offshore being notable exceptions. Second, the heterogeneous, orthotropic behavior of FRP and other composite materials has hindered the use of the pipe stress analysis algorithms developed for homogeneous, isotropic materials associated with crystalline structures. A lack of generally accepted analytical procedures has contributed to a general reluctance to use FRP piping for critical applications. Stress analysis of FRP components must be viewed on many levels. These levels, or scales, have been called Micro-Mini-Macro levels, with analysis proceeding along the levels according to the "MMM" principle (Reference 4). CAESAR II User's Guide 929 Technical Discussions Micro-Level Analysis Stress analysis on the "Micro" level refers to the detailed evaluation of the individual materials and boundary mechanisms comprising the composite material. In general, FRP pipe is manufactured from laminates, which are constructed from elongated fibers of a commercial grade of glass, E-glass, which are coated with a coupling agent or sizing prior to being embedded in a thermosetting plastic material, typically epoxy or polyester resin. This means, on the micro scale, that an analytical model must be created which simulates the interface between these elements. Because the number and orientation of fibers is unknown at any given location in a FRP sample, the simplest representation of the micro-model is that of a single fiber, extending the length of the sample, embedded in a square profile of matrix. Micro Level GRP Sample -- Single Fiber Embedded in Square Profile of Matrix Evaluation of this model requires use of the material parameters of: 1. the glass fiber 2. the coupling agent or sizing layer normally of such microscopic proportion that it may be ignored 3. the plastic matrix It must be considered that these material parameters might vary for an individual material based upon tensile, compressive, or shear applications of the imposed stresses, and typical values vary significantly between the fiber and matrix (Reference 5): Young's Modulus Ultimate Strength Coefficient of Thermal Expansion tensile (MPa) tensile (MPa) m/m/ºC 3 Glass Fiber 72.5 x10 1.5 x 103 5.0 x 10-6 Plastic Matrix .07 x 103 7.0 x 10-6 Material 2.75 x 103 The following failure modes of the composite must be similarly evaluated to: 930 failure of the fiber failure of the coupling agent layer failure of the matrix CAESAR II User's Guide Technical Discussions failure of the fiber-coupling agent bond failure of the coupling agent-matrix bond Because of uncertainties about the degree to which the fiber has been coated with the coupling agent and about the nature of some of these failure modes, this evaluation is typically reduced to: failure of the fiber failure of the matrix failure of the fiber-matrix interface You can evaluate stresses in the individual components through finite element analysis of the strain continuity and equilibrium equations, based upon the assumption that there is a good bond between the fiber and matrix, resulting in compatible strains between the two. For normal stresses applied parallel to the glass fiber: f = m = af / Ef = am / Em af = am Ef / Em Where: f = Strain in the Fiber = Strain in the Matrix af = Normal Stress Parallel to Fiber, in the Fiber Ef = Modulus of Elasticity of the Fiber am = Axial Normal Stress Parallel to Fiber, in the Matrix Em = Modulus of Elasticity of the Matrix Due to the large ratio of the modulus of elasticity of the fiber to that of the matrix, it is apparent that nearly all of the axial normal stress in the fiber-matrix composite is carried by the fiber. Exact values are (Reference 6): af = L / [ + (1-)Em/Ef] am = L / [Ef/Em + (1-)] Where: L = nominal longitudinal stress across composite = glass content by volume CAESAR II User's Guide 931 Technical Discussions The continuity equations for the glass-matrix composite seem less complex for normal stresses perpendicular to the fibers, because the weak point of the material seems to be limited by the glass-free cross-section, shown below: Stress Intensification in Matrix Cross-Section For this reason, it would appear that the strength of the composite would be equal to that of the matrix for stresses in this direction. In fact, its strength is less than that of the matrix due to stress intensification in the matrix caused by the irregular stress distribution in the vicinity of the stiffer glass. Because the elongation over distance D1 must be equal to that over the longer distance D2, the strain, and thus the stress at location D1 must exceed that at D2 by the ratio D2/D1. Maximum intensified transverse normal stresses in the composite are: Where: b = intensified normal stress transverse to the fiber, in the composite = nominal transverse normal stress across composite m = Poisson's ratio of the matrix Because of the Poisson effect, this stress produces an additional 'am equal to the following: 'am = Vmb 932 CAESAR II User's Guide Technical Discussions Shear stress can be allocated to the individual components again through the use of continuity equations. It would appear that the stiffer glass would resist the bulk of the shear stresses. However, unless the fibers are infinitely long, all shears must eventually pass through the matrix in order to get from fiber to fiber. Shear stress between fiber and matrix can be estimated as Where: ab = intensified shear stress in composite T = nominal shear stress across composite Gm = shear modulus of elasticity in matrix Gf = shear modulus of elasticity in fiber Determination of the stresses in the fiber-matrix interface is more complex. The bonding agent has an inappreciable thickness, and thus has an indeterminate stiffness for consideration in the continuity equations. Also, the interface behaves significantly differently in shear, tension, and compression, showing virtually no effects from the latter. The state of the stress in the interface is best solved by omitting its contribution from the continuity equations, and simply considering that it carries all stresses that must be transferred from fiber to matrix. After the stresses have been apportioned, they must be evaluated against appropriate failure criteria. The behavior of homogeneous, isotropic materials such as glass and plastic resin, under a state of multiple stresses is better understood. Failure criterion for isotropic material reduces the combined normal and shear stresses (a, b, c, ab, ac, bc) to a single stress, an equivalent stress, that can be compared to the tensile stress present at failure in a material under uniaxial loading, that is, the ultimate tensile stress, Sult. Different theories, and different equivalent stress functions f(a, b, c, ab, ac, bc) have been proposed, with possibly the most widely accepted being the Huber-von Mises-Hencky criterion, which states that failure will occur when the equivalent stress reaches a critical value the ultimate strength of the material: eq = {1/2 [(a - b)2 + (b - c)2+ (c - a)2 + 6(ab2+ ac2+ bc2)} Sult This theory does not fully cover all failure modes of the fiber in that it omits reference to direction of stress, that is, tensile versus compressive. The fibers, being relatively long and thin, predominantly demonstrate buckling as their failure mode when loaded in compression. CAESAR II User's Guide 933 Technical Discussions The equivalent stress failure criterion has been corroborated, with slightly non-conservative results, by testing. Little is known about the failure mode of the adhesive interface, although empirical evidence points to a failure criterion which is more of a linear relationship between the normal and the square of the shear stresses. Failure testing of a composite material loaded only in transverse normal and shear stresses are shown in the following figure. The kink in the curve shows the transition from the matrix to the interface as the failure point. Mini-Level Analysis Mini-Level Analysis Fiber Distribution Models Although feasible in concept, micro level analysis is not feasible in practice. This is due to the uncertainty of the arrangement of the glass in the composite the thousands of fibers that might be randomly distributed, semi-randomly oriented, although primarily in a parallel pattern, and of randomly varying lengths. This condition indicates that a sample can truly be evaluated only on a statistical basis, thus rendering detailed finite element analysis inappropriate. For mini-level analysis, a laminate layer is considered to act as a continuous hence the common reference to this method as the "continuum" method, material, with material properties and failure modes estimated by integrating them over the assumed cross-sectional distribution, which is, averaging. The assumption regarding the distribution of the fibers can have a marked effect on the determination of the material parameters. Two of the most commonly postulated 934 CAESAR II User's Guide Technical Discussions distributions are the square and the hexagonal, with the latter generally considered as being a better representation of randomly distributed fibers. The stress-strain relationships, for those sections evaluated as continua, can be written as: aa = aa/EL - (VL/EL)bb - (VL/EL)cc bb = -(VL/EL)aa + bb/ET - (VT/ET)cc cc = -(VL/EL)aa - (VT/ET)bb + cc/ET ab = ab / 2 GL bc = bc / 2 GT ac = ac / 2 GL Where: ij = strain along direction i on face j ij, ab = stress (normal, shear) along direction i on face j EL = modulus of elasticity of laminate layer in longitudinal direction VL = Poisson’s ratio of laminate layer in longitudinal direction ET = modulus of elasticity of laminate layer in transverse direction VT = Poisson’s ratio of laminate layer in transverse direction GL = shear modulus of elasticity of laminate layer in longitudinal direction GT = shear modulus of elasticity of laminate layer in transverse direction These relationships require that four modules of elasticity, EL, ET, GL, and GT, and two Poisson’s ratios, VL and V, be evaluated for the continuum. Extensive research (References 4 - 10) has been done to estimate these parameters. There is general consensus that the longitudinal terms can be explicitly calculated; for cases where the fibers are significantly stiffer than the matrix, they are: EL = EF + EM(1 - ) GL = GM +/ [ 1 / (GF - GM) + (1 -) / (2GM)] VL = VF + VM(1 - ) You cannot calculate parameters in the transverse direction. You can only calculate the upper and lower bounds. Correlations with empirical results have yielded approximations (Reference 5 and 6): ET = [EM(1+0.85f2) / {(1-VM2)[(1-f)1.25 + f(EM/EF)/(1VM2)]} GT = GM (1 + 0.6) / [(1 - )1.25 + (GM/GF)] VT = VL (EL / ET) Use of these parameters permits the development of the homogeneous material models that facilitate the calculation of longitudinal and transverse stresses acting on a laminate layer. The resulting stresses can be allocated to the individual fibers and matrix using relationships developed during the micro analysis. CAESAR II User's Guide 935 Technical Discussions Macro-Level Analysis Macro to Micros Stress Conversion Where Mini-level analysis provides the means of evaluation of individual laminate layers, Macro-level analysis provides the means of evaluating components made up of multiple laminate layers. It is based upon the assumption that not only the composite behaves as a continuum, but that the series of laminate layers acts as a homogeneous material with properties estimated based on the properties of the layer and the winding angle, and that finally, failure criteria are functions of the level of equivalent stress. Laminate properties may be estimated by summing the layer properties (adjusted for winding angle) over all layers. For example Where: ExLAM = Longitudinal modulus of elasticity of laminate tLAM = thickness of laminate E⊥k = Longitudinal modulus of elasticity of laminate layer k Cik = transformation matrix orienting axes of layer k to longitudinal laminate axis Cjk = transformation matrix orienting axes of layer k to transverse laminate axis tk = thickness of laminate layer k After composite properties are determined, the component stiffness parameters can be determined as though it were made of homogeneous material that is, based on component cross-sectional and composite material properties. Normal and shear stresses can be determined from 1) forces and moments acting on the cross-sections, and 2) the cross-sectional properties themselves. These relationships can be written as: aa = Faa / Aaa ± Mba / Sba ± Mca / Sca bb = Fbb / Abb ± Mab / Sab ± Mcb / Scb cc = Fcc / Acc ± Mac / Sac ± Mbc / Sbc ab = Fab / Aab ± Mbb / Rab 936 CAESAR II User's Guide Technical Discussions ac = Fac / Aac ± Mcc / Rac ba = Fba / Aba ± Maa / Rba bc = Fbc / Abc ± Mcc / Rbc ca = Fca / Aca ± Maa / Rca cb = Fcb / Acb ± Mbb / Rcb Where: ij = normal stress along axis i on face j Fij = force acting along axis i on face j Aij = area resisting force along axis i on face j Mij = moment acting about axis i on face j Sij = section modulus about axis i on face j ij = shear stress along axis i on face j Rij = torsional resistivity about axis i on face j Using the relationships developed under macro, mini, and micro analysis, these stresses can be resolved back into local stresses within the laminate layer, and from there, back into stresses within the fiber and the matrix. From these, the failure criteria of those microscopic components, and hence, the component as a whole, can be checked. Implementation of Macro-Level Analysis for Piping Systems The macro-level analysis described above is the basis for the preeminent FRP piping codes in use today, including Code BS 7159 (Design and Construction of Glass Reinforced Plastics Piping Systems for Individual Plants or Sites) and the UKOOA Specification and Recommended Practice for the Use of GRP Piping Offshore. BS 7159 BS 7159 uses methods and formulas familiar to the world of steel piping stress analysis in order to calculate stresses on the cross-section, with the assumption that FRP components have material parameters based on continuum evaluation or test. All coincident loads, such as thermal, weight, pressure, and axial extension due to pressure need be evaluated simultaneously. Failure is based on the equivalent stress calculation method. Because one normal stress (radial stress) is traditionally considered to be negligible in typical piping configurations, this calculation reduces to the greater of (except when axial stresses are compressive): (when axial stress is greater than hoop) (when hoop stress is greater than axial) A slight difficulty arises when evaluating the calculated stress against an allowable, due to the orthotropic nature of the FRP piping normally the laminate is designed in such a way to make the pipe much stronger in the hoop, than in the longitudinal, direction, providing more than one allowable stress. This difficulty is resolved by defining the allowable in terms of a design strained, rather than stress, in effect adjusting the stress allowable in proportion to the strength CAESAR II User's Guide 937 Technical Discussions in each direction. In other words, the allowable stresses for the two equivalent stresses above would be (ed ELAMX) and (ed ELAMH) respectively. In lieu of test data, system design strain is selected from Tables 4.3 and 4.4 of the Code, based on expected chemical and temperature conditions. Actual stress equations as enumerated by BS 7159 display below: 1. Combined stress straights and bends: C = (f 2+ 4S2)0.5 dELAM or C = (X2 + 4S2)0.5 dELAM Where: ELAM = modulus of elasticity of the laminate; in CAESAR II, the first equation uses the modulus for the hoop direction and in the second equation, the modulus for the longitudinal direction is used. C = combined stress Φ = circumferential stress = ΦP + ΦB S = torsional stress = MS(Di + 2td) / 4I X = longitudinal stress = XP + XB ΦP = circumferential pressure stress = mP(Di + td) / 2 td ΦB = circumferential bending stress = [(Di + 2td) / 2I] [(Mi SIFΦi)2 + Mo SIFΦo)2] 0.5 for bends, = 0 for straights MS = torsional moment on cross-section Di = internal pipe diameter td = design thickness of reference laminate I = moment of inertia of pipe m = pressure stress multiplier of component P = internal pressure Mi = in-plane bending moment on cross-section SIFΦi= circumferential stress intensification factor for in-plane moment M = out-plane bending moment on cross-section SIFΦo = circumferential stress intensification factor for out-plane moment XP = longitudinal pressure stress = P(Di+ td) / 4 td 938 CAESAR II User's Guide Technical Discussions XB = longitudinal bending stress = [(Di + 2td) / 2I] [(Mi SIFxi)2 + Mo SIFxo)2]0.5 SIFxi = longitudinal stress intensification factor for in-plane moment SIFxo = longitudinal stress intensification factor for out-plane moment 2. Combined stress branch connections: CB = ((ΦP + bB)2 + 4SB2)0.5 d ELAM Where: CB = branch combined stress ΦP = circumferential pressure stress = mP(Di + tM) / 2 tM bB = non-directional bending stress = [(Di + 2td) / 2I] [(Mi SIFBi)2 + Mo SIFBo)2]0.5 SB = branch torsional stress = MS(Di + 2td) / 4I tM = thickness of the reference laminate at the main run SIFBi = branch stress intensification factor for in-plane moment SIFBo = branch stress intensification factor for out-plane moment 3. When longitudinal stress is negative (net compressive): Φ - VΦx x Φ ELAMΦ Where: VΦx = Poisson’s ratio giving strain in longitudinal direction caused by stress in circumferential direction Φ = design strain in circumferential direction ELAMΦ= modulus of elasticity in circumferential direction CAESAR II User's Guide 939 Technical Discussions BS 7159 also dictates the means of calculating flexibility and stress intensification (k- and i) factors for bend and tee components, for use during the flexibility analysis. 940 CAESAR II User's Guide Technical Discussions BS 7159 imposes a number of limitations on its use, the most notable being: the limitation of a system to a design pressure of 10 bar, the restriction to the use of designated design laminates, and the limited applicability of the k- and i- factor calculations to pipe bends (that is, mean wall thickness around the intrados must be 1.75 times the nominal thickness or less). This code appears to be more sophisticated, yet easy to use. We recommend that its calculation techniques be applied even to FRP systems outside its explicit scope, with the following recommendations: Pressure stiffening of bends should be based on actual design pressure, rather than allowable design strain. Design strain should be based on manufacturer’s test and experience data wherever possible (with consideration for expected operating conditions). Fitting k- and i- factors should be based on manufacturer’s test or analytic data, if available. UKOOA The UKOOA Specification is similar in many respects to the BS 7159 Code, except that it simplifies the calculation requirements in exchange for imposing more limitations and more conservatism on the piping operating conditions. CAESAR II User's Guide 941 Technical Discussions Rather than explicitly calculating a combined stress, the specification defines an idealized envelope of combinations of axial and hoop stresses that cause the equivalent stress to reach failure. This curve represents the plot of: (x / x-all)2 + (hoop / hoop-all)2 - [x hoop / (x-all hoop-all)] 1.0 Where: x-all = allowable stress, axial hoop-all = allowable stress, hoop The specification conservatively limits you to that part of the curve falling under the line between x-all (also known as sa(0:1)) and the intersection point on the curve where hoop is twice sx-(a natural condition for a pipe loaded only with pressure), as shown in the following figure. An implicit modification to this requirement is the fact that pressure stresses are given a factor of safety (typically equal to 2/3) while other loads are not. This gives an explicit requirement of: Pdes f1 f2 f3 LTHP Where: Pdes = allowable design pressure f1 = factor of safety for 97.5% lower confidence limit, usually 0.85 f2 = system factor of safety, usually 0.67 f3 = ratio of residual allowable, after mechanical loads = 1 - (2 ab) / (r f1 LTHS) ab = axial bending stress due to mechanical loads r = a(0:1)/a(2:1) a(0:1) = long term axial tensile strength in absence of pressure load a(2:1) = long term axial tensile strength under only pressure loading LTHS = long term hydrostatic strength (hoop stress allowable) LTHP = long term hydrostatic pressure allowable 942 CAESAR II User's Guide Technical Discussions This has been implemented in the CAESAR II pipe stress analysis software as: Code Stress ab (f2 /r) + PDm / (4t) Code Allowable (f1 f2 LTHS) / 2.0 Where: P = design pressure D = pipe mean diameter t = pipe wall thickness K and i-factors for bends are to be taken from the BS 7159 Code, while no such factors are to be used for tees. The UKOOA Specification is limited in that shear stresses are ignored in the evaluation process; no consideration is given to conditions where axial stresses are compressive; and most required calculations are not explicitly detailed. CAESAR II User's Guide 943 Technical Discussions FRP Analysis Using CAESAR II Practical Applications CAESAR II has had the ability to model orthotropic materials such as FRP almost since its inception. It also can specifically handle the requirements of the BS 7159 Code, the UKOOA Specification, and more recently ISO 14692. FRP material parameters corresponding to those of many vendors’ lines are provided with CAESAR II. You can pre-select these parameters to be the default values whenever FRP piping is used. Other options, as to whether the BS 7159 pressure stiffening requirements should be carried out using design strain or actual strain can be set in CAESAR II’s configuration module as well. 944 CAESAR II User's Guide Technical Discussions CAESAR II User's Guide 945 Technical Discussions Selecting material 20 — Plastic (FRP) – activates CAESAR II’s orthotropic material model and brings in the appropriate material parameters from the pre-selected materials. The orthotropic material model is indicated by the changing of two fields from their previous isotropic values: Elastic Modulus (C) changes to Elastic Modulus/axial and Poisson's Ratio changes to Ea/Eh*Vh/a. These changes are necessary because orthotropic models require more material parameters than do isotropic. For example, there is no longer a single modulus of elasticity for the material, but now two: axial and hoop. There is no longer a single Poisson’s ratio, but again two: Vh/a (Poisson’s ratio relating strain in the axial direction due to stress-induced strain in the hoop direction) and Va/h (Poisson’s ratio relating strain in the hoop direction due to stress-induced strain in the axial direction). Also, unlike isotropic materials, the shear modulus does not follow the relationship G = 1 / E (1-V), so that value must be explicitly input. To minimize input, a few of these parameters can be combined due to their use in the program. Generally, the only time that the modulus of elasticity in the hoop direction or the Poisson’s ratios is used during flexibility analysis is when calculating piping elongation due to pressure (note that the modulus of elasticity in the hoop direction is used when determining certain stress allowables for the BS 7159 code): dx = (x / Ea - Va/h * hoop / Eh) L Where: dx 946 = extension of piping element due to pressure CAESAR II User's Guide Technical Discussions x = longitudinal pressure stress in the piping element E = modulus of elasticity in the axial direction Va/h = Poisson’s ratio relating strain in the axial direction due to stressinduced strain in the hoop direction hoop = hoop pressure stress in the piping element Eh = modulus of elasticity in the hoop direction L = length of piping element This equation can be rearranged, to require only a single new parameter, as: dx = (x - Va/h hoop * (Ea / Eh )) * L / Ea In theory, that single parameter, Vh/a is identical to (Ea / Eh * Va/h) giving: dx = (x Vh/ahoop) * L / Ea The shear modulus of the material is required in ordered to develop the stiffness matrix. In CAESAR II, this value, expressed as a ratio of the axial modulus of elasticity, is brought in from the pre-selected material, or can be changed on a problem-wise basis using the Special Execution Parameter (see "Special Execution Parameters" on page 287) dialog box accessed by the Environment menu from the piping spreadsheet (see figure). This dialog box also shows the coefficient of thermal expansion (extracted from the vendor file or user entered) for the material, as well as the default laminate type, as defined by the BS 7159 Code: Type 1 – All chopped strand mat (CSM) construction with an internal and an external surface tissue reinforced layer. Type 2 – Chopped strand mat (CSM) and woven roving (WR) construction with an internal and an external surface tissue reinforced layer. Type 3 – Chopped strand mat (CSM) and multi-filament roving construction with an internal and an external surface tissue reinforced layer. The latter is used during the calculation of flexibility and stress intensification factors for piping bends. You can enter bend and tee information by using the auxiliary spreadsheets. CAESAR II User's Guide 947 Technical Discussions You can also change bend radius and laminate type data on a bend by bend basis, as shown in the corresponding figure. Specify BS 7159 fabricated and molded tee types by defining CAESAR II tee types 1 and 3 respectively at intersection points. CAESAR II automatically calculates the appropriate flexibility and stress intensification factors for these fittings as per code requirements. Enter the required code data on the Allowables auxiliary spreadsheet. The program provides fields for both codes, number 27 – BS 7159 and number 28 – UKOOA. After selecting BS 7159, CAESAR II provides fields for entry of the following code parameters: SH1 through SH9 = Longitudinal Design Stress = d ELAMX Kn1 through Kn9 = Cyclic Reduction Factor (as per BS 7159 paragraph 4.3.4) Eh/Ea = Ratio of Hoop Modulus of Elasticity to Axial Modulus of Elasticity K = Temperature Differential Multiplier (as per BS 7159 paragraph 7.2.1) 948 CAESAR II User's Guide Technical Discussions After selecting UKOOA, CAESAR II provides fields for entry of the following code parameters: SH1 through SH9 = hoop design stress = f1 * LTHS R1 through R9 = ratio r = (a(0:1) / a(2:1)) f2 = system factor of safety (defaults to 0.67 if omitted) K = temperature differential multiplier (same as BS 7159) These parameters need only be entered a single time, unless they change at some point in the system. Performing the analysis is simpler than the system modeling. <Product> evaluates the operating parameters and automatically builds the appropriate load cases. In this case, three are built: Operating includes pipe and fluid weight, temperature, equipment displacements, and pressure. This case is used to determine maximum code stress/strain, operational equipment nozzle and restraint loads, hot displacements, and so forth. Cold (same as above, except excluding temperature and equipment movements). This case is used to determine cold equipment nozzle and restraint loads. Expansion (cyclic stress range between the cold and hot case). This case may be used to evaluate fatigue criteria as per paragraph 4.3.4 of the BS 7159 Code. After analyzing the response of the system under these loads, CAESAR II displays a menu of possible output reports. Reports may be designated by selecting a combination of load case and results type (displacements, restraint loads, element forces and moments, and stresses). From the stress report, you can determine at a glance whether the system passed or failed the stress criteria. CAESAR II User's Guide 949 Technical Discussions For UKOOA, the piping is considered to be within allowable limits when the operating stress falls within the idealized stress envelope this is illustrated by the shaded area in the following figure. Conclusion A pipe stress analysis program with worldwide acceptance is now available for evaluation of FRP piping systems as per the requirements of the most sophisticated FRP piping codes. This means that access to the same analytical methods and tools enjoyed by engineers using steel pipe is available to users of FRP piping design. References 1. Cross, Wilbur, An Authorized History of the ASME Boiler an Pressure Vessel Code, ASME, 1990 2. Olson, J. and Cramer, R., "Pipe Flexibility Analysis Using IBM 705 Computer Pro\-gram MEC 21, Mare Island Report 277-59," 1959 3. Fiberglass Pipe Handbook, Composites Institute of the Society of the Plastics Indus\try, 1989 4. Hashin, Z., "Analysis of Composite Materials a Survey," Journal of Applied Mechanics, Sept. 1983 5. Greaves, G., "Fiberglass Reinforced Plastic Pipe Design," Ciba-Geigy Pipe Systems 6. Puck, A. and Schneider, W., "On Failure Mechanisms and Failure Criteria of FilamentWound Glass-Fibre/Resin Composites," Plastics and Polymers, Feb. 1969 7. Hashin, Z., "The Elastic Moduli of Heterogeneous Materials," Journal of Applied Mechanics, March 1962 8. Hashin, Z. and Rosen, B. Walter, "The Elastic Moduli of Fibre Reinforced Materials," Journal of Applied Mechanics, June 1964 9. Whitney, J. M. and Riley, M. B., "Elastic Properties of Fiber Reinforced Composite Materials," AIAA Journal, Sept. 1966 10. Walpole, L. J., "Elastic Behavior of Composite Materials: Theoretical Foundations," Advances in Applied Mechanics, Volume 21, Academic Press, 1989 11. BS 7159: 1989 British Standard Code of Practice for Design and Construction of Glass Reinforced Plastics GRP Piping Systems for Individual Plants or Sites. 12. UK Offshore Operators Association Specification and Recommended Practice for the Use of GRP Piping Offshore., 1994 950 CAESAR II User's Guide Technical Discussions Code Compliance Considerations This section comprises general notes that cover code compliance. The first several pages contain information that applies to all of the codes. The last pages contain code-specific discussions. Review the general notes, highlighting those that apply to your problem. Also, review the notes for the piping code that you need. Configuration and Environment (on page 45) gives details about the various parameters that you can use in the CAESAR II setup file. Many of these parameters are discussed from an "application point-of-view" in the text that follows. For more information on the CAESAR II setup file, see Configuration and Environment (on page 45). General Comments on Configuration Settings' Effect on Piping Code Calculations Stress Intensification Factors (SIF) for all codes Use the table below to determine which SIF value you need. If you have... then use an SIF Value of ... threaded joints 2.3 double welded slip-on flanges 1.2 lap joint flanges with B16.9 stub ends 1.6 Calculate Bonney Forge sweepolet and insert weldolet fittings Use the Weld ID on the SIF & TEE Auxiliary dialog box to calculate the sweepolet and insert weldolet fittings. If you can verify that the welds for these fittings are finished or dressed, then specifying the weld ID lowers the SIF. Bend SIF overrides User-defined bend SIF overrides affect the entire cross section of the bend, and as such you cannot use them to specify a single point on the bend curvature. You must specify the SIFs for the bend TO node. CAESAR II will apply this SIF, in place of the code SIF, over the entire bend curvature, from weldline to weldline. The default value for Fiberglass-Reinforced Plastic (FRP) bend and intersection SIFs is 2.3. Use this value for all user-modified bends and intersections. The default flexibility factor value for FRP bends is 1.0. If you modify these values, and generate the SIFs using the steel fatigue tests you might not be able to use them as a basis for SIFs with FRP fittings. CAESAR II does not permit the use of SIF values less than 1.0. CAESAR II User's Guide 951 Technical Discussions WRC 329 The only piping codes that cannot take advantage of the WRC 329 options, or the option to use the ASME NC and ND rules for reduced intersections, are BS806 and the Swedish Power Method 1. These codes do not use the effective section modulus, and any extrapolation of the ASME methods into these codes is unwarranted. There is a small difference between Use WRC329 and Reduced Intersection = WRC329. Use Use WRC329 for all full and reduced intersections that are not welding tees or reinforced tees. Use Reduced Intersection =WRC329 for reduced fittings that are not welding tees or reinforced fabricated tees. A fitting is reduced when d/D is less than 0.975. WRC 329 impact on use with B31.3, B31.4, B31.11, or B31.1 (1967) codes 1. Include torsional stresses in all stress calculations (sustained and occasional). 2. Use a torsional SIF of (r/R) io. 3. Compute i(ib) use 0.6(R/T)2/3 [1+0.5(r/R)3](r/rp). 4. For i(ob) use 1.5(R/T)2/3 (r/R)1/2 (r/rp) and i(ob)(t/T)>1.5 when (r/R) < 0.9 use 0.9(R/T)2/3 (r/rp) and i(ob)(t/T)>1.0 when (r/R) = 1.0 and use interpolation when 1.0 > (r/R) > 0.9 5. For ir use 0.8 (R/T)2/3 (r/R), and ir > 2.1 6. If the radius at the junction provided is greater than the larger of t/2 or T/2, then divide the calculated SIFs by 2.0, but with ib>1.5 and ir>1.5. WRC 329 impact on use with B31.1, B31.8, ASME III NC, ASME III ND, Navy 505, Z183, Z184, or Swedish Method 2 codes 1. For ib use 1.5(R/T)2/3 (r/R)1/2 (r/rp), and ib(t/T)>1.5 when (r/R) < 0.9 use 0.9(R/T)2/3 (r/rp), and ib(t/T)>1.0 when (r/R) = 1.0 and use interpolation when 1.0 > (r/R) > 0.9 2. For ir use 0.8 (R/T)2/3 (r/R), and ir > 2.1 3. If a radius at the provided junction is greater than the larger of t/2 or T/2, then divide the calculated SIFs by 2.0, but with ib>1.5 and ir>1.5. Bonney Forge Sweepolets tend to be a little more conservative because they are used for fittings in the nuclear industry. Bonney Forge Sweepolet equations can generate SIFs less than one because they are stronger than the girth butt weld used as the unity basis for the code fitting SIFs. CAESAR II does not permit SIFs of less than 1.0. If you generate a Bonney Forge Sweepolet SIF that is less than 1.0, the default value 1.0 is used. The Bonney Forge SIF Data came from the technical flyer: "Bonney Forge Stress Intensification Factors" Bulletin 789/Sl-1, Copyright 1976. Although CAESAR II allows the specification of two element intersections, you cannot specify two SIFs at a single node and get an increased SIF. For example, you cannot specify a socket weld SIF and an intersection SIF at the same point. 952 CAESAR II User's Guide Technical Discussions Stress calculations for under-specified fittings For two element joints use the largest diameter and the smallest wall thickness, when discrepancies exist between the two adjoining pipes. For two element fittings modeled as socket welds use the largest wall thickness. Both of these selections generate the largest SIFs and the most conservative stress calculations for under-specified fittings. The mismatch given for girth butt welds is the average mismatch and not the maximum mismatch. You must verify that any maximum mismatch requirements are satisfied. If a fillet leg is given in conjunction with a socket weld SIF definition, then both socket weld types result in the same SIF. B31.3 sustained case SIF The B31.3 sustained case SIF factor in the setup file affects all of the following codes: B31.4, B31.8, B31.11, Navy 505, Z662, and B31.1 (1967). The default value for the B31.3 SUS case SIF factor is 1.0. Corrosion Calculate the corroded effective section modulus by using (r2)te Where: r is the average cross sectional radius of the non-corroded pipe (te) is the corroded thickness. Select the thickness (te) based on the non-corroded thicknesses of the branch and header, in other words, the lesser of Th and iTb. The resulting value has the corrosion subtracted from it before the effective section modulus calculation is made. Always use the corroded wall thickness to calculate the Maximum Shear Stress regardless of the setting of the All Stress Cases Corroded option located in the setup file. Using more than one Piping Code If you use different piping codes in one job, the code that displays at the top of the Output Stress report is the last code used during model input. SIFs, allowables, and code equations are all computed in accordance with the code that varies with the input. When there are multiple piping codes in the same piping job, and a piping code change occurs at an intersection, if the intersection is completely defined with three pipes framing into the intersection then the piping code used to generate the SIF equations will be that one associated with the first header pipe framing into the intersection. If the intersection is only partially defined, then the piping code will be selected from the first pipe framing into the intersection point. Axial Stress in the Expansion Stress Range The ASME piping codes primarily combine moments for thermal expansion stresses. When there is any tendency for large axial forces to exist in the pipe these code equations are not adequate. An example of this is for buried or partially buried pipe. Here the axial stresses can be very high. B31.4 directs you to compute a longitudinal stress for completely restrained pipe. CAESAR II enables you to specify just how much of the pipe is buried. This longitudinal stress is then added to the stress calculations for thermal and contributes to a failure prediction that might have otherwise been ignored. Similar effects can be achieved in CAESAR II by using the axial CAESAR II User's Guide 953 Technical Discussions soil restraint and telling the setup file to include F/A components in the stress calculations. Be aware that for any type of problem, if large axial loads are developed because of the design, the piping code might not be adequately considering it. Application of Torsion in Stress Calculations The piping codes that do not, by default, include torsion in the sustained or occasional stress calculations display below: B31.3 Navy 505 B31.4 Z662 B31.8 B31.1 (1967) B31.11 GPTC/Z380 These codes tell you to add the longitudinal stresses due to weight, pressure, and other sustained loadings so torsion is not added. Torsional shear stresses are not longitudinal stresses. You can request that torsion is added into the sustained and occasional stress equations by including the Add Torsion in SL Stress option in the setup file. The torsion stress is still not intensified as it is in the power piping codes. This lack of intensification is considered an oversight and is corrected in WRC 329. You can include this fix by running any of the above codes and including the Use WRC330 option in the setup file. Radius Entry for Mitered Joints The radius given in CAESAR II is always the equivalent closely spaced miter radius. Only use the radius calculation for widely spaced miters in the piping codes after breaking the widely spaced miter bend down into individual single cut miters as recommended. Reduced intersection calculations Use reduced intersection calculations when d/D < 0.975. Where: d = Outside Diameter of the Branch D = Outside Diameter of the Header B31.1 and the ASME Section III piping codes provide stress intensification factors for reduced branch ends. None of the other piping codes provide these SIFs. The Reduced Intersection option in the setup file enables other piping code users to access improved SIFs for reduced fittings. You should review the notes associated with the B31.1 and the ASME Section III codes that follow to verify that any other parameters or input associated with the reduced intersection calculations are set as necessary. Pressure Stiffening If you request pressure stiffening for those codes that do not normally provide it, CAESAR II applies pressure stiffening for all bends and for both miter types. 954 CAESAR II User's Guide Technical Discussions Occasional Load Factors The defaults occasional load factor from the setup file used in the evaluation of the allowable stress, display the text that follows for each of the piping codes. B31.1: The occasional load factor is 1.15. B31.3: The occasional load factor is 1.33. B31.4: This is 0.8Sy as defined in the most recent edition of B31.4. OCC does not affect a B31.4 analysis in CAESAR II. B31.5: The occasional load factor is 1.33. B31.8: Occasional cases are not specifically defined. If you enter an OCC load case the allowable defaults to 1.0 times the sustained allowable stress in other words OCC=1.0. B31.11: This is 0.88Sy as defined in the most recent edition of B31.11 OCC does not affect a B31.11 analysis in CAESAR II. ASME Section III NC and ND: The default value of OCC is 1.2, the occasional stress allowable is 1.8 (1.2 X 1.5)Sh but not greater than 1.5Sy. If OCC is 1.5 or 2.0, the allowable is set to the minimum of 2.25Sh/1.8Sy (Level C) or 3.0Sh/2.0Sy (Level D). Note in the latter two cases, enter Sm for Sh. Navy 505: Occasional cases are not addressed but defaults to the method used in B31.1, and an OCC value of 1.15 is the default. Z662: The occasional case is not defined, but if you make an entry the allowable for the case defaults to 1.0 times the sustained allowable. BS806: The occasional load case is not defined, but if you make an entry the allowable stress for the OCC load case is KSh. This is the occasional load factor times the sustained allow\-able. The default value for k is 1.0. Swedish Method 1: OCC is not used. The load cases are not differentiated. The same allowable Sigma(ber)/1.5 is used for all load cases. Swedish Method 2: Uses an OCC default of 1.2 as recommended in the Swedish Piping Code. B31.1(1967): OCC default is 1.15. Stoomwezen: OCC default is 1.2. RCC-M C&D: OCC default is 1.2. CODETI: OCC default is 1.15. NORWEGIAN: OCC default is 1.2. FBDR: OCC default is 1.15 BS 7159: The occasional load case is not defined. UKOOA: The occasional load case is not defined. IGE/TD/12: Table 4 of the code addresses occasional stress increases. The occasional factor in the setup file has no bearing on this code. EN-13480: The occasional load factor varies from 1.0 to 1.8, depending on the loading. Refer to Section 12.3.3 for details. CAESAR II User's Guide 955 Technical Discussions GPTC/Z380: Occasional cases are not specifically defined. If you enter an OCC load case the allowable defaults to 1.0 times the sustained allowable stress in other words OCC=1.0. HPGSL: The occasional load factor is 1.33. JPI: The occasional load factor is 1.33. You can change the occasional load factor from the program defaults by using the setup file. Enter the value as a percent. To get an occasional load factor of 1.5, you must type 50.0. Code-Specific Notes B31.1 Calculate pressure stiffening using B31.1 Pressure stiffening is defined by default in the code. You can exclude pressure stiffening on bends in the analysis by including the Use Pressure Stiffening=No option in the setup file. Flanged end modifications using B31.1 Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. CAESAR II does not verify the B31.1 criteria "B" length for closely spaced miters. B31.1 does not by default add F/A into the stress calculation. F/A and the pressure stresses are added to the bending stress, whether the tensile or compressive component of bending, to produce the largest longitudinal stress component. This is true for all codes where the addition of axial and pressure terms are concerned. You can include the axial force terms into the code stress by inserting the Add F/A In Stress=Yes option in the setup file. The F/A forces are structural forces developed in the pipe independent of the pressure PD/4t forces. Calculate reduced branch stress intensification factors (SIFs) using B31.1 In 1980, B31.1 added a reduced branch SIF equation to Appendix D. This equation came from ASME Section III. However, B31.1 continued to use the effective section modulus calculation for the branch. The ASME Section III rules clearly stated that the branch section modulus, not the effective section modulus should be used with the new SIF. B31.1 continued use of the effective section modulus produced unnecessarily high calculated stresses. This error was corrected in the 1989 version of B31.1. Prior to CAESAR II version 3.0, you had two options: Use the pre-1980 version of the B31.1 SIF rules Use the very conservative post-1980 B31.1 SIF rules These options also exist in version 3.0 and later except that the section modulus problem is corrected. If you need to run version 3.0 and later without the section modulus correction, then include the B31.1 Reduced Z Fix=No option in the setup file. Calculate reduced intersection branch using B31.1 Reduced intersection branch SIFs were not intended for reinforced or welding tees. Conservative results are produced, but the original researchers did not intend for SIFs to be used for these fittings. You can disable the reduced branch fitting calculations for reinforced or 956 CAESAR II User's Guide Technical Discussions welded tees by including the No Reduced SIF for RFT and WLT option in the setup file. This produces less conservative results, but can in some cases be justified. B31.1 102.3.2 (c) says to divide the allowable stresses coming from the stress tables in Appendix A by the applicable weld joint factors listed in Paragraph 102.4.3. Calculate the B31.1 stress allowables Use the equations below to calculate the stress allowables. Expansion Allowable = f [ (1.25/Eff)(Sc+Sh) - Sl ] Sustained Allowable = Sh/Eff Occasional Allowable = Sh/Eff * (Occ) Where: f = Cyclic Reduction Factor Eff = Longitudinal Weld Joint Efficiency Sc = Cold Allowable Stress Sh = Hot Allowable Stress Sl = Sustained Stress Occ = Occasional Load Factor Default is 1.15 Calculate stress intensification factors (SIFs) for intersections using B31.1 Inplane and outplane SIFs for intersections are the same. B31.1 reducer default values The default flexibility factor value is 1.0. Use the following equation to determine the SIF value: maximum of 2.0 or 0.5 + .01*Alpha* SQRT(D2/t2). Where: D1- Diameter of the Large End t1- Thickness of the Large End D2 - Diameter of the Small End t2 - Thickness of the Small End Alpha - the Reducer Cone Angle in Degrees. Where: Alpha = atan[ 0.5 * (D1-D2) / (length of the sloped portion of the reducer) ] Alpha is the slope of the reducer transition in degrees. If left blank, the value is set from an estimated slope equal to the arc tangent times 1/2 the change in diameters times sixty percent of the entered reducer length. Alpha cannot exceed 60° and the larger of D1/t1 and D2/t2 cannot exceed 100. CAESAR II User's Guide 957 Technical Discussions B31.3 Flanged end modifications using B31.3 Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. Calculate stress intensification factors (SIFs) for intersections using B31.3 In-plane and out-plane SIFs for intersections are separate and unique. B31.3 piping code gives the equation for the expansion stress. Because that equation does not include the longitudinal stress due to axial loads in the pipe, CAESAR II does not include the F/A component of the stress in the expansion stress equation. The code also says that you can add the F/A component where it is significant. Change this by including the Add F/A In Stress option in the setup file. The F/A longitudinal stress components are added by default to the code stress component for all other stress categories. B31.3 girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate socket welds using B31.3 B31.3 makes no distinction between socket welds with undercut and socket welds without undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3 for all B31.3 socket welds. Calculate the B31.3 stress allowables Use the equations below to calculate the stress allowables. Expansion Allowable = f [ (1.25)(Sc+Sh) - Sl ] Sustained Allowable Occasional Allowable = = Sh Sh * (Occ) Where: f = Cyclic Reduction Factor Sc = Cold Allowable Stress Sh = Hot Allowable Stress (as selected) Sl = Sustained Stress Occ = Occasional Load Factor Default is 1.33 Calculate corroded stress using B31.3 By default, B31.3 applied corrosion to section modulus calculation for sustained and occasional stress calculation. Specifying All Stress Cases Corroded in the setup file performs the corroded stress calculations for all stress calculations. 958 CAESAR II User's Guide Technical Discussions Calculate pressure effects on miters using B31.3 Pressure effects on miters are allowed in the B31.3 piping code. B31.3 reducer default values The default SIF value is 1.0. The default flexibility factor value is 1.0. B31.4 Calculate pressure stiffening using B31.4 Pressure stiffening is defined by default in the code. You can exclude pressure stiffening on bends in the analysis by including the Use Pressure Stiffening on Bends in the setup file. Flanged end modifications using B31.4 Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. B31.4 girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate stress intensification factors (SIFs) for intersections using B31.4 In-plane and out-plane SIFs for intersections are separate and unique. Calculate the B31.4 stress allowables Use the equations below to calculate the stress allowables. Expansion Allowable = (0.72)(Sy) Sustained Allowable = (0.75)(0.72)(Sy) Occasional Allowable = (0.8)(Sy) Operating Allowable = (0.9)(Sy) if the axial stress is compressive, no code check is done if axial stress tensile Where: Sy = Specified Minimum Yield Stress B31.4 does not use EFF, (found in the Allowable Stress auxiliary field). The minimum yield stress is all that is required to compute flexibility stress allowables. Calculate effective section modulus using B31.4 B31.4 has no provision for using an effective section modulus calculation at intersections. Calculate liberal allowable using B31.4 B31.4 does not include a provision for the liberal allowable. This particular option is not used for B31.4 stress allowable calculations. The occasional load factor, used in the other piping codes CAESAR II User's Guide 959 Technical Discussions for determining the allowable stress for occasional load sets, is not used in B31.4, as the default allowable stress is 0.8 times the minimum yield stress. CAESAR II assumes that 419.6.4(b) establishes a requirement for the allowable operating stress at 90% of Sy; when the net axial stress is compressive (for example, when longitudinal pressure stresses can be ignored in underground pipes). The last sentence in the paragraph establishes that: "Beam bending stresses shall be included in the longitudinal stress for those portions of the restrained line which are supported above ground." You have two options for including the axial stress in your analyses: 1. Include axial friction restraints and include the ADD_F/A parameter into the setup file. Set Fac to 0.001 to indicate that the line is buried, so longitudinal pressure stresses are not present, so the hoop stress component must be considered. 2. Use the Fac value to have CAESAR II compute the "axially-restrained" stress and include it during stress calculations. If you enter a nonzero Fac value, then multiply the pressure plus axial loads in the pipe by (1-Fac). This gives a more realistic estimation of the axial stress in the pipe when you include both of the effects above. Paragraph 419.6.4(b) requires 1) the reduction of the axial expansion stress by the product of Poisson's ratio and the pressure hoop stress, and 2) the addiction of the hoop stress to the axial stress. The latter represents the calculation of stress intensity when the axial stress is compressive, implying that there is no longitudinal pressure stress in buried pipe (the pressure loads are transmitted directly to the soil). CAESAR II handles this case in the Operating Load Case, where the hoop stress is added in and the allowable stress is set to 0.9 Sy whenever the axial stress is compressive. If Fac is 0.001, the piping element is considered buried, so the longitudinal pressure stress is replaced by the product of Poisson’s ratio and the hoop stress, in keeping with the spirit of paragraph 419.6.4(b). "Fac" is automatically set to 0.001 when B31.4 pipe is sent through the Buried Pipe Modeler. The stress due to axial force is also included for these elements. The Fac variable should probably not be set to 1.0 with B31.4 and thermal expansion cases where you are going from one thermal state to another state. In other words, where the case is of the form: L1-L2, and both L1 and L2 contain temperatures. In this case, the thermal expansion used in the restrained pipe calculation comes from the last thermal specified in the load case definition. In the example above the thermal expansion associated with the L2 load case. The Base Hoop Stress On OD flag in the setup file is used by B31.4 when the hoop stress is calculated for the restrained pipe longitudinal stress calculation. The default is to base the hoop stress calculation on the average diameter, and the equation PD/2t. In the mechanical stress calculations the hoop stress is based on the inside diameter. This is the hoop stress that is printed in the extended CAESAR II Stress report. B31.4 reducer default values The default SIF value is 1.0. The default Flexibility Factor value is 1.0. 960 CAESAR II User's Guide Technical Discussions B31.4 Chapter IX Chapter IX presents the offshore requirements of the B31.4 (on page 959). Calculate Stress Intensification Factors (SIFs), flexibility factors, and section moduli Calculate all SIFs, flexibility factors, and section moduli exactly as stated in the standard B31.4 code. Calculate stress using B31.4 Chapter IX Use the uncorroded wall thickness to make stress calculations. Calculate load cases using B31.4 Chapter IX There is no provision for a code check for the expansion load case, so no expansion cases are generated under this code. Operating, sustained, or occasional load cases are treated identically. Do three stress calculations for these load cases, each with a different allowable limit. The Stress Report displays the calculation causing the highest percent of allowable along with its specific allowable. These three stress checks are: Hoop Stress: Sh F1 Sy Longitudinal Stress: |SL| 0.8 Sy Equivalent Stress: Se 0.9 Sy Where: Sh = (Pi – Pe) D / 2t Pi = Internal Pressure Pe = External Pressure D = Outer Diameter t = Wall Thickness F1 = Hoop Stress Design Factor 0.60 or 0.72, see Table A402.3.5(a) of the B31.4 Code Sy = Specified Minimum Yield Strength SL = Sa + Sb or Sa - Sb, whichever results in greater stress value Sa = Axial Stress Positive Tensile and Negative Compressive Sb = Bending Stress Se = 2[((SL - Sh)/2)2 + St2]1/2 St = Torsional Stress CAESAR II User's Guide 961 Technical Discussions B31.5 B31.5 reducer default values The default SIF value is 1.0. The default flexibility factor value is 1.0. B31.8 Restrained Pipe (as defined in Section 833.1): For Straight Pipe: Both SL and SC < 0.9ST (OPE) Both SL, and SC < 0.9ST (SUS) SL < 0.9ST and Sc < ST (OCC) and * The Stress Report displays the calculation causing the highest percent of allowable along with its specific allowable. For All Other Components SL < 0.9ST (OPE, SUS, OCC) Unrestrained Pipe (as defined in Section 833.1): SL < 0.75ST (SUS, OCC) SE < f[1.25(SC + SH) – SL] (EXP) Where: SL = SP + SX + SB SP = 0.3SHoop (for restrained pipe); 0.5SHoop (for unrestrained pipe) SX = R/A SB = MB/Z (for straight pipe/bends with SIF = 1.0); MR/Z (for other components) SC = Max (|SHoop – SL|, sqrt[SL2 – SLSHoop + SHoop2]) MR = sqrt[(0.75iiMi)2 + (0.75ioMo)2 + Mt2] SE = ME/Z ME = sqrt[(0.75iiMi)2 + (0.75ioMo)2 + Mt2] S = Specified Minimum Yield Stress T = Temperature Derating Factor SH = 0.33SUT SC = 0.33SU SU = Specified Minimum Ultimate Tensile Stress B31.8 distinguishes between restrained and unrestrained piping for the purposes of stress computations. To implement B31.8 you must define which sections of the piping system are 962 CAESAR II User's Guide Technical Discussions restrained, as per Code Section 833.1. In general, restrained piping is piping in which the soil or supports prevent axial displacement of flexure at bends. Conversely, unrestrained piping is piping that is free to displace axially or flex at bends. For more information, see Section 833.1. Processing a B31.8 model through the Buried Pipe Modeler designates the buried sections as restrained. For restrained pipe, B31.8 specifies that the operating case stresses should include the thermal axial stress component, a constant stress due to linear thermal expansion, but exclude thermal bending stresses from the SB component. Because CAESAR II cannot go back and segregate internal thermal forces and moments from those of other loads, the thermal axial stresses are calculated and included as part of SX (as opposed to added as a constant), and thermal bending stresses are conservatively included in SB. Bending stress SB is defined differently for straight pipe or "large-radius" bends than it is for other components. CAESAR II resolves the ambiguity of exactly what constitutes a "largeradius" bend by considering any bend having an SIF of 1.0 as being a "large-radius" bend. Occasional load default values The occasional load default value for B31.8 is 1.111 (1/0.9) and is only applied to the allowable for SC combined stress calculated only in straight pipes. The allowable in this case is ST as opposed to 0.9ST. There is no provision for increasing or decreasing this allowable. In the case of occasional stresses in straight pipes, there are potentially two stresses (SL and SC) to be compared against two different allowable limits. CAESAR II only prints the one that provides the greater ratio of calculated stress versus allowable stress. You can visually determine which stress prints by examining the magnitude of the allowable. Calculate pressure stiffening using B31.8 Pressure stiffening is included by default in the code. You can exclude pressure stiffening on bends in the analysis by setting the Use Pressure Stiffening switch in the setup file. Modifications to the flexibility factor and Stress Intensification Factor (SIF) using B31.8 Modifications to the flexibility factor and SIF of bends resulting from flanged ends are permitted by the code. Calculate socket welds using B31.8 B31.8 makes no distinction between socket welds with undercut and socket welds without undercut. Unless you are specifying a fillet weld leg length, use a default SIF value of 2.1 for all B31.8 socket welds. Using reducers with B31.8 Use of reducers is subject to the following limitations: Alpha the reducer cone angle is limited to 60° The larger of D1/SQRT(t1) and D2/SQRT(t2) cannot exceed 100 where D1/t1 and D2/t2 are the diameters and thicknesses of the large and small ends, respectively. CAESAR II User's Guide 963 Technical Discussions B31.8 Chapter VIII Chapter VIII discusses the offshore requirements of B31.8. For more information, see B31.8 (on page 962) Calculate the Stress Intensification Factors (SIFs), flexibility factors, and section moduli using B31.8 Chapter VIII Calculate all SIFs, flexibility factors, and section moduli exactly as in the standard B31.8 Code. Make all stress calculations using the non-corroded wall thickness for the hoop and longitudinal stresses. Use the corroded thickness for the combined stress. Calculate the expansion load case using B31.8 Chapter VIII There is no provision for a code check for the expansion load case, so no expansion cases are generated under this code. Calculate the operating, sustained, or occasional load cases using B31.8 Chapter VIII Operating, sustained, or occasional load cases are treated identically. For these load cases, you must perform three stress calculations, each with specific allowable limits. The stress calculation causing the highest percent of allowable displays in the stress report along with its specific allowable. The stress checks are: Hoop Stress: Sh F1ST Longitudinal Stress: |SL| 0.8S Equivalent Stress: Se 0.9S Where: Sh = (Pi – Pe) D / 2t Pi = Internal Pressure Pe = External Pressure D = Outer Diameter t = Wall Thickness F1 = Hoop Stress Design Factor 0.50 or 0.72 see Table A842.22 of B31.8 S = Specified Minimum Yield Strength T = Temperature Derating Factor see Table 841.116A of B31.8 The product of S and T, the yield stress at operating temperature, is required in the SH field of the CAESAR II Input: SL = Maximum Longitudinal Stress Positive Tensile and Negative Compressive Se = 2[((SL - Sh)/2)2 + Ss2]1/2 Ss = Torsional Stress 964 CAESAR II User's Guide Technical Discussions B31.9 Notes Paragraph 919.4.1.b states that for analysis methods follow B31.1. For more information, refer to B31.1. B31.11 Calculate pressure stiffening using B31.11 Pressure stiffening is included by default in the code. You can exclude pressure stiffening on bends in the analysis by setting the Use Pressure Stiffening switch in the setup file. Flanged end modifications using B31.11 Modifications resulting from flanged ends are permitted in the code provided the bend is not a widely spaced miter. B31.11 girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate stress intensification factors (SIFs) for intersections using B31.11 In-plane and out-plane SIFs for intersections are separate and unique. Calculate the B31.11 allowable stresses Use the equations below to calculate the stress allowables. Expansion Allowable = (0.72)(Sy) Sustained Allowable = (0.75)(0.72)(Sy) Occasional Allowable = (0.88)(Sy) Operating Allowable = (0.9)(Sy) if the axial stress is compressive; no code check done if the axial stress is tensile Where: Sy = Specified Minimum Yield Stress B31.11 does not use EFF, found on the Allowable Stress Auxiliary field. The minimum yield stress is all that is required to compute flexibility stress allowables. Calculate effective section modulus using B31.11 B31.11 has no provision for using an effective section modulus calculation at intersections. Calculate liberal allowable using B31.11 B31.11 does not include a provision for the liberal allowable. This option is not used for B31.11 stress allowable calculations. The occasional load factor, used in the other piping codes for determining the allowable stress for occasional load sets, is also not used in B31.11, as the allowable stress is 0.88 times the minimum yield stress. CAESAR II User's Guide 965 Technical Discussions CAESAR II assumes that 1119.6.4(b) establishes a requirement for the allowable operating stress at 90% of Sy when the net axial stress is compressive (when longitudinal pressure stresses can be ignored in underground pipes). The last sentence in the paragraph establishes that: "Beam bending stresses shall be included in the longitudinal stress for those portions of the restrained line which are supported above ground." You have two options for including this axial stress in your analyses: 1. Include axial friction restraints and include the Add F/A option in the setup file. Set Fac to 0.001 to indicate that the line is buried, so longitudinal pressure stresses are not present, and so the hoop stress component is considered. 2. Use Fac to tell CAESAR II to compute the axially-restrained stress and include it during stress calculations. If you enter a nonzero Fac, the pressure plus axial loads in the pipe are multiplied by (1-Fac). This gives a more realistic estimation of the axial stress in the pipe when you have included both of the effects above. Paragraph 1119.6.4(b) requires 1) the reduction of the axial expansion stress by the product of Poisson’s ratio and the pressure hoop stress, and 2) the addition of the hoop stress to the axial stress. The latter represents the calculation of stress intensity when the axial stress is compressive, implying that there is no longitudinal pressure stress in buried pipe (the pressure loads are transmitted directly to the soil). CAESAR II handles this case in the operating load case, where the hoop stress is added in and the allowable stress is set to 0.9 Sy whenever the axial stress is compressive. If Fac is 0.001, the piping element is considered buried, so the longitudinal pressure stress is replaced by the product of Poisson’s ratio and the hoop stress, in keeping with the spirit of paragraph 1119.6.4(b). Fac is automatically set to 0.001 when B31.11 pipe is sent through the buried pipe modeler (on page 483). The stress due to axial force is also included for these elements. Do not set Fac to 1.0 when using B31.11with thermal expansion cases where you are going from one thermal state to another state. In other words where the case is of the form: L1-L2, and both L1 and L2 contain temperatures. In this case the thermal expansion used in the restrained pipe calculation comes from the last thermal specified in the load case definition. In the example above the thermal expansion associated with the L2 load case. When calculating the hoop stress for the restrained pipe longitudinal stress calculation use the Base Hoop Stress On option in the setup file. The default is to base the hoop stress calculation on D = average diameter in the equation PD/2t. In mechanical stress calculations the hoop stress is based on the inside diameter. This is the hoop stress that displays in the extended CAESAR II Stress report. B31.11 reducer default values The default SIF value is 1.0. The default flexibility factor value is 1.0. 966 CAESAR II User's Guide Technical Discussions ASME III Subsections NC and ND Calculate pressure stiffening using NC and ND Pressure stiffening is not defined by default in this code. You can include pressure stiffening on bends in the analysis by including the Use Pressure Stiffening=Yes option in the setup file. Flanged end modifications using NC and ND Modifications resulting from flanged ends are permitted in this code providing the bend is not a widely spaced miter. Minimum SIF for reinforced and unreinforced fabricated tees using NC and ND The minimum SIF for reinforced and unreinforced fabricated tees is 2.1. Calculate B1 and B2 using NC and ND Calculate B1 and B2 according to the equations in ASME NC and ND. Calculate liberal allowable using NC and ND If you are using this piping code and define a dynamic load case as a “Expansion”, a request for Liberal Allowable is ignored and the (Sh-Sl) term is removed from the allowed limit (see below). This is a programming decision rather than an interpretation of the piping code or a recommendation for doing dynamic analysis. Calculate stress intensification factors (SIFs) for intersections using NC and ND Inplane and outplane SIFs for intersections are the same. Using WRC 329 with NC or ND For all intersections that are not welding tees or reinforced fabricated tees use the equation *r2*t to calculate the approximate section modulus for the stress calculations. This includes all reduced intersections and all d/D ratios. Determine the branch SIF using NC or ND If you do not want to use the branch SIF of the Code for welding and reinforced reducing tees, include the No Reduced SIF for RFT and WLT flag in the setup file. Calculate the NC and ND stress allowables Use the equations below to calculate the stress allowables. Expansion Allowable = f(1.25Sc + 0.25Sh) + (Sh-Sl) Sustained Allowable = 1.5Sh If not at an intersection Occasional Allowable = 1.8Sh not greater than 1.5Sy, if OCC=1.2; 2.25Sh not greater than 1.8Sy, if OCC=1.5; 3.0Sh not greater than 2.0Sy, if OCC=2.0 CAESAR II User's Guide 967 Technical Discussions Where: f = Cyclic Reduction Factor Sc = Cold Allowable Sh = Hot Allowable Sl = Sustained Stress from PD/4t+0.75iMb Sy = Material Yield Stress OCC = Occasional Factor from the CAESAR II configuration file Calculate two pipe intersections using NC and ND For two pipe intersections, for example butt welds or socket welds, B1 and B2 factors are 1.0. If the ratio of the average branch to average run radius is less than 0.5, then apply the reduced intersection rules to the B1 and B2 calculations regardless of the intersection type. If the reduced intersection rules do not apply then use the following rules for butt welded fittings: B2b = 0.4 * (R/T)**2/3 but not < 1.0 B2r = 0.5 * (R/T)**2/3 but not < 1.0 You can modify the values for B1 and B2 for any node in the SIF&TEE auxiliary field. Any changes you make to B1 and B2 on an auxiliary field only apply for that element, regardless of whether the node is an intersection or not. Calculate the ratio of r/R using NC and ND When r/R < 0.5 use the following equations for B1 and B2: B2b = 0.50 C2b but not < 1.0 B2r = 0.75 C2r but not < 1.0 C2b = 3(R/T)2/3 (r/R)1/2 (t/T)(r/rp), but not < 1.5 C2r = 1.15(r/t)1/4 but not < 1.5 Branch SIFs using NC and ND WRC 329 produces smaller branch SIFs than ASME NC and ND, and the same run SIFs. The branch SIFs are smaller by a factor of 2. This is when d/D<0.5 and WRC 329 corrects the Mob (out of plane bending) inconsistency when d/D is between 0.5 and 1. In the lower ranges of d/D ratios WRC 329 is less conservative than the present codes and in the higher ranges WRC 329 is more conservative than the present codes. Calculate Pvar using NC and ND Pvar represents the difference between the operating pressure and Pmax, which is used in eq 11. CAESAR II forms occasional stresses by adding the sustained stress including pressure, and the occasional stress including the stress difference between the operating pressure and the peak pressure. 968 CAESAR II User's Guide Technical Discussions Limit for expansion stress range To satisfy equations 10 or 11, the expansion stress, iMc/Z, must remain below the maximum of either f(1.25Sc + 0.25Sh) or f(1.25Sc + 0.25Sh) + (Sh-Sl) where Sl is the sustained stress as defined by equation 11: Sl= PDo/4tn+0.75iMa/Z. Calculate moment summations using NC and ND The approach taken by CAESAR II for moment summations at inter\-sections to satisfy equations 8 and 9 is to use the SRSS of the moments at each end of the pipe framing into the intersection. You do not have to adhere to the cumulative moment summation rules for a single intersection as per NB 3683.1. In addition, use the effective section modulus rules of NC and ND for all intersection stress calculations like equations 8 and 9. Use subsection NB to get the values for B1 and B2 only, and to compute the local flexibility if requested. Because of the use of this approach in CAESAR II, there is no allowable calculated for intersection points and sustained or occasional loads. Determine sustained case SIF using NC and ND Do not use the SIF in the ASME class 2 or 3 sustained stress calculations. NC and ND reducer default values The default flexibility factor value is 1.0. Use the following equation to determine the SIF value: 2.0 max or 0.5 + .01*alpha* SQRT(D2/t2). Where: D1- Diameter of the Large End t1- Thickness of the Large End D2 - Diameter of the Small End t2 - Thickness of the Small End Alpha - the reducer cone angle in degrees Where: Alpha = atan[ 0.5 * (D1-D2) / (length of the sloped portion of reducer) ] Alpha is the slope of the reducer transition in degrees. If left blank, the value is set from an estimated slope equal to the arc tangent times 1/2 the change in diameters times sixty percent of the entered reducer length. Alpha cannot exceed 60º. The larger of D1/t1 and D2/t2 cannot exceed 100. B1=.5 if alpha 30º, 1.0 if 30º < alpha 60º; B2 = 1.0. There is an error in the code, the code states note 12 however, they meant note 14. Alpha cannot exceed 60º. CAESAR II User's Guide 969 Technical Discussions CANADIAN Z662 Calculate pressure stiffening using Z662 Pressure stiffening is not defined by default in the code. You can include pressure stiffening on bends in the analysis by including the Use Pressure Stiffening=Yes option in the setup file. Flanged end modifications using Z662 Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. Pad thickness using Z662 There is no limit in Z662 for the beneficial effect of the pad on an intersection. Most codes limit the pad thickness to 1.5 times the header thickness. For Z662, CAESAR II does not limit the pad thickness. Z662 girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. In-plane and out-plane stress intensification factors for intersections are the same. Calculate socket welds using Z662 Z662 makes no distinction between socket welds with undercut and socket welds without undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3. Calculate effective section modulus using Z662 Z662 has no provision for using an effective section modulus calculation at intersections. Calculate the CANADIAN Z662 allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = (0.72)(T)(Sy) Sustained Allowable = (Fac)(T)(L)(Sy) Occasional Allowable = (Occ)(Fac)(T)(L)(Sy) Operating Allowable = 0.9(T)(Sy), if pipe is buried and axial stress is compressive Operating Allowable = (T)(Sy), if pipe is not buried and axial stress is compressive Where: Sy = Specified Minimum Yield Stress Fac = Construction Design Factor T = Temperature De-rating Factor Occ = Occasional Load Factor (Default is 1.0) L = Location Factor 970 CAESAR II User's Guide Technical Discussions CAESAR II assumes that Section 4.6.2 of the Z662 code establishes a requirement for the allowable operating stress of 0.9 x S x T whenever the net axial stress is compressive in the absence of bending stress, and an allowable operating stress of S x T when the net axial stress is compressive in the presence of bending stress. Section 4.6.2 requires the following: 1. The reduction of the axial expansion stress by the product of Poisson’s Ratio and the pressure hoop stress. 2. The addition of the hoop stress to the axial stress. The latter represents the calculation of stress intensity when the axial stress is compressive, implying that there is no longitudinal pressure stress in buried pipe (the longitudinal pressure thrust loads are transmitted directly to the soil). CAESAR II handles these requirements, in the operating load case, in the following manner: 1. If FAC is 1.0, the piping system is fully restrained in the axial direction as described in Section 4.6.2.1, and the operating stress is calculated as: Sh + E a (T2 - T1) - v Sh < 0.9 S x T 2. If FAC is 0.001, the piping system is buried, but the soil supports are modeled (rather than just assumed to be fully rigid). This setting removes the longitudinal pressure stress from the equation (as described above), and takes bending stresses into consideration, as required by Section 4.6.2.2.1. In this case, the operating stress is calculated as: Sh +Fax/A + Sb - v Sh < S x T 3. If FAC is 0.0, the piping system is either not restrained, or is a freely spanning or above ground portion of a restrained line, as described in Section 4.6.2.2.1. In this case, the longitudinal pressure stress is restored, so this formula only comes into effect if the net axial stress including pressure is compressive, in which case the operating stress is calculated as: Sh +Slp + Fax/A + Sb < S x T 4. CAESAR II does not do an operating code stress check for those elements for which the net axial stress is longitudinal. 5. CAESAR II does not check for buckling, as required by Section 4.6.2.2.2. Z662 reducer default values The default SIF value is 1.0. The default flexibility factor value is 1.0. NAVY 505 Calculate pressure stiffening using Navy 505 Pressure stiffening is not defined by default in the Code. You can include pressure stiffening on bends in the analysis by including the parameter Use Pressure Stiffening in the setup file. Flanged end modifications using Navy 505 Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. CAESAR II User's Guide 971 Technical Discussions Navy 505 girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate effective section modulus using Navy 505 Navy 505 has no provision for using an effective section modulus calculation at intersections. Calculate stress intensification factors (SIF)s for intersections using Navy 505 In-plane and out-plane SIFs for intersections are the same. Calculate liberal allowable using Navy 505 Navy 505 has no provision for a liberal allowable, that is, adding the difference between Sh and Sl to the allowed expansion stress range. This feature from the control parameter spreadsheet has no effect on 505 runs. Calculate cold and the hot allowable using Navy 505 Navy 505 uses longitudinal weld joint efficiency (Eff) to compute the cold and the hot allowable stress. The use of this parameter is subject to some speculation however. Calculate the Navy 505 allowable for occasional loads Navy 505 has no specific allowable for occasional loads. An occasional load factor (k), similar to the B31.1 code is used, and the occasional allowable calculated from kSh. Calculate the Navy 505 allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = [f(1.25Sc + 0.25Sh)]/Eff Sustained Allowable = Sh/Eff Occasional Allowable = k*Sh/Eff Where: f = Cyclic Reduction Factor Eff = Joint Efficiency (Not explicitly in the Code) Sc = Cold Allowable Stress Sh = Hot Allowable Stress k = Occasional Load Factor, Defaults to 1.15 Use the B31.3 SUS Case SIF Factor option to multiply the SIFs for sustained and occasional loads to be more in line with the current B31.1 practice. 972 CAESAR II User's Guide Technical Discussions BS806 For BS806, the maximum hot stress case is considered to be the operating load case. Operating load case allowables are only given as per BS806 when the creep rupture strength governs the stress range allowable. See BS806 sect 4.11.2. Stress Intensification Factors (SIFs) using BS806 BS806 SIFs printed are labeled fti and fto for bends, and Bi and Bo for intersections. Calculate pressure stiffening using BS806 Pressure stiffening is not defined by default in the code. You can include pressure stiffening on bends in the analysis by including the Use Pressure Stiffening option in the setup file. Pad thickness using BS806 There is no limit in BS806 for the beneficial effect of the pad on an intersection. Most codes limit the pad thickness to 1.5 times the header thickness. For BS806, CAESAR II does not limit the pad thickness. Flanged end modifications using BS806 The code permits modifications due to flanged ends for all bend types. This includes closely and widely spaced mitered bends. BS806 girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate the BS806 allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = lesser of (H)(Sc)+(H)(Sh) <or> (H)(Sc)+F Sustained Allowable = Sy Occasional Allowable = (Sy)(Occ) Operating Allowable = S avg rupture at design temperature Where: H = Multiplication Factor 0.9 or 1.0 from CAESAR II Sc = 0.2% Proof Stress at Room Temperature Sh = 0.2% Proof Stress at Design Temperature F = Mean Stress to Failure in Design Life at Design Temperature Occ = Occasional Load Factor Default is 1.0 Calculate pressure at intersections using BS806 The pressure calculation at the intersections is made as required in BS806 4.8.5.1 Eq. (17). The pressure stress as per Eq. (17) is computed and then combined with the bending and torsional CAESAR II User's Guide 973 Technical Discussions moment at each of the intersection ends 1, 2 and 3 respectively. The m factor is computed as required with a value of n=1, in other words, for non-interacting intersections. BS806 does not address reducers for SIF calculations. Other BS806 Notes When there is more than one thermal case to evaluate, read the following note carefully concerning CAESAR II and the application of BS806. Regarding BS806 4.11.3.1 paragraph 2, for sectionalized systems: CAESAR II only makes the moment summation on a load case by load case basis, and does not take the largest moments for an axis for any combination of load cases. The CAESAR II method is designed to enable you to set up and combine the effects of each of the load transients that the piping system undergoes. This method, for the most part is used in the B31/ASME piping codes. The BS806 method is conservative in that it uses what is basically a shakedown approach and computes a single worst case moment difference. The CAESAR II method satisfies the shakedown theory but, also computes the moment range for each different load traversed. The BS806 method of combining the maximum moment range is more conservative. The BS806 method also eliminates the need to know where on the pipe the stress is the highest. Use the moment tables in Appendix F, to get the moment difference between any two load cases. However, you cannot use the moment tables to get the maximum moment difference for any of the three moment axes as requested by the sectionalized piping rules. To satisfying 4.11.3.1(a) CAESAR II uses the moment difference between the cold and the hot case to compute the stress. You can only enter a single modulus of elasticity for a single element in each job. Different elements can have different moduli of elasticity, but you cannot vary that modulus between load cases in the same run. Also, you cannot use cold and a hot moduli of elasticity in the same run at this time. For BS806 in 4.11.5.2 the value of n is 1.0.for all branches of the non-interacting type. See the fourth paragraph 4.11.4.2 for the definition of n for interacting branches. 974 CAESAR II User's Guide Technical Discussions The CAESAR II equation modeling of the BS806 SIF curves for bends displays in the following plots. Swedish Method 1 and 2 Calculate pressure stiffening using Swedish Method 1 and 2 Pressure stiffening is not defined by default in the code. You can include pressure stiffening on bends in the analysis by including the parameter Use Pressure Stiffening in the setup file. Flanged end modifications using Swedish Method 1 and 2 Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. WRC329 recommendations Swedish Method 1 cannot take advantage of the WRC 329 recommendations. WRC 329, if requested, is ignored. Calculate effective section modulus using Swedish Method 1 Swedish Method 1 has no provision for using an effective section modulus calculation at intersections. CAESAR II User's Guide 975 Technical Discussions Calculate stress intensification factors (SIFs) for intersections using Swedish codes Inplane and outplane SIFs for intersections are the same. Swedish Code item 9 is dealt with as a US tapered transition. Also, items 10 and 11 in the Swedish table 9:2 correspond to items 8 and 9 in the CAESAR II nomenclature. Calculate the allowable stress limits using Method 1 Use the equations below to calculate the stress allowables. Sber = lesser of Sh or F Allowable = (Fac)(Sber) / 1.5 Where: Sh = Yield Stress at Temperature F = Creep Rupture Stress at Temperature Fac = Usually 1.5 for Pre-stressed Pipe Use 1.35. Calculate the allowable stress limits using Method 2 Expansion Allowable = f ( 1.17S1 + 0.17S2 ) Sustained Allowable = Sh Occasional Allowable = Occ * Sh Where: f = Cyclic Reduction Factor S1 = Lesser of Sc or 0.267Sy S2 = Lesser of Sh or 0.367Sy Sc = Allowable Stress at Room Temperature (Stn2) Sh = Allowable Stress at Design Temperature (Stn1) Sy = Ultimate Tensile Strength at Room Temperature Occ = Occasional Load Factor Default is 1.2 Default girth butt welds for Swedish Method codes If the weld is ground flush inside and out then the default SIF value for a girth butt weld is 1.0. Pressure Variation in Swedish Codes Swedish methods 1 and 2 Beta in the code is entered in the Pvar field on the Allowable Stress Auxiliary dialog box. Enter the value for Pvar in percent, for example 10.0 for ten percent. If left blank, the default is 10.0 percent. Limits on the reasonable Betas that you may enter for the Swedish piping code is 10% to 25%. Anything less than 0.1 is taken to be 10% and anything entered greater than 0.25 is taken to be 25%. 976 CAESAR II User's Guide Technical Discussions Pressure Stress in Swedish Codes Include the Use PD/4t option in the setup file to tell CAESAR II to use the thin walled equations for stress calculations for Swedish Method 1 code compliance. Default occasional load factor for Swedish Method 2 The default value for the occasional load factor for Swedish Method 2 is 1.2. Pad thickness using the Swedish Method 1 and 2 The pad thickness on an intersection reduces stresses up to pad thickness of 2.5 times the header wall thickness. Calculate reducers using the Swedish Method 1 and 2 The default value for the flexibility factor is 1.0 and the equation to calculate reducer SIFs is: 2.0 max or 0.5 + .01*alpha* SQRT(D2/t2) Where D1 and t1 are the diameter and thickness of the large end and D2 and t2 are the diameter and thickness of the small end. Alpha is the reducer cone angle in degrees. Where: Alpha = atan[ 0.5 * (D1-D2) / (0.60 * length of sloped portion of the reducer) ] Alpha is the slope of the reducer transition in degrees. If left blank, the value is set from an estimated slope equal to the arc tangent times 1/2 the change in diameters times sixty percent of the entered reducer length. Other Swedish Notes If you are using Swedish Method 1 to calculate the CAESAR II allowable, assume that the SIGMA(tn) multiplier is 1.5 for piping that is not pre-stressed. If you use pre-stressed or cold sprung pipe change Fac on the Allowable Stress Auxiliary field to 1.35 as per the Swedish code. Use the corroded section modulus for all stress calculations as per the definition of Di in the Swedish code. B31.1 (1967) Calculate full-sized intersections for both the header and the branch using B31.1 (1967) B31.1 (1967) uses ii = io for full-sized intersections for both the header and the branch, and for reduced intersections uses ii = 0.75io + 0.25 for both the header and the branch. Calculate pressure stiffening using B31.1 (1967) Pressure stiffening is not defined by default in this code. You can include pressure stiffening on bends in the analysis by including the Use Pressure Stiffening option in the setup file. CAESAR II User's Guide 977 Technical Discussions Flanged end modifications using B31.1 (1967) Modifications resulting from flanged ends are permitted in the code providing the bend is not a widely spaced miter. B31.1 (1967) girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate socket welds using B31.1 (1967) B31.1 (1967) makes no distinction between socket welds with undercut and socket welds without undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3. Calculate the B31.1 (1967) allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = f [ (1.25/Eff)(Sc+Sh) - Sl ] Sustained Allowable = Sh/Eff Occasional Allowable = Sh/Eff * Occ Where: f = Cyclic Reduction Factor Eff = Longitudinal Weld Joint Efficiency Sc = Cold Allowable Stress Sh = Hot Allowable Stress Sl = Sustained Stress Occ = Occasional Load Factor (Default is 1.15) Stoomwezen 978 Sc = The yield stress at room temperature is referred to as Re in the code. Sh1 = The yield stress at design temperature is referred to as Re (um) in the code. Sh2 = not used Sh3 = not used FN = The average creep stress to produce one percent set is referred to as Rrg in the code. F2 is the average creep tensile stress to produce rupture and is referred to as Rmg in the code. F3 is the minimum creep tensile stress to produce rupture and is referred to as Rmmin in the code. Eff = The cyclic reduction factor is referred to as Cf in the code. CAESAR II User's Guide Technical Discussions Sy = The tensile strength at room temperature is referred to as Rm in the code. Fac = A constant whose value is either 0.44 or 0.5. For more information, refer to Stoomwezen Section 5.2. Pvar = The Cm coefficient in the code whose value is usually 1.0. Calculating reducers using Stoomwezen Stoomwezen does not mention reducers for Stress Intensification Factor (SIF) calculations. RCC-M Subsection C and D Calculate pressure stiffening using RCC-M Subsection C and D Pressure stiffening is not defined by default in the code. You can enable pressure stiffening on bends in the analysis by including the Use Pressure Stiffening option in the configuration file. Flanged end modifications using RCC-M Modifications resulting from flanged ends are permitted providing the bend is not a widely spaced miter. Calculate stress intensification factors (SIFs) for intersections using RCC-M Inplane and outplane SIFs for intersections are the same for these piping codes. Calculate SIF for branch connection using RCC-M If you do not want to use the SIF for branch connections, found in Figure C3680.1 of the code for welding and reinforced reduced tees, include the No Reduced SIF For RFT and WLT option in the configuration file. Calculate the RCC-M allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = F (1.25Sc + 0.25Sh)+(Sh SSL) Sustained Allowable = Sh Occasional Allowable = OCC * Sh OCC defaults to 1.2 for Level B OCC defaults to 1.8 for Level C OCC defaults to 2.4 for Level D CAESAR II User's Guide 979 Technical Discussions Where: F = Cyclic Reduction Factor Sc = Cold Allowable Sh = Hot Allowable SSL = Sustained Stress (PD/4t + 0.75i Mb/Z) OCC = Occasional Factor from the CAESAR II configuration file Calculate Pvar using RCC-M Pvar represents the difference between the operating pressure and Pmax, which is used in eq 10. To satisfy equations 7 or 8 use iMc/Z stress as the maximum of either F(1.25Sc + 0.25Sh) or F(1.25Sc + 0.25Sh) + (Sh - Ssl) where Ssl is the sustained stress as defined by equation 6. Calculate reducers using RCC-M For reducers RCC-M states that the flexibility factor is 1.0. The code also states that the SIF is: The minimum of 2.0 or 0.5 + .01*alpha* SQRT(D2/t2) Where: D2 - Diameter of the Small End t2 - Thickness of the Small End Alpha is the reducer cone angle in degrees. If not specified: Alpha = atan[ 0.5 * (D1-D2) / (0.60 * length of the reducer element) ] Alpha cannot exceed 60° and the larger of D1/t1 and D2/t2 cannot exceed 100. CODETI Modifications resulting from flanged ends using CODETI Modifications resulting from flanged ends are permitted in the code for all bends, including widely spaced miters. Calculate stress intensification factors (SIFs) for intersections using CODETI CODETI provides two separate equations to calculate the in-plane and out-plane SIFs for intersections. Calculate expansion stress using CODETI CODETI provides an equation to calculate the expansion stress. This equation does not include calculations for the longitudinal stress due to axial loads in the pipe. CAESAR II does not include the F/A longitudinal stress component for stress in the expansion stress equation. You can change this by setting Add F/A In Stress to the configuration file. The program adds the F/A longitudinal stress component, by default, to the code stress component for all other stress categories. 980 CAESAR II User's Guide Technical Discussions Calculate the CODETI allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = F [1.25 (Sc + Sh)] - Sl Sustained Allowable = Sh Occasional Allowable = OCC * Sh Where: F = Cyclic Reduction Factor Sc = Cold Allowable Stress Sh = Hot Allowable Stress Sl = Sustained Stress OCC = Occasional Load Factor from Configuration - Defaults to 1.15 Pressure stiffening using CODETI Pressure stiffening of bends is automatically included as directed by the code. You can disable pressure stiffening on bends in the analysis by excluding the Use Pressure Stiffening option in the configuration file. SIFs and flexibility coefficients using CODETI Flexibility coefficients and SIFs are phased in for bends with an included angle between 15° and 45°. The default value for bends smaller than 15° is 1.0. SIFs and fabricated tees using CODETI To determine the SIF of a fabricated tee having an angle of incidence other than 90°divide it by (sin a)3/2 CODETI recommended occasional load factor values Recommended occasional load factor values are 1.15, 1.2, and 1.3, as per Code Table C3.3. CODETI requires that when "the design temperature is such that the creep characteristics are determinant, and if a section of the piping presents locally weaker characteristics," the sum of the primary and secondary stresses must not exceed the value flexibility factor (from Section C1.4.3). CAESAR II does not implement this requirement and is left for you to verify. CODETI reducer default values The default SIF value is 1.0. The default flexibility factor value is 1.0. Norwegian (TBK 5-6) Calculate pressure stiffening using TBK 5-6 Pressure stiffening of bends is required for flexibility factors only and is done by default. You can disable pressure stiffening by excluding the Use Pressure Stiffening option in the setup file. CAESAR II User's Guide 981 Technical Discussions You can enable pressure stiffening for stress intensification factors (SIF)s as well by including the Use Pressure Stiffening option. Expansion stress in TBK 5-6 Summing the longitudinal component F/A into the stress calculation is not defined by default in the code. You can enable the axial force term in the code stress by including the Add F/A In Stress option in the configuration file. The code uses a circumferential weld strength factor (Z) when calculating longitudinal pressure stress. Enter this value as Eff. Calculate cyclic reduction factor using TBK 5-6 You can calculate the cyclic reduction factor using the following equation: F = (7000/Ne)0.2 Where Ne = Number of Anticipated Cycles F may be as high as 2.34 but not greater than 1.0 when Rm governs the expansion stress allowable. Calculate SIFs for bends and intersections using TBK 5-6 In-plane and out-of-plane SIFs for bends and intersections use the same stress equation. Calculate the Norwegian allowable stress limits Use the equations below to calculate the stress allowables. Expansion Allowable = Sr + F2 - SSUS Sustained Allowable = F2 Occasional Allowable = Occ * F2 Where: Sr = Minimum of 1.25F1 + 0.25F2; Fr * Rs - F2; or Fr (1.25 R1 + 0.25 R2) The latter for higher temperatures; above 425°C for austenitic stainless steel, or above 370°C for other materials. F2 = Hot Allowable Stress (entered in Sh) OCC Occasional Load Factor from the configuration file (defaults to 1.2) SSUS = Sustained Stress 982 F1 = Allowable Stress at Ambient (entered in Sc) Fr = Cyclic Reduction Factor RS = Permissible Extent of Stress for 7000 Cycles (from Code Table 10.2) R1 = Lesser of F1 and 0.267 RM CAESAR II User's Guide Technical Discussions R2 = Lesser of F2 and 0.367 RM Rm = Ultimate Tensile Strength at room temperature Calculate SIFs using TBK 5-6 As of this writing, SIFs or fitting types 6 (branch with raised edge radius), 7 (branch on locally thickened pipe), 13 (conical reducer with knuckles), and 14 (reducer without knuckles) have not been implemented in CAESAR II so you must enter them manually. The Norwegian code offers an alternative stress analysis method in Appendix D. However, CAESAR II does not implement this method. TBK 5-6 reducer default values Calculate the SIFs by using the following equation: 2.0 max or 0.5 + .01*alpha* SQRT(D2/t2). Where: D2 - Diameter of the Small End t2 - Thickness of the Small End alpha - the slope of the reducer TBK 5-6 flexibility factor default value The default flexibility factor value is 1.0. FDBR FDBR is similar to B31.1 in most requirements. For more information, see B31.1. Calculate reinforced tees using FDBR FDBR limits the pad thickness to a maximum equal to the header thickness. If you enter a pad thickness that is greater than the header thickness the program overrides it with the header thickness. Calculate reduced intersections using FDBR Treat intersections similar to ASME NC. For more information, see ASME NC. Calculate butt welds using FDBR Use either 1.0 or 1.8 depending on the thickness. Calculate flexibility analysis using FDBR You must use the Hot Modulus of Elasticity in your flexibility analysis. Calculate the expansion case allowable stress using FDBR Additionally, when computing the expansion case allowable stress you must include the ratio of Ehot to Ecold. You can override the program computed ratio by manually entering a value for Fac. CAESAR II User's Guide 983 Technical Discussions Calculate reducers using FDBR The value for the flexibility factor is 1.0 and the equation to calculate reducer SIFs is: 2.0 max or 0.5 + .01*alpha* SQRT(D2/t2) Where: D1 - Diameter of the Large End t1 - Thickness of the Large End D2 - Diameter of the Small End t2 - Thickness of the Small End Alpha - Reducer Cone Angle in Degrees When not entered: Alpha = atan[ 0.5 * (D1-D2) / (0.60 * length of the reducer element) ] Alpha cannot exceed 60° and the larger of D1/t1 and D2/t2 cannot exceed 100. BS 7159 BS 7159 for Fiberglass Reinforced Plastic (FRP) pipe requires that you evaluate the operating load case only. You must verify the following operating load case combined stress requirements are met: If Sx is tensile: (OPE) and (OPE) or if Sx is compressive: If Fx/A > P(Dm)/(4t) and it is compressive (OPE) and 984 CAESAR II User's Guide Technical Discussions (OPE) Circumferential Stress for straight pipes for bends for tees Dm and t are always for the Run Pipe Calculate the allowable stress limits using BS 7159 BS 7159 allowables are based on material design strain d. Therefore allowable stresses differ in the axial and hoop directions by the ratio of the axial and hoop moduli of elasticity: Sh = dEx SHOOP = (dEx) (Eh/Ex) Enter the ratio Eh/Ex in the allowable stress Eff field. If left blank, the value defaults to 1.0 for isotropic materials. Calculate pressure stiffening using BS 7159 Pressure stiffening of bends is done assuming the bends are fully pressurized up to the design strain of the components. You can exclude pressure stiffening on bends by including the Use Pressure Stiffening option in the configuration file. BS 7159 does not by default add F/A into the stress calculation (unless this puts an element into compression as described above). Use the Add F/A in Stress option to tell CAESAR II to include the axial force term into the code stress. Calculate the fatigue factor using BS 7159 The fatigue factor Kn is used inversely relative to the cyclic reduction factor in most codes, so its value should be greater than or equal to 1.0 (allowable stress is divided by this number). K n is calculated as: Kn = 1.0 + 0.25 (As/n) (Log10(n) - 3.0) Where: As = Stress Range During Fatigue Cycle n = Maximum Stress During Fatigue Cycle n = Number of Cycles During Design Life Enter Kn in the Cyclic Reduction Factor fields. CAESAR II User's Guide 985 Technical Discussions BS 7159 requires that you consider the thermal strain of the pipe material as being from 80% 85% below the true material strain due to insulation effects of the pipe wall. Enter this reduction factor K in the allowable stress FAC field. If left blank, this value defaults to 1.0. Calculate the stress intensity and flexibility factors of bends using BS 7159 The stress intensity and flexibility factors of bends vary based on laminate type: All chopped strand mat (CSM) construction with internal and external surface tissue reinforced layer. CSM and woven roving (WR) construction with internal and external surface tissue reinforced layer. CSM and multi-filament roving construction with internal and external surface tissue reinforced layer. You can enter the laminate type in the Bend Type field, or set the type default on the Special Execution Parameter dialog box. Calculate SIFs for Reducers using BS 7159 BS 7159 does not mention reducers for SIF calculations. UKOOA The United Kingdom Offshore Operators Association (UKOOA) Specification and Recommended Practice for the Use of GRP Piping Offshore is similar in many respects to the BS 7159, except that it simplifies the calculation requirements in exchange for imposing more conservatism on the piping operating conditions. Rather than explicitly calculating a combined stress, the specification defines an idealized envelope of combinations of axial and hoop stresses which cause the equivalent stress to reach failure. This curve represents the plot of: (x / -all)2 + hoop / hoop-all)2 - [x hoop / (x-all hoop-all)] 1.0 Where: x-all = Allowable Stress Axial hoop-all = Allowable Stress Hoop The specification conservatively limits you to that part of the curve falling under the line between x-all also known as a(0:1) and the intersection point on the curve where hoop is twice x a natural condition for a pipe loaded only with pressure. An implicit modification to this requirement is the fact that pressure stresses are given a factor of safety typically equal to 2/3 while other stresses are not. This gives an explicit requirement of: Pdes f1 f2 f3 LTHP Where: Pdes = Allowable Design Pressure f1 = Factor of Safety for 97.5% Lower Confidence Limit Usually 0.85 f2 = System Factor of Safety Usually 0.67 f3 = Ratio of Residual Allowable After Mechanical Loads = 1 - (2 sab) / (r f1 LTHS) 986 CAESAR II User's Guide Technical Discussions sab = Axial Bending Stress Due to Mechanical Loads r = a(0:1) / a(2:1) a(0:1) = Long Term Axial Tensile Strength In Absence Of Pressure Load a(2:1) = Long Term Axial Tensile Strength Under Pressure Loading Only LTHS = Long Term Hydrostatic Strength Hoop Stress Allowable LTHP = Long Term Hydrostatic Pressure Allowable This is implemented in the CAESAR II using the following equations: Code Stress ab (f2 /r) + PDm / (4t) Code Allowable (f1 f2 LTHS) / 2.0 Where: P = Design Pressure Dm = Pipe Mean Diameter t = Pipe Wall Thickness On the Allowable auxiliary dialog box, the product of f1 and LTHS is entered in the SH1, SH2, SH3 fields; r is entered in the F1, F2, F3 fields; f2 is entered in the Eff field; and the temperature reduction factor K (described for BS 7159 above) is entered in the Fac field if omitted, it defaults to 1.0. K- and i-factors for bends and tees, and bending and pressure stresses are calculated as described for the BS 7159. Calculate SIFs using UKOOA UKOOA refers to BS 7159 for SIF calculations. IGE/TD/12 CAESAR II performs calculations as per the IGE/TD/12 Edition 2 code requirements. The complexity of these requirements far exceeds what can be described here. We recommend that you acquire a copy of this code from the International Institution of Gas Engineers & Managers. Det Norske Veritas (DNV) This code is entitled "Rules for Submarine Pipeline Systems." The Allowable Stress Design (ASD) provisions of the code are implemented here, rather than the limit state requirements. Calculate the Stress Intensification Factors (SIFs), flexibility factors, or section moduli using DNV DNV does not provide any guidance on calculating SIFs, flexibility factors, or section moduli. An informal poll of DNV experts and users was taken and the decision was made to use the B31.1 Power Code. Make all stress calculations using the corroded wall thickness. CAESAR II User's Guide 987 Technical Discussions Calculate the expansion load case using DNV There is no provision for a code check for the expansion load case, so no expansion cases are generated under this code. Calculate the operating, sustained, or occasional load cases using DNV Treat the operating, sustained, or occasional load cases identically. For these load cases, you must perform three stress calculations with different allowable limits. The stress calculation causing the highest percent of allowable is reported in the stress report, along with its specific allowable. These stress checks are: Hoop Stress: Sh ns SMYS Hoop Stress: Sh nu SMTS Longitudinal Stress: SL n SMYS Equivalent Stress: Se n SMYS Where: Sh = (Pi – Pe) (D – t) / 2t Pi = Internal Pressure Pe = External Pressure D = Outer Diameter t = Wall Thickness ns = Hoop Stress Yielding Usage Factor; see Tables C1 and C2 of the DNV Code SMYS = Specified Minimum Yield Strength at Operating Temperature nu = Hoop Stress Bursting Usage Factor; see Tables C1 and C2 of the DNV Code SMTS = Specified Minimum Tensile Strength at Operating Temperature SL = Maximum Longitudinal Stress n = Equivalent Stress Usage Factor; see Table C4 of the DNV Code Se = [Sh2 + SL2 - ShSL + 3t2]1/2 t = Torsional Stress Calculate reducers using DNV DNV does not mention reducers for SIF calculations. EN-13480 Flexibility calculations using EN-13480 EN-13480 uses the hot modulus of elasticity in the flexibility calculations (Sect 12.1.7.2). The expansion allowable stress is subsequently modified by the ratio of Eh/Ec. 988 CAESAR II User's Guide Technical Discussions Calculate the flexibility stresses using EN-13480 EN-13480 provides two methods of determining the flexibility stresses. The CAESAR II default implementation is to use Sections 12.3.2 through 12.3.6, which perform an SRSS of the bending moments with a single SIF. As an alternative, the flexibility stresses can be determined by distinguishing between in and out of plane bending, using distinct SIFs, as discussed in Section 12.3.1. The option to implement this alternative can be found on the "SIF & Stress" tab of the configuration module. EN-13480 pressure stiffening EN-13480 does not consider pressure stiffening effects on bends. GPTC/Z380 The recommendations of this code apply only to above ground steel piping through 450°F. GPTC/Z380 and B31.8, prior to 2004, recommendations are similar in many ways. The differences between GPTC/Z380 and B31.8 display below: The longitudinal joint factors vary slightly between B31.8 Table 841.115a and GPTC/Z380 Table 192.113. The design factor in B31.8 Table 841.114b provides more detail than GPTC/Z380 Table 192.11. The allowable for the combined stress calculation in GPTC/Z380 Section 192.159-1.5e includes a "0.75" factor, while B31.8 Section 833.4 does not. GPTC/Z380 uses a single stress intensification factor (SIF) for both in-plane and out-of-plane loads, while B31.8 distinguishes between in-plane and out-of-plane SIFs. ISO-14692 ISO-14692 addresses the analysis of Fiber Reinforced Plastic (FRP) pipe. Qualification is based on the comparison of actual stresses, hoop and axial, to a failure envelope. See BS 7159 (on page 984) for the CAESAR II approach for FRP pipe analysis. HPGSL Calculate stress intensification factors (SIFs) for intersections using HPGSL HPGSL provides two separate equations to calculate the in-plane and out-plane stress intensification factors (SIFs) for intersections. Calculate expansion stress using HPGSL HPGSL provides an equation to calculate the expansion stress. This equation does not include calculations for the longitudinal stress due to axial loads in the pipe. CAESAR II does not include the F/A longitudinal stress component for stress in the expansion stress equation. You can change this by including the Add F/A In Stress option in the configuration file. The program adds the F/A longitudinal stress component, by default, to the code stress component for all other stress categories. CAESAR II User's Guide 989 Technical Discussions HPGSL girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate socket welds using HPGSL HPGSL makes no distinction between socket welds with undercut and socket welds without undercut. Codes that do differentiate use 1.3 for socket welds with no undercut, and 2.1 for all others. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3. Calculate the HPGSL stress allowables Use the equations below to calculate the stress allowables. Expansion Allowable = f [ (1.25/Eff)(Sc+Sh) - Sl ] Sustained Allowable Sh/Eff = Occasional Allowable = (Occ)*Sh/Eff Where: f = Cyclic Reduction Factor Eff = Weld Joint Efficiency Minimum Wall Thickness Only Sc = Cold Allowable Stress Sh = Hot Allowable Stress SI = Sustained Stress Occ = Occasional Load Factor Default is 1.33 When specifying a corrosion allowance, do not use a corrosion value in the sustained and occasional stress calculations. HPGSL reducer default values The default SIF value is 1.0. The default Flexibility Factor value is 1.0. HPGSL Pressure effects Pressure effects on miters are allowed in this piping code. JPI Calculate stress intensification factors (SIFs) for intersections using JPI JPI provides two separate equations to calculate the in-plane and out-plane SIFs for intersections. Calculate expansion stress using JPI JPI provides an equation to calculate the expansion stress. However, this equation does not include calculations for the longitudinal stress due to axial loads in the pipe. CAESAR II does not include the F/A longitudinal stress component for stress in the expansion stress equation. 990 CAESAR II User's Guide Technical Discussions The program adds the F/A longitudinal stress component, by default, to the code stress component for all other stress categories. JPI girth butt welds default value The default SIF value for a girth butt weld is 1.0. This is also Markl’s original basis for SIFs. Calculate socket welds using JPI JPI makes no distinction between socket welds with undercut and socket welds without undercut. Unless you are specifying a fillet weld leg length, use a default SIF value of 1.3. Calculate the JPI Stress allowables Expansion Allowable = f [ (1.25/Eff)(Sc+Sh) - Sl ] Sustained Allowable = Sh/Eff Occasional Allowable = (Occ)*Sh/Eff Where: f = Cyclic Reduction Factor Eff = Weld Joint Efficiency minimum wall thickness only Sc = Cold Allowable Stress Sh = Hot Allowable Stress SI = Sustained Stress Occ = Occasional Load Factor Default - 1.33 When specifying a corrosion allowance, do not use a corrosion value in the sustained and occasional stress calculations. JPl reducer default value The default SIF value is 1.0. The default Flexibility Factor value is 1.0. Pressure effects and JPl Pressure effects on miters are allowed in this piping code. Local Coordinates Many analytical models in engineering are based upon being able to define a real physical object mathematically. This is accomplished by mapping the dimensions of the physical object into a similar mathematical space. Mathematical space is usually assumed to be either two-dimensional or three-dimensional. For piping analysis, the three dimensional space is necessary, because almost all piping systems are three dimensional in nature. CAESAR II User's Guide 991 Technical Discussions Two typical three-dimensional mathematical systems are shown below in Figure 1. Both of these systems are "Cartesian Coordinate Systems". Each axis in these systems is perpendicular to all other axes. Figure 1 – Typical Cartesian Coordinate Systems In addition, for these Cartesian coordinate systems the "right hand rule" is used to define positive rotation about each axis and the relationship, or ordering, between the axes. Before illustrating the "right hand rule", there are several traits of the systems in Figure 1 that should be noted. Each axis can be thought of as a "number line", where the zero point is the point where all of the axes intersect. While only the positive side of each axis is shown in Figure 1, each axis has a negative side as well. The direction of the arrow heads indicates the positive direction of each axis. In Figure 1, the X-axis has one arrowhead, the Y-axis has two arrowheads, and the Z-axis has three arrowheads. The circular arcs labeled RX, RY, and RZ define the direction of positive rotation about each axis. (This point will be dis\-cussed later.) Any point in space can be mapped to these coordinate systems by using its position along the number lines. For example, a point 5 units down the X-axis would have a coordinate of (5.0, 0.0, 0.0). A point 5 units down the X-axis and 6 units down the Y-axis would have a coordinate of (5.0, 6.0, 0.0). Notice that if the system on the right side of Figure 1 is rotated a positive 90-degrees about the X axis, the result is the system on the left side of Figure 1. The coordinate system on the left side of Figure 1 is the default CAESAR II global coordinate system. In this system, the X and Z axes define the horizontal plane, and the Y-axis is vertical. The other coordinate system in Figure 1 can be obtained in CAESAR II by selecting the Z-axis Vertical option, discussed later in this section. All further discussion in this section targets this default coordinate system, unless other\wise noted. 992 CAESAR II User's Guide Technical Discussions Other Global Coordinate Systems There are other types of coordinate systems that can be used to mathematically map a physical object. A Polar coordinate system maps points in a two dimensional space using a radius and a rotation angle (r, theta). A Cylindrical coordinate system maps points using a radius, a rotation angle, and an elevation (r, theta, z). The origin in this system could be considered the center of the bottom of a cylinder. Cylindrical coordinates are convenient to use when there is an axis of symmetry in the model. A Spherical coordinate system maps points using a radius and two rotation angles (r, theta, phi). The origin in this system could be considered the center of a sphere. Spherical coordinatesare convenient to use when there is a point which is the center of symmetry in the model. Typically, none of these coordinate systems are easily used to map piping systems. Most piping software deals exclusively with the Cartesian coordinate system. The Right Hand Rule In the Cartesian coordinate system, each axis has a positive and a negative side, as previously mentioned. Translations, straight-line movement, can be defined as movement along these axes. Rotation can also occur around these axes, as illustrated by the arcs in Figure 1. A standard rule must be applied in order to define the direction of positive rotation about these axes. The right hand rule is used as the standard. Put the thumb of your right hand along the axis, in the positive direction of the axis. The direction your fingers curl is positive rotation about that axis. This is best illustrated in Figure 2. Figure 2 – The Right Hand Rule The right hand rule can also be used to describe the relationship between the three axes. Mathematically, the relationship between the axes can be defined as: X cross Y = Z (EQ 1) Y cross Z = X (EQ 2) Z cross X = Y (EQ 3) Where cross indicates the vector cross product. CAESAR II User's Guide 993 Technical Discussions Physically, using your right hand, what do the above equations mean? This question is best answered by Figure 3. Figure 3 – The Right Hand Rule - Continued The left pane of Figure 3 corresponds to vector equation 3 above. Similarly, the center pane in Figure 3 also corresponds to vector equation 3 above. The right pane in Figure 3 corresponds to vector equation 2 above. All panes of Figure 3 refer to the left hand image of Figure 1. Straight-line movement along any axis can be therefore described as positive or negative, depending on the direction of motion. This straight-line movement accounts for three of the six degrees of freedom associated with a given node point in a model. Analysis of a model requires the discretization of the model into a set of nodes and elements. Depending on the analysis and the element used, the associated nodes have certain degrees of freedom. For pipe stress analysis, using 3D Beam Elements, each node in the model has six degrees of freedom. The other three degrees of freedom are the rotations about each of the axes. In accordance with the right hand rule, positive rotation about each axis is defined as shown in Figures 1 and 2. When modeling a system mathematically, there are two coordinate systems to deal with, a global or model coordinate system and a local (or elemental) coordinate system. The global or model coordinate system is fixed, and can be considered a constant characteristic of the analysis at hand. The local coordinate system is defined on an elemental basis. Each element defines its own local coordinate system. The orientation of these local systems varies with the orientation of the elements. An important concept here is the fact that local coordinate systems are defined by, and therefore associated with, elements. Local coordinate systems are not defined for, or associated with, nodes. 994 CAESAR II User's Guide Technical Discussions Pipe Stress Analysis Coordinate Systems As noted previously, most pipe stress analysis computer programs use the 3D Beam Element. This element can be described as an infinitely thin stick, spanning between two nodes. Each of these nodes has six degrees of freedom three translations and three rotations. Piping systems models are constructed by defining a series of elements, connected by nodes. These pipe elements are typically defined as vectors, in terms of delta dimensions referenced to a global coordinate system. Several example pipe elements are shown below in Figure 4. Figure 4 - Example Pipe Elements For most pipe stress applications, there are two dominant global coordinate systems to choose from, either Y-axis or Z-axis up. These two systems are depicted in Figure 1. As previously noted, the global coordinate system is fixed. All nodal coordinates and element delta dimensions are referenced to this global coordinate system. For example, in Figure 4 above, the pipe element spanning from node 10 to node 20 is defined with a DX (delta X) dimension of 5 ft. Additionally, node 20 has a global X coordinate 5 ft. greater that the global X coordinate of node 10. Similar statements could be made about the other two elements in Figure 4, only these elements are aligned with the global Y and global Z axes. In CAESAR II, you can choose between the two global coordinate systems shown in Figure 1. By default, the CAESAR II global coordinate system puts the global Y-axis vertical, as shown in the left half of Figure 1, and in Figure 4. There are two ways to change the CAESAR II global coordinate system so that the global Z-axis is vertical. CAESAR II User's Guide 995 Technical Discussions The first method is to modify the configuration file in the current data directory. This can be accomplished from the Main Menu, by selecting Tools>Configure Setup. After the configuration dialog appears, select the Geometry tab, as shown in Figure 5. On this tab, click the Z-axis Vertical check box, as shown in the figure below. Figure 5 - Geometry Configuration After the Z axis Vertical check box is selected, the CAESAR II global coordinate system is in accordance with the right half of Figure 1. This configuration affects all new jobs created in this data directory. Existing jobs with the Y-axis vertical are not affected by this configuration change. 996 CAESAR II User's Guide Technical Discussions The second method to obtain a global coordinate system with the Z-axis vertical is to switch coordinate systems from within the input for the specific job at hand. This can be accomplished from the Special Execution Parameters dialog box of the piping input processor. This dialog box is shown below in Figure 6. Figure 6 - Special Execution Parameters Dialog Checking the Z Axis Vertical check box immediately changes the orientation of the global coordinate system axis, with corresponding updates to the element delta dimensions. However, the relative positions and lengths of the elements are not affected by this switch. CAESAR II User's Guide 997 Technical Discussions Defining a Model Using the CAESAR II default coordinate system (Y axis vertical), and assuming the system shown below in Figure 7, the corresponding element definitions are given in Figure 8. Figure 7 - Sample Piping Model Figure 8 - Sample Piping Model Element Definitions For this sample model, most of the element definitions are very simple: The first element, 10-20, is defined as 5 ft. in the positive global X direction. This element starts at the model origin. The second element, 20-30, is defined as 5 ft. in the positive global Y direction. This element begins at the end of the first element, because both elements share node 20. The third element, 30-40, is defined as 5 ft. in the negative global Z direction. Note in Figure 8 that the delta dimension for this element is a negative number. This is necessary to define the element in a negative direction. The fourth element, 40-50, runs in both the positive global X and negative global Y directions. This element slopes to the right and down, and is defined with delta dimensions in both the DX and DY fields. Notice that these delta dimensions are equal in magnitude; therefore this element slopes at 45 degrees. Continuing the model, from node 50, along the same 45 degree slope can be rather tedious, because most often only the overall element length is known, not its components in the global directions. In CAESAR II this can be best accomplished by activating the Edit Deltas dialog box, shown below in Figure 9. The Edit Deltas dialog box can be activated by clicking the Browse button next to the DX field. Using this dialog box, you can enter the element length, and 998 CAESAR II User's Guide Technical Discussions CAESAR II determines the appropriate components in the global directions, based on the current direction cosines, which default to those of the preceding element. Figure 9 - Edit Deltas Dialog Box CAESAR II provides an additional coding tool, for longer runs of pipe with uniform node spacing. Element Break enables you to break an element into equal length segments, given a node number increment. In the preceding example, the model is defined solely using delta dimensions. By constructing the model in this fashion, it is assumed that the world coordinates of node 10 the first node in the model are at (0., 0., 0.). This assumption is acceptable in all but one instance, when environmental loads are applied to the model. In this instance, the elevation of the model is critical to the determination of the environmental loads, and therefore must be specified. In CAESAR II, the specification of the starting node of the model can be accomplished using the Alt+G key combination, and all nodal coordinates are displayed as absolute coordinates. Regardless of whether or not the global coordinates of the starting node are specified, the relative geometry of the model will plot the same. After a model has been defined, there are a number of operations that can be performed on the entire system, or on any section of the system. These operations include: Translating the model: translation can be accomplished by specifying the global coordinates of the starting node of the model. If the model consists of disconnected segments, CAESAR II requests the coordinates of the starting node of each segment. Rotating the model: by using the List processor or by clicking List Input . The List processor presents the model in a spreadsheet, format, as shown in Figure 8. Options in this processor allow you to rotate the model about any of the three global axes, or a specified amount. For example, if the model shown in Figures 7 and 8 is rotated a negative 90 degrees about the global Y-axis, the result is as shown in Figure 10. CAESAR II User's Guide 999