Code notes

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FOR THE POWER,

PROCESS AND

RELATED INDUSTRIES

The COADE Mechanical EngineeringNews Bulletin is published twice a yearfrom the COADE offices in Houston,Texas. The Bulletin is intended to provideinformation about software applicationsand development for MechanicalEngineers serving the power, process andrelated industries. Additionally, the Bulletinserves as the official notificationvehicle for software errors discovered inthose Mechanical Engineering programsoffered by COADE.

2002 COADE, Inc. All rights reserved.

V O L U M E 3 2 F E B R U A R Y 2 0 0 2

Whats New at COADEPVElite Version 4.30 and CodeCalc 6.4

Released .................................................... 1CADWorx Version 2002 Released ................ 4TANK Version 2.30 ........................................ 6

Technology You Can UseComparison of Response Spectrum and

Static methods uisng ASCE 7-98 .............. 6Coordinate Systems in CAESAR II ................ 9Frequency / Phase Pairs in CAESAR II ....... 18PC Hardware for the Engineering User

(Part 32) ................................................... 24

Program SpecificationsCAESAR II Notices ...................................... 25TANK Notices .............................................. 26CodeCalc Notices ........................................ 26PVElite Notices ............................................ 26

I N T H I S I S S U E :

PVElite 4.3 and CodeCalc 6.4Released!CodeCalc 6.4 released in January 2002 introduced many new features, someof the significant ones are:

Interactive computation of results on the input screen Trunnion design Leg baseplate design WRC 368 (local stress in the nozzle-cylinder junction due to internal

pressure)

On-screen calculations are introduced in this version, to aid in faster designand estimation. As the data is entered the calculation is automatically performed.Once the data is consistent and complete, the results are displayed on thestatus bar in color. A failure in design is indicated in red to bring it to theusers attention. The following figure shows an internal/external cylindricalshell analysis with the results displayed on the status bar. This interactivefeature is implemented in the shell/head, nozzle and flange modules.

COADE Mechanical Engineering News February 2002

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Lifting trunnion analysis was also implemented in this version.Stresses in the trunnion are computed and compared to theirrespective allowables. An option to perform an automatic localstress evaluation per the WRC 107 method is available. In thisversion the leg baseplate can also be designed. The features discussedabove were available to the PVElite users in the component analysismodule in the September release.

Features, which are new for both the CodeCalc and PVElite users(in the component analysis module) are:

Simplified input and analysis for the non-radial nozzles.

Split screen graphics.

Tailing lug analysis.

Improved registration procedure.

ASME A-2001 update

Visit www.coade.com for a complete list.

Input for non-radial nozzles has been simplified. Nozzles can beeasily located around the vessel by specifying the angle between thevessel and nozzle centerline and the nozzle offset, as illustrated inthe following figure.

Figure 2 Nozzle angle input

To illustrate lets consider a 6 in. tangential nozzle located on a 60in. ID elliptical head. The nozzle is offset from the head centerlineby 20 in. Appropriate data input and the CodeCalc graphic for thiscase is shown in Figure 3.

Additionally, CodeCalc now checks the design in both thelongitudinal and the circumferential planes for Hillside nozzles inthe same analysis. Lateral nozzles or Y-angle on cones or cylinderscan also be easily specified.

Figure 3 Nozzle input and corresponding graphic for atangential nozzle.

February 2002 COADE Mechanical Engineering News

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As seen in Figure 1, the split screen graphic is back by populardemand. This provides instant visual check of the input. Thesplitter bar that separated the screen areas can be used to adjust thesize of the input tabbed dialog and the graphic.

CodeCalc can now perform a tailing lug analysis. The tailing lug,which is attached to the basering, is used for lifting vertical vessels.

Another enhancement in CodeCalc version 6.4 is the improvedproduct registration procedure. A link is provided in the softwarethat allows users to register with COADE. By registering, importantnews about builds, new versions etc. is emailed to those whoregistered. Contact information can be modified or updated anytime through this web interface.

Significant new features in PVElite version 4.3 are:

Added top head platform and caged ladder

PD5500 Annex F Nozzle calculations

IBC 2000 Earthquake code added

Modal Natural frequency solver

Added Dynamic Response Spectrum for earthquake loadcalculation

ASME A-2001 update

The following figure shows a vessel with a rectangular platform and2 caged ladders. Modal natural frequency solver and computationof earthquake loading using the dynamic response spectrum method,helps to accurately model the vessel. This can provide considerablesavings in material cost, especially for tall vertical vessels. Thesefeatures are discussed in another article (Comparison of ResponseSpectrum and Static Methods using ASCE 7-98) in this newsletter.

As previously advised, beginning with PVElite Version 4.3,there will only be one update of the software per year.

Figure 4 A Vessel modeled with PVElite 4.3


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CADWorx 2002 Released!The CADWorx development team is excited to announce the releaseof CADWorx 2002, the latest advancements in COADEs plantdesign and automation software. The new version is packed withfeatures many of them requested by existing CADWorx users.Here is a brief overview of CADWorx 2002.

CADWorx PIPE and P&ID 2002

Windows style tool tips have been added. Hover over acomponent and view information about that component withoutrunning any command. The tool tips displayed can becustomized to include only information you need.

Figure 1: Tool Tip Data Selection In CADWorx PIPE

Editing a component is easier than ever before. Just double-click on it and change any information including long, shortdescriptions etc.

CADWorx now supports various languages. All prompts anddialogs can now be localized with different languages. Initiallanguages available include French and Spanish. Futurelanguages are also planned. Below are examples of twodialogs one in Spanish and one in French.

Figure 2: CADWorx PIPE Setup Dialog In French

Figure 3: CADWorx P&ID Setup Dialog In Spanish

Enforce specification and size limitation using the new variableSpecSizeOveride in the configuration file.

New HTML Help system has been implemented and onlinehelp is available from dialogs and the command line.


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CADWorx PIPE 2002

A fully integrated live database has been added. Completeintegration with AutoCAD commands like COPY, ERASE isincluded to make database operation seamless. The databaseis updated immediately. Make your changes in the drawing orin the database and you will not lose any information! Usingthe SYNC command, CADWorx will update your drawingswith the information from the database. CADWorx supportsMicrosoft Access, Oracle and Microsoft SQL Server databases.

The ISOOUT command has been enhanced dramatically toimprove speed. In addition, a special component STOPSIGNhas been added to break ISOs at specified points along lines.

Creating new data files is now easy with the new Templatebutton in the Specification Editor. Just select the componenttype, pick a location to save the data file and a brand newtemplate data file is created. All you have to do is fill it withthe sizes you need.

A new variable IsometricColor has been added. Set thisvariable to make all your ISOs come out in the same color.

The Auto Isometric Configuration dialog has been improvedand records the last used configuration file.

Convert your CADWorx Modelspace/Paperspace AutoISOinto a 2D flat drawing using the new 2DISO command. Thiscommand requires the use of AutoCAD express tools.

The ZOOMLOCK command has been improved to lock allMVIEWs in Paperspace.

Flange placement has been enhanced to prevent the flangeface from being placed on buttweld side of a component.Previous versions of the program required the user to changethe option at the command line during flange placement.

Specifications can be set to a particular color in advance usingthe SpecColor setting. Previous versions of the programrequired the spec color to be entered every time the spec wasset in a new drawing.

New commands have been added to set the current main size,reduction size, specification and/or line number based on anexisting component.

GCEDIT (Global Component Edit) now shares the sameoptions as CEDIT (Component Edit) including newly addedBOM Item Type.

Sort your Bill of Material in any order with the new SORT BYbutton in the BOMSETUP dialog.

You can now start your BOM tag numbers at any value youspecify.

Several commands including ISOOUT, DBFGEN now havethe ability to select multiple line numbers at the same time.

The ROUTER command has been enhanced to allow a constantslope to be set, maintain the crosshairs at the elevation of thelast point picked, and allow a sloped segment at the beginningof a routing line.

Importing a PCF file using PCFIN has been improved withmore components and with less clean up required.

The menu file was updated to allow easy activation of toolbarsby simply right clicking on a docked PIPE toolbar.

CADWorx P&ID 2002

Create specification driven P&IDs. CADWorx can nowread information from specifications and automatically updatethe database as you draw your P&ID drawing. This feature iscontrolled by the SpecControl variable in the configurationfile.

Change process line priority using the new PROCESSASSIGNcommand.

Embedded instruments can now be copied with the correctnumber of entries created in the database.

Added flanged, socketweld valves and function symbols tomenu.

New SyncOnStartUp variable has been added to theconfiguration file. This variable allows you to alwayssynchronize on opening a drawing, never synchronize orprompt for user response.

The XDATAADD is used to convert existing P&ID drawingsinto CADWorx P&ID drawings. XDATAADD now has theoption of adding component information to user-definedtables.

If any user created text styles contain the phrase No Change,CADWorx P&ID will no longer change the text style to thecurrent style when inserting components into the drawing.

The SETVISIBILITY command has new options. You cannow hide all objects with an entry in the database. You canalso isolate a single object based on its database ID. TheSETVISIBILITY command allows you to only view a subsetof all objects in a drawing.

REMOVEITEM is a new command that removes the linkbetween valves or other objects and process lines.


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UNCOMBINELINE is a new command that creates individualentries in the database for each broken segment of a processline. This command is the opposite of COMBINELINE thatcreates one entry in the database for broken process linesegments.

The menu file was updated to allow easy activation of toolbarsby simply right clicking on a docked P&ID toolbar.

All CADWorx users under current UMS, (Upgrades, Maintenanceand Support), contract should receive CADWorx 2002 shortly. Ifyou are not already using CADWorx, now is a great time to start.Visit www.coade.com and download an evaluation version or call281-890-4566 to request a demo CD. If you are ready to buyCADWorx, contact your local CADWorx dealer or contact us.

Register with us (www.coade.com/updates.htm) and keep up-to-date with the latest releases and builds of CADWorx.

TANK Version 2.30TANK Version 2.30 should be ready to ship by the first part ofFebruary 2002. This new release of TANK includes the followingchanges and modifications.

New input options exist to disable the output of annular baseplate information, and to exclude the wind moment in F.4.2computations.

Rafter supported cone roof (no columns) design has beenadded.

In the wind girder report, the actual distances below the topof the tank have been added.

In the tank layout graphics, the shell course thicknesseshave been added.

TANK output can now be sent directly to Microsoft WORD,with subsequent reformatting.

The configuration dialog now includes [D]efault buttons,allowing users to reset the directive to its default value with asingle click.

The Error Checker module has been modified to notify usersof fatal errors when run in batch mode.

Use of user defined materials has been simplified. The usermaterial file no longer needs to be manually merged with theCOADE supplied material database. This operation isperformed in memory by the input processor when necessary.

Software registration is now handled directly on-line. Thisprovides better abilities to notify users when software updatesbecome available.

Comparison of the ResponseSpectrum Analysis and StaticMethods using the ASCE 7-98Earthquake Code

By: Scott Mayeux

PVElite version 4.3 was released in January 2002 and incorporatesa variety of new features including earthquake analysis utilizing theResponse Spectrum Method.

What is the Response Spectrum Method (RSM) and why is ituseful?

The response spectrum method computes forces and moments on astructure utilizing matrix solution methods and shock spectra datato yield a more accurate result than the static equivalent buildingcode technique. The vessel is modeled as an elastic, multipledegree of freedom system and the equations of motion for eachdegree of freedom are solved. The resulting equations of motion(matrices) are integrated in time to obtain the simulated response ofthe structure. To understand the difference between the methods, itis important to understand how a static earthquake analysis works.Generally, when using a typical building code it is necessary toobtain basic parameters such as the seismic zone, soil factors, siteclass, etc. to solve for a base shear force. In the case of our examplebelow, the ASCE 7-98 building code was selected. After enteringthe input, PVElite was utilized to analyze a tall process tower.Selected results appear in the tables below. Note the value of V(16823 lb.). This is the base shear. It is an equivalent static inertialhorizontal load. With a known base shear and element masses, alateral force (Element Load) can be computed for each element,based on a weighted mass distribution summation equation. Afterthese loads are computed, bending moments and subsequent bendingstresses at each node can be calculated. These bending stressescause both tensile and compressive stresses in the tower elements.These stresses are ultimately combined with other types such aspressure and weight stresses, which are then compared to appropriatecode allowables.

It is known that a flexible structure such as a freestanding tallvertical vessel or piping system can have many modes of vibration.


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Using traditional methods of structural analysis in pressure vesseldesign, only the first mode of vibration is considered. Thisfundamental mode of vibration is used in both wind and seismiccalculations. PVElite 4.3 incorporates advanced technology thatallows it to solve for multiple frequencies under 100 cycles persecond using the Eigen Solution method. This method solves amass/stiffness matrix problem iteratively until a mode of vibrationis successfully extracted. Computing several modes of vibration isimportant because the elemental mass may contribute differentlybased on the mode of interest. This is obviously not a considerationusing the static method. After PVElite extracts the modes andmode shapes, it can determine the shear forces, axial forces and thecorresponding moments. Additionally, the dynamic displacementsat each node point (typically a weld seam) can now be computed.

Since ASCE 7-98 addresses both the RSM and the static equivalentmethod, it was chosen because it allows a direct comparison of thetwo techniques. For our test, a 112 feet tall (34 meters) processtower tall was selected. The task of interest is to compare theresulting bending moments throughout the tower. At the base of thetower a moment of 519629 ft-lbs was computed using the RSM,while a moment of 1,100,000 ft-lbs was computed using thetraditional method. This is quite a remarkable difference, less thanhalf! If the governing thickness requirement is based upon seismicrequirements, this analysis could reduce the thickness of the skirtand shell courses. The thickness savings become especially importantif the vessel is constructed of an expensive material, such aszirconium, titanium, stainless steel or other. Additional benefitssuch as lower foundation loads, smaller anchor bolts, chair caps etc.are also realized.

It is also interesting to note that the wind moment changed. This isdue to the change in the natural frequency and resulting energydissipation difference. When the RSM is chosen, PVElite willalways use the Eigen Solver to extract the various modes of vibration.Note that there is a slight difference here, 1.115189 hz (using theFreese Method) versus 1.1682 hz using the Eigen method. Thedifference is very small but does have an impact on the wind loadcalculation. Another important advantage of the Eigen solver is thatit does not rely on the assumption that the structure is supported atthe base, which is a requirement of the Freese method. The newer,advanced technique in PVElite allows for accurate solutions oflug, intermediate skirt and leg supported vessels. For newlycreated vessels, the program uses this method as the default.

In addition to the ASCE and IBC 2000 earthquake types using theRSM, a table of data points for Period or Frequency versusDisplacement, Velocity or Acceleration can be entered into theprogram. The United States Nuclear Regulatory Commissions guide1.60 shock spectra and ElCentro are also built into PVElite. Themissing mass correction factor is included as an option.

In conclusion, the Response Spectrum Method can provide vesseldesigners with more accurate stress and deflection results whencompared to the older, more traditional analysis techniques. Theresulting calculations are shown for each case below.

Earthquake Analysis Results per ASCE 7-98 (static method)

User Entered Table Value 9.4.1.2.4a Fa 1.000User Entered Table Value 9.4.1.2.4b Fv 1.400Max. Mapped Acceleration Value for Short Periods Ss 1.00Max. Mapped Acceleration Value for Long Periods S1 0.400Moment Reduction Factor Tau 1.000Force Modification Factor R 3.000Importance Factor I 1.000Seismic Design Category C

Check the Period (1/Frequency) from 9.5.3.3-1Ta = Ct * hn^(3/4) where Ct = 0.020 and hn = total Vessel HeightTa = 0.020 * ( 114.0697 ^(3/4) = 0.698 seconds

The Coefficient Cu from Table 9.5.3.3 is 1.300

Check the Min. Value of T which is the Smaller of Cu*Ta and TT = Min. Value of ( 1.300 * 0.698, 1/ 1.152 ) = 0.8681 per9.5.3.3

Compute the Seismic Response Coefficient Cs per 9.5.3.2.1Cs = Sds / ( R / I )Cs = 0.6667 / ( 3.0000 / 1.0000 ) = 0.2222

Check the minimum value of Cs per eqn. 9.5.3.2.1-3Cs = Maximum Value of ( 0.1433, 0.044 * 1.00 * 0.6667 ) =0.1433

Compute the Total Base Shear V = Cs * Total WeightV = 0.1433 * 117364.1 = 16823.69 lb.

Distribute the Base shear force to each element according tothe equations Fx = Cvx * V (eqn. 9.5.3.4-1 ) and the verticaldistribution factor Cvx = Wx*hx^k/( Sum of Wi*hi^k ) and k isan exponent which is related to the period of Vibration.In this case, the value of k was 1.1841.

The Natural Frequency for the Vessel (Ope...) is 1.15189 Hz.

Wind/Earthquake Shear, Bending

| | Elevation | Cummulative| Earthquake | Wind | Earthquake |From| To | of To Node | Wind Shear| Shear | Bending | Bending | | | ft. | lb. | lb. | ft.lb. | ft.lb. | 10| 20| 10.5000 | 29821.4 | 16823.7 | 1.639E+06 | 1.100E+06 | 20| 30| 21.0833 | 23674.9 | 15684.7 | 1.077E+06 | 758759. | 30| 40| 25.3333 | 23635.2 | 15554.8 | 1.073E+06 | 756156. | 40| 50| 30.2500 | 21573.5 | 14825.4 | 884802. | 629573. | 50| 60| 36.0000 | 20744.9 | 14531.6 | 853063. | 607555. | 60| 70| 46.0000 | 18671.6 | 13305.0 | 655981. | 468372. | 70| 80| 56.0000 | 16512.6 | 11861.0 | 480060. | 342542. | 80| 90| 66.0000 | 13173.5 | 9789.46 | 331629. | 234289. | 90| 100| 76.5000 | 10871.9 | 7980.78 | 211403. | 145438. | 100| 110| 87.5000 | 7566.71 | 5437.96 | 109991. | 71635.1 | 110| 120| 94.0000 | 4281.93 | 2566.15 | 44823.1 | 27612.5 | 120| 130| 104.267 | 3874.40 | 2291.62 | 36666.8 | 22754.7 | 130| 140| 113.742 | 80.1298 | 157.889 | 21.4870 | 55.9972 | 140| 150| 114.010 | 17.8717 | 86.1383 | 1.07035 | 5.15889 |


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Tensile and Bending Stresses due to Earthquake Moments

Analyzing Stresses for Load Case : EQ Stress Units: psiFrom Tensile All. Tens. Comp. All. Comp. Tens. Comp.Node Stress Stress Stress Stress Ratio Ratio

10 6961.37 14700.00 -6961.37 -18940.33 0.4736 0.3675 20 4428.13 21000.00 -4428.13 -20215.11 0.2109 0.2191 30 4412.93 17850.00 -4412.93 -20215.11 0.2472 0.2183 40 3674.19 17850.00 -3674.19 -20215.11 0.2058 0.1818 50 4936.62 17850.00 -4936.62 -21000.00 0.2766 0.2351 60 4686.55 17850.00 -4686.55 -21000.00 0.2626 0.2232 70 3870.30 17850.00 -3870.30 -21000.00 0.2168 0.1843 80 3555.63 17850.00 -3555.63 -20763.93 0.1992 0.1712 90 3334.83 17850.00 -3334.83 -19806.43 0.1868 0.1684 100 1642.56 17850.00 -1642.56 -19806.43 0.0920 0.0829 110 357.88 17850.00 -357.88 -21000.00 0.0200 0.0170 120 2488.57 15300.00 -2488.57 -18000.00 0.1627 0.1383 130 6.12 21000.00 -6.12 -21000.00 0.0003 0.0003 140 0.25 21000.00 -0.25 -21000.00 0.0000 0.0000

Maximum Stress ratio: 0.4736, tension at node 10, moment1,100,000 ft-lbs

Response Spectrum Analysis per ASCE 7-98

Computed Natural Frequencies (OPE): 11 Mode Freq (Hz) Freq (Rad/Sec) Period (Sec)

1 1.1682 7.3398 0.8560 2 4.0176 25.2430 0.2489 3 7.4993 47.1197 0.1333 4 14.0766 88.4458 0.0710 5 24.7993 155.8188 0.0403 6 31.0785 195.2722 0.0322 7 39.9319 250.8992 0.0250 8 58.1019 365.0652 0.0172 9 70.5193 443.0861 0.0142 10 78.7207 494.6167 0.0127 11 100.0587 628.6871 0.0100

Mass Participation Factors: 11 Mode X Y

1 10.95138983 0.00000029 2 0.93197919 -0.00000003 3 -0.25465900 0.00000000 4 0.04770686 -0.00000018 5 0.00704619 0.00000005 6 0.00000000 0.01942145 7 -0.00126486 0.00000000 8 0.00033505 0.00000000 9 0.00000000 -0.00152696 10 0.00010016 0.00000000 11 -0.00003331 0.00000000

Computed EigenVectors Report Deleted for Brevity

Mass Percentages: Included(X) Included(Y) Added(X) Added(Y)

82.82 80.48 0.00 0.00

NOTE: In the following reports, Max Contrib displays thecontribution of the Mode/Load combination having the maximum impacton the total (and names that Mode/Load combination).

Restraint Loads: Node Fx(lb.) Fy(lb.) Mz(ft.lb.)

10 8586.4 10787.0 519629.0 Max 6192.2 10645.1 485676.4 Contrib 1 (X) 6 (Y) 1 (X)

Element Forces and Moments: [Report Abbreviated] Node Fx(lb.) Fy(lb.) Mz(ft.lb.)

10 8586.4 10787.0 519629.0 Max 6192.2 10645.0 485676.4 Contrib 1 (X) 6 (Y) 1 (X) 20 8586.4 10787.0 362310.7 Max 6192.2 10645.0 355640.6 Contrib 1 (X) 6 (Y) 1 (X)

Displacements: [Report Abbreviated] Node Dx(in.) Dy(in.) Rz(Deg)

10 0.0000 0.0000 0.0000 Max 0.0000 0.0000 0.0000 Contrib 1 (X) 6 (Y) 1 (X)

20 0.1342 0.0017 0.0548 Max 0.1266 0.0017 0.0525 Contrib 1 (X) 6 (Y) 1 (X)

Wind/Earthquake Shear, Bending

Wind/Earthquake Shear, Bending | | Elevation | Cummulative| Earthquake | Wind | Earthquake |From|To | of To Node | Wind Shear| Shear | Bending | Bending | | | ft. | lb. | lb. | ft.lb. | ft.lb. | 10| 20| 10.5000 | 29733.4 | 8586.43 | 1.634E+06 | 519629. | 20| 30| 21.0833 | 23607.6 | 7696.16 | 1.074E+06 | 362311. | 30| 40| 25.3333 | 23568.0 | 7491.96 | 1.070E+06 | 361184. | 40| 50| 30.2500 | 21513.3 | 7153.78 | 882358. | 306675. | 50| 60| 36.0000 | 20685.9 | 6820.82 | 850708. | 297297. | 60| 70| 46.0000 | 18619.5 | 6179.39 | 654181. | 237813. | 70| 80| 56.0000 | 16467.9 | 5440.72 | 478744. | 184079. | 80| 90| 66.0000 | 13136.3 | 4691.29 | 330723. | 136472. | 90| 100| 76.5000 | 10842.4 | 3909.20 | 210829. | 95293.3 | 100| 110| 87.5000 | 7546.04 | 2766.40 | 109693. | 58549.6 | 110| 120| 94.0000 | 4270.26 | 1902.53 | 44703.1 | 33256.5 | 120| 130| 104.267 | 3864.10 | 1604.81 | 36568.8 | 29811.4 | 130| 140| 113.742 | 79.8592 | 150.120 | 21.4144 | 68.9268 | 140| 150| 114.010 | 17.8114 | 53.2318 | 1.06674 | 6.37673 |

Analyzing Stresses for Load Case : EQ Stress Units: psi From Tensile All. Tens. Comp. All. Comp. Tens. Comp. Node Stress Stress Stress Stress Ratio Ratio

10 3324.08 14700.00 -3324.08 -18940.33 0.2261 0.1755 20 2114.45 21000.00 -2114.45 -20215.11 0.1007 0.1046 30 2107.87 17850.00 -2107.87 -20215.11 0.1181 0.1043 40 1789.76 17850.00 -1789.76 -20215.11 0.1003 0.0885 50 2415.65 17850.00 -2415.65 -21000.00 0.1353 0.1150 60 2379.57 17850.00 -2379.57 -21000.00 0.1333 0.1133 70 2079.87 17850.00 -2079.87 -21000.00 0.1165 0.0990 80 2071.12 17850.00 -2071.12 -20763.93 0.1160 0.0997 90 2185.03 17850.00 -2185.03 -19806.43 0.1224 0.1103 100 1342.51 17850.00 -1342.51 -19806.43 0.0752 0.0678 110 431.03 17850.00 -431.03 -21000.00 0.0241 0.0205 120 3260.33 15300.00 -3260.33 -18000.00 0.2131 0.1811 130 7.54 21000.00 -7.54 -21000.00 0.0004 0.0004 140 0.31 21000.00 -0.31 -21000.00 0.0000 0.0000

Maximum Stress ratio: 0.2261, tension at node 10, moment519629 ft-lbs


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Coordinate Systems inCAESAR II

By: Richard Ay

Introduction

This article discusses coordinate systems, and how they relate topiping systems and pipe stress analysis. Additional information onthis subject can be found in two issues of COADEs MechanicalEngineering News - December 1992 and November 1994. Theseissues can be found on the COADE web site athttp://www.coade.com.

Many analytical models in engineering are based upon being able todefine a real physical object mathematically. This is accomplishedby mapping the dimensions of the physical object into a similarmathematical space. Mathematical space is usually assumed to beeither two-dimensional or three-dimensional. For piping analysis,the three dimensional space is necessary, since almost all pipingsystems are three dimensional in nature.

Two typical three-dimensional mathematical systems are shownbelow in Figure 1. Both of these systems are Cartesian CoordinateSystems. Each axis in these systems is perpendicular to all otheraxes.

Figure 1 Typical Cartesian Coordinate Systems

In addition, for these Cartesian coordinate systems, the right handrule is used to define positive rotation about each axis, and therelationship, or ordering, between the axes. Before illustrating theright hand rule, there are several traits of the systems in Figure 1that should be noted.

Each axis can be thought of as a number line, where thezero point is the point where all of the axes intersect. Whileonly the positive side of each axis is shown in Figure 1, eachaxis has a negative side as well.

The direction of the arrow heads indicates the positivedirection of each axis.

In Figure 1, the X axis has one arrowhead, the Y axis hastwo arrowheads, and the Z axis has three arrowheads. Thecircular arcs labeled RX, RY, and RZ define the directionof positive rotation about each axis. (This point will bediscussed later.)

Any point in space can be mapped to these coordinate systemsby using its position along the number lines. For example, apoint 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 unitsdown 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 rotateda positive 90 degrees about the X axis, the result is thesystem on the left side of Figure 1.

The coordinate system on the left side of Figure 1 is the defaultCAESAR II global coordinate system. In this system, the X andZ axes define the horizontal plane, and the Y axis is vertical.(The other coordinate system in Figure 1 can be obtained inCAESAR II by selecting the Z-axis Vertical option, discussedlater in this article.) All further discussion in this article will targetthis default coordinate system, unless otherwise noted.

Other Global Coordinate Systems

There are other types of coordinate systems that can be used tomathematically map a physical object.

A Polar coordinate system maps points (in a two dimensionalspace) 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 inthis system could be considered the center of the bottom of acylinder. Cylindrical coordinates are convenient to use whenthere is an axis of symmetry in the model.

A Spherical coordinate system maps points using a radiusand two rotation angles, (r, theta, phi). The origin in thissystem could be considered the center of a sphere. Sphericalcoordinates are convenient to use when there is a pointwhich is the center of symmetry in the model.

Typically, none of these coordinate systems are easily used to mappiping systems. Most piping software deals exclusively with theCartesian coordinate system.


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The Right Hand Rule

In the Cartesian coordinate system, each axis has a positive and anegative side, as previously mentioned. Translations, straight-linemovement, can be defined as movement along these axes. Rotationcan also occur around these axes, as illustrated by the arcs inFigure 1.

A standard rule must be applied in order to define the direction ofpositive rotation about these axes. This standard rule (known as theright hand rule) is: Put the thumb of your right hand along theaxis, in the positive direction of the axis. The direction your fingerscurl is positive rotation about that axis. This is best illustrated inFigure 2.

Figure 2 The Right Hand Rule

The right hand rule can also be used to describe the relationshipbetween the three axes. Mathematically, the relationship betweenthe axes can be defined as:

X cross Y = Z eq 1Y cross Z = X eq 2Z cross X = Y eq 3Where cross indicates the vector cross product.

Physically, using your right hand, what do the above equationsmean? 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 vectorequation 3 above. The right pane in Figure 3 corresponds to vectorequation 2 above. All panes of Figure 3 refer to the left hand imageof Figure 1.

Straight-line movement along any axis can be therefore describedas positive or negative, depending on the direction of motion. Thisstraight-line movement accounts for three of the six degrees offreedom associated with a given node point in a model. (Analysisof a model requires the discretization of the model into a set ofnodes and elements. Depending on the analysis and the elementused, the associated nodes have certain degrees of freedom. Forpipe stress analysis, using 3D Beam Elements, each node in themodel has six degrees of freedom.) The other three degrees offreedom are the rotations about each of the axes. In accordancewith the right hand rule, positive rotation about each axis isdefined as shown in Figures 1 and 2.

When modeling a system mathematically, there are two coordinatesystems to deal with, a global (or model) coordinate system and alocal (or elemental) coordinate system. The global or modelcoordinate system is fixed, and can be considered a constantcharacteristic of the analysis at hand. The local coordinate systemis defined on an elemental basis. Each element defines its own localcoordinate system. The orientation of these local systems varieswith the orientation of the elements. An important concept here(which will be reiterated later) is the fact that local coordinatesystems are defined by, and therefore associated with, elements.Local coordinate systems are not defined for, or associated with,nodes.


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Pipe Stress Analysis Coordinate Systems

As noted previously, most pipe stress analysis computer programsutilize the 3D Beam Element. This element can be described as aninfinitely thin stick, spanning between two nodes. Each of thesenodes has six degrees of freedom - three translations and threerotations. Piping systems (models) are constructed by defining aseries of elements, connected by nodes. These pipe elements aretypically defined as vectors, in terms of delta dimensions referencedto a global coordinate system. Several example pipe elements areshown below in Figure 4.

Figure 4 - Example Pipe Elements

For most pipe stress applications, there are two dominant globalcoordinate 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 andelement delta dimensions are referenced to this global coordinatesystem. For example, in Figure 4 above, the pipe element spanningfrom node 10 to node 20 is defined with a DX (delta X) dimensionof 5 ft. Additionally, node 20 has a global X coordinate 5 ftgreater that the global X coordinate of node 10. Similar statementscould be made about the other two elements in Figure 4, only theseelements are aligned with the global Y and global Z axes.

In CAESAR II, the user can choose between the two globalcoordinate systems shown in Figure 1. By default, the CAESAR IIglobal coordinate system puts the global Y axis vertical, as shownin the left half of Figure 1, and in Figure 4. There are two ways tochange the CAESAR II global coordinate system so that the globalZ axis is vertical.

The first method is to modify the configuration file in the currentdata directory. This can be accomplished from the Main Menu, byselecting Tools\Configure Setup. Once the configuration dialogappears, select the Geometry tab, as shown in Figure 5. On thistab, check the Z Axis Up check box, as shown in the Figure.

Figure 5 - Geometry Configuration

Once the Z Axis Vertical switch is activated, the CAESAR IIglobal coordinate system will be in accordance with the right half ofFigure 1. This configuration affects all new jobs created in this datadirectory. Existing jobs with the Y axis vertical are not affectedby this configuration change.

The second method to obtain a global coordinate system with theZ axis vertical is to switch coordinate systems from within theinput for the specific job at hand. This can be accomplished fromthe Special Execution Parameters dialog of the piping inputprocessor. This dialog is shown below in Figure 6.

Figure 6 - Special Execution Parameters Dialog


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Checking the Z Axis Vertical checkbox will immediately changethe orientation of the global coordinate system axis, withcorresponding updates to the element delta dimensions. However,the relative positions and lengths of the elements are not affected bythis switch.

Defining a Model

Using the CAESAR II default coordinate system (Y axis vertical),and assuming the system shown below in Figure 7, the correspondingelement 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 verysimple:

The first element, 10-20, is defined as 5 ft in the positive globalX direction. This element starts at the model origin.

The second element, 20-30, is defined as 5 ft in the positiveglobal Y direction. This element begins at the end of thefirst element, since both elements share node 20.

The third element, 30-40, is defined as 5 ft in the negativeglobal Z direction. Note in Figure 8 that the delta dimensionfor this element is a negative number. This is necessary todefine the element in a negative direction.

The fourth element, 40-50, runs in both the positive globalX and negative global Y directions, this element slopes tothe right and down. This element is defined with deltadimensions in both the DX and DY fields. Notice that thesedelta dimensions are equal in magnitude; therefore this elementslopes at 45 degrees.

Continuing the model, from node 50, along the same 45degree slope can be rather tedious, since most often only theoverall element length is know, not its components in theglobal directions. In CAESAR II this can be best accomplishedby activating the Direction Cosine dialog box, shown belowin Figure 9. (The Direction Cosine dialog can be activatedby clicking on the button next to the DY field.) Usingthis dialog box, the element length can be entered, andCAESAR II will determine the appropriate components inthe global directions, based on the current direction cosines(which default to those of the preceding element).

Figure 9 - Direction Cosine Dialog


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CAESAR II provides an additional coding tool, for longerruns of pipe with uniform node spacing. An element breakoption is provided, which allows an element to be broken intoequal length segments, given a node number increment.

In the preceding example, the model is defined solely using deltadimensions. By constructing the model in this fashion, it is assumedthat the world coordinates of node 10 (the first node in the model)are at (0., 0., 0.). This assumption is acceptable in all but a oneinstance, when environmental loads are applied to the model. Inthis instance, the elevation of the model is critical to the determinationof the environmental loads, and therefore must be specified. InCAESAR II, the specification of the starting node of the model canbe accomplished using the [Alt+G] key combination, and all nodalcoordinates will be displayed as absolute coordinates. Regardlessof whether or not the global coordinates of the starting node arespecified, the model relative geometry will plot the same.

Once a model has been defined, there are a number of operationsthat can be performed on the entire system, or on any section of thesystem. These operations include:

Translating the model: translation can be accomplished byspecifying the global coordinates of the starting node of themodel. If the model consists of disconnected segments,CAESAR II requests the coordinates of the starting node ofeach segment.

Rotating the model: rotation can be accomplished by using the

[LIST] processor(by clicking on the zbutton in thetoolbar). The [LIST] processor presents the model in aspreadsheet, or grid, format, as shown in Figure 8. Options inthis processor allow the model (or any sub-section of themodel) to be rotated about any of the three global axes, aspecified amount. For example, if the model shown in Figures7 and 8 is rotated a (negative) -90 degrees about the global Yaxis, the result is as shown in Figure 10.

Figure 10 - Example of Model Rotation

Duplicating the model: duplication can also be accomplishedby using the [LIST] processor. The entire model, or any sub-section of the model, can be duplicated.

Using Local Coordinates

When analyzing a piping system, there are a number of items thatmust be checked and verified. These items include:

Operating loads on restraints and terminal points Maximum operating displacements Hanger design results Codes stresses for code cases Equipment evaluation Vessel nozzle evaluation Expansion joint evaluation

Restraint loads and displacements are checked in the globalcoordinate system. This is necessary because restraint loads anddisplacements are nodal quantities. Element loads and stresses aremost often evaluated in their local coordinate system. A goodexample illustrating the use of a local (element) coordinate systemis the free body diagram, of forces and moments. The forces andmoments in this free body diagram remain the same, regardless ofthe position of the element in the global coordinate system. Notehowever, that each element has its own local coordinate system.Furthermore, the local coordinate system of one element may bedifferent from the local coordinate system of a different element.

While the global coordinate system is typically referred to using thecapital letters X, Y, and Z, local coordinate systems use avariety of nomenclature. In almost all cases, local coordinatesystems use lower case letters. Typical local coordinate systemaxes are: xyz, abc, and uvw. CAESAR II uses xyz todenote the local element coordinate system.

The local coordinate system for an element is related to the globalcoordinate system through a rule. There may be a number of suchrules, depending on the type of element. In CAESAR II, thefollowing rules are used to define the local coordinate systems ofthe piping elements in a model.

CAESAR II Local Coordinate Definitions

Rule 1 - Straight Pipe: For straight pipe elements, the local xaxis always points from the From Node to the To Node. Thelocal y axis can be found by the vector cross product of the localx axis with the global Y axis. Applying the right hand rule,this local y axis can be found by:

1. Lay your right hand on the pipe, with the wrist at the FromNode, and the fingers pointing to the To Node.

2. Align or rotate your hand so that the global Y axis pointsperpendicularly out from the palm.

3. The thumb is now aligned with the local y axis for thiselement.

The local z axis can be found by the vector cross product of thelocal x and local y axes.


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An exception to this rule is the case of a vertical element. In thiscase, the local x axis is still aligned in the From - To direction.However, you cant cross a vertical element into global Y, sothe local y axis was arbitrarily assigned to align with the globalX axis.

The straight elements of the model in Figure 7 are reproducedbelow in Figure 11, along with their local coordinate systems.Notice that each of these straight elements has its own localcoordinate system, and that in this model, they are all aligneddifferently.

Figure 11 - Local Coordinate Systems for Straight Elements (1)

In Figure 11, the positive direction of the local x axis for eachelement is defined according to the From - To definition of theelement. For example, the local x axis of element 10-20 isaligned with the positive global X axis, because that is the directiondefined in moving from node 10 to node 20. The local x axis ofelement 30-40 is aligned with the negative global Z axis, becausethat is the direction defined in moving from node 30 to node 40.Figure 11 should be studied to ensure a good understanding of howthe local element coordinate system can be defined based on thedefinition of the element, especially with regard to the skewedelement 40-50.

As an additional example, the local element coordinate systems forthe rotated system of Figure 10 are shown below in Figure 12.

Figure 12 - Local Coordinate Systems for Straight Elements (2)

Rule 2 - Bend Elements: For the near weld line of bendelements, the local x axis is directed along the incoming tangent,in the From To direction. The local z axis points to the centerof the circle described by the bend. For the far weld line of bendelements, the local x axis is directed along the outgoing tangent,in the From To direction. The local z axis points to the centerof the circle described by the bend. In both cases, the local y axiscan be found by applying the right hand rule. The local coordinatesystem for the bends in the example model of Figure 7 are shownbelow in Figure 13.

Figure 13 Local Coordinate Systems for Bend Elements


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Rule 3 - Tee Elements: For tees, there is no element or fitting asthere is in a CAD application. Rather designating a node as a teesimply applies code defined SIFs at that point, for the three elementsframing into the tee node. As usual, the local x axis is defined bythe element From - To direction. The local y axis coincideswith the line that defines the in-plane plane of the tee (in otherwords, the local y axis is perpendicular to the plane of the threetee elements). The positive direction of the local y axis is foundby (vectorally) crossing the local x axis of the header elementwith the local x axis of the branch, and then (strangely enough)reversing the sign (direction). (In those cases where the two headerelements have opposite local x axes, CAESAR II chooses thefirst one that it finds.) The local z axis can then be determinedusing the right-hand rule.

Note that the local z axis coincides with the out-of-plane axis ofthe tee, for each element. Examples of local coordinates for elementsframing into tees are depicted below in Figure 14.

Figure 14 - Local Coordinate Systems for Tee Elements

Applications - Utilizing Global and Local Coordinates

Global coordinates are used most often when dealing with pipingmodels. Global coordinates are used to define the model andreview nodal results. Even though element stresses are defined interms of axial and bending directions, which are local coordinatesystem terms, local coordinates are rarely used. A typical pipinganalysis scenario is as follows.

A decision is made as to how the global coordinate system forthe piping model will align with the plant coordinate system.Usually, one of the two horizontal axes is selected to correspondto the North direction. However, if this results in a majorityof the system being skewed with respect to the global axes, oneshould consider realigning the model. It is best to have mostof the system aligned with one of the global coordinate axes.

The piping system is then assigned node points at locationswhere: there is a change in direction, a support, a terminalpoint, a point of cross section change, a point of load application,or any other point of interest.

Once the nodes have been assigned the piping model can bedefined using the delta dimensions as dictated by theorientation of the global coordinate system. Analysts shouldtake advantage of the tools provided by CAESAR II inconstructing the model - this includes the element breakoption, the LIST rotate and duplicate options, and the directioncosine facility.

After verifying the input, confirming the load cases, andanalyzing the model, output review commences.

Output review involves checking various output reports to ensurethe system responds within certain limits. These checks include:

Checking that operating displacements make sense and arewithin any operational limits (to avoid ponding etc.).Displacements being nodal quantities, are reviewed in theglobal coordinate system. There is no local coordinatesystem associated with nodes. For the model defined inFigures 7 and 8, the operating displacements are shown inFigure 15 below.

Figure 15 - Operating Displacements

This report shows the movements of all of the nodes in the model, ineach of the six degrees of freedom, in the global coordinate system.

Checking that the restraint loads for the structural loadcases are reasonable. This includes ensuring that the restraintscan be designed to carry the computed load. Restraints beingnodal quantities, are reviewed in the global coordinatesystem. There is no local coordinate system associated withrestraints. For the model defined in Figures 7 and 8, theoperating / sustained restraint summary is shown in Figure 16below.


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Figure 16 - Operating / Sustained Restraint Summary

This report shows the loads on the anchor at 10 and the nozzle at 50,for all six degrees of freedom, for the two selected structural loadcases, in the global coordinate system.

Checking the Code cases for codes stress compliance.Typically the code stress is compared to the allowablestress for each node on each element. Occasionally, whenthere is an overstress condition, a review of axial, bending,and torsion stresses are necessary. These stresses (axial,bending, and torsion) are local coordinate system terms,and therefore relate to the elements local coordinate system.For the model defined in Figures 7 and 8, a portion of thesustained stress report is shown in Figure 17 below.

Figure 17 - Sustained Stress Report

These reports provide sufficient information to evaluate the pipeelements in the model, to ensure proper behavior and codecompliance. However, the analysts job is not complete, loads andstress must still be evaluated at terminal points, where the pipingsystem connects to equipment or vessel nozzles. Depending on thetype of equipment or nozzle, various procedures and codes areapplied. These include API-610 for pumps and WRC-107 forvessel nozzles, as well as others. In the case of API-610 and WRC-107, a local coordinate system specific to these codes is employed.These local coordinate systems are defined in terms of the pump ornozzle/vessel geometry.

When the equipment coordinate system aligns with the globalcoordinate system of the piping model, the nozzle loads from therestraint report (node 50 in Figure 14) can be used in the nozzleevaluation. However, when the equipment nozzle is skewed (as it isin the case of node 50 in Figure 14), the application of the loads ismore difficult. In this case, it is best to use the loads from theelements force/moment report, in local coordinates. The onlything to remember here is to flip the signs on all of the forces andmoments, since the element force/moment report shows the loadson the pipe element, not on the nozzle. For the element from node40 to node 50, the local element force/moment report is shown inFigure 18 below.

Figure 18 - Local Element Force/Moment Report


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Because the correlation between the pipe models coordinate systemsand those of equipment codes (API, WRC, etc) are often timestedious and error prone, CAESAR II provides an option in itsequipment modules to acquire the loads on the nozzle directly fromthe static output. The user simply has to select the node and the loadcase; CAESAR II will acquire the loads and rotate them into theproper coordinate system as defined by the applicable equipmentcode. The user really does not have to be concerned with thetransformation from global to local coordinates, even for skewedcomponents. This is illustrated below, in Figure 19. In this figure,the API-610 nozzle loads at node 50 have been acquired by clickingon the [Get Loads from Output File] button.

Notice that the loads shown in Figure 19 are in the CAESAR IIglobal coordinate system. This can be easily verified by comparingthese values to those in the restraint summary (for the Operatingload case) as shown previously in Figure 16.

Figure 19 - API-610 Nozzle Load Acquisition

In the corresponding output report for this API-610 analysis, boththe global and API local loads are reported. This is shown below inFigure 20.

Figure 20 - API-610 Nozzle Output Report Segments

Notice in Figure 20, that each report segment indicates whichvalues are related to the global coordinate system and which arerelated to the local API coordinate system.

Transforming from Global to Local

Converting (or transforming) values from the CAESAR II globalcoordinate system to a local coordinate system involves applying anumber of rotation matrices to the global values. Matrix mathematicsis not a trivial task, and one must exercise the utmost care to arriveat the correct result. For those that want to undertake this taskthemselves, a small utility (discussed in the July 2001 issue ofCOADEs Mechanical Engineering News) can be downloaded fromthe COADE web site to perform this transformation. The use of thisutility (GlbtoLocal) is illustrated here, using the nozzle at node 50as an example.


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The element 40-50 is defined with the delta coordinates of:

DX = 3 ft. 6.426 inDY = -3 ft. 6.426 inDZ = 0.0

The global restraint forces at node 50, in global coordinates, for theoperating case are:

FX = 323. MX = -953.FY = 4. MY = -9.FZ = -271. MZ = -548.

Using this data as input to GlbtoLocal, the utility yields the forceson the restraint in the elements local coordinate system. This isshown in Figure 21 below.

Figure 21 - Example Global to Local Transformation

The set of values labeled Rotated Displacements / Load Vectorcan be compared with the Local Element Force / Moment report,as shown in Figure 18. Note however, that a change in sign isnecessary, since the restraint report shows loads acting on therestraint, while the element report shows loads acting on the element.

Frequently Asked Questions

What are global coordinates? Global coordinates define themapping of a physical system into a mathematical system. For anygiven model, the global coordinate system is fixed for the entiremodel. In CAESAR II, there are two alternative global coordinatesystems that can be applied to a model. Both coordinate systemsfollow the right hand rule and use X, Y, and Z as mutuallyperpendicular axes. The first alternative uses the Y axis vertical,while the second uses the Z axis as vertical.

What are local coordinates? Local coordinates represent themapping for a single element. Local coordinate systems are used todefine positive and negative directions and loads on elements.Local coordinate systems are aligned with the elements, and thereforevary throughout the model.

What coordinates are used to plot and view the model? Themodels global coordinate system is used to generate plots of themodel. This is necessary since each element has its own localcoordinate system, and these local systems can vary from element toelement. Local coordinate systems are an element property, not asystem property.

How do you obtain restraint loads in local coordinates? Ingeneral, you dont - this doesnt make any sense. Restraint loads area nodal property. Nodes dont have local coordinate systems,elements do. While an argument can be made that the localcoordinate system of the connecting element should be used, this isonly valid if one single element frames into the restraint. As soon asmultiple elements frame into the restraint, there are multiple localcoordinate systems to deal with. The lone exception is when asingle element frames into a nozzle. In this instance, the restraintloads in this single elements coordinate system can be obtainedfrom the elements local force / moment report, with a change insign.

How do you obtain nodal displacements in local coordinates? Ingeneral, you dont - this doesnt make any sense. Displacements area nodal property. Nodes dont have local coordinate systems,elements do. Refer to the preceding discussion on restraint loadsfor additional details.

What do you do with local coordinates? In most instances nothing.The only time local coordinates are useful in CAESAR II is whendealing with a skewed nozzle. The CAESAR II software interfacemakes the use of local coordinates unnecessary except in this oneinstance.


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Frequency / Phase Pairsin CAESAR II

By: Dave Diehl

Introduction

The harmonic analysis included with the initial release ofCAESAR II was simple in one way yet complex in another. It wassimple in that it did not account for system damping. Therefore, themaximum system response occurred at the same instant as themaximum applied load. But these ideal systems, systems withoutdamping, are capable of producing infinite response when drivenexactly at a natural frequency. Of course, a CAESAR II modelwith infinite response would not mimic the real world. What madeit more complex was the way we addressed this damping term. Atthe time, we offered an equation to adjust the forcing frequency tosimulate the damping that was missing from the analysis. It workedwell enough for those users who understood the theory behind it all.

Then in Version 3.22, back in 1995, Tom1 added damping toCAESAR II harmonic analysis2 . Now that frequency shift is nolonger required for an accurate analysis. But with damping themaximum response no longer happens at the same time as themaximum load. So Tom added a few more screens to the harmonicsprocessor to search for and display the maximum system response,no matter when it occurs. This search and display is performed foreach loading frequency in the analysis. All this data is presented tothe user along with two choices 1) let CAESAR II sort throughthe data and report the significant results, or, 2) allow the user topick through the numbers and choose. As you might imagine, mostusers simply have CAESAR II select frequency/phase pairs. Wesee it time and again here at COADE; as we add more sophisticationto our programs, more user input and knowledge is required tosuccessfully utilize these analysis improvements. This articledescribes what those additional harmonic analysis screens hold,how to use them, and why you may want to select your ownfrequency/phase pairs.

Harmonic Analysis

A few basics in harmonic analysis are worth reviewing. First of all,the system response to a harmonic load (either force or displacement)has the same frequency as the applied load. The equations may notmake this obvious but the real world does. Consider an orchestra onstage. All the instruments can tune up independent of the hall in

1 Tom Van Laan, President of COADE

2 Rayleigh damping is incorporated by adjusting the systemstiffness. This approximation works well when the forcingfrequency is close to a system natural frequency which is usuallythe case of interest.

which they are played. The frequency or pitch produced on stagewill reach your ear in the audience. Of course, the sound producedon stage will change before it reaches your ear. It may be amplifiedor attenuated by the room dynamics and there are delays in soundsthat have traveled farther before reaching your ear. But a C playedon stage will still be a C when you hear it. Your piping systemdynamics are analogous to the acoustics in that concert hall. Theresponse exhibits the same frequency as the applied load.

Heres another basic the system response is always changing. Ifwe apply a harmonic load to a piping system, we can take a snapshotof that system at any point in time and the magnitude of systemresponse will vary according to the frequency of the applied loadand the time of the snapshot. Now this may sound overly simple butit is often overlooked. CAESAR II output the system deflections,loads and stresses varies according to when you take that snapshot.Using some non-maximum value as the amplitude of the responsewould underestimate the system response. We want to report themaximum response, reporting results at any other time would notshow the true amplitude of the response. Refer to Figure 1 andidentify proper report times to display response amplitude. Thenodal response reported at snapshot B can be used for the systemamplitude as can D. Reports generated for a given point in thesystem at time A would not show maximum response and shouldnot be used to predict things like fatigue life. Time C illustrates areport that would have zero response for the selected node.

Harmonic Analysis with Damping

Remember that with no system damping, the system response followsthe load exactly when the load is maximum, the response ismaximum. This would have report times A, B, C & D above keyeddirectly to the load itself. Figure 2a shows another way of lookingat this. Here we are watching the response at the tip of the cantileverfor an undamped system. The response of the tip (and any otherpoint in this undamped system) tracks the applied load identically.


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Figure 2a

We can show this in equation:

)cos(= Aload ; )cos(= Bresponse 3

Where A is the magnitude of applied load (force or deflection) is the forcing frequencyB is the nodal response (deflection, load, stress)

But when damping is introduced in this system4 , there is a lag in theresponse. The frequency of response still matches the applied loadbut there is a phase shift. The maximum response of any node nolonger occurs at the same instant as the maximum applied load.This point is illustrated in Figure 2b. The base of the cantilever isapproaching its maximum positive value while the tip is comingfrom is minimum position as it approaches zero deflection.

3 Its a little more complicated than this. In the ideal, with nodamping, the response is either exactly in phase or 180 degreesout of phase (points B & D in Figure 1) with the applied load. Itis in phase when the forcing frequency is less than a systemnatural frequency and out of phase when the forcing frequency isgreater than a system natural frequency. Since we are interestedin the absolute maxima, the numbers come out the same.

4 So whats a good number for the critical damping ratio for piping?The default value displayed in the CAESAR II dynamic inputcontrol parameters is 0.03. This is on the high side for most piping.The U.S. A.E.C. Regulatory Guide 1.61 states that piping with anominal OD of 12 inches and lower has a damping value (percent ofcritical damping) of 1 (thats 0.01 in CAESAR II input) and largerpiping has a damping value of 2. These values are for seismicdesign for an operating basis earthquake. ASME BPVC Section III(Nuclear) Div. 1 Appendix N (Dynamic Analysis Methods)mimicked these values until the 1999 addendum. In 1999 theNuclear code changed the damping value to 5 for all pipe sizes andearthquake magnitudes. While this newer information is useful inselecting the magnitude of the ground response, the older data isstill applicable for the harmonic analysis we are running here.

Figure 2b

This lag in the response is the phase shift (f) at the tip of thecantilever. The equations now include this phase shift:

)cos(= Aload ; )cos( += BresponseWhere is the phase shift at the node in question.

We Want the Maximum Response

With no damping the response will match the timing of the appliedload. Theres no reason to fool with a phase angle; the responsechanges over time but the maximum response is known to match themaximum applied load. The early version of harmonic analysis,without damping, did not require a search for the maximum response.But because of the associated phase shift, damping alters thissimple view.

Fortunately, CAESAR II monitors the maximum displacementof every node for each exciting frequency and tracks the phase shiftassociated with this nodal response. When you have CAESAR IIselect frequency/phase pairs late in the harmonic analysis, a reportis displayed for each analyzed frequency at the phase angle thatproduced the largest overall displacement. For each forcingfrequency analyzed, CAESAR II lists the node with greatestdisplacement, that displacement and phase angle of this response5 .This frequency/phase pair, as we call it, can also be selected byhand and this is discussed later. When the user has CAESAR IIselect the frequency/phase pairs the report tabulating these results(shown in Figure 3) is displayed before control is passed to theoutput processor.

5 The program also lists the real and imaginary terms of thisdisplacement. Think of the real term as the X axis and the imaginaryterm as the Y axis in an X-Y plot. The magnitude of the response isplotted as a vector with its base at (0,0) and this vector is rotated offthe +X axis by the phase angle, where positive is counterclockwise.


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The real term is )cos(magnitude and the imaginary term is)sin(magnitude .

Figure 3

Rather than analyzing a single frequency, the user should typicallysweep through a range of loading frequencies. This wouldaccommodate any inaccuracies in the dynamic (mass & stiffness)model and any uncertainties in the loading frequency. This presentsa lot of data to review. Using CAESAR IIs snapshot at eachfrequency; the task of data review is greatly simplified. Figure 3shows that 15 frequencies were analyzed from 7.0 to 7.7 Hz. Thiswill produce 15 load cases for review in the output processor eachhaving the usual complement of reports of displacements, restraintloads, internal loads and stresses. The maximum response up to 7.5Hz is at node 25 and beyond that node 58 has the maximumdisplacement. The phase angle of these maxima increases from 8degrees at 7.0 Hz to 165 degrees at 7.7 Hz. These snapshots of thesystem at these point in time (in other words, at this phase angle)will display, and report the system response based on these selectedmaximum nodal displacements.

Thats what you want to see6.

6 In most cases the maximum displacement of a system node willproduce the maximum stress but this is not necessarily true. Most ofour concerns regarding harmonic analysis center on lower modes ofsystem vibration modes that usually display simple cantileverbending. Higher modes of vibration may produce higher bendingstresses with a smaller maximum deflection. Also, higher modescould develop high stresses at intermediate points along the pipebetween existing node numbers. Without the node number defined,these high stresses cannot be reported.

Other Information in this Report

Response increases exponentially as the forcing frequencyapproaches a system natural frequency and fades as the forcingfrequency increases beyond a system natural frequency. Figure 4shows this relationship in equation and plot. The plot displays thisresponse for a 1% critically damped system in terms of amplitudeversus ratio of forcing frequency to natural frequency. When asystem is driven exactly at a natural frequency the amplitude of theresponse simplifies to: )2(1 =A ; where is the critically dampedratio. Here, where is 0.01 (not atypical for piping systems), theamplification factor is 50.

Figure 4

Of course, if you are looking for maximum response as you sweepthrough a range of frequencies, you would only need to review theresults at one frequency the driving frequency closest to a systemnatural frequency.

This report in Figure 3 also indicates which forcing frequency isclosest to the natural frequency, but not directly. In the example,the response at node 25 builds exponentially from 4.2 mm at 7.0 Hzup to 20.2 mm at 7.45 Hz and then drops off. You will also note thatthe phase shift for each frequency increases with the forcingfrequency. A useful key here is that as the forcing frequencyapproaches a system natural frequency, the phase shift in themaximum response approached 90 degrees. This is true for anyamount of system damping. Keep an eye on the phase shift in themaximum response and you can easily pick out the forcingfrequencies of greatest significance. In our example, a naturalfrequency of this piping system is somewhere between 7.45 Hz and7.50 Hz. Our attention will focus on the 7.45 Hz report since thatone shows the greatest displacement at node 25. With this


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information, you could also go back to the harmonic input and run afiner sweep between 7.45 Hz and 7.50 Hz, confident that this wouldget you closer to the system maximum response at node 25.

The stress report at the frequency/phase pair of 7.45 Hz and 69degrees (or anything closer to the natural frequency) will show thestress amplitudes at every node. With the appropriate fatigue curve,this information could be used to estimate the number of cycles tosystem failure.

Selecting Your Own Frequency/Phase Pairs

The discussion so far concerns the programs selection of frequency/phase pairs. The user is also offered the choice of selecting thesedata by hand as shown in Figure 5.

Figure 5

Once you know signs to look for, you can select your own frequenciesto report maximum system response. In our example, we will selectour own frequency/phase pairs using the 7.45 Hz load. Figures 6aillustrates this selection.

Figure 6a

After selecting the frequency to monitor, you then select a node. Inour example we will monitor node 25. Again, the CAESAR IIselection shown earlier indicated that node 25 exhibited the maximumdisplacement at 7.45 Hz. Once you choose a node the followingscreen appears (Figure 6b).

Figure 6b


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You see that 18 different reports each at a different phase angle can be displayed for this single forcing frequency of 7.45 Hz. Thereport at Index #4 (the first column in the report), with a phase angleof 69.13, is the one that CAESAR II selected earlier but you canreview the others as well. Watching the DZ column, you see thenode cycle through its displacement in Z. Index #13 is just theopposite of #4. Index #9 essentially shows zero deflection as does#18. All the others show intermediate results. Looking back atFigure 1, you could say report times A, B, C & D correlate toIndices 17, 4, 18 & 13.

Note how these 18 reports are based on phase angles pretty muchrunning between 0 and 340 degrees at 20 degree increments. Thedisplayed displacement will equal (maximum displacement)*cos(-) where is phase angle and runs through 0, 20, 40,340.There are four exceptions to this pattern that shift the phase angle tocatch the maximum, minimum and two zero response times forthe node in question. These four phase angles replace the closestreports. In Figure 6b you see that the report at phase angle 60 isreplaced by a report at 69.13 degrees to catch the maximum response.Likewise, the reports at 160, 240 and 340 degrees are also replacedby more significant events. Stars are added to the screen capture tomark these four reports. A plot of these responses in Figure 7reinforces this point. The two curves represent the applied harmonicload defined and the response at node 25. The response at node 25lags node 5 by 69.13 degrees. CAESAR II provides reports at the18 phase angles indicated by the circles. The stars highlight thereport shifts to catch those significant points. The shifts to catch themaximum and minimum response are obvious while the zero pointsare not apparent with the scale used. These are the 18 phasesolutions or reports discussed in the program text shown inFigure 5.

Figure 7

So Why Would You Want to Select Your Own Frequency/Phase Pairs?

If CAESAR II can find the frequency/phase pairs producing themaximum displacement, why would you want to get in the way andselect your own? I can think of three reasons.

1. If you wanted to reduce the amount of reports listed in theoutput, simply select the same node and phase shift asCAESAR II but only for the forcing frequencies close to anatural frequency.

2. If you are interested in a specific node (a point of failure?),you can select your node here. You will note that the phaseangle associated with maximum response changes from nodeto node.

3. If you simply wanted to exercise the processor to increaseyour understanding of harmonic analysis in CAESAR II.

Conclusion

You must remember the cyclic nature of harmonic results. Thesnapshot we see in the CAESAR II output is time or phasedependant. Our goal is to display the maximum response based onthe proper frequency/phase pair. This article described theimportance of that frequency/phase pair and how you can useCAESAR II to confirm you are looking at the proper results.

Most vibration texts provide good background in forced harmonicvibration. One such book is Theory of Vibrations with Applicationsby William T. Thompson published by Prentice-Hall, now in 5thEdition.


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PC Hardware/Software for theEngineering User (Part 32)Keeping Your System Up to Date

Recently, Microsoft published a document titled Windows DesktopProduct Lifecycle Guidelines. This document (available at http://www.microsoft.com/windows/lifecycleconsumer.asp) discusses thelife cycle of the various Microsoft operating systems. As explainedin this document, the operating system life cycle consists of threephases; mainstream phase, extended phase, and non-supported phase.

In the non-supported phase, support for the operating system isavailable only online, and Microsoft may terminate this afterproviding 12 months notice. The following operating systems arecurrently listed in the un-supported phase of their life cycle: MSDOS, Windows 3.xx, Windows 95, Windows NT 3.5x. Of theseoperating systems, current COADE software will only run onWindows 95.

From this Microsoft document:

When a Windows desktop operating system enters the Non-Supported phase, does that mean new applications wont run onthe older operating system?

There is no direct correlation between when an operating systementers the Non-Supported phase and when new applications andnew hardware will no longer work with the older operating system.However, the older an operating system is, the less likely it is thatnew applications will run well on it. As happens today, to offercustomers products that take advantage of the complete functionalityof the latest operating systems, hardware and softwaremanufacturers may choose to only have their products work withthe most recent operating systems and discontinue supporting theirproducts on older operating systems.

Register Your COADE Product!

Keeping with the latest builds and versions of COADE products isboth important and highly recommended. The developers at COADEare constantly adding new features and fixing problems found byusers and us. These updates are available for download from ourwebsite. Visit www.coade.com/updates.htm and register yourselfto receive timely e-mail notices informing you about newly availablebuilds, versions and other important product information.

As always, the information you share with us is used solely byCOADE Inc. and is not sold or provided to any outside sources.For more information, visit www.coade.com and click PrivacyPolicy to review our privacy policy.

For those users running Norton Anti-Virus, ensure youre-enable scripting from the "options" tab. Failure to dothis will prevent COADE products from sending output toMicrosoft Word.


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CAESAR II Notices

Listed below are those errors & omissions in the CAESAR IIprogram that have been identified since the last newsletter. Thesecorrections are available for download from our WEB site.

1) Stress Computation Modules:

Modified the computation of the minimum Sh value forB31.8 Ch VIII allowable computation

Modified the handling of rotational restraint stiffnesses foranchors and displacements so as to use the default specifiedin the configuration.

2) Animation Module:

Modified to address dual monitors.

3) Element Generator:


4) Error Checker Module:

Corrected the diameter/thickness checks to ensure zerovalues are properly reported as errors.


Corrected the specification of user entered SIF values forthe TD/12 piping code.

Corrected the specification of user entered SIF values forTD/12 pressure stresses.

Corrected the units conversion of the API-650 delta Tvalue when printing the nozzle report directly to the printer.

5) Input Echo / Neutral File Module:

Corrected to address the Z axis up setting..

6) Intergraph Interface:

Modified to handle alpha-numeric pipe scheduledesignations.

Corrected temperature/pressure data storage allocation.

Refined the tolerance used to determine English nominaldiameters from metric values.

7) Static Load Case Setup Module / Dynamic Input:

Increased memory allocation for force sets whenperforming force spectrum analysis.

Removed a restriction limiting the number of static loadcases that could be referenced in a combination case

Corrected wave plots to properly label Z axis up.

Corrected load case error message when introducing springhanger design.

Corrected scalar/absolute warning to show only once.

8) Output Modules:


Corrected the operation of the Find dialog, for the on-screen mode (unity/mass) reports.

Corrected input echo generation when reporting allowablestress data for output modules.

Corrected a problem accessing the two line user titles,following report export to MS Word.

Corrected a problem causing the cumulative usage andcode compliance reports to print more than once.

Corrected a problem where if MS Word was implementedfirst, data was not available for plotting.

9) PCF Interface:

Modified to allow the conversion of multiple neutral files ina single session.

10) CADPIPE Interface:

Implemented additional intersection checks to improveolet location

Corrected the placement of the downstream leg of bendswhen terminating at tees.

Added an additional 18 entity types per latest CADPIPEversion.

11) PIPENET Interface:

Corrected the interface to properly put forces set values inthe CAESAR II dynamic input file..


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12) Miscellaneous Processor:

Added handling of Z axis up for EJMA routines

Corrections to the flange routine; nubbin width definition,conversion of B and G to user units, applied momentunits conversion, ring joint width from gasket dimensions.

13) Piping Input Module:

Corrected temperature, pressure, diameter, and wallthickness window close operations.

Corrected the operation of the node marker on/off switch.

Corrected the hanger run control data when upgradinginput files from previous versions.

Added handling of skewed restraints when performing amirror duplication.

14) MS Word Templates:

Updated to address Win95/Office97 table of contents issues.

15) Eigen Solver:

Corrected the execution of the out-of-core solver.

TANK NoticesListed below are those errors & omissions in the TANK programthat have been identified since the last newsletter. These correctionsare available for download from our WEB site.

1) Input Module:

Corrected a problem preventing the sizing scratchpadfrom displaying output. Corrected for the 2.30 release.

CodeCalc NoticesListed below are those errors & omissions in the CodeCalc programthat have been identified since the last newsletter.

1) TEMA Tubesheet: Corrected an error related to tubesheet classselection.

2) Flange: Corrected the Flange MDMT computation.

3) Cone: The external pressure required thickness calculation forcones with half-apex angle greater than 60 degrees, is per the flathead formula, as outlined in the code.

4) ASME Tubesheet: Corrected the tube allowable stresses forTemperature + Pressure cases. This only affected the fixedtubesheet design and was a conservative error.

PVElite NoticesListed below are those errors & omissions in the PVElite programthat have been identified since the last newsletter. These correctionsare available for download from our WEB site.

1) Nozzle Dialog - Depending on the path taken through the nozzledialog a program abort could occur, specifically if one of thelookup buttons was pressed before tabbing past the nozzlediameter.

2) Detail Properties - Under BS:5500, the allowable stresses fordetail components was not being updated if the design temperaturewas changed.

3) Nozzle Analysis - The strength reduction factor for set on(abutting) nozzles when constructed of different materials wasnot handled in the Division 2 area of replacement calculations .

4) The corroded hydrotest option was not handled by the programfor the Zick analysis in the test condition.

5) The distance for stiffening ring inclusion in conical calculationswas not computed correctly due to a units problem.

6) For vessels with intermediate skirts that had large differences inelement diameter diameters, the natural frequency calculationwas in error. This usually resulted in very low natural frequency.

7) For Horizontal vessels where -Y forces were specified, theprogram was subtracting the applied force from the saddle loadand not adding to it.

8) For Division 2 vessels with reinforcing pads, the program wasnot properly considering the reduced pad area in the two thirdsarea calculation.


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12777 Jones Rd. Suite 480 Tel: 281-890-4566 Web: www.coade.comHouston, Texas 77070 Fax: 281-890-3301 E-Mail: [email protected]

COADE Engineering Software

What's New at COADEPVElite Version 4.30 and CodeCalc 6.4 ReleasedCADWorx Version 2002 ReleasedTANK Version 2.30

Technology You Can UseComparison of Response Spectrum and Static methods using ASCE 7-98Coordinate Systems in CAESAR IIFrequency / Phase Pairs in CAESAR IIPC Hardware for the Engineering User (Part 32)

Program SpecificationsCAESAR II NoticesTANK NoticesCodeCalc NoticesPVElite Notices

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