GUIA_DE_USO

CAESAR IIApplications

Guide

CAESAR II, VERSION 4.40 Copyright(c) COADE/Engineering Physics Software, Inc., 1984-2002, all rights reserved.

(LAST REVISED 5/2002)

CAESAR II - Applications Guide

Contents

�� Overview A1 - 2Program Support / User Assistance A1 - 2COADE Technical Support Contact Information A1 - 2

��

Bend Definition A2 - 2Single and Double Flanged Bends or Stiffened Bends A2 - 4180 Degree Return (Fitting-To-Fitting 90 Deg. Bends) A2 - 6Mitered Bends A2 - 7Closely Spaced Mitered Bend A2 - 8Widely Spaced Mitered Bend A2 - 10

Example: Widely Spaced Miter A2 - 11Example: Widely Spaced Miter ...Continued A2 - 12

Elbows - Different Wall Thickness A2 - 13Example: Thick Elbow A2 - 13

Bend Flexibility Factor A2 - 14

�� Anchors A3 - 2Anchors with Displacements A3 - 3Flexible Anchors A3 - 5Flexible Anchors with Predefined Displacements A3 - 6Flexible Nozzle (WRC Bulletin 297) A3 - 8

Flexible Nozzle with Predefined Displacements A3 - 11Flexible Nozzle with Complete Vessel Model A3 - 12

Double-Acting Restraints A3 - 17Double-Acting Restraints (Translational) A3 - 17Double-Acting Restraint (Rotational) A3 - 18

Single-Directional Restraints A3 - 19Guides A3 - 20Limit Stops A3 - 22Windows A3 - 24Rotational Directional Restraints with Gaps A3 - 25Single-Directional Restraint with Predefined Displacement A3 - 26Single-Directional Restraint and Guide A3 - 27Restraint Settlement A3 - 28Skewed Double-Acting Restraint A3 - 29Skewed Single-Directional Restraint A3 - 31Restraint Between Two Pipes (Use of CNodes) A3 - 32Restraint Between Vessel and Pipe Models A3 - 33Restraints on a Bend at 45 Degrees A3 - 34

i


Restraints on a Bend at 30 and 60 Degrees A3 - 35Vertical Dummy Leg on Bends A3 - 36

Near/Far Point Method A3 - 36On Curvature Method A3 - 36Offset Element Method A3 - 36

Vertical Leg Attachment Angle A3 - 39Horizontal Dummy Leg on Bends A3 - 40Large Rotation Rods (Basic Model) A3 - 42Large Rotation Rods (Chain Supports) A3 - 44Large Rotation Rods (Spring Hangers) A3 - 45Large Rotation Rods (Constant Effort Hangers) A3 - 46Large Rotation Rods (Struts) A3 - 47Bilinear Restraints A3 - 47"Static" Snubbers A3 - 51Plastic Hinges A3 - 52Sway Brace Assemblies A3 - 53

�� General Information A4 - 2Simple Hanger Design A4 - 3Single Can Design A4 - 4Constant Effort Support Design A4 - 5Inputting Constant Effort Supports (No Design) A4 - 6Entering Existing Springs (No Design) A4 - 7Multiple Can Design A4 - 8Old Spring Redesign A4 - 9Pipe and Hanger Supported From Vessel A4 - 10Hanger Design with Support Thermal Movement A4 - 11Hanger Between Two Pipes A4 - 12Hanger Design with Anchors in the Vicinity A4 - 13Hanger Design with User-Specified Operating Load A4 - 14Spring Can Models with “Bottom-Out” and “Lift-Off” Capability A4 - 15Spring Hanger Model With Rods, “Bottom-Out,” and “Lift-Off” A4 - 19Simple "Bottomed-Out" Spring A4 - 23Modeling Spring Cans with Friction A4 - 24

�� Simple Bellows with Pressure Thrust A5 - 2Tied Bellows (Simple vs. Complex Model) A5 - 4Tied Bellows Expansion Joint (Simple Model) A5 - 6Tied Bellows Expansion Joint (Complex Model) A5 - 8Universal Expansion Joints (Simple Models) A5 - 10Universal Joint (Comprehensive Tie Rod) A5 - 16Universal Joint with Lateral Control Stops (Comprehensive Tie Rod Model) A5 - 17Hinged Joint A5 - 18

ii


Slotted Hinge Joint (Simple) A5 - 20Slotted Hinge Joint (Comprehensive) A5 - 21 Slip Joint A5 - 23Gimbal Joints A5 - 25Dual Gimbal A5 - 29Pressure-Balanced Tees and Elbows A5 - 31

�� Reducers A6 - 2Ball Joints A6 - 5Jacketed Pipe A6 - 6Cold Spring A6 - 8

�� ! �Example 1: Harmonic Analysis (TABLE) A7 - 2

Harmonic Analysis of this System A7 - 4Example 2: Relief Valve Loads (RELIEF) A7 - 7

CAESAR II Gas Thrust Load Calculations A7 - 9Relief Valve Example Problem Setup A7 - 10

Relief Valve Loading - Output Discussion A7 - 14Example 3: Dynamic Analysis of Water Hammer Loads (HAMMER) A7 - 20

Notes for Analyzing Water Hammer Loads A7 - 28Water Hammer Loading - Output Discussion A7 - 30

Mass Participation Report A7 - 30Displacement Report A7 - 30Restraint/Force/Stress Reports A7 - 30Combination Cases A7 - 30

Problem Solution A7 - 31Example 4:Dynamic Analysis of Independent Support Earthquake Excitation (CRYISM) A7 - 36

Cryogenic Piping Dynamics Example A7 - 36Discussion of Results A7 - 45

Example 5: Structural Analysis (FRAME) A7 - 47Example 6: Dynamic Analysis (NUREG9) A7 - 58

NRC Example NUREG9 A7 - 58Example 7: Omega Loop Modeling (OMEGA) A7 - 66Example 8: Jacketed Piping (JACKET) A7 - 72

Step 1 - Modeling Plan A7 - 73Step 2 - Layout of Nodes A7 - 73Step 3 - Input of Core Piping A7 - 75Step 4 - Input of Jacket, 1st Half A7 - 76Step 5 - Input of Jacket, 2nd Half A7 - 80

Example 9: WRC 107 A7 - 82Converting Forces/Moments in CAESAR II Global Coordinates to WRC 107 Local Axes A7 - 83

Example 10: NEMA SM23 A7 - 95NEMA Example PT69M A7 - 95Nozzle Results for PT69M A7 - 99

iii


Nozzle Load Summation Report A7 - 100

"��# �System Overview A8 - 2

Preparing the Drawing A8 - 3Generating CAESAR II Input A8 - 5Input Review A8 - 20Ending the Input Session A8 - 25Performing the Static Analysis A8 - 26

Reviewing the Static Results A8 - 29Static Analysis Output Listing A8 - 34

Conclusions A8 - 42

"��$ �Evaluating Pump Discharge Loads A9 - 2Creating a More Accurate Model A9 - 12Checking Nozzle Loads A9 - 22System Redesign A9 - 25Conclusion A9 - 34

iv

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Overview CAESAR II - Applications Guide

1-2 Introduction

OverviewThe CAESAR II Applications Guide is intended to serve as an example guide, showing the application of the CAESAR II program. Users should refer to this manual for exam-ples of specific piping components, as well as complete example jobs.

Chapters 2 through 6 of this manual illustrate the techniques and methods used to model individual piping components, restraints, and attached equipment. These chapters should be referenced often when modeling seldom-used components or unusual geometries. Users should recognize that the numeric data used in these examples is not necessarily applicable in all cases. In general, the numeric values used in these examples are fictitious quantities, unless otherwise noted.

Chapter 7 is a chapter of worked examples, illustrating the application of CAESAR II to various piping problems. These examples illustrate modeling, problem solving, and pro-gram operation.

Chapters 8 and 9 contain a tutorial that walks the user through the modeling and analysis of a complete system.

Users are urged to work through these chapters, especially if a particular analysis has never been previously attempted. The component modeling examples in Chapters 2 through 6 are especially useful, for both modeling techniques and general program under-standing. The examples in Chapter 7 also provide engineering guidelines and indicate where assumptions must be made in attempting to solve real-world problems.

Program Support / User AssistanceCOADE’s staff understands that CAESAR II is not only a complex analysis tool but also, at times, an elaborate process — one that may not be obvious to the casual user. While our documentation is intended to address the questions raised regarding piping analysis, sys-tem modeling, and results interpretation, not all the answers can be quickly found in these volumes.

COADE understands the engineer’s need to produce efficient, economical, and expedi-tious designs. To that end, COADE has a staff of helpful professionals ready to address any CAESAR II and piping issues raised by all users. CAESAR II support is available by telephone, facsimile, website discussion forum, and by e-mail; literally hundreds of sup-port calls are answered every week. COADE provides this service at no additional charge to the user. It is expected, however, that questions focus on the current version of the pro-gram.

Formal training in CAESAR II and pipe stress analysis is also available from COADE. For many years now, COADE has scheduled regular training classes in Houston and pro-vided in-house and open attendance training around the world. These courses focus on the expertise available at COADE—modeling, analysis, and design.

COADE Technical Support Contact InformationPhone: 281-890-4566 Fax: 281-890-3301

E-Mail: [email protected] WEB: www.coade.com

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Bend Definition CAESAR II - Applications Guide

Bend DefinitionBends are defined by the element entering the bend and the element leaving the bend. The actual bend curvature is always physically at the To end of the element entering the bend.

The input for the element leaving the bend must follow the element entering the bend. The bend angle is defined by these two elements.

Bend radius defaults to 1 1/2 times the pipe nominal diameter (long radius), but may be changed to any other value.

Specifying a bend automatically generates two additional intermediate nodes, at the 0-degree location and at the bend mid-point (M).

For stress and displacement output the To node of the element entering the bend is located geometrically at the far-point on the bend. The far-point is at the weldline of the bend, and adjacent to the straight element leaving the bend.

The 0-degree point on the bend is at the weldline of the bend, and adjacent to the straight element entering the bend.

The From point on the element is located at the 0-degree point of the bend (and no 0-degree node point will be generated) if the total length of the element as specified in the DX, DY, and DZ fields is equal to:

R tan (β / 2)

where β is the bend angle, and R is the bend radius of curvature to the bend cen-terline.

Nodes defined in the Angle and Node fields are placed at the given angle on the bend cur-vature. The angle starts with zero degrees at the near-point on the bend and goes to β degrees at the far-point of the bend.

Angles are always entered in degrees. Entering the letter "M" as the angle designates the bend midpoints.

2-2 Bends

CAESAR II - Applications Guide Bend Definition

Nodes on the bend curvature cannot be placed closer together than specified by the Mini-mum Angle to Adjacent Bend parameter in the Configure-Setup—Geometry section. This includes the spacing between the nodes on the bend curvature and the near and far-points of the bend.

The minimum and maximum total bend angle is specified by the Minimum Bend Angle and Maximum Bend Angle parameters in the Configure Setup—Geometry section.

Bends 2-3

Single and Double Flanged Bends or Stiffened Bends CAESAR II - Applications Guide

Single and Double Flanged Bends or Stiffened BendsSingle and double flanged bend specifications only effect the stress intensification and flexibility of the bend. There is no automatic rigid element (or change in weight) gener-ated for the end of the bend.

Single- and double-flanged bends are indicated by entering 1 or 2 (respectively) for Type in the bend auxiliary input. Rigid elements defined before or after the bend will not alter the bend’s stiffness or stress intensification factors.

When specifying single flanged bends it doesn’t matter which end of the bend the flange is on.

If the user wishes to include the weight of the rigid flange(s) at the bend ends, then he/she should put rigid elements (whose total length is the length of a flange pair) at the bend ends where the flange pairs exist.

As a guideline, British Standard 806 recommends stiffening the bends whenever a compo-nent that significantly stiffens the pipe cross section is found within two diameters of either bend end.

2-4 Bends

CAESAR II - Applications Guide Single and Double Flanged Bends or Stiffened Bends

The flanges in the figures below are modelled only to the extent that they effect the stiff-ness and the stress intensification for the bends.

Example: Flanged Bends

Bends 2-5

180 Degree Return (Fitting-To-Fitting 90 Deg. Bends) CAESAR II - Applications Guide

180 Degree Return (Fitting-To-Fitting 90 Deg. Bends)Two 90-degree bends should be separated by twice the bend radius.

The far-point of the first bend is the same as the near-point of the second (following) bend.

The user is recommended to put nodes at the mid point of each bend comprising the 180 degree return. (See the example below.)

Example: 180-degree Bend

2-6 Bends

CAESAR II - Applications Guide Mitered Bends

Mitered BendsEvenly spaced mitered bends, whether closely or widely spaced, are uniquely defined by two parameters:

• Number of cuts (changes in direction)

• Equivalent radius <or> miter spacing.

For closely spaced miters the equivalent radius is equal to the code defined “R1” for B31.3 and “R” for B31.1. The equation relating the equivalent radius to the spacing for evenly spaced miters is:

Req = S / [ 2 tan(θ) ]

where:

Req -equivalent miter bend radius

S -spacing of the miter cuts along the centerline

θ -code defined half-angle between adjacent miter cuts:

θ = α / 2N

where:

α - total bend angle

N - number of cuts

An additional parameter B (length of miter segment at crotch) is checked for closely spaced miters when using B31.1. B may be found for evenly spaced miters from:

B = S [ 1 - ro / Req ]

where:

ro - outside radius of pipe cross-section.

Bends 2-7

Closely Spaced Mitered Bend CAESAR II - Applications Guide

Closely Spaced Mitered BendMiter bends are closely spaced if:

S < r [ 1 + tan (θ) ]

where:

S - miter spacing

r - average pipe cross section radius: (ri+ro)/2

θ -one-half the angle between adjacent miter cuts.

B31.1 has the additional requirements that:

B > 6 tn

θ ≤ 22.5 deg.

B- length of the miter segment at the crotch.

tn- nominal wall thickness of pipe.

Closely spaced miters regardless of the number of miter cuts may be entered as a single bend. CAESAR II will always calculate the spacing from the bend radius. If the user has the miter spacing and not the bend radius, the radius must be calculated as shown above.

The mitered bend shown below has 4 cuts and a spacing of 15.913 in.

Req = S / [ 2 tan (θ) ]

θ = α / 2N

= 90 / [2(4)]

= 11.25 deg.

Req = 15.913 / [2 tan (11.25 deg.)]

= 40

2-8 Bends

CAESAR II - Applications Guide Closely Spaced Mitered Bend

Example: Closely spaced miter bend.

Bends 2-9

Widely Spaced Mitered Bend CAESAR II - Applications Guide

Widely Spaced Mitered BendMitered bends are widely spaced if:

S ≥ r * [1 + tan (θ)]

S - spacing between miter points along the miter segment centerline.

r - average cross section radius. (ri+ro)/2

θ - one-half angle between adjacent miter cuts.

B31.1 has the additional requirement that:

θ ≤ 22.5 deg.

In CAESAR II, widely spaced miters must be entered as individual, single cut miters, each having a bend radius equal to:

R = r [1 + cot (θ)] / 2

R - reduced bend radius for widely spaced miters.

During error checking, CAESAR II will produce a warning message for each mitered component which does not pass the test for a closely spaced miter. These components should be re-entered as a group of single cut joints.

2-10 Bends

CAESAR II - Applications Guide Widely Spaced Mitered Bend

Calculate the coordinates to get from the tangent intersecting point of the single cut miter bend at node 10 to the single cut miter bend at node 15.

∆

Example: Widely Spaced Miter

Pipe O.D. = 10.375 in.

Pipe Thk. = 0.500 in.

Bend angle = 90 deg.

Cuts = 2

Req = 45 in.

Assuming closely spaced:

θ = a / 2N = 90 / (2 * 2) = 22.5 deg.

r = [10.3750 - .5] / 2 = 4.9375

S = Req [2 tan(θ)] = 45(2) tan(90/4) = 37.279Find that 37.279 > 6.9826 (Check the Closely Spaced Miter requirements).

The bend is widely spaced. The reduced miter bend radius is needed to define widely spaced bends in CAESAR II.

Rr 1 θcot+[ ]

2---------------------------- 8.4288″= =

g=37.279 sin 45 deg

Bends 2-11

Widely Spaced Mitered Bend CAESAR II - Applications Guide

Example: Widely Spaced Miter ...Continued

Input widely spaced miters as individual straight pipe elements, with bends specified, having one miter cut.

Input for element from Node 5 to Node 10.



2-12 Bends

CAESAR II - Applications Guide Elbows - Different Wall Thickness

Elbows - Different Wall ThicknessWhen the fitting thickness in the bend auxiliary field is input, CAESAR II changes the thickness of the curved portion of the bend element only. The thickness of any preceding or following straight pipe is unaffected.

The specified fitting thickness applies for the current elbow only and is not carried on to any subsequent elbows in the job.

Stresses at the elbow are calculated based on the section modulus of the matching pipe as specified in the B31 codes. However, stress intensification factors and flexibility factors for the bend are based on the elbow wall thickness.

The elbow at 10 has a thickness larger than the matching pipe wall. The matching pipe has a thickness of 0.5.

Example: Thick Elbow

Bends 2-13

Bend Flexibility Factor CAESAR II - Applications Guide

Bend Flexibility FactorNormally bend flexibility factors are calculated according to code requirements. However, the user may override the code calculation by entering a value in the K-factor field. For example, if the user enters 1.5 in this field, the bend will be 1.5 times as flexible as a straight pipe of the same length.

2-14 Bends

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Anchors CAESAR II - Applications Guide

AnchorsThe following are general guidelines and information concerning anchors:

• The anchor default stiffness for translational and rotational degrees of freedom is defined in the Configuration file.

• Connecting nodes can be used with anchors to rigidly fix one point in the piping sys-tem to any other point in the piping system.

• Entries in the Stif field apply to all 6 anchor degrees of freedom.• Displacements should not be specified at an anchor. If the displacements of a particu-

lar point are known, they should be input directly without any additional restraints or anchors.

• Accurate input of the piping boundary conditions (i.e. restraints) is probably the single most important part of system modeling, requiring experience both with piping fabri-cation and erection, and with CAESAR II.

The first group of examples illustrates a large number of boundary condition applications and their proper modeling using CAESAR II.

0101-C2ARigid anchor input

Nozzle connection modeled as anchor

Example: Rigid Anchor at Node 5

3-2 Restraints

CAESAR II - Applications Guide Anchors with Displacements

Anchors with DisplacementsFollow these general guidelines to model anchors with displacements:

• Enter only displacements for the node.• Do not specify restraints or anchors at the node to be displaced.• For anchors with displacements, make sure all 6 degrees of freedom at the node are

defined.

Note Degrees of freedom not defined (left blank) in any displacement vector are assumed to be free in all load cases.

Up to 9 different displacement vectors (i.e., D1...D9) may be defined.

Non-zero displacements are usually part of the thermal expansion effects and, if so, should normally be added into any analysis case containing the corresponding thermal, i.e. W+P1+T1+D1. The CAESAR II recommended load cases do this automatically.

The translations and/or rotations for any nodal degree of freedom having displacements specified in any displacement vector will be zero for load cases not containing that vector as part of the load case identification, and the specified non-zero value for load cases con-taining the vector as part of the load case identification. For instance, defined displace-ments are used if the load case is W+P1+T1+D1 (OPE) and those displacements are held to zero if the load case is W+P1 (SUS).

Restraints 3-3

Anchors with Displacements CAESAR II - Applications Guide

Once a degree of freedom has been fixed in one displacement vector, it cannot be free in another displacement vector at the same node (leaving a displacement field blank will default to zero in this case).

0102-C2A

Predefined displacements on an anchor

Anchor displacement input

Example: Anchor with Predefined Displacements

3-4 Restraints

CAESAR II - Applications Guide Flexible Anchors

Flexible AnchorsFollow these guidelines to model flexible anchors:

• Use six flexible restraints.• Put four restraints on one spreadsheet and the last two restraints on the next element

spreadsheet.• See the following flexible nozzle examples to improve modeling methods for intersec-

tions of this type.

Example: Flexible Restraints for Nozzle and Shell

0103-C2A

Restraints 3-5

Flexible Anchors with Predefined Displacements CAESAR II - Applications Guide

Flexible Anchors with Predefined DisplacementsTo model flexible anchors with predefined displacements, implement the following requirements:

• Use six flexible restraints.• Put four restraints on one spreadsheet and the last two restraints on the next element

spreadsheet.• Define a unique connecting node (CNode), at each of the six restraints. All six

restraints should have the same connecting node.• Specify the displacements at the connecting node.

Example: Flexible Anchor with Predefined Displacements

0104-C2A

The connecting node here is 1005. Connect-ing node numbers may be selected at the user’s convenience, but must be unique.

3-6 Restraints

CAESAR II - Applications Guide Flexible Anchors with Predefined Displacements

Restraints 3-7

Flexible Nozzle (WRC Bulletin 297) CAESAR II - Applications Guide

Flexible Nozzle (WRC Bulletin 297)Adhere to these requirements when modeling flexible nozzles:

• Frame only one pipe element into the nozzle node.• Do not place restraints at the nozzle node.• Do not place anchors at the nozzle node.• Do not specify displacements for the nozzle node. (See the following example for dis-

placements at flexible nozzles.)

CAESAR II automatically performs the following functions:

• calculates nozzle flexibilities for the nozzle/vessel data entered by the user • calculates and inserts restraints to simulate the nozzle flexibilities• calculates flexibilities for the axial translations, circumferential, and longitudinal

bending

The user must perform the error check process to view these calculated values.

CAESAR II uses the following criteria for its calculations:

• Shear and torsional stiffnesses are assumed rigid.• Nozzle configurations outside of the WRC 297 curve limits are considered rigid. It is

not unusual for one stiffness value to be rigid because of curve limits, and the others to be suitably flexible.

• The vessel temperature and material fields on the WRC 297 auxiliary data area may be used to optionally compute a reduced modulus of elasticity for the local stiffness calculations.

3-8 Restraints

CAESAR II - Applications Guide Flexible Nozzle (WRC Bulletin 297)

Example: Schematic of Nozzle and Vessel to be Modeled with WRC 297

0105-C2A

Restraints 3-9


0105-C2A

Figure 1-5b—WRC297 input for example

Figure 1-5c—WRC297 output for example

3-10 Restraints


Flexible Nozzle with Predefined Displacements

Follow these guidelines to model flexible nozzles with predefined displacements (WRC 297):

• Define a unique vessel node on the Nozzle spreadsheet.• Apply the predefined displacements to the vessel node.

Note These displacements can be given on any element spreadsheet (the displacement node does not need to be on an element that defines it).

The CAESAR II generated nozzle/vessel flexibilities will be inserted in restraints that act between the nozzle node and the vessel node.

Example: Flexible Nozzle with Predefined Displacements

Displacements defined on vessel node

Restraints 3-11


Flexible Nozzle with Complete Vessel Model

Follow these guidelines for modeling a flexible nozzle that includes a complete vessel:

• Define a unique vessel node on the Nozzle Spreadsheet. • Run a rigid element between the vessel node defined on the Nozzle Spreadsheet and

the centerline of the vessel. The outside diameter of the rigid element should be approximately equal to the outside diameter of the vessel. The weight of the rigid ele-ment should be zero.

• Model the actual vessel length using pipe elements. The vessel diameter and wall thicknesses should be modeled as accurately as possible

• Use an anchor to model the vessel anchorage point.

The CAESAR II generated nozzle/vessel flexibilities will be inserted between the nozzle node and the vessel node.

3-12 Restraints


0107-C2A

Example: Full WRC 297 Model Schematic

Restraints 3-13


Pipe entering nozzle WRC 297 auxiliary input

Example: Full WRC 297 and Vessel Model

0107-C2A

3-14 Restraints


Example (continued): Full WRC 297 and Vessel Model

Rigid weight is blank (0.0)

Vessel element

Vessel skirt element

0107-C2A

Rigid element specification for vessel radius

Restraints 3-15


WRC 297 results found at end of error checking

3-16 Restraints

CAESAR II - Applications Guide Double-Acting Restraints

Double-Acting RestraintsDouble-acting restraints are those that act in both directions along the line of action. Most commonly used restraints are double-acting.

CNode is the connecting node. If left blank then the restrained node is connected via the restraint stiffness to a rigid point in space. If CNode is entered then the restrained node is connected via the restraint stiffness to the connecting node.

If a gap is specified, it is the amount of free movement along the positive or negative line of action of the restraint before resistance to movement occurs. A gap is a length, and so is always positive.

Double-Acting Restraints (Translational)

Restraint acts along both the positive and negative directions.

Friction at double-acting restraints acts orthogonally to the line of action of the restraint.

Example: Double-Acting Restraint at Node 55 in the Z Direction

Schematic Input

0108-C2A

Restraints 3-17

Double-Acting Restraints CAESAR II - Applications Guide

Double-Acting Restraint (Rotational)

Behavior is similar to double-acting translational restraints.

Friction is not defined for rotational restraints.

Example: Hinged-End Rod Free to Rotate about Z-Axis

Four restraints on element spreadsheet con-taining node 105 and remaining restraint on next spreadsheet.

0109-C2A

3-18 Restraints

CAESAR II - Applications Guide Single-Directional Restraints

Single-Directional RestraintsThe following are some important facts pertaining to single-directional restraints:

• The sign on the single-directional restraint gives the direction of “free” movement; that is, a +Y restraint may move freely in the positive Y direction and will be restrained against movement in the negative Y direction.

• Single-directional restraints may define restraint along positive, negative, or skewed axes.

• Any number of single-directional restraints may act along the same line of action. (If more than one single directional restraint acts along the same line of action, then there are usually two in opposite directions and they are used to model unequal leg gaps.)

• CNode is the connecting node. If left blank then the restrained node is connected via the restraint stiffness to a rigid point in space. If CNode is entered then the restrained node is connected via the restraint stiffness to the connecting node.

• Friction and gaps may be specified with single-directional restraints.

Example: Rigid Single-Directional Restraint in Y at Node 20

The sign on the restraint gives the direc-tion of "free" movement. Since the stiff-ness is omitted, the restraint will be rigid.

0111-C2A

Restraints 3-19

Guides CAESAR II - Applications Guide

GuidesThe following are some important facts pertaining to Guides in CAESAR II.

• Guides are double-acting restraints with or without a specified gap. • Connecting Nodes (CNode) can be used with guides.• Guides may be defined using the global system coordinates or with the restraint type

GUI.• A "guided" pipe in the horizontal or skewed direction will have a single restraint, act-

ing in the horizontal plane, orthogonal to the axis of the pipe.• A “guided” vertical pipe will have both X and Z direction supports.• Direction cosines for guides are computed by CAESAR II. Guide direction cosines

entered by the user are ignored.

Example: Guide on Horizontal Pipe with Single Directional Restraint

Node 25 is guided in Z with a gap of 2.5 in. A single-directional restraint in the Y direction also exists. Both restraints are rigid.

0112-C2A

Note: Replacing the Guide restraint type is the same thing as replacing the Z restraint type.

3-20 Restraints

CAESAR II - Applications Guide Guides

Example: Guided Pipe in Both Horizontal and Vertical Directions

0113-C2A

Restraints 3-21

Limit Stops CAESAR II - Applications Guide

Limit StopsThe following are important facts pertaining to Limit Stops:

• Limit Stops are single- or double-acting restraints whose line of action is along the axis of the pipe.

• The sign on the single-directional restraint gives the direction of unlimited free move-ment.

• Limit Stops/Single Directional Restraints can have gaps. The gap is the distance of permitted free movement along the restraining line of action.

• A gap is a length, and is always positive. Orientation of the gap along the line of action of the restraint is accomplished via the sign on the restraint.

• Connecting Nodes (CNode) may be used with any Limit Stop model.• Limit stops may be defined using the restraint type LIM.• Limit Stops provide double or single-acting support parallel to the pipe axis. Limit

Stops may have gaps and friction. The positive line of action of the Limit Stop is defined by the From and To node on the element.

• Direction cosines for orthogonal or skewed limit stops are computed by CAESAR II. Limit Stop direction cosines entered by the user are ignored.

0115-C2A

Example: Directional Limit Stop with a Gap

3-22 Restraints

CAESAR II - Applications Guide Limit Stops

Restraints 3-23

The stop at 195 permits unlimited free move-ment in the minus X direction, and 1.0 in. of free movement in the plus X direction before the Limit Stop becomes active.

The stop at 45 permits unlimited free movement in the plus X direc-tion, and 1.0 in. of free movement in the minus X direction before the Limit Stop becomes active.

Example: Two Limit Stops that Act in Opposite Directions

0114-C2A

Windows CAESAR II - Applications Guide

WindowsKeep in mind the following facts when modeling Windows in CAESAR II.

• Equal leg windows are modeled using two double-acting restraints with gaps orthogo-nal to the pipe axis.

• Unequal leg windows are modeled using four single-acting restraints with gaps orthogonal to the pipe axis. (See the following example.)

• The gap is always positive. The direction of movement before the gap closes is deter-mined by the sign on the restraint. If there is no sign, then the restraint is double-acting and the gap exists on both sides of the line of action of the restraint. If there is a sign on the restraint then the gap exists on the “restrained” line of action of the restraint, i.e. a +Y restraint is restrained against movement in the -Y direction, and any gap associ-ated with a +Y restraint is the free movement in the -Y direction before the restraint begins acting.

Example: Window Modeled with Four Single Directional Restraints with Gaps

0116-C2A

3-24 Restraints

CAESAR II - Applications Guide Rotational Directional Restraints with Gaps

Rotational Directional Restraints with Gaps These restraints can be considered specialty items and are typically only used in sophisti-cated expansion joint or hinge models.

Example: Rotational Restraints

Allowable rotation of 5 degrees in either direc-tion about the z-axis before resistance to rota-tion is encountered.

Hinge assembly at node 50 can rotate relative to assembly at node 55 only in the positive direction about the z-axis.

Bi-directional rotational restraint with gap

Hinge assembly with directional rotational restraint

0117-C2A

Restraints 3-25

Single-Directional Restraint with Predefined Displacement CAESAR II - Applications Guide

Single-Directional Restraint with Predefined DisplacementDefine the one-directional restraint as usual, and enter a unique node number in the CNode field. Specify the predefined displacements for the CNode.

Example: Single-Directional Restraint with Predefined

Piping at node 55 rests on top of the restraint that is displaced in the y-direction (node 1055).

1018-C2A

3-26 Restraints

CAESAR II - Applications Guide Single-Directional Restraint and Guide

Single-Directional Restraint and Guide with Gap and Predefined Displacement

Define the single-directional restraint and guide as usual. Put a unique node number in the CNode field for the single-directional restraint and the guide. The same unique node num-ber should be entered in both CNode fields. Specify the predefined displacements for the CNode.

Guided piping at mode 70 rests on a struc-tural member (node 1070). The structure undergoes a predefined displacement.

Example: Guide Plus Single-Directional Restraint with Predetermined Displacement

0119-C2A

Restraints 3-27

Restraint Settlement CAESAR II - Applications Guide

Restraint SettlementKeep in mind the following facts when modeling restraint settlements:

• Model using a single-directional restraint with predefined displacements. The magni-tude of the predefined displacement is the amount of anticipated settlement in the minus Y direction.

• The Displacement Load Case is used to include the effect of the settlement (non ther-mal).

• The settlement displacements are prescribed for the connecting node at the single directional restraint. (Refer to single-directional Restraint with Predefined Displace-ment.)

Example: Settlement of a Restraint

The weight of this pipe at node 95 exerts a sufficient load on the foundation (node 1095) to cause a calculated.325-in. set-tlement.

0120-C2A

3-28 Restraints

CAESAR II - Applications Guide Skewed Double-Acting Restraint

Skewed Double-Acting RestraintThe following are some important considerations for modeling skewed restraints:

• Direction vectors or direction cosines can be used to define the line of action of the restraint. If direction vectors are used, CAESAR II will immediately convert them to direction cosines.

• Direction cosines may be quickly checked in the graphics processor. • Any translational axis can be used in the restraint description. The “redefinition” of

the axis does not affect any other restraint description for the element.• Particular attention should be paid to skewed direction input data. A common mistake

is to specify an axial instead of transverse restraint when modeling a skewed guide. Plotted section views of the restrained nodes can be an extremely useful check of the skewed direction specification.

• The sense of the direction or cosine unit vector is unimportant. In the definition of double-acting restraints, the direction vector and cosines are only used to define the restraint line of action and are not concerned with a direction along that line.

• A simple rule can be used for finding perpendicular, skewed, direction vectors. The restraint is to be perpendicular to the pipe. If the pipe has skewed delta dimensions DX and DZ, the perpendicular restraint directions vector will be (-DZ, 0, DX).

0121-C2A

Example: Skewed Double-Acting Restraint with Gap

Z

Restraints 3-29

Skewed Double-Acting Restraint CAESAR II - Applications Guide

Example (continued): Skewed Double-Acting Restraint with Gap

Input using unit direction vectors

Input using direction cosines

Input using perpendicular vector

Input using guide restraint type

0121-C2A

3-30 Restraints

CAESAR II - Applications Guide Skewed Single-Directional Restraint

Skewed Single-Directional RestraintThe following are some important considerations regarding skewed single-directional restraints:

• Skewed restraints may be nonlinear.• Direction vectors or direction cosines may be used to define the line of action of the

restraint. If direction vectors are used CAESAR II will immediately convert them to direction cosines.

• The direction of the cosines or the direction vector is along the positive line of action of the (+) restraint. (See the figure for clarification.)

• Direction cosines may be quickly checked in the graphics processor.• Connecting nodes (CNode) can be used with any skewed single-directional restraint.

0122-C2A

Example: Skewed Single-Directional Restraint

Restraints 3-31

Restraint Between Two Pipes (Use of CNodes) CAESAR II - Applications Guide

Restraint Between Two Pipes (Use of CNodes)

Note For these two examples, the directive Connect Geometry Through CNodes must be turned off to avoid plotting and geometry errors.

Nonlinear or linear restraints can act between two different pipe nodes. The Cnode effec-tively represents what the "other end of the restraint" is attached to.

0124-C2A

Example: Nonlinear Restraint Between Two Pipes

Saddle modeled as a + y restraint

3-32 Restraints

CAESAR II - Applications Guide Restraint Between Vessel and Pipe Models

Restraint Between Vessel and Pipe ModelsThe following are some important facts that pertain to restraints’ acting between vessel and pipe:

• Use a restraint with connecting node to link the pipe to the rigid element extending from the vessel shell.

• Any number of restraints may be specified between the restrained node and the con-necting node.

• Restraints may be linear or nonlinear with gaps and/or friction.

Example: Restraint Between Vessel and Piping

0125-C2A

The "far point" of the elbow at node 20 is linked, via the restraint, to the structural attachment point at 185.

Restraints 3-33

Restraints on a Bend at 45 Degrees CAESAR II - Applications Guide

Restraints on a Bend at 45 DegreesLinear and/or non-linear restraints can act at any point on the bend curvature. Points on the bend curvature are like any other point in the piping system.

The following figure shows a bend supported vertically by a rigid rod. The rod will be allowed to take tensile loads only and so will be modeled as a single directional restraint that can move freely in the +Y direction. (See the Chapter on "Bends" if the actual posi-tions of the nodes 19 and 20 are not clear.)

The line of action of the rod is really shifted away from the node 19. Note that a downward force at node 15 will produce a positive Z moment about 20 in the system as modeled, and a negative Z moment about the point 20 in real life.

The magnitude of this moment is a function of the load and the moment area (the amount of the shift). If this is considered significant, then a rigid element with zero weight could be placed between node 19 and the actual point of rod attachment. The restraint would then be placed at the actual point of rod attachment.

Example: 90-Degree Bend Restrained at Midpoint

0126-C2A

3-34 Restraints

CAESAR II - Applications Guide Restraints on a Bend at 45 Degrees

Restraints on a Bend at 30 and 60 Degrees

Up to three (3) nodes can be defined at any angle on the bend curvature so long as the points are more than five degrees apart. Restraints may be modeled on any of these nodes. If necessary one of these points can be at the zero degree point on the bend. The zero degree point on a bend is the bend “near” point.

The To node of the bend is placed at the tangent intersection point for geometric construc-tion but is placed at the bend "far" point for analysis purposes. Therefore, specifying a node at the bend far-weld point will generate an error.

Nodes and angles on the bend curvature can be specified in any order.

Example: Restraints on Intermediate Points Along a Bend

0127-C2A

Restraints 3-35

Vertical Dummy Leg on Bends CAESAR II - Applications Guide

Vertical Dummy Leg on BendsDummy legs on bends can be modeled several ways. The three most common methods used to model dummy legs are outlined below:

Near/Far Point Method• Easy input• Dummy leg acts along centerline of vertical run • Dummy leg does not act at the proper place on the bend curvature

On Curvature Method• Easy input• Dummy leg acts at the proper place on the bend curvature • Dummy leg does not act along the centerline of the vertical run

Offset Element Method• Difficult input• Dummy leg acts at the proper place on the bend curvature • Dummy leg acts along centerline of vertical run

The element immediately after the bend must define the downstream side of the bend. Do not define dummy legs on the element spreadsheet immediately following the bend speci-fication spreadsheet.

Dummy legs and/or any other elements attached to the bend curvature should be coded to the bend tangent intersection point. The length of the dummy leg will be taken directly from the DX, DY, and DZ fields on the dummy leg’s pipe spreadsheet. There will be no automatic alteration of the dummy leg length due to the difference between the bend tan-gent intersection point and the actual point on the bend curvature where the dummy leg acts. The true length of the dummy leg should be input in the DX, DY, and DZ fields on the dummy leg element spreadsheet.

Input and output plots of the dummy leg always show it going to the bend tangent intersec-tion point.

3-36 Restraints

CAESAR II - Applications Guide Vertical Dummy Leg on Bends

For each dummy leg/bend model a warning message is generated during error checking. The user should make sure that the warning message description of the bend is accurate.

The bend shown is entered from the top left corner of the control station (nodes 80 to 85), and exits horizon-tally to the right (nodes 85 to 90). The dummy leg is attached at the 45-degree point on the bend, and the centerline of the dummy leg should line up with the centerline of the vertical run of pipe entering the bend (node 80 to 85).

0128-C2A

Example: Vertical Dummy Leg on Bend

α

Restraints 3-37

Vertical Dummy Leg on Bends CAESAR II - Applications Guide

Example (continued): Dummy Leg on Bend

0128-C2AOffset element method

On curvature method

Near point method

3-38 Restraints

CAESAR II - Applications Guide Vertical Leg Attachment Angle

Vertical Leg Attachment Angle

0129-C2A

Example: Dummy Leg Attachment Angle Calculation

Restraints 3-39

Horizontal Dummy Leg on Bends CAESAR II - Applications Guide

Horizontal Dummy Leg on BendsThe element leaving the bend must define the downstream side of the bend. Do not define dummy legs on the element spreadsheet immediately following the bend specification spreadsheet.

The true length of the dummy leg should be input in the DX, DY, and DZ fields on the dummy leg pipe spreadsheet.

Input and output plots of the dummy leg always show the dummy leg going to the bend tangent intersection point.

For each dummy leg/bend model a warning message is generated during error checking. The user should make sure that the warning message description of the dummy leg is accurate.

Dummy leg is defined as a zero-weight rigid supported on one end by a spring can.

0129-C2A

Example: Horizontal Dummy Leg on Midpoint of Bend

3-40 Restraints

CAESAR II - Applications Guide Horizontal Dummy Leg on Bends

0129-C2A

Example: Node Position Definition for Points on the Bend Curvature

Restraints 3-41

Large Rotation Rods (Basic Model) CAESAR II - Applications Guide

Large Rotation Rods (Basic Model)Large rotation rods are used to model relatively short rods, where large orthogonal move-ment of the pipe causes shortening of the restraint along the original line of action.

Large rotation rods can be entered in any direction. The user picks the XROD, YROD, or ZROD from the type list. When CAESAR II detects that a rod is being input, the restraint field is changed: Gap is changed to Len and Mu is changed to Fi. Len is the length of large rotation swing. Fi is the initial load on the restraint if used to model a variable sup-port spring hanger. (See some of the later rod examples.) The user can imagine the large rotation rod as providing a “bowl” in which the pipe node is free to move.

Large rotation rods should only be entered where needed. Repeated use where not neces-sary may cause the system to become unstable during the nonlinear iteration. The system should first be analyzed without the large rotation rods, then large rotation rods added where horizontal movement at support points is greatest. Usually only one rod should be added in an area at a time.

The rod angle tolerance is currently set at 1.0 degree.

Large rotation is generally considered to become significant when the angle of swing becomes greater than 5 degrees.

Connecting nodes may be used for large rotation rods just like for any other support. Graphically, the connecting nodes and the restraint node do not have to be at the same point in space. There is no plot connectivity forced between large rotation rod nodes and connecting nodes.

The signs on the large rotation rod are significant and determine the orientation of the swing axis. A +YROD is equivalent to a YROD and indicates that the concave side of the curvature is in the positive Y direction.

0129g-C2A

3-42 Restraints

CAESAR II - Applications Guide Large Rotation Rods (Basic Model)

In the example below, the rod pivots about the structural steel support. There is a very short swing arm, and so even a small amount of horizontal movement will produce a rela-tively large swing. In the output report for this restraint, the user will see X and Y direction loads.

Example: Large Rotation Rod

0129-C2A

Restraints 3-43

Large Rotation Rods (Chain Supports) CAESAR II - Applications Guide

Large Rotation Rods (Chain Supports)See the Large Rotation (Basic Model) example for a discussion of large rotation rod fun-damentals.

In the model below, the user wants the large rotation swing only in the plane of the chain support (the Y-Z plane). The two pipes should move freely relative to each other in the axial direction (the Y-X plane). Three restraints with connecting nodes are used. The first is the large rotation rod with its connecting node, which in turn is connected to the second and third linear restraints that allow only Y-Z interaction between the large rotation rod connecting node and the top pipe node.

0130-C2A

Example: Chain Support

3-44 Restraints

CAESAR II - Applications Guide Large Rotation Rods (Spring Hangers)

Large Rotation Rods (Spring Hangers)See the Large Rotation (Basic Model) example for a discussion of large rotation rod fun-damentals.

The Stif, Len, and Fi fields must be filled in to model large rotation variable springs. CAESAR II will design a spring at a location where the user suspects that large rotation will be a factor, but once the spring has been designed, the user must transfer the spring design data into large rotation restraint data. (The spring design algorithm will not include large rotation effects in a to-be-designed spring.)

Springs can be particularly susceptible to the large rotation effect because they are often pulled along horizontally rather than through the large rotation arc. This direct horizontal movement can cause considerable extension of the spring, changing the spring load and possibly even causing bottoming out of the spring. CAESAR II properly calculates this change in the spring load and its direction of application. The user must, however, make sure that the spring stays within the design limits. (This is not difficult to do. The maxi-mum computed load on the spring is compared to the manufacturer’s load limits).

Large rotation variable support spring hanger models can be used with or without connect-ing nodes.

Steam line hangers are particularly susceptible to large rotation because they typically experience large horizontal movement, and tend to pull the hanger along with the pipe.

In the following example, the pipe movement, if it follows the path from A to B, will change the line of action of the spring force, but not significantly alter the spring load. If the pipe “pulls” the hanger along in the horizontal plane along the path from A to C, both the line of action of the spring force and the magnitude of the spring load can change. It is this type of “pulling along” that is potentially the most dangerous to the spring.

0130-C2A

Example: Spring Modeled as Large Rotation Rod

Restraints 3-45

Large Rotation Rods (Constant Effort Hangers) CAESAR II - Applications Guide

Large Rotation Rods (Constant Effort Hangers)See the Large Rotation (Basic Model) example for a discussion of large rotation rod fun-damentals.

To model large rotation constant effort springs, the Stif, Len, and Fi fields must be filled in. CAESAR II will design constant effort supports at a location where the user suspects that large rotation will be a factor, but once the spring has been designed, the user must transfer the hot load data into large rotation restraint data. (The spring design algorithm will not include large rotation effects in a to-be-designed spring. Remember that constant effort springs are designed by CAESAR II by specifying a very small maximum allowed travel limit on the spring hanger design spreadsheet).

Constant effort support large rotation spring models are built just like the variable support model, except that the spring stiffness is set to some small number. The piping system must be very stable with respect to these hangers.

Springs can be particularly susceptible to the large rotation effect because they are often pulled along horizontally rather than through the large rotation arc. This direct horizontal movement can cause considerable extension of the spring, possibly bottoming it out. The user must make sure that bottoming out does not occur.

Large rotation constant effort spring hanger models can be used with or without connect-ing nodes.

Steam line hangers are particularly susceptible to large rotation because they typically experience large horizontal movement, and tend to pull the hanger along with the pipe.

For English units a spring stiffness of 1 lb./in. is usually a suitably small spring stiffness. The design load for the constant effort support is 2,334 lb. The spring is at node 105.

0131-C2A

3-46 Restraints

CAESAR II - Applications Guide Large Rotation Rods (Struts)

Large Rotation Rods (Struts)See the Large Rotation (Basic Model) example for a discussion of large rotation rod fun-damentals.

For the example problem shown on the next page, the amount the rods pulls up on the sys-tem as a result of the large rotation effect, is important, because a large axial load can be produced for a very small vertical movement.

Note The lengths for Len are always positive. The sign, or orientation of the swing, is given by the sign in the Type field.

Bilinear RestraintsBilinear restraints have the digit 2 following the direction in the restraint TYPE field.

When a bilinear spring is entered the restraint fields change as follows: Stif changes to K1, which is the Initial Stiffness, Gap changes to K2, which is the Yield Stiffness, and Mu changes to Fy, which is the Yield Load.

Bilinear restraints are used most often to model soil support where some soil ultimate load bearing capacity can be calculated.

Both the yield stiffness (K2) and the yield load (Fy) are required entries. The initial stiff-ness (K1) may be left blank, and a rigid initial stiffness assumed. The yield stiffness may be negative if necessary. Some subsea pipeline resistance tests have shown that load carry-ing capacity drops after the “ultimate” load is reached, and displacement continues.

More detailed use of these spring types to model underground piping systems is illustrated in the Underground Pipe Modeler chapter.

Restraints 3-47

Bilinear Restraints CAESAR II - Applications Guide

0132-C2A

Example: Strut Modeled as Large-Rotation Rod

The cumulative gap that is assumed to exist between the rod ends and the clamp, etc., is 1/4 in.

3-48 Restraints

CAESAR II - Applications Guide Bilinear Restraints

0133-C2A

Example: Characteristics of Bi-Linear Supports

Restraints 3-49

Bilinear Restraints CAESAR II - Applications Guide

Example: Pipe in a Trench--Bi-Linear Restraint Modeling

0134-C2A

3-50 Restraints

CAESAR II - Applications Guide "Static" Snubbers

"Static" Snubbers "Static" snubbers (or static analysis snubbers) have SNB following a translational direc-tion in the restraint Type field.

When a snubber is entered, the restraint fields change as follows: Gap and Mu are dis-abled.

Static snubbers are translational restraints that provide resistance to displacement in static analysis of occasional loads only. It is assumed that this occasional loading is dynamic in nature, such as a static seismic, or static wind loading. THESE SNUBBERS ARE INAC-TIVE FOR ALL EXPANSION, SUSTAINED, AND OPERATING STATIC CASES, AND ARE ACTIVE FOR ALL TYPES OF TRUE DYNAMIC ANALYSES, i.e. HAR-MONIC, MODAL, OR SPECTRAL. These restraints are active in all static load cases defined as OCCasional in the load case list.

Static snubbers may be directional, i.e. may be preceded by a plus or minus sign.

Restraints 3-51

Plastic Hinges CAESAR II - Applications Guide

Plastic HingesThe steps in setting up a plastic hinge are illustrated below. The leg from A to B is over-heated, causing bending of the B-D support leg. This example models the plastic deforma-tion at cross-section E-E. The plastic hinge is formed between the nodes 10 and 15. The expansion joint is used to provide translational and torsional rigidity at the plastic hinge junction. Two bi-linear supports are used to model rigid resistance to bending until a breakaway force (yield force) is exceeded at which point bending is essentially free.

Example: Plastic Hinge in Support Leg *

Expansion joint element is zero length

The yield force is determined from

Fy = SyZ(SF)

where:

Sy is the Yield Stress

Z is the section modulus

SF is the safety factor

* The plastic hinge modeled as a zero length expansion joint with rotational bi-linear restraints.

0110-C2A

3-52 Restraints

CAESAR II - Applications Guide Sway Brace Assemblies

Sway Brace AssembliesThe sway brace is commonly used to allow unrestrained thermal movements while “tun-ing” the system dynamically to eliminate vibration. In this respect sway brace resembles a spring: it may be pre-loaded in the cold (installed) position, so that after thermal pipe growth it reaches the neutral position and the load on the system in the operating condition is zero or negligible.

The sway brace is composed of a single compression spring enclosed between two mov-able plates. The spring is pre-compressed a full inch providing an initial force that instan-taneously opposes vibration. Any movement from the sway brace neutral position is opposed by a load equal to the pre-load plus travel from neutral position times the sway brace spring constant. Once maximum allowed travel (usually 3-in. in either direction) is reached the sway brace locks preventing additional movement.

Manufacturers typically recommend a specific size sway brace for a given pipe nominal diameter.

A more specific sway brace selection is possible when the exact restraining force required to control the piping vibration is known. The energy necessary to control the piping is pro-portional to the mass, amplitude of movement, and the force causing the vibration. From this relation the exact restraining force required to control the piping vibration may be cal-culated and an appropriate sway brace size selected.

Once selected, the sway brace may be modeled in CAESAR II using a combination of a bi-linear restraint and a translational restraint:

Restraints 3-53

Sway Brace Assemblies CAESAR II - Applications Guide

In the event that the sway brace is to be installed in the operating condition (or the neutral position is to be adjusted in the operating position), the modeling is CAESAR II is a little more complex. In this case, before modeling the sway brace, you must analyze the piping system without the sway brace to obtain displacements from the cold to neutral operating position:

Run analysis on the system without the sway brace to obtain the displacements from cold to operating condition. For the sake of this example, let’s assume the CAESAR II calcu-lated displacement from cold to operating position is 0.5 in.

In the SUS case the displacement D2 (vector 2) represents the pre-load in cold position. Under shutdown conditions, the pipe returns to its cold position and the brace exerts a force as previously described.

Sustained case restraint loads on sway brace = Pre-Load + Hot Deflection * Spring Rate

In OPE the displacement allows thermal expansion and the sway assumes neutral position exerting zero or negligible load on the pipe.

Operating case restraint loads on sway brace =~ 0.0 (does not restrain thermal expansion)

Example: Sway Brace Installed in the Cold Position

Sway Brace Installed in neutral position as shipped

Spring rate: 150 lb./in.

Initial loading: 150 lb.

Allowed movement: 3 in.

3-54 Restraints

CAESAR II - Applications Guide Sway Brace Assemblies

Example: Sway Brace Installed in Operating Condition

Sway Brace opposing compression force (movement occurs after pre-load is overcome)

Spring rate: 150 lb./in.

Initial loading: 150 lb.

Allowed movement: 3.0 in.

Calculated displacement: .5 in.

Note Be sure to include D2 in the sus-tained and operating cases.

Restraints 3-55

Sway Brace Assemblies CAESAR II - Applications Guide

3-56 Restraints

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General Information CAESAR II - Applications Guide

General InformationSelect Model—Hanger Design Control Data from the menu on the Input Spreadsheet to enter parameters affecting hanger design throughout the model. The hanger control spreadsheet items, with default values, are shown below. Complete descriptions of each item can be found in the Technical Reference Manual. These items can greatly affect the hangers designed and should be reviewed carefully at least one time so that the user is aware of the capability available.

Whenever CAESAR II designs a “zero load constant effort support,” a proposed spring location is found to be holding the pipe down at that point. In this case, that hanger loca-tion is removed from the analysis, and the restrained weight case is rerun to redistribute the weight loads.

There are instances where the stiffness of the adjacent piping and the hanger location restraints in the restrained weight case unfavorably interact, producing an undesirable dis-tribution of loads. Often these load distribution problems can be eliminated by reducing the stiffness used to compute the hanger loads in the restrained weight run. The default for this stiffness is 1.0E12. Values on the order of 50,000 or 75,000 have been used success-fully to relax the system somewhat and redistribute these piping loads. This stiffness can be changed through the Computation Control tab of the Configuration/Setup item of the Main Menu.

The operating case for hanger travel (free thermal case) can be analyzed either with no spring stiffness at the hanger locations, or with the stiffness of the selected springs inserted at those locations (in the latter case, the springs are selected through an iterative process). This is controlled via the Include Spring Stiffness in Hanger OPE Travel Cases option of the Configuration/Setup item of the Main Menu. Inserting the actual hanger stiffness into the Operating Case for Hanger Travel may give a technically more accurate result, but may introduce convergence problems as well. Also, please note that in the latter case, it is very important that the hanger load in the cold case (in the physical system) be adjusted to match the reported hanger Cold Load.

4-2 Hangers

CAESAR II - Applications Guide Simple Hanger Design

Simple Hanger DesignDouble-click the Hanger checkbox on the pipe spreadsheet to enter the spring hanger data for a particular node.

For a simple hanger no additional input is required. Note that a number of the parameters from the hanger control sheet also show up on the individual hanger auxiliary data fields. These items may be set globally (in hanger control) for all springs, or overridden locally (on each hanger auxiliary data area).

Example: Simple Hanger Design

Hangers 4-3

Single Can Design CAESAR II - Applications Guide

Single Can DesignIndicate that the pipe is supported from below by entering a negative number in the Hanger/Can Available Space field on the hanger spreadsheet.

The magnitude of the number in the available space field represents the distance between the pipe support and the concrete foundation, or baseplate. See the Technical Reference Manual for each of the manufacturer’s definitions of available space. If the available space is not really a criteria in the hanger design, then input a large negative value (i.e -1000).

CAESAR II input plots will use a different symbol for these base supports.

Example: Design of single can at one node

4-4 Hangers

CAESAR II - Applications Guide Constant Effort Support Design

Constant Effort Support DesignDesign a constant effort support by specifying a very small allowable travel. A typical value to use is (0.001 in.).

Example: Design of a Constant Effort Supports

Hangers 4-5

Inputting Constant Effort Supports (No Design) CAESAR II - Applications Guide

Inputting Constant Effort Supports (No Design)Follow these steps to enter the constant effort support information:

1. Enter the constant effort support load (per hanger) in the Predefined Hanger Data field.

2. Enter the number of constant support hangers at the location.

Do not enter spring rate or theoretical cold load.

Hangers completely predefined will not be designed by the hanger design algorithm.

Note Any other data entered on this hanger spreadsheet will be ignored.

Example: Multiple Predefined Constant Effort Supports

The two constant effort supports at node 377 should carry 10484 lb. each.

4-6 Hangers

CAESAR II - Applications Guide Entering Existing Springs (No Design)

Entering Existing Springs (No Design)Follow these steps to enter existing springs information:

1. Enter the Spring Rate and the Theoretical Cold Load (installation load, on a per hanger basis) in the Predefined Hanger Data fields.

2. Enter the number of Variable Support Hangers at the location.

Hangers completely predefined will not be designed by the hanger design algorithm. Any other data can exist for the spring location but this data is not used. Entered spring rates and theoretical cold loads will be multiplied by the number of hangers at this location. CAESAR II requires the Theoretical Cold (Installation) Load to pre-define the spring. Theoretical Cold Load = Hot Load + Travel * Spring Rate, where upward travel is posi-tive.

Example: Predefined Spring Hanger

Known Information:

Spring Rate: 590 lb./in.

Hot Load: 2000 lb.

Design Travel:1.375 in.

Calculate the Theoretical Cold Load:

Cold Load = (2000) + (1.375 * 590) = (2811)lb.

Hangers 4-7

Multiple Can Design CAESAR II - Applications Guide

Multiple Can DesignEnter the number of hangers or cans as a positive number in the No. of Hangers at Location field.

Placing a negative number in that field allows CAESAR II to design up to that number of hangers at the location.

All other hanger design parameters are still active.

Example: Trapeze Hanger Assembly

Power Piping springs

Allowable load variation: 15%,

Rigid Support Displacement Criteria: 0.05 in.

Note The program will design up to three cans at the sup-port if the load is too high for a single or double can configuration.

4-8 Hangers

CAESAR II - Applications Guide Old Spring Redesign

Old Spring RedesignThis option is used to determine if the old spring can still be used. If the old spring can be used then the new preset (initial cold load) is determined. If the old spring cannot be used then a new spring design is recommended.

The old spring is always left in the problem for subsequent load case analysis. The old hanger information needed for the re-design is

• the hanger table

• the number of springs at the location

• the old spring rate

The old spring rate is entered in the Spring Rate field under Predefined Hanger Data. The Theoretical Cold Load must not be specified.

Example: Old Spring Redesign

3 springs at node 97 and each has a spring rate of 1105 lb./in.

Hangers 4-9

Pipe and Hanger Supported From Vessel CAESAR II - Applications Guide

Pipe and Hanger Supported From VesselConnecting nodes associated with hangers and cans function just like connecting nodes with restraints.

Connecting node displacements are incorporated in the hanger design algorithm.

Example: Pipe Supported by Hanger from Vessel

Spring hanger is supported from the vessel at node 135. The hanger supports the pipe at node 550. Bergen-Paterson springs.

4-10 Hangers

CAESAR II - Applications Guide Hanger Design with Support Thermal Movement

Hanger Design with Support Thermal MovementUnique connecting node numbers that do not exist on any pipe element are input on the hanger spreadsheet in the Hanger Connecting Node field. The hanger is designed to act with one end at the Hanger Node and with one end at the Hanger Connecting Node.

Thermal growth of the hanger connecting node can be specified on any pipe element spreadsheet.

The hanger at node 9 is supported from a structural steel extension off of a large vertical vessel. The vessel at the point where the hanger is attached grows thermally in the plus Y direction approximately 3.5 in.

Example: Hanger with Support Thermal Movement

The vessel and the structural support are not modelled.

Hangers 4-11

Hanger Between Two Pipes CAESAR II - Applications Guide

Hanger Between Two PipesPart of the weight of the lower pipe is supported by a pipe crossing overhead.

The node on the pipe passing overhead is entered into the hanger spreadsheet as the CNode.

When using hangers with connecting nodes to design springs, users should be particularly careful that CAESAR II’s design hot load is accurate. To find the hot load, CAESAR II puts a rigid element between the pipe node and the support node (which may be another pipe node as in the example below), and runs a weight case. If in the weight run both nodes are expected to deflect, then the hanger weight loads will be distributed to other parts of the piping system, and not to the hanger. In this case it might be necessary for the user to estimate the loads on the hanger in an independent run, and then enter by hand the operating load on the particular spring hanger spreadsheet with the connecting node.

If zero load constant effort supports are designed for a spring location with a connecting node, the user is recommended to switch the hanger node and the connecting node. In this situation, in the weight run the pipe node tends to deflect downward less than the connect-ing node. To CAESAR II this looks like the connecting node is pushing down on the hanger node, thus “holding the pipe down.” Switching the hanger node and the hanger connecting node eliminates this problem.

Note The directive Connect Geometry through CNodes must be turned off in the Configuration Setup to avoid plot and geometry errors.

Example: Hanger Between Two Pipes

The pipe at 65 is supported via a spring hanger by the pipe at 470.

4-12 Hangers

CAESAR II - Applications Guide Hanger Design with Anchors in the Vicinity

Hanger Design with Anchors in the VicinityHangers are designed to support a given weight load through a specified travel with a min-imum of load variation.

Most often the weight load is that of the pipe between an anchor and the hanger.

The travel is the displacement of the hanger node as it thermally expands away from the anchor. When weight sensitive anchors (e.g. equipment nozzles) are relatively close to the hangers (less than 4 or 5 pipe diameters in the horizontal plane), the anchors should prob-ably be freed during the hanger restrained weight run. When the anchors are freed, the weight of the pipe between the anchor and the hanger should fall almost in its entirety on the hanger.

Anchor nodes to be released are entered on the specific hanger design spreadsheet. The anchor degrees of freedom are released according to the specified Free Code.

Anchor degrees of freedom are released for the hanger design Restrained Weight run only.

If the Free Code is not specified for an anchor or restraint to be freed, all degrees of free-dom associated with the anchor or restraint will be released for the restrained weight solu-tion.

Restraints as well as anchors can be freed to cause additional weight to be carried by the hanger.

Only linear restraints may be freed.

Example: Hanger Design in Vicinity at Equipment or Vessel Nozzle.

the anchor at 5 is freed in the Y-direction, the anchor at 105 is freed in all directions.

Hangers 4-13

Hanger Design with User-Specified Operating Load CAESAR II - Applications Guide

Hanger Design with User-Specified Operating LoadIn certain situations around equipment nozzles, and usually where the piping leaving the nozzle is very complex or very rigid, the hanger design algorithm will select operating loads that are too small. In these cases the user can override CAESAR II’s calculated operating (hot) loads. The design algorithm will proceed normally, except that the user’s entered hot load will be substituted for CAESAR II’s calculated value for both the hanger design and all post hanger design analysis load cases.

Example: Hanger Design with User-Specified Operating Load

In this configuration, freeing the anchors at 5 and 60 didn’t help the thermal case nozzle loads. It was postulated that, due to the stiff-ness of the overhead branches, the hanger calculated hot load was not sufficient. The calculated hot load was 2376 lb. A new hot load of 4500 lb. is tried here.

4-14 Hangers

CAESAR II - Applications Guide Spring Can Models with “Bottom-Out” and “Lift-Off”

Spring Can Models with “Bottom-Out” and “Lift-Off” CapabilityThe spring can must be fully pre-defined to describe bottom-out, or lift-off attributes (i.e. the spring can stiffness and theoretical cold load must be known.)

The spring can to be illustrated is a Grinnell, fig. B268, size 10.

The theoretical cold load: 1023 lb.

The spring rate from the spring table: 260 lb./in.

The smallest load in the spring table: 910 lb.

The largest load in the spring table: 1690 lb.

To get from the installed condition to the “bottom-out” condition the can must displace in the minus Y direction:

To get from the installed condition to the initiate “lift-off” condition the can must displace in the positive Y direction:

To get from the initiate “lift-off” condition to the completely “lifted-off” condition the pipe node must displace in the positive Y direction an additional:

Values for the gaps shown in the Stiffness Characteristics Graph on the following page are

g1 = 0.4346

g2 = 0.4346 + 9.1E -06

g3 = 2.5650

in 565.2260

)10231690(

Rate Spring

Load) (Installed - Load) Table (Max.�

��

in. 0.4346260

910)(1023

Rate Spring

Load) Table (Min. -Load) (Installed�

��

in. 06- 9.1E08 1E

910

Stiffness PlateAnnular Can Spring Est.

Load Table Min.��

Hangers 4-15

Spring Can Models with “Bottom-Out” and “Lift-Off” Capability CAESAR II - Applications Guide

Example: Spring Can Characteristics

Bottom out

4-16 Hangers

CAESAR II - Applications Guide Spring Can Models with “Bottom-Out” and “Lift-Off”

Example: Input for Lift-off and Bottom-out Spring Can model

Notes when building the model:

• Use displacements to prevent the rigid elements between 6 and 106, model-ing the spring can body, from translating or rotating laterally. (i.e. displace-ments should be defined at node 106 for the X, Z, RX, RY, and RZ directions).

• The spring is not defined in the spring hanger spreadsheet. (It could have been, but doing it as shown keeps the modelling simpler and in the same place.)

• When the pipe “lifts-off” of the spring support, the load on the spring assemblage should be equal and opposite, and its magnitude equal to the smallest load in the spring hanger table.

• When the restraint “bottoms-out”, the total restraint load will be distributed over the “spring” restraint and the +Y restraint with the gap.

Hangers 4-17

Spring Can Models with “Bottom-Out” and “Lift-Off” Capability CAESAR II - Applications Guide

Example: Input for Lift-off and Bottom-out Spring Can Model (continued)

Note The gap field in the restraints auxiliary data area rounds off values to 3 decimal places for display only. Internally, CAESAR II stores values to 7 digits for calculations. Therefore the gap corre-sponding to the -Y restraint in this exam-ple was input as 0.4346 + 9.1e-06 and this value will be retained in memory for calculations.

0.4346

0.4346 + 9.1 E -06

4-18 Hangers

CAESAR II - Applications Guide Spring Hanger Model With Rods, “Bottom-Out,” and

Spring Hanger Model With Rods, “Bottom-Out,” and “Lift-Off”To define “lifting-off” and “bottoming-out” the hanger should be fully pre-defined.

See the previous example for additional details modelling “bottom-out” and “lift-off” in spring supports.

The following example illustrates a Grinnell Fig. B268, size 9 hanger.

The spring rate = 200 lb./in.

The theoretical cold load = 1011 lb.

The smallest load in the spring table= 600 lb.

The largest load in the spring table = 1300 lb.

“Bottom-out” displacements:

“Initiate lift-off” displacements:

“Initial to final lift-off” displacements:

The following are notes for building the model:

• When modeling a spring between two different nodes in the piping system, note how the initial spring load must be applied equally, but in opposite directions at the two internal hanger nodes 20 and 25.

• The distributed length expansion joint is used to provide an estimated lateral stiffness for the spring hanger, and to define the hanger’s spring rate.

• Since the expansion joint is used to model the spring hanger stiffness, only three restraints are needed for the hanger model, instead of the four needed for the can model.

in 445.1200

)10111300(

Rate Spring

Load) (Installed - Load) Table (Max.�

��

.in 2.055200

)6001011(

Rate Spring

Load) Table (Min. - Load) (Installed�

��

in. 06- 0E.608 1E

600

Stiffness PlateAnnular Can Spring Est.

Load Table Min.��

Hangers 4-19

Spring Hanger Model With Rods, “Bottom-Out,” and “Lift-Off” CAESAR II - Applications Guide

Example: Spring Hanger Model with Rods, Bottom-out, and Lift-off

4-20 Hangers

CAESAR II - Applications Guide Spring Hanger Model With Rods, “Bottom-Out,” and

Example: Bottom-out and Lift-off Spring Hanger Model with Rods

Dummy rigid modeled between nodes 10 and 15. Pipe connected to the rod through a +Y restraint.

Rod modeled as solid pipe.

Hangers 4-21

Spring Hanger Model With Rods, “Bottom-Out,” and “Lift-Off” CAESAR II - Applications Guide

Example: Bottom out and Lift off Spring Hanger Model with Rods (continued)

No bending stiffness. Effective ID is zero (this eliminates pressure thrust)

Gap on -Y support at node 25 is .000001 in. The display does not show this value but calculations will be performed correctly.

4-22 Hangers

CAESAR II - Applications Guide Simple "Bottomed-Out" Spring

Simple "Bottomed-Out" Spring Spring supports that may "bottom out" have SPR following a translational direction in the restraint Type field. (For example, YSPR for a vertical “bottomed-out” spring.)

When a bottom out spring is entered, the restraint auxiliary screen changes as follows: The Gap field changes to x, the permitted travel, and the Mu field changes to F, the initial spring load. The direction of permitted travel is assumed opposite to the initial load on the pipe. These definitions were setup almost exclusively to handle vertical springs, and as such x and F inputs are always entered as positive, as shown in the following example.

Used most often to conveniently enter predefined springs into the piping system model. These spring restraints provide a “bottoming-out” capability that occurs when the spring has exceeded its maximum travel limit.

The user should always enter the stiffness Stif, the allowed travel x, and the initial load on the spring F, to properly utilize the "bottomed-out" spring model. If the travel x is not entered it defaults to zero. If the initial load is not entered it also defaults to zero, and its sign is taken as positive.

Note that no hanger should be entered at the same position as a bottomed-out spring.

Hangers 4-23

Modeling Spring Cans with Friction CAESAR II - Applications Guide

Modeling Spring Cans with Friction In many systems, portions of the pipe are supported by spring cans. These spring cans per-form the same function as spring hangers, only they are below the pipe, pushing up. In some models, these spring cans are allowed to slide on their foundation, subjecting the system to friction forces.

Basically, each support of this type needs the following:

• A rigid element from the pipe center to the top of the can. Length equals pipe radius + insulation thickness + shoe height + any trunnion height.

• A Cnode to connect to the spring. Except for the vertical spring stiffness, all other DOFs are rigidly connected.

• A rigid element representing the spring can height.

These points are illustrated in the model below.

Alternatively, element 15-20 may be omitted, with the +Y restraint (with friction) placed directly on node 15.

This modeling technique can also be applied to situations where the shoe or trunnion slides on top of a bolted spring can.

Example: Model of Spring Can with Friction

4-24 Hangers

��6 4�� B ��

� ��"��&�"" ��!�� !��&�"" �� 4�� B ��=��"��%�� "�4�. ��"? �� )��"� 4�� B �� +��"�B ��=� ��!��, ��. ��"? �� -��"�B ��:��"�� "�� /@��B �� *�" ��@��B ��=��"�?�� +�" ��@��B ��=� ��? �� "��B �� 39��'�"�B �� 6��"�9��'�" �� 8��&�"��!��C�� "' �� 3

!��'�� ,�� "�� 4�� D ��%

Simple Bellows with Pressure Thrust CAESAR II - Applications Guide

CAESAR II’s Expansion Joint Modeler can model many different expansion joint assem-blies quickly and accurately. This chapter reviews variations on those models.

Simple Bellows with Pressure ThrustBellows expansion joints can be modeled with either a zero or a finite length. When finite length bellows are used, either the bending or the transverse stiffness must be left blank. CAESAR II will calculate the exact stiffness coefficient for the term left blank.

For finite length expansion joints, the user is recommended to leave the bending stiffness field blank, and to enter the lateral stiffness given by the manufacturer into the transverse stiffness field on the expansion joint spreadsheet. The lateral stiffness may be computed from the axial stiffness (if not provided) from the equation:

KTR = (3/2) (KAX) (D/L) 2

If the bending stiffness is given, its value should be approximately (within 1%) equal to:

KBEND =(1/2) (KAX) (D2) (π/180)

KAX is the axial stiffness of the expansion joint

D - is the effective diameter of the expansion joint

L - is the flexible length of the joint.

For zero length expansion joints:

KBEND = (1/8) (KAX) (D2) (π/180)

When a zero length expansion joint is used, CAESAR II will use either the preceding or the following element to determine the axial direction of the bellows stiffnesses. The pre-ceding element is checked first.

Bellows are very fragile under torsional loading. It is recommended that accurate torsional stiffnesses and allowable torsional rotations be obtained from the vendor.

Systems using untied bellows should either be of very low pressure or adequately anchored to withstand the possibly large thrust loads developed due to the unrestrained bellows.

Bellows and any other miscellaneous weights should be added to flanges on either side of the bellows (or can be added as concentrated forces). This is particularly true when the bellows is part of a hanger sizing weight calculation.

A zero or blank Bellows ID results in a zero pressure thrust.

The Bellows ID is the diameter used to find the area for pressure thrust calculations. The total thrust load is applied at the From and To ends of the bellows, and is used to “open” the bellows (providing the pressure is positive). The magnitude of the thrust load is P * A, where P is the pressure in the pipe above atmospheric, and A is the area, found from

A = π/4 * (Bellows ID) 2

Many manufacturers specify the effective area of the bellows. The bellows ID for CAESAR II input may be calculated by using the following equation:

Bellows ID = 4π---

EffectiveArea

5-2 Expansion Joints

CAESAR II - Applications Guide Simple Bellows with Pressure Thrust

In the system shown below, the untied bellows runs between the nodes 8 and 9. The elbow at 11 is anchored to take the thrust load developed in the bellows. The manufacturer’s specification for the joint’s axial stiffness is 6530 lb./in. with a transverse stiffness of 3250 lb./in. The bending stiffness is left blank, and will be calculated by CAESAR II since the bellows has a finite length. The pump and the baseplate at 5 must be able to withstand the large axial force that may develop due to pressure thrust in the bellows.

Example: Bellows with Pressure Thrust

Aeff = 67.5 in2

P = 175 psi

Thrust = 67.5(175) = 11812 lb. (will be auto-matically applied by CAESAR II)

Bellows ID = = 9.28 in.

Expansion Joints 5-3

Tied Bellows (Simple vs. Complex Model) CAESAR II - Applications Guide

Tied Bellows (Simple vs. Complex Model)Complex models of expansion joints are much more difficult to build than simple models. Unfortunately there are no hard and fast rules for when to use simple models and when to use complex models. The following guidelines are presented to aid the engineer in making this decision.

• Complex models are used whenever a failure is being investigated.

• Complex models are normally used when the pipe diameter and number of convolu-tions become large.

• Complex models are used when nuts are only on the outside of the flange, allowing the tie bars to only carry tension.

• Complex models give good values for the load distribution in the tie bars. Simple models give no indication of the load distribution. In some cases, where the tie bars combine to resist relative bending of the joint ends, one pair of tie-bars can be in com-pression while the other pair is in tension. This effective redistribution of load in the tie bars will never be observed in a simple model. When this does occur, and if the tie bars are very long, buckling of the rods in the complex model should be investigated (evaluate whether the rods can withstand the compressive forces reported in the output report).

The single tied bellows is designed to absorb movement by lateral deflection only. There is no axial deflection or relative bending rotations at the joint ends.

These simple models should only be used where the tie bars are either guaranteed to be carrying tension, or have nuts on either side of the flange and so will carry compression if needed.

Be sure to enter the lateral instead of the bending spring rate from the manufacturer’s cat-alog. See the previous discussion for a simple bellows for more information about bellows stiffnesses.

The weights of the bellows and associated hardware should be added to the flange weights on either side of the bellows. This is particularly true if the expansion joint is between a hanger to be sized and an anchor.

The expansion joint user should be sure to check the displacement limits for the expansion joint once the protected equipment loads are within the allowables. CAESAR II has a pro-cessor called EJMA Expansion Joint Rating accessible through the Analysis option of the Main Menu, which helps the user to compute relative bellows movements for evaluating the bellows distortion.

Simple models of single tied bellows are built by entering a large axial stiffness. This axial stiffness simulates the tie bars, preventing relative axial movement of the bellows. Tie rods may also be modeled with a single rigid element along the centerline of the bellows, with zero weight and rotational restraints, prevents the ends of the joint from rotating relative to one another. In reality the tie bars being offset from the centerline prevent this rotation.

The complex models are built by running pipe elements whose diameter is equal to the diameter of the tie-bars, and whose wall thickness is equal to half of the tie-bar diameter, between rigid elements that extend normal to the pipe axis and from the centerline and to their intersection with the tie-bar centerline (See the following illustration).


CAESAR II - Applications Guide Tied Bellows (Simple vs. Complex Model)

Some manufacturers feel that friction at the tie bar ends, plus other effects serve to limit the overall lateral flexibility of this joint. For lack of a better value, a 30% increase in lat-eral stiffness is sometimes used to compensate for these frictional effects.

Field situations such as loose nuts on tie-bars, etc. can be modeled using the complex expansion joint model.


Tied Bellows Expansion Joint (Simple Model) CAESAR II - Applications Guide

Tied Bellows Expansion Joint (Simple Model)STEP 1—Need to compute the lateral stiffness for the bellows:

The flexible length of the bellows is not listed in most expansion joint catalogs. The listed lengths include the rigid end pieces such as flanges or pipe ends. Since the transverse stiff-ness is based on the flexible length, the flexible length must be known. A very simple way of pulling this value from the catalog is to examine the incremental increase in overall length of the joint as additional convolutions are added. With all convolutions the same length, this incremental length can be used to calculate the total flexible length. In this example the total length of a 4 convolution joint is 8 in. and the total length of an 8 convo-lution joint is 12 in. This means that the extra four convolutions add 4 in., so the length of all twelve convolutions is 12 in. (This also indicates that the rigid end pieces on this joint of 4, 8, or 12 convolutions is 4 in.)

Deff = (4Aeff/π )1/2 = 10.0 in.

KTR= (3/2) (KAX) (Deff/L)2

L = Flexible Convolution Length = 12 in.

KTR= (3/2) (850) (12.0/12.0)2

= 1,275 lb./in.

STEP 2—Build the CAESAR II model of the flexible portion of the expansion joint. Note how the rotational restraints between nodes 29 and 30 keep the two flanges parallel. In the field, the tie bars at four points around the expansion joint will keep the flanges parallel. (The flanges and the tie bars forms a parallelogram upon lateral deflection.)

Axial Stiffness: 848 lb./in.No. Convolutions: 12Leff: 12 in.

Aeff: 78.4 in2

Zero-weight rigid element (tie rod)

Example: Tied Bellows (simple model)


CAESAR II - Applications Guide Tied Bellows Expansion Joint (Simple Model)

Example: Tied Bellows (simple model—


Tied Bellows Expansion Joint (Complex Model) CAESAR II - Applications Guide

Tied Bellows Expansion Joint (Complex Model)In the system shown below the flexible joint is between the nodes 30 and 35. The flanged ends of the joint are modeled as the rigid elements 20 to 30 and 35 to 45. Additional rigid elements, perpendicular to the pipe axis, extend from each flange. The tie bars are 1-in. in diameter. The following nodal layout and input is used to build a comprehensive model of the tied bellows.

Example: Tied Bellows (complex model)


CAESAR II - Applications Guide Tied Bellows Expansion Joint (Complex Model)

Example: Tied Bellows (complex model—continued)

Weightless rigid elements extend from flange centerline to outside edge of flanges where tie rods are attached. (only 2 of 8 element inputs shown).


Universal Expansion Joints (Simple Models) CAESAR II - Applications Guide

Universal Expansion Joints (Simple Models)Please refer to the previous models of bellows expansion joints for specific notes relating to individual bellows designs, and to some comparisons of simple and complex expansion joint input.

The tied universal bellows is designed to absorb movement by lateral deflection only. There is no axial deflection or relative bending rotations at the joint ends.

Lateral instead of the bending spring rates from the manufacturer’s catalog should be entered. See the discussion for a “simple bellows” for more information about bellows stiffnesses.

Manufacturers publish a wide variety of data for universal expansion joints. In most cases the published spring rates are for the universal joint as a whole assembly. When the lateral stiffness is given for the whole assembly the simple or complex models of single bellows can be used. In this case the manufacturer must also provide a cumulative assembly dis-placement limit so that the piping designer can make sure that neither of the bellows are over-extended.

Many universal expansion joint assemblies have stops along the tie-bars that are con-nected to the center spool-piece. These stops are designed to prevent over-extension of the bellows and can be modeled in the complex universal joint model. For the simple univer-sal joint model, the user must check the results to make sure that the stops are not engaged. Stops should typically be considered a safety feature, and should not be included as a working part of the design, unless particular attention is paid to the design surrounding the stop components.

The expansion joint user should be sure to check the displacement limits for each of the expansion joints once the protected equipment loads are within the allowables. CAESAR II has a program called EJMA Expansion Joint Rating which helps the user to compute relative bellows movements for evaluating the convolution’s strength. This pro-gram only works on single bellows, however, and so the user would need to model and then check each bellows in the universal assembly.

Some manufacturers feel that friction at the tie bar ends, plus other effects serve to limit the overall lateral flexibility of this joint. For lack of a better value, a 10% increase in overall lateral stiffness is sometimes used to compensate for these frictional effects.

The complex models are built by running pipe elements, whose diameter is equal to the diameter of the tie-bars, and whose wall thickness is equal to half of the tie-bar diameter, between rigid elements that extend normal to the pipe axis and from the centerline and to their intersection with the tie-bar centerline. See the next example.

The weights of the bellows and associated hardware should be added to the flange weights on either side of the bellows. This is particularly true if the expansion joint is between a hanger to be sized and an anchor.

In-situ field effects like loose nuts on tie-bars, etc., can be modeled using the complex expansion joint model.

Descriptions of some various universal models are shown in the following figures. The two models shown have example input given on the following pages. Simple models should only be used when the user knows that both ends of the tie-bars will be fixed to the flanges, i.e. when there are nuts on both sides of the flange. (The top drawing shows nuts


CAESAR II - Applications Guide Universal Expansion Joints (Simple Models)

on only one side of the flange at the left end. This configuration should be modeled with a complex joint model unless the user is sure that all tie-bars will remain in tension.)

The top model is used when the analyst is provided with global assembly data for the uni-versal, i.e. the assembly lateral stiffness.

The second model is used when the analyst is given angular spring rates for each of the two bellows used in the model.



When provided individual bellows angular stiffness:



Note This model does not show the addition of any extra hardware or bellows weights which could affect weight load distribution and spring hanger design in the area.

Example: Universal Expansion Joint (simple model)



When provided individual bellows angular stiffness



Example: Universal Expansion Joint (simple model—individual bellows)

Note The rigid tie bar(s) should be mod-eled at the ambient temperature.

Note This model does not show the addition of any extra hardware or bellows weights which could affect weight load distribution and spring hanger design in the area.


Universal Joint (Comprehensive Tie Rod) CAESAR II - Applications Guide

Universal Joint (Comprehensive Tie Rod)The comprehensive universal joint model involves defining, as accurately as possible, all tie rods and connections between tie rods and end plates.

The following groups illustrate the method used in constructing the universal expansion joint model shown above.

——Rigid Elements (Flanges) —

15-17 / 31-33

——Rigid Elements normal to the pipe axis, and between the pipe and tie bar centerlines. At the end where there are nuts on either side of the flange, fixing the tie-bar to the flange.

33-1033 / 33-2033 / 33-3033

——Rigid Elements normal to the pipe axis, and between the pipe and tie-bar centerlines. At the end where there are nuts only on the backside of the flange.

15-1015 / 15-2015 / 15-3015

——Intermediate lateral tee supports (Rigid) —

23-1023 / 23-2023 / 23-3023

25-1025 / 25-2025 / 25-3025

——Tie-bars —

1033-1034-1035-1036

2033-2034-2035-2036

3033-3034-3035-3036

— Restraints with connecting nodes at the tension-only flange end.——

RESTR NODE = 1036 CNODE = 1015 TYPE = -X , Y , Z



— Restraints with connecting nodes at the intermediate support points.

RESTR NODE = 1035 CNODE = 1023 TYPE = Y , Z







CAESAR II - Applications Guide Universal Joint with Lateral Control Stops (Compre-

Universal Joint with Lateral Control Stops (Comprehensive Tie Rod Model)

Double-acting restraints with connecting nodes and gaps are used to model stop gaps along the tie bars.

Stops along the tie-bars are installed to restrict lateral motion at each end of the universal joint.

The following groups illustrate the method used in constructing the universal joint with lateral stops shown above. Only the right side tie rod elements are shown below.

— Standard pipe elements —

34-36 / 36-38

— Rigid flange elements —

30-32 / 40-42

— Bellows elements —

32-34 / 38-40

— Rigid elements from the pipe to the tie-bar centerline —

(Normal to the pipe axis)

30-1030 / 36-1036 / 42-1042

— Tie-bar elements —

1003-1002 / 1002-1001

— Restraints with connecting nodes —

RESTR NODE=1001 CNODE = 1042 TYPE = +Y , X , Z

RESTR NODE=1002 CNODE = 1036 TYPE = Y w/gap=1.5 , X , Z


Hinged Joint CAESAR II - Applications Guide

Hinged JointThe relationship between the rotational bellows stiffness used in the model and the axial bellows stiffness should be approximately:

Kbend = (1/8) (Kax) (D2)(π/180)

This is typically the value given in expansion joint manufacturers’ catalogs. This equation and the bending stiffness value from most manufacturers’ catalogs should only be used with a zero length expansion joint.

The hinged joint is defined using a zero length expansion joint with axial, transverse, and torsional stiffnesses rigid. The bending stiffness is set equal to the bending stiffness of the hinge.

Hinge directions are defined using restraints and connecting nodes. The restraint line of action is always normal to the hinge axis.

Hinged joints are designed to take pressure thrust. The analyst should make sure that the joint manufacturer is aware of the design loads in the hinges.

Some expansion joint manufacturers believe that the hinge friction can provide consider-able additional resistance to bending. Certainly as the axial load the hinge is to carry becomes large, this “hinge friction” effect will increase. Approximations to this increase in bending stiffness can be made by increasing the stiffness of the bellows in proportion to the axial load on the hinge. The expansion joint manufacturer can hopefully provide assis-tance here.

Several typical geometries for hinged expansion joints are shown in the figures below:


CAESAR II - Applications Guide Hinged Joint

In the example that follows, the hinged joint is zero length and is defined between nodes 45 and 46. “X” is the hinge axis, i.e. all relative rotations are permitted between 45 and 46 about the X axis. 45 and 46 are fixed rotationally relative to each other in the “Y” axis. (See the second note above.)


Slotted Hinge Joint (Simple) CAESAR II - Applications Guide

Slotted Hinge Joint (Simple)The hinged joint is defined using a zero length expansion joint and rigid elements with zero weight to define the interaction of the hinge geometry.

Hinge directions are defined using restraints with connecting nodes. The restraint line of action is always normal to the hinge axis.

Example: Slotted Hinged Joint (simple model)

Elements from 10 to 15 and from 16 to 20 are weightless 9-inch long rigids.


CAESAR II - Applications Guide Slotted Hinge Joint (Comprehensive)

Note In this model, the relative rotation at the hinge about the “Y” axis is assumed to be zero. The slots on either side will provide some limit to this Y rotation. In most applications of this type, the relative Y rotation is zero because the problem is kept planar using guides. A good first pass can be made using the model shown, then if the analysis shows that the RY restraint between nodes 15 and 16 is sup-porting load, a further refinement to the model can be made.

Slotted Hinge Joint (Comprehensive)This model is somewhat different from the previous model because of the need to provide for the non-hinge axis rotation due to the slots on either side of the joint. The schematic below illustrates the extra input required to incorporate this effect.

Example: Slotted Hinge Joint (comprehensive)


Slotted Hinge Joint (Comprehensive) CAESAR II - Applications Guide

Zero weight rigid elements defining the hinge assembly are listed below:

10 - 15 Normal to pipe axis to centerline of hinge assy.

10 - 35 "

55 - 30 "

55 - 50 "

15 - 20 Parallel to pipe axis to centerline of hinge axis.

35 - 40 "

50 - 45 "

30 - 25 "

The finite length bellows must be defined accurately between nodes 10 and 55. This typi-cally means entering the correct flexible length and using the manufacturer’s axial and lat-eral spring rates. Remember that manufacturer’s angular spring rates should not be used in finite length expansion joint models.


CAESAR II - Applications Guide Slip Joint

Slip JointLarge slip joints are usually difficult to install and difficult to accurately model.

Smaller diameter slip joints are telescoping, axial displacement devices, that permit con-siderable axial displacement of the slip joint ends and moderately rigid resistance to pipe bending.

Smaller slip joints are usually categorized by having two annular packing glands separated axially along the joint by a dead air space, or by a small bellows sleeve.

The following figure shows the cross-section of a typical large slip joint. The stiffnesses between nodes 15 and 25 are a function of the packing stiffness for transverse and rota-tional relative deformation and of packing stiffness and tightening for axial relative defor-mation.

Example: Slip Joints


Slip Joint CAESAR II - Applications Guide

ote 3

Note 1: Typical delta dimensions are:

5 - 10 The distance from the closest guide or support to the end of the joint. (Same values would also be used for 25 - 30.)

10 - 15 The effective length of the joint if known, or the travel expected plus 4", or a 12" estimate if nothing else is known.

Note 2: K1 is the spring stiffness for forces below the yield force, FY.

Note 3: K2 is the spring stiffness (for joint compression) for forces greater than FY. The best estimate for this resistance is cumulative friction effects of guides and supports, given by the vendor.

Where (N) is the nominal pipe diameter in inches, and (a) is the thermal expansion at the operating temperature in inches per 100 ft.

Note 4: Fy is the joint friction thrust from the vendor catalog. Typical values are given as 400 lbs times the nominal pipe size.

K2 100( )N( ) a( )⁄= (Approximation)

Note 2 Note 4

N


CAESAR II - Applications Guide Gimbal Joints

Gimbal Joints Gimballed joints are designed to resist pressure thrust. The analyst should make sure that the joint manufacturer is aware of the design loads on the gimbals.

There are two basic types of Gimballed expansion joints:

• Those designed to take angular deformation only.

• Those designed to take angular deformation and transverse offsets.

Typically, gimbals in the smaller sizes absorb only angular deformation. The difference between the two types of joints can be seen by counting the total number of hinges. Gim-bal joints which take angular deformation have two hinges. Gimbal joints which take angular deformation and transverse offsets have four hinges.

Modeling for the two types of gimballed joints is completely different.

Angular-only gimbals are by far the most common and are most often used in pairs. Single gimbal, angular-only joints are very easy to model provided the correct angular spring rates are used. The analyst is generally discouraged from using the manufacturer’s angular spring rates, but in this case (and for all point expansion joint applications) it is precisely the angular spring rate that should be used.

The angular-only gimbal can be input as a zero length expansion joint with rigid axial, transverse, and torsional stiffnesses. The bending stiffness is set equal to the rotational stiffness specified in the manufacturer's catalog.

Angular and Offset gimbals should probably be thoroughly modeled as shown in the fol-lowing figures. Angular and Offset gimballed joints are usually installed in large diameter lines where lumped property assumptions for the bellows may not be within reasonable engineering accuracy.


Gimbal Joints CAESAR II - Applications Guide

Example: Angular-only Gimballed Joint

Rigid elements between nodes 105 and 110 and nodes 111 and 115 each con-taining half the weight of the hinge mechanism.


CAESAR II - Applications Guide Gimbal Joints

Example: Angular and Offset Gimbal Joint

Bellows Assembly nodes are above on illustration

Hinge Assembly nodes are below on illustration

All 3 expansion joints are defined the same (as above)

Rigid Elements from node 5 to 10, node 11 to 15, node 16 to 20, and node 21 to 25.

Hinge Assembly Inputs


Gimbal Joints CAESAR II - Applications Guide

Example: Angular and Offset Gimbal Joint

Rigid elements between nodes 5 and 105, nodes 110 and 115, and nodes 120 and 25.

Expansion Joints for both elements have same auxiliary data as shown. These are NOT zero length.

Bellows Assembly Input


CAESAR II - Applications Guide Dual Gimbal

Dual GimbalDual gimbal joints are two, usually angular-only, gimballed joints in series in the pipeline. Putting two (or even three) angular-only gimballed joints together provides for an ability to absorb lateral and possibly axial deformation.

(An elementally linear piping program will never be able to model the axial-only compo-nent of the possible deformation because it requires large rotation of the expansion joint components—something not considered in such programs.)

The single “angular deformation only” gimbal should always be used in series with at least one other gimballed joint. It is only in series that the “angular deformation only” gimbal provides for any lateral movement.

Gimballed joints are designed to take pressure thrust. The analyst should make sure that the joint manufacturer is aware of the design loads on the gimbals.

Each individual angular-only gimbal joint should be modelled as a zero length expansion joint with rigid axial, transverse, and torsional stiffnesses. The bending stiffness should be equal to the manufacturer's published rotational stiffness term. See the notes for a single gimballed expansion joint for a more complete discussion.

The minimum required distance “L” between adjacent single gimballed joints (shown as 8-7 in the following example), is principally a function of the angular and rotational defor-mation to be absorbed, the diameter, and the number of corrugations per joint.

The following figure shows a dual gimbal comprised of two angular-only gimbals. The bending stiffness for each gimballed joint is 490.0 in.lb./deg.


Dual Gimbal CAESAR II - Applications Guide

Example: Dual Gimbal (Angular-Only)


CAESAR II - Applications Guide Pressure-Balanced Tees and Elbows

Pressure-Balanced Tees and ElbowsPressure balanced tees and elbows are used primarily to absorb axial displacements at a change in direction, without any associated pressure thrust. Pressure balanced tees can also be used in universal type configurations to absorb axial and lateral movement.

The example below shows briefly the coding of a pressure-balanced tee in a turbine exhaust line. The bottom side of the tee is blanked off. The tee is a standard unreinforced fabricated tee. The tie bars will only act in tension.


Pressure-Balanced Tees and Elbows CAESAR II - Applications Guide


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Reducers CAESAR II - Applications Guide

ReducersThere are two common ways to model reducers:

1. Enter a data point at the center of the reducer and change the diameter and wall thick-ness on the following element.

2. Enter a data point at both ends of the reducer fitting. The diameter and wall thickness of this element should be equal to the average diameter and average wall thickness of the mating pipes.

Method 2 above is recommended. The axial stiffness of this model is exact and the bend-ing stiffness approximate.

Where eccentric reducers are used, the reducer element should show a corresponding change in elevation. The centerlines of the mating pipes should be correctly represented.

B31.1 Table D-1 gives the following equation for calculating the stress intensification fac-tor for concentric reducers as per B16.9:

SIF = 0.5 + 0.01(a)(D2/t2)1/2

where (a) is the cone angle and does not exceed 60 degrees, D2 is the outside diameter of the small end of the reducer, and t2 is the wall thickness of the small end of the reducer. Additionally, the larger of D1/t1 and D2/t2 should not exceed 100, and the wall thickness throughout should not be less than t1 except in and immediately adjacent to the cylindrical portion of the small end, where the thick-ness shall not be less than t2. The maximum SIF is 2.0.

The stress intensification factors should be specified for each end of the reducer element. The user should activate the SIFs & TEEs field on the pipe spreadsheet, leave the TYPE field blank, and enter the SIFs in the SIF(i) and SIF(o) fields.

6-2 Miscellaneous Models

CAESAR II - Applications Guide Reducers

Example: Concentric Reducer Modeling

B31.1 maximum SIFs for concentric reducers are used here.

Miscellaneous Models 6-3

Reducers CAESAR II - Applications Guide

Example: Eccentric Reducer Modeling

B31.1 does not specify SIFs for eccentric reducers so same as concentric are used in lieu of a more suitable value


CAESAR II - Applications Guide Ball Joints

Ball JointsBall joints can be modeled with zero length expansion joints, or with restraints and con-necting nodes.

When using expansion joints, each ball and socket is defined with one zero length expan-sion joint having rigid axial and transverse stiffnesses, and essentially zero bending and torsional stiffnesses.

When bending and torsional stiffnesses should be small, a value of (1.0) should be used.

Results are invalid for large rotations.

Example: Two methods of modeling a Ball Joint

Modeling a ball joint between nodes 20 and 21 using a zero length expan-sion joint

Modeling a ball joint between nodes 20 and 21 using axial and translational restraints with Cnodes.

Modeling a ball joint between nodes 20 and 21 using a torsional restraint.


Jacketed Pipe CAESAR II - Applications Guide

Jacketed PipeJacketed piping systems are input by running the jacket elements directly on top of the core elements where the two are concentric.

A very simple way to generate a jacketed pipe model is to run through the entire core and then duplicate the core piping using a proper node increment (such as 1000). This will pro-duce a second run of pipe which will be modified to build the jacket model. For the jacket, change pipe size, temperature, bend radii, etc., to finish the model. The jacket and core can then be attached by changing node numbers and adding restraints.

Typically, the end caps connecting the core to the jacket pipe are much stiffer than either the core or the jacket. For this reason node pairs like (10 and 1010), (25 and 1025), (35 and 1035), and (40 and 1040) are often joined by using the same node for each, i.e. the dis-placements and rotations at the end of the core pipe are assumed to be the same as the dis-placements and rotations at the end of the jacket pipe.

Internal spiders offer negligible resistance to bending and axial relative deformation. Node 15 might be connected to node 1015 via a restraint with connecting node. For an X run of pipe, rigid restraints would exist between the two nodes for the Y and Z degrees of free-dom.

The +Y support acting on the jacket at node 1020 does not cause any stiffnesses to be inserted between 20 and 1020. Node 20 is included in the model so that outside diameter interference can be checked at the 20-1020 cross section. Should there be any concern about interference, or interference-related stresses at the 20-1020 nodes, then restraints with connecting nodes and gaps can be used to approximate the pipe-inside-a-pipe with a clearance geometry.

Since CAESAR II constructs the jacketed piping model by associating nodal DOFs, the program really does not know one pipe is inside of another. Therefore the following items should be considered.

If both the jacket and the core are fluid-filled, the fluid density of the jacket must be reduced, to avoid excess (incorrect) weight.

If wind loads are specified, the wind or wave loading must be deactivated for the core, or else the core will pick up wind load.

The core pipe should probably have its insulation thickness set to zero.


CAESAR II - Applications Guide Jacketed Pipe


Cold Spring CAESAR II - Applications Guide

Cold SpringSee the CAESAR II Technical Reference Manual for a detailed discussion of the method for analyzing Cold Spring.

Material 18 is used for Cut Short (Material 19 for Cut Long). Material is changed back on element 11 to 15 to actual material. Cold spring will be considered in all load cases that contain load vector CS.

Example: Cut Short


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Example 1: Harmonic Analysis (TABLE) CAESAR II - Applications Guide

Example 1: Harmonic Analysis (TABLE)This problem is taken from the following source:

I. S. Tuba and W. B. Wright, “Pressure Vessel and Piping 1972 Computer Programs Verification An Aid To Developers and Users.” The American Society of Mechanical Engineers. New York, 1972. Problems 6 and 2.

It is assumed that the user reviewing this example is familiar with the basic CAESAR II input. Only the input germane to the dynamic analysis is discussed.

The following model is to be analyzed first for natural frequencies and second for har-monic loads imposed on the top of the structure at nodes 8 and 13.

Enter the model as shown and set the material density on the pipe spreadsheet to be zero. (All weights are input as concentrated masses.) Do not enter bends, but rather only straight elements.

Member Properties:

Pipe Outside Diameter: 2.375 in.

Pipe Wall Thickness: 0.154 in.

Elastic Modulus: 27.9E+06 psi

Poisson’s Ratio: 0.3

Run the static case and then access the Dynamic Input.

First, additional masses may be added, or degrees of freedom deleted. In the eigensolution of larger systems the deletion of un-needed degrees of freedom may be a very important

7-2 Examples

CAESAR II - Applications Guide Example 1: Harmonic Analysis (TABLE)

factor in keeping the run times reasonable. In most normal cases, however, masses must neither be added nor deleted. The mass of the piping, fluid, and insulation is automatically calculated and included by CAESAR II. For the current example the weight of the pipe is zero and all masses are concentrated and prespecified as lumped masses.

Next, modify the Control Parameters as shown below:

Examples 7-3


By turning off the Frequency Cutoff and setting the value of the maximum number of Eigenvalues we are guaranteed to acquire the first five natural frequencies in our results.

When the eigensolution is completed, the calculated natural frequencies are printed on the screen:

Choose Output-View Animation from the main menu to view the animations of the 5 modes of vibration. The first mode is back and forth along the x-axis, the second mode is transverse along the z-axis and the third mode is a twisting about the y-axis. The next two modes are combinations of the previous three.

Harmonic Analysis of this System

Assume a 120 Hz electric motor sits on the piping structure and acts:

FX @ 8 = ( -95 cos ω t ) lb.

FX @ 13 = ( 95 cos ω t ) lb.

What is the largest stress in the small piping structure subject to these dynamic loads?

7-4 Examples

CAESAR II - Applications Guide Example 1: Harmonic Analysis (TABLE)

Note The 120 Hz vibration falls between the structural resonant frequencies 115 Hz and 137 Hz. The torsional mode will most likely be excited because the sign differ-ence on the forces promotes a twisting of the structure. The model has already been built and so dynamic input is simply modified. There is only a single har-monic frequency of excitation to be investigated.

Harmonic loads are input next. The user is first asked for harmonic forces, and then har-monic displacements. Harmonic forces act at points (8) and (13) on the example piping system. The forces act in the “X” direction, with an opposite sense, and with a magnitude of 95 lb. The force acting at point (8) can be plotted as a function of time as shown in the following figure:

Harmonic force data input is shown as follows. Harmonic displacements may exist in the same problem with harmonic forces if necessary. The example problem has harmonic forces only.

For the example problem, there are 120 cycles per second.

Examples 7-5


Note The same force effect could have been achieved by entering +95.0 lb at each node, but entering a phase angle of 180.0 degrees at node 13.

Calculations for the example problem take less than 30 seconds to complete. The user may view the structure in animated motion or view standard displaced shape plots from the Dynamic Output using the Display Graphical Results option (shown below). Additionally, for harmonic results, restraint loads, forces, and stresses can accurately be calculated for the maximum displacements due to the harmonic loads.

7-6 Examples

CAESAR II - Applications Guide Example 2: Relief Valve Loads (RELIEF)

Example 2: Relief Valve Loads (RELIEF)PROBLEM: Analyze the two relief valve systems, shown as follows, subject to the

simultaneous firing of both valves.

Process steam conditions: 450 psi, @ 650°F

Relief Valve Orifice: JOHNSON #34A-06 2.141 in. ID.

Valve Opening Time: 8.0 milliseconds

Valve Closing Time: 8.0 milliseconds

Relief Duration: 1.0 sec.

Examples 7-7

Example 2: Relief Valve Loads (RELIEF) CAESAR II - Applications Guide

7-8 Examples


CAESAR II Gas Thrust Load Calculations

Examples 7-9


Relief Valve Example Problem Setup

REQUIRED: Compute the support loads, forces, and stresses in the vent piping system when the relief valves fire simultaneously.

GIVEN: Venting steam stagnation properties are given. The CAESAR II “RELIEF LOAD SYNTHESIS” option is run to compute the maximum thrust load magnitude at the vent pipe exit. This dynamic load will act downward at the vent elbow nodes 65 and 100. Venting will last for approximately one second, and the opening and closing time for the relief valve (as provided by the manufacturer) is 8.0 milliseconds. A static load case is run first to perform spring hanger sizing at node 22. The static load case #3 is the operating case, and will be used to set the nonlinear restraints for the dynamic analysis.

SOLUTION: The spectrum table name is arbitrarily selected as “Relief” and is defined as having a Frequency range and a Force ordinate. (A # sign precedes the name in the spectrum definition because the shock table is to be read from an ASCII file on the hard disk.) The spectrum definition follows:

The DLF Spectrum Generator builds the ASCII file “Relief” that contains the relief valve spectrum table. Input to the DLF Spectrum Generator is the filename, maximum table fre-quency, number of points, and the time-history waveform. For this example a maximum frequency of 33 Hz and 20 data points are used to generate the table. The points in the time

7-10 Examples


history waveform are entered as shown as follows. These points represent the valve’s opening, its one second vent time, and its closing.

Examples 7-11


The resulting DLF Spectrum is shown below. The Frequency vs. Dynamic Load Factors are written to the file "Relief."

The thrust loads act at points 65 and 100. These loads are defined as Force Sets and are entered as shown as follows:

There is only a single Spectrum Load Case defined as follows:

7-12 Examples


There is one static/dynamic combination case of interest and that is the combination of the sustained static load case with our one dynamic load case. This is defined as follows:

Only one item needs to be set on the Control Parameter spreadsheet. It defines the static load case to be used for setting the nonlinear restraints, (3). Alternatively, the modal com-bination method could have been set to ABS instead of SRSS to produce unquestionably conservative results.

Examples 7-13


Relief Valve Loading - Output Discussion

There are four key reports for a relief valve analysis:

Mass Participation Report. This report illustrates how sensitive each of the piping system’s modes are to the relief valve firing. High modal participation factors indicate that the mode is easily excited by the applied dynamic forces. If subsequent displacement, restraint, or stress reports indicate excessive dynamic responses, then the modes having high participation must be dampened or eliminated. Once a particular mode is targeted as

7-14 Examples


being a problem, it may be viewed tabularly via the mode shape report, or graphically via the animated mode shape plots.

Examples 7-15


Displacement Report. This report gives the maximum possible positive or negative displacement that may occur at some time during the relief valve’s firing. Values in this report are always positive.

7-16 Examples


Restraint Report. This report gives the maximum dynamic load the support should be designed for. The top value is the maximum support reaction. The second value is the larg-est support reaction due to any one mode. The last number on the left tells which mode.

Stress Report. This report gives the maximum dynamic stress due to the relief valve fir-ing. Stresses from a dynamic shock load case should be combined with the sustained stresses from a static analysis and the result compared with the code defined occasional stress for the material.

The Participation Factor report shows which modes tend to be excited by the applied dynamic load.

The Displacement Report shows the maximum displacements that occur due to the relief loads. These displacements may actually be positive or negative. Their true sign is indeter-minate and always shown positive in the displacement report.

The following Stress Report shows element stresses due to the dynamic relief loads. The top value is the maximum stress due to the interaction of all the system modes. The second value is the largest stress due to any one mode. The bottom number on the left tells which mode.

For example:

Examples 7-17


The maximum stress at node 5 is 1486 psi. The stress at node 5 due only to mode #1 was 1288 psi.

The maximum stress at node 40 on the 40-50 element is 5864 psi. The stress at node 40 due to mode #4 was 3982 psi. Mode #4 was the largest contributor to the stress at node 40.

Support reactions due to the combination of the static sustained and the dynamic solutions.

7-18 Examples


Stresses due to the combination of the static sustained and the dynamic solutions. This stress combination can be compared to the B31 code allowables for occasional stresses.

Examples 7-19

Example 3: Dynamic Analysis of Water Hammer Loads (HAMMER) CAESAR II - Applications Guide

Example 3: Dynamic Analysis of Water Hammer Loads (HAMMER)

PROBLEM: The cooling water supply line shown as follows suffers a pressure surge when the turbine driven pump drops offline due to a bearing temperature problem. The elbow at node 45 is observed to “jump” 6 to 8 in. in the “X” direction when the turbine trip occurs.

Design an alternative support scheme to eliminate the large field displacements associated with the turbine trip.

Fluid Properties: 250 psi @ 140°F

Flow Velocity: 6 fps

Water Bulk Modulus: 313000 psi

SOLUTION: The magnitude of the pump supply side pressure wave which emanates from the pump discharge at node 5 can be estimated from

dp = ρ c dv

where:

7-20 Examples

CAESAR II - Applications Guide Example 3: Dynamic Analysis of Water Hammer Loads

dp - the pressure rise due to the pump’s “instantaneous” stopping

ρ - the fluid density

c - the speed of sound in the fluid

dv - the change in velocity of the fluid

The speed of sound in the fluid can be estimated from

c = [Ef / (ρ + ρ(Ef / E) (d/t) )] 0.5

where:

Ef - is the bulk modulus of the fluid (313000 psi)

E - is the modulus of elasticity of the pipe (30E6 psi)

d - is the pipe mean diameter

t - is the pipe wall thickness

ρ - is the fluid density (62.4 lbm/ft3)

ρ + ρ(Ef / E)(d/t) = 62.4 lbm/ft3 [1 + (313000/30E6) (8.625 -0.322)/0.322 ]

= 79.1875 lbm/ft3

c = (313000 lbf/ in2) (ft3/79.1875 lbm) (32.2 lbm ft/lbf sec2) (144in2 /ft2)1/2 = 4281 ft/sec

Note See the PIPING HANDBOOK, Crocker & King, Fifth Edition, McGraw-Hill pp. 3-189 through 3-191 for a more detailed discussion and evaluation of the speed of sound.

Apply the equation above for the magnitude of the water hammer pressure wave.

dp = ρ c dv = (62.4 lbm/ft3) (4281 ft/sec) (6.0 ft/sec)

= (62.4 lbm/ ft3) (4281 ft/sec) (6.0 ft/sec) (lbf sec2/32.2 lbm ft) ( ft2/144 in2)

= 345.6 psi

There are two distinct pressure pulses generated when a flowing fluid is brought to a stop. One pulse originates at the supply side of the pump, and the other pulse originates at the discharge side of the pump. This example only deals with the supply side water hammer effect, but the magnitude and impact of the discharge side water hammer load should like-wise be investigated when in a design mode.

Examples 7-21


The time history wave form for both types of water hammer pulses is shown as follows:

Pod - Discharge pressure

Ps - Source (tank or static) pressure

Pos - Suction pressure (while running)

dp - Pressure fluctuation due to the instantaneous stoppage of flow through the pump

pv - Liquid vapor pressure at flow temperature

There will be an unbalanced load on the piping system due to the time it takes the pressure wave to pass successive elbow-elbow pairs. The magnitude of this unbalanced load can be computed from:

F unbalanced = dp * Area

The duration of the load is found from t = L/c; where L is the length of pipe between adja-cent elbow-elbow pairs. For this problem the elbow-elbow pairs most likely to cause the large deflections at node 45 are 45-75 and 90-110.

The rise time for the unbalanced dynamic loading should be obtained from the pump man-ufacturer or from testing and can be determined from graphs such as those shown above. For this problem a rise time of 5 milliseconds is assumed.

CALCULATIONS:

L 45-75 = 7 + 4(20) + 4 = 90 ft.

L 90-110 = 3(20) + 15 = 75 ft.

Area = p /4 di2 ; di = 8.625 - (2) (0.322) = 7.981 in.

Area = p /4 (7.981)2 = 50.0 in2

F unbalanced = dp * Area = (345.6) (50.0) = 17289 lbf

t duration = L/c

= (90) / (4281) = 21 milliseconds, on leg from 45 to 75

= (75) / (4281) = 17.5 milliseconds, on leg from 90 to 110

t rise = 5.0 milliseconds

7-22 Examples


Because the piping in this example is ductile low carbon steel, the major design variable will be the large displacement; i.e. the problem will be assumed to be solved when the restraint system is redesigned to limit the large displacements due to water hammer with-out causing any subsequent thermal problem due to over-restraint.

First we generate the DLF Spectrum Files as follows.

Examples 7-23


7-24 Examples


Next we define the Spectrum:

Then we define the force sets as follows:

Three Spectrum load cases are of interest here: Each spectrum separately and the two of them in combination as follows:

Examples 7-25


The sustained static load case is now combined with each dynamic load case for code stress checks. Note that for operating restraint loads the static operating case would be combined with each dynamic load case as well. That is left for the user to investigate.

7-26 Examples


The Control Parameters should be set as follows:

Examples 7-27


Notes for Analyzing Water Hammer Loads

On the pump or valve supply side the magnitude of the pressure wave is calculated as shown in this example using: dp = ρ c dv.

On the pump or valve discharge side the maximum magnitude of the pressure wave is the difference between the fluid vapor pressure and the line pressure.

On the supply side a positive pressure wave moves away from the pump at the speed of sound in the fluid. The magnitude of the pressure wave is equal to the sum of the suction side pressure and “dp.”

On the discharge side a negative pressure wave moves away from the pump at the speed of sound in the fluid. The maximum magnitude of this “negative” pressure wave is the differ-ence between the pump discharge pressure and the fluid vapor pressure. Once the pump shuts down, the pressure at the discharge begins to drop. The momentum of the fluid in the downstream piping draws the discharge pressure down. If the fluid reaches its vapor pres-sure the fluid adjacent to the pump flashes. As the negative pressure wave moves away from the pump these vapor bubbles collapse instantly. This local vapor “implosion” can cause extremely high pressure pulses. In addition, there may be a fluid backflow created due to the rapid drop in pressure. In this case the backflow “slap” at the idle pump can be accentuated by the collapse of created vapor bubbles, resulting in an extremely large downstream water hammer loading.

Water hammer loadings will cycle to some extent. The pressure wave passes through the system once at full strength. Reflections of the wave may then cause secondary pressure transients. Without a transient fluid simulation or field data the usual procedure is to assume one or two significant passes of the pressure wave.

Where critical piping is concerned or where the maximum loads on snubbers and restraints is to be computed, the independent effect of a single pass of the pressure wave should be analyzed for each elbow-elbow pair in the model. A separate force spectrum load set is defined for the elbow with the highest pressure as the wave passes between the elbow-elbow pair. The direction of the applied force is away from the elbow-elbow pair. An indi-vidual dynamic load case is run for each separate force set, combinations of different force sets are usually not run. This approach has proved satisfactory when applied to large, hot steam piping systems that have very few fixed restraints, and a high number of low modes of vibration. Extrapolation to other types of piping systems should be made at the designers discretion.

CAESAR II does not check the integrity of the piping system due to the local increase in hoop stress that occurs as the fluid pressure wave passes each pipe cross-section.

The magnitude of the water hammer loads can be reduced by slowing the mechanism that tends to reduce the flowrate. In the case of valve closing, this means slowly closing the valve. In the case of a pump going off line, this means slowly removing power from the pump. “Slowly” in each of these instances can be estimated from:

T = 2L/c

where T = time of one wave cycle sec.

L = Characteristic length of the piping system. Usually taken as the length between the pump or valve and the source or sink.

c = Speed of sound in the fluid.

7-28 Examples


If the pump or valve stops in a time shorter than “T” then the water hammer should be ana-lyzed as shown in this example for “instantaneous” closure. Calculations for this problem are given as follows:

Of primary interest is the largest time that must be used to close a valve, or bring a pump flowrate to a halt such that water hammer type pressure pulses are not generated. Calcula-tions using the lengths of several reflecting systems will be made to get a “feel” for the variation of the computed “T’s.” The longest time will be for the wave to leave the supply side at node 5 and move to the tank connection at node 125. This represents a total “L” of about 270 ft.

T = (2) (270) ft./(4281)ft/sec = 126 milliseconds

The length through which the wave passes that causes the most trouble is thelength between nodes 45 and 75:

T = (2) (90)/(4281) = 42 milliseconds

So, if the pump or valve can slow down in greater than 126 milliseconds, the tendency for water hammer in the piping system will probably be abated. If the pump or valve can slow down in greater than 42 milliseconds then the tendency for water hammer in the 45-75 length will be abated.

Water hammer excitation initially produces axial acoustic waves in the steel pipe wall that can induce locally very high, very short duration forces and stresses. These short duration loads are usually not a design problem in ductile steel piping systems. Where crack propa-gation in welds and material due to water hammer loads is a concern the following rules should be followed:

• A very high number of natural frequencies must usually be included in the analysis. Cutoff frequencies of 300 Hz are not unusual. These are the axial natural modes of the pipe between the excited elbow-elbow pairs. Higher modes must be computed until the inclusion of extra modes doesn’t produce an appreciable change in the force/stress response. The maximum frequency cutoff can be estimated from SQRT (E/ρ)/L where: E = Pipe material modulus of elasticity, ρ = Pipe material density, L = Length of a single pipe element in the primary run that is to have accurate stresses computed due to the passing of the water hammer originated acoustic stress wave. Calculation of the maximum cutoff frequency for the 45-75 elbow-elbow pair for the 20 ft pipe lengths is given as follows:

f cutoff = SQRT (E/ρ)/L

= SQRT ((30E6)(32.2)(12)/(0.283))/20

= (202388 in./sec) / (20 ft. 12 in/ft)

= (843.3 rad./sec) / (2 π rad./cycles)

= 134.2 Hz.

Alternatively, including the Missing Mass Correction will approximate the contribu-tion from the omitted modes.

Examples 7-29


• The length of any element in the primary axial runs should not be greater than about ct/4, where c equals the speed of sound in the pipe and "t" equals the duration of the water hammer load. Calculation of the greatest element length for the 45-75 elbow-elbow pair is given as follows:

Lmax = ct/4

= (4281) ft/sec (0.021) sec/(4)

= 22.5 ft.

and so, to get an accurate estimate of the stresses due to the passing of the stress wave in the pipe, individual element lengths should be smaller than about 20 ft. Shorter duration loads require shorter elements to monitor the passing of the stress wave.

• The inclusion of the response due to the higher modes will not affect the displacement results (only the force and stress results). Displacement results, such as the 6 to 8 in. in the example can usually be computed accurately after the inclusion of the low fre-quency modes with participation factors greater than about 0.01.

Water Hammer Loading - Output Discussion

Mass Participation Report

This report illustrates how sensitive each of the piping system’s modes are to the water hammer dynamic loading. High modal participation factors indicate that the mode is eas-ily excited by the applied dynamic forces. If subsequent displacement reports indicate high dynamic responses then the modes having high participation must be dampened or eliminated. Once a particular mode is targeted as being a problem, it may be viewed tabu-larly via the mode shape report, or graphically via the animated mode shape plots.

Displacement Report

This report gives the maximum possible positive or negative displacement that may occur at some time during the event. Values in this report are always positive.

Restraint/Force/Stress Reports

If high modes are included, as discussed in the notes in this section, then these reports give the maximum values of the forces and stresses in the system due to gross deformation and the propagation of an acoustic stress wave in the pipe. If the high modes are not included, then these reports give the maximum values of forces and stresses in the system due to gross deformation alone.

Combination Cases

The force spectrum approach to the water hammer problem does not include consideration of the time relationship between modal or directional maximums. Completely conserva-tive results can be guaranteed by taking the absolute summation of both the modal and directional response properties. Running one load case for each main piping run, and a final load case including all of the individual load cases typically gives the analyst a “good feel” for where problems exist.

7-30 Examples


In this example the main piping run between nodes 45 and 75 added the major contribu-tion to the system dynamic responses. The combination load case including the 45-75 and 90-110 contributions together yielded little extra information.

Problem Solution

A guide and axial limit stop at nodes 45 and 105 produces little increase in thermal stresses (which were low to begin with), and serves to attenuate the large axial displace-ments in the line due to the water hammer load. Loads on this support due to the low mode displacements are seen to be small. Local, very short duration loads may not be so small. The restraint should be designed with this in mind. A few simple design rules are usually sufficient:

• Flexible is better. The restraint should only be stiff enough to sufficiently attenuate the low frequency gross deformation.

• Areas of local discontinuities, such as the weld of the support to the pipe, should have extra weld or support plate area (Discontinuities at other restraints in a problem area should probably also be “beefed up” to withstand the local passing of the impact stress wave.)

Examples 7-31


Portions of the CAESAR II output reports for this job are shown as follows:

7-32 Examples


Examples 7-33


7-34 Examples


Examples 7-35

Example 4: Dynamic Analysis of Independent Support Earthquake Excitation (CRYISM)CAESAR II - Appli-

Example 4: Dynamic Analysis of Independent Support Earthquake Excitation (CRYISM)

PROBLEM: The cryogenic piping system shown on the following page is to be designed in accordance with B31.3 using the ground, building, and enve-lope spectra shown. Two analyses are to be run:

• Assume the pipe (structural steel) supports are rigid.

• Include the flexibility of the structural steel supports by including the steel frames in the analysis.

Finally, compare the results from the two analysis.

Design parameters are:

Ambient Temperature: 100°F

Operating Temperature: -59°F

Pipe: 8-in. Sch 10S

Insulation: 4-in. 22.3 lb/cu ft

Fluid: 0.232 SG

Columns: W14x82

Beams: W10x12

Cryogenic Piping Dynamics Example

The isometric of the complete model is shown in the following figure. This drawing shows the piping, pipe supports, and the structural steel frames.

7-36 Examples

CAESAR II - Applications Guide Example 4: Dynamic Analysis of Independent Support

The excitation spectra to be applied to this model are

Ground Response Spectra Building Response Spectra Envelope Response Spectra “Ground Response” “Building Response” “Envelope Response”

T, sec V, in/sec T, sec V, in/sec T, sec V, in/sec

0.05 0.787 0.05 0.787 0.05 0.7870.2 7.874 0.2 1.3 0.2 7.8740.5 21.653 0.5 3.4 0.5 21.6531 39.37 1 27.3 1 39.372 18.89 2 30.4 2 30.43.5 43.7 3.5 21.12 3.5 43.75 11.8 5 21.3 5 21.3

10 5.9 10 5.359 10 5.9

Examples 7-37


The necessity for the various spectra can be best understood by investigating the differ-ence between independent support excitation and uniform support excitation. These exci-tation methods are shown in the following figures.

7-38 Examples


For the analysis with steel supports, the structural steel must be included as part of the pip-ing model. This can be accomplished by using the Include Structural Input Files option from the KAUX feature of the CAESAR II spreadsheets.

The structural steel model for this problem can be generated by invoking the structural input from the Main Menu. The input listing from the structural input session is shown as follows:

SECID=1, W14 X 82; COLUMN CROSS SECTION

SECID=2, W10 X 12; BEAM CROSS SECTION

MATID=1, YM=29E6 POIS=0.3 G=11E6 DENS=0.283

DEFAULT SECID=1

ANGLE=90

EDIM 1038 1039 DY=15-0; DEFINE ALL COLUMNS

EDIM 1043 1044 DY=15-0

EDIM 1048 1049 DY=15-0

EDIM 1053 1054 DY=15-0

DEFAULT SECID=2

ANGLE=0

EDIM 1039 1040 DZ=-2-0;DEFINE ALL BEAMS

Examples 7-39


EDIM 1044 1045 DZ=-2-0

EDIM 1054 1055 DZ=-2-0

FIX 1038 ALL

FIX 1043 ALL

FIX 1048 ALL

FIX 1053 ALL

The dynamics input for this problem is summarized in the figure that follows. Details of the dynamics input are contained on the following pages.

7-40 Examples


Examples 7-41


In order to keep the documentation for this example brief, the only results presented are those for the “uniform support excitation” case. Using this load case, the model with and without structural steel supports will be compared. The results from these two models are shown in the tables that follow:

7-42 Examples


DISPLACEMENTS

X Y Z RX RY RZ

35 with 0.4253 0.0336 1.5831 0.4298 0.5932 0.0622

without 0.0049 0.0076 1.0334 0.2902 0.3832 0.0033

45 with 0.4240 0.0379 3.7952 0.2311 0.5550 0.0412

without 0.0036 0.0 1.9555 0.1635 0.2576 0.0007

50 with 0.4219 0.0447 3.7435 0.1911 0.5695 0.1220

without 0.0020 0.0 1.4764 0.0817 0.4083 0.0002

60 with 0.3799 1.4247 0.5930 0.3613 0.3534 0.2322

without 0.0366 0.5838 0.0635 0.0292 0.0425 0.0236

75 with 0.8484 1.3529 1.3033 0.5127 0.4247 0.4924

without 0.6447 0.5631 1.1291 0.4482 0.3346 0.2114

90 with 0.5927 0.4228 0.2087 0.3816 0.5229 0.4461

without 0.4689 0.3414 0.1815 0.3425 0.4236 0.2465

RESTRAINT LOADS

X Y Z RX RY RZ

5 with 241 319 523 4761 981 1133

without 207 353 353 3114 647 1001

40 with 146 1118

without 18 597

45 with 229without 4

50 with 754

without 1

55 with 2029 1939 1154 1536 384819

without 976 1408 596 434 8100 11638

Examples 7-43


65 with 956 1101

without 580 560

70 with 538 895

without 500 743

80 with 236

without 110

115 with 743 253 429 2531 1568 4025

without 504 200 359 2286 1339 2701

STRESSES

AXIAL BENDING TORSION MAX OCT CODE

20F with 80 20614 1742 9834 20639without 88 13344 1151 6363 13350

35F with 22 13454 571 6366 13468without 17 8558 280 4041 8559

40 with 164 7179 571 3431 7211without 122 4779 280 2265 4782

45 with 297 11001 571 5246 11081without 193 7963 280 3762 7966

55 with 429 16435 571 7832 16582without 232 11664 280 5504 11667

55 with 140 15886 1009 7600 16024without 86 17125 148 8114 17210

60F with 340 20784 696 9920 21114without 357 12164 414 5911 12520

75F with 69 11489 375 5448 11539without 59 6208 281 2963 6267

7-44 Examples


Discussion of Results

These comparison tables illustrate the differences that can exist when the structural steel models are not included in the analysis. In some cases, the results with the structural steel included are many times higher than the results computed without the structural steel. The steel models add flexibility to the piping system. More flexibility means lower natural fre-quencies and more modes to be excited by the shock. A comparison of the natural frequen-cies of the two models is given as follows:

NATURAL FREQUENCIES

No. With Structure Without Structure

1) 1.307 1.706

2) 2.244 2.533

3) 2.520 3.371

4) 3.149 3.936

5) 3.443 4.384

6) 4.206 5.294

7) 4.404 5.929

8) 5.250 8.957

9) 5.675 11.849

10) 5.761 16.367

11) 5.988 16.564

12) 6.594 20.588

13) 7.992 22.954

14) 11.855 23.474

15) 14.086 25.582

16) 14.086 29.685

17) 14.086 35.083

18) 16.504

19) 15.554

20) 20.333

21) 20.589

22) 20.909

23) 20.909

24) 20.909

25) 23.052

26) 23.475

27) 25.582

Examples 7-45


28) 38.085

In the above table, there are only five extra mode shapes for the system which includes the structure.

The restraint moment at node 55 in the Z direction is much larger without the steel model than it is with the steel model. Even though the piping is tied to the steel, the steel frame will not support much moment in the Z direction. The steel frame bends slightly about the Z axis, and the moment is carried through from the pipe. In the “piping only” model, the rigid anchor at node 55 will not rotate about the Z axis (or any other axis) and so ends up carrying all of the moment load.

7-46 Examples

CAESAR II - Applications Guide Example 5: Structural Analysis (FRAME)

Example 5: Structural Analysis (FRAME)

PROBLEM: Analyze the braced frame shown below subjected to the givenuniform load and self weight.

Column section data: area = 15 in2 inertias = 250 in.4

Beam section data: area = 10 in2 inertias = 500 in.4

Brace section data: area = 5 in2 inertias = 1 in.4

Material density: 490 pcf

Beam loading: 200 lb/in.

This example shows how to model a structure using the CAESAR II structural preproces-sor.

The figure below shows a single bay, braced space frame. All beam and column lengths are 50 in. as shown. This frame is subjected to its own weight load as well as a uniform load of 200 pounds per inch on all of the top level beams. We wish to know the displace-ments, reactions, and element forces for three load cases: self weight, uniform load, and self weight plus uniform load.

This example will illustrate how to use most of the keyword directives in the structural preprocessor. A standard finite element modeling approach will be followed, where the system nodes are defined, then materials and section properties, then elements, and finally the loading.

Examples 7-47

Example 5: Structural Analysis (FRAME) CAESAR II - Applications Guide

To process the input file Frame.str start the structural preprocessor by selecting option File-Open from the Main Menu then select the type of file as Structure and select the examples directory to find the file.

Next, select Input-Structural Steel from the Main Menu to enter the input window shown (only the input portion of the window shown here). Press the Save button or choose File-

7-48 Examples


Save from the structural processor to error check and save the model. You may also want to view the plot of the model before you exit.

Examples 7-49


After the input has been saved and error checked exit the structural steel input processor to go back to the Main Menu. The analysis can be started immediately by selecting option Analysis-Statics. At this point CAESAR II will read the binary files created by the struc-tural preprocessor and recommend load cases. Note, in all probability you will not want to analyze the structure with the recommended load cases. CAESAR II recommends load cases to satisfy piping code compliance. Therefore occasional loads (like the current uni-form load) will not be used. Edit the load cases as shown below. Note that load case 2 con-sists of only U1 and that it is designated as an operating case. It is purely a construction case and is segregated here only because it may be interesting to see the loads produced by the Uniform Load solely.

7-50 Examples


The results for this analysis are shown in the following nine figures:

Examples 7-51


7-52 Examples


Examples 7-53


7-54 Examples


Examples 7-55


7-56 Examples


Examples 7-57

Example 6: Dynamic Analysis (NUREG9) CAESAR II - Applications Guide

Example 6: Dynamic Analysis (NUREG9)PROBLEM: Analyze the piping system shown on the following page subjected to a

series of shock spectra.

This problem is one of the NRC benchmark problems run to verify the dynamic capabili-ties of CAESAR II. The detailed input will not be shown or discussed in this example. Users will find the necessary input files on the examples diskette. For those users inter-ested, this problem was taken from: NUREG/CR -1677, BNL-NUREG-51267, VOL II, August 1985.

NRC Example NUREG9

This problem is a three-branch system, composed of 20 pipe elements and 14 support ele-ments. The support elements are divided into four groups corresponding to four distinct input excitation spectra sets. This problem demonstrates the independent support motion feature of CAESAR II.

In modeling this problem, the 14 support elements were input as restraints with stiffnesses. All bend elements include a node at the “near” point to insure mass and stiffness computa-tions consistent with the NRC example. Users should note that in addition to the pipe den-sity, there is a single lumped mass applied at node 18.

For this example, the contributions from the pseudo-static anchor point displacements are not included. The three solutions presented represent the following:

• envelope spectrum; spatial then modal combinations

• ISM (independent support motion); directional, spatial, then modal combinations using SRSS

• ISM; directional, spatial, then modal combinations using ABS

7-58 Examples

CAESAR II - Applications Guide Example 6: Dynamic Analysis (NUREG9)

Examples 7-59


NRC BENCHMARK SERIES

NRC BULLETIN NUREG-51267 VOL.II 1980.

NRC PROBLEM 2A CAESAR II JOB NUREG9

NATURAL FREQUENCY REPORT (Hz)

MODE NRC CAESAR II

1 9.360 9.362

2 12.71 12.708

3 15.38 15.379

4 17.80 17.800

5 21.60 21.606

6 25.10 25.102

7 32.03 32.039

8 38.07 38.075

9 40.29 40.299

10 48.90 48.905

11 57.51 57.524

12 61.50 61.510

13 62.54 62.550

14 69.35 69.359

15 77.44 77.456

16 78.88 78.893

17 101.7 101.731

18 103.6 103.598

19 108.0 107.983

20 115.1 115.116

21 135.2 135.265

22 155.2 155.244

23 160.6 160.626

24 203.8 203.820

7-60 Examples


25 209.9 209.957



TRANSLATIONS (in)

DX DY DZ

NODE NRC CAESAR II NRC CAESAR II NRC CAESAR II

2 .0105 .0105 .0 .0 .0250 .0250

4 .0431 .0431 .0049 .0049 .0907 .0907

6 .0475 .0475 .0253 .0252 .0327 .0327

8 .0280 .0280 .0379 .0379 .0491 .0491

10 .0108 .0107 .0249 .0249 .0631 .0631

12 .0285 .0285 .0186 .0186 .0633 .0633

14 .0849 .0849 .0085 .0085 .0635 .0635

16 .0476 .0476 .0001 .0001 .0402 .0401

18 .0286 .0286 .0318 .0138 .0421 .0421

20 .0131 .0131 .0095 .0095 .0001 .0001

ROTATIONS (deg)

RX RY RZ


2 .0457 .0457 .0260 .0260 .0190 .0190

4 .0515 .0515 .0688 .0688 .0269 .0268

6 .0389 .0389 .1012 .1012 .0268 .0267

8 .0309 .0309 .0950 .0949 .0217 .0217

10 .0201 .0201 .0289 .0289 .0203 .0203

12 .0105 .0105 .0328 .0328 .0224 .0224

14 .0102 .0102 .0514 .0511 .0299 .0299

16 .0359 .0359 .0496 .0496 .0476 .0476

18 .0105 .0105 .0343 .0343 .0128 .0127

20 .0215 .0214 .0273 .0273 .0090 .0090

Examples 7-61




SUPPORT FORCES (lb)

FX FY FZ


1 90 90 65 64 177 177

7 0 0 0 0 708 707

9 446 445 0 0 0 0

11 0 0 206 206 0 0

13 0 0 164 164 0 0

15 188 187 188 187 263 262

17 58 58 198 197 103 103

21 378 377 192 191 245 245

TRANSLATIONS (in)

DX DY DZ

NODE NRC CAESAR II NRC CAESAR II NRC CAE-SAR II

2 .0064 .0064 .0002 .0 .0158 .0158

4 .0267 .0267 .0031 .0031 .0574 .0574

6 .0295 .0295 .0162 .0162 .0207 .0207

8 .0170 .0170 .0242 .0242 .0311 .0311

10 .0029 .0029 .0152 .0152 .0399 .0399

12 .0103 .0103 .0110 .0110 .0400 .0400

14 .0530 .0530 .0053 .0053 .0401 .0401

16 .0301 .0301 .0001 .0001 .0255 .0255

18 .0103 .0103 .0187 .0187 .0267 .0267

20 .0033 .0033 .0057 .0057 .0 .0

7-62 Examples


NRC BULLETIN NUREG-51267 VOL.II 1980

NRC PROBLEM 2B CAESAR II JOB NUREG9

ROTATIONS (deg)

RX RY RZ


2 .0289 .0289 .0165 .0165 .0116 .0116

4 .0326 .0326 .0435 .0435 .0172 .0171

6 .0247 .0247 .0641 .0640 .0171 .0171

8 .0199 .0199 .0599 .0598 .0132 .0132

10 .0134 .0134 .0075 .0075 .0120 .0120

12 .0071 .0071 .0204 .0204 .0134 .0134

14 .0062 .0062 .0307 .0307 .0184 .0184

16 .0228 .0228 .0276 .0276 .0301 .0301

18 .0070 .0070 .0208 .0208 .0079 .0079

20 .0128 .0128 .0074 .0074 .0053 .0053

SUPPORT FORCES (lb)

FX FY FZ


1 53 53 46 46 113 112

7 0 0 0 0 441 440

9 257 256 0 0 0 0

11 0 0 123 123 0 0

13 0 0 98 98 0 0

15 111 111 111 111 156 155

17 32 32 124 123 66 66

21 103 103 114 113 116 115

Examples 7-63


NRC BENCHMARK SERIES


NRC PROBLEM 2C CAESAR II JOB NUREG9

TRANSLATIONS (in)

DX DY DZ


2 .0090 .0090 .0 .0 .0220 .0220

4 .0373 . 0372 .0044 .0044 .0800 .0800

6 .0411 . 0411 .0235 .0235 .0289 .0288

8 .0237 . 0237 .0355 .0355 .0434 .0434

10 .0043 . 0043 .0227 .0227 .0556 .0556

12 .0148 . 0148 .0164 .0164 .0558 .0558

14 .0741 . 0740 .0074 .0074 .0560 .0560

16 .0420 . 0420 .0001 .0001 .0355 .0355

18 .0148 . 0148 .0281 .0372 .0372 .0372

20 .0049 . 0049 .0085 .0085 .0001 .0001

ROTATIONS (deg)

RX RY RZ


2 .0402 .0402 .0229 .0229 .0163 .0163

4 .0456 .0455 .0606 .0605 .0244 .0244

6 .0347 .0346 .0894 .0893 .0252 .0252

8 .0282 .0282 .0835 .0835 .0196 .0196

10 .0197 .0197 .0112 .0112 .0179 .0179

12 .0104 .0104 .0285 .0285 .0199 .0199

14 .0092 .0092 .0429 .0429 .0260 .0260

16 .0318 .0317 .0387 .0387 .0421 .0420

18 .0104 .0104 .0291 .0291 .0116 .0116

20 .0191 .0191 .0110 .0110 .0079 .0079

7-64 Examples



NRC PROBLEM 2C CAESAR II JOB NUREG9

SUPPORT FORCES (lb)

FX FY FZ


1 76 76 70 69 156 155

7 0 0 0 0 607 607

9 350 350 0 0 0 0

11 0 0 184 184 0 0

13 0 0 146 146 0 0

15 151 151 151 151 212 211

17 45 45 169 168 91 90

21 152 151 170 169 158 157

Examples 7-65

Example 7: Omega Loop Modeling (OMEGA) CAESAR II - Applications Guide

Example 7: Omega Loop Modeling (OMEGA)PROBLEM: The “Omega” expansion loop consists of a series of back to back 135

degree bends. Generate a piping model of an Omega loop according to the following sketches.

DESIGN PARAMETERS:

Pipe: 3-in., standard wall

Bend Radius: 24 in.

Material: low carbon steel

Temperature: 200°F, 300°F, 400°F

The objective of this example is to illustrate the techniques necessary to code a series of back to back bends. For this example, we will use an Omega loop as shown below.

The given dimensions are the 6-ft 10-in. height, the 2-ft bend radius, and the bend angles of 135 degrees and 270 degrees. From this information the other dimensions shown in the figure can be derived.

In coding a series of back to back bends it is important to remember that the delta dimen-sions should be measured from tangent intersection point (TIP) to tangent intersection point. (See Chapter 2 of the Applications Guide for additional information on the proper coding of bends.)

Figure 1

7-66 Examples

CAESAR II - Applications Guide Example 7: Omega Loop Modeling (OMEGA)

Figure 2 shows the node points which will be coded on the spreadsheets to model the Omega loop. (The model will be anchored at nodes 1 and 35.) The first bend (lower left bend) will span between nodes 5 and 10. Note that the TIP 10, is far to the right of the bend. For analysis and output, the actual location of node 10 is at the far weld line, as shown in Figure 3.

The second bend (upper left bend) will span between nodes 10 and 15. Recall that we code TIP to TIP. Therefore the delta coordinates entered on the spreadsheet are the X and Y dis-tances between nodes 10 and 15 on Figure 2. The actual location of node 15 is at the far weld line, shown in Figure 3. Node 15 is the TIP for this bend, and lies to the left of the pipe.

The third bend (upper right bend) spans between nodes 15 and 20, where node 20 is TIP. In coding from TIP to TIP, only a delta X is required. Figure 3 shows the actual location of node 20 on the pipe.

The fourth and final bend (lower right bend) spans between nodes 20 and 25. In this case, a delta X and a delta Y are required. The actual location of node 25 is shown on Figure 3. The element from 25 to 30 is a straight element necessary to finish off the bend. (Recall a

Figure 2

Examples 7-67


bend in CAESAR II requires an element beyond the far weld line to determine its orienta-tion.)

Below is an input listing for the model. The delta dimensions shown were obtained from Figure 1. Note that 3 additional, equally spaced points are located on each bend.

Note This example requires a change in Configuration/Setup to allow the error checker to accept large angle (> 95 deg.) bends.

Figure 3

7-68 Examples


Examples 7-69


The following figures depict line and volume input plots from the CAESAR II preproces-sor. It should now be obvious why volume plot should always be reviewed. This will insure the model is as the analyst thinks it is.

7-70 Examples


Examples 7-71

Example 8: Jacketed Piping (JACKET) CAESAR II - Applications Guide

Example 8: Jacketed Piping (JACKET)This example is intended to serve as a guide for modeling techniques used in the analysis of jacketed piping systems. Where applicable, various alternatives are discussed that may be benefit specific systems or problems.

The piping system to be analyzed is shown in the following figure. The piping system con-sists of an 8-in., schedule-40 crude oil line and a 12-in., schedule-40 steam jacket. The section of piping from the pump to the valve is completely jacketed, while the section from the valve to the vessel has only the straight sections jacketed. (This variation in the jacket is used to illustrate the two common types of jacketed systems.) The core pipe is supported in the jacket through the use of spiders. These spiders provide translational restraints in two directions, normal to the axis of the pipe. For this system, the spiders are located at each elbow weld line, and in the straight runs such that the spider spacing does not exceed 6 ft. For this system, both the jacket and the core are low carbon steel.

Note In some systems, the jacket and the core consist of different materials. This condi-tion must be modeled very carefully, since the thermal growth in the core will be different from the thermal growth of the jacket. Improper axial restraints in such a system can cause extremely large loads in the pipe.

7-72 Examples

CAESAR II - Applications Guide Example 8: Jacketed Piping (JACKET)

Step 1 - Modeling Plan

The first step in modeling any system is to consider the most efficient way to create the input, and more importantly, how to best review the results. By deciding how to best review the results, the input node numbering scheme can be setup. From the node number-ing scheme, one can decide how to generate the model to take advantage of the various rotate, duplicate, and include options.

For this example system, the core piping will be modeled using node numbers from 1000 to 1999, and the jacket will be modeled using node numbers starting at 2000. Additionally, similar locations on the two systems will have the same base node number, i.e. 1110 and 2110 describe the same point on both the core and the jacket. Setting up the node numbers in this manner enables one of the systems to be generated from the other, using either the duplicate or the include options of the input preprocessor. The systems can also be viewed individually in the plot by using the Range command and breaking the model at 1999. The other advantage to this scheme is that when reviewing output we can tell immediately from the node number whether the point in question belongs to the core or the jacket.

Although not necessary for a small system such as this, additional node number ranges can be employed to differentiate parts of the model. To illustrate this concept, the following additional constraints will be placed on the node numbers. The ground level piping will have nodes in the 100-400 series, while the second level piping will have nodes in the 500-900 series. For example, node 1110 will be a core node at ground level, and node 2550 will be a jacket node on the second level. To indicate locations where external supports are applied to the system, node numbers will end in 5, all other points will be multiples of 10. Similar node numbering schemes can be used to differentiate branches from headers, pipe from structural steel, and various line sizes. A little thought and planning at the start of a model can ease both input verification and output review. For example, consider review-ing the input for this system and finding a spring hanger at node 1530. This should quickly be recognized as an error since the 1000 series nodes make up the core piping, and can’t utilize spring hangers. Additionally, a support node should end with a 5.

Step 2 - Layout of Nodes

The system as defined in the preceding figure consists of nine segments of piping. Each segment is shown in the following figure with the node numbers assigned to the various points for the core piping. Each segment is discussed in the following paragraphs.

Please note, the term segments is used solely to assist in discussing this example.

CAESAR II does not require the segregation of a piping system into segments. There are no such input requirements or restrictions in CAESAR II.

Examples 7-73


Core Pipe Layout

Segment A

This segment runs from the pump to the first elbow. Since this section is at ground level the 100 series nodes will be used. Since the pump acts as an anchor, the start node of this segment will end in 5, thus the pump is assigned node 1105. The length of the segment requires an intermediate node point for a spider, thus node 1110 is assigned 5 ft from the pump. Nodes 1120 and 1115 are assigned to the elbow. Note that the +Y support is not at node 1115, since 1115 is part of the core piping. The +Y will be applied at node 2115 (the jacket), and therefore we assign the “5” to this node point.

Segment B

This segment is the six foot vertical section, beginning with the elbow at 1120. This sec-tion can be simply modeled by coding to the top elbow and assigning nodes 1500 and 1510. Note that we are using the 500 series nodes here, because we are now modeling the 2nd level piping.

Segment C

The first horizontal run in the 2nd level requires a node at mid-span to accommodate a spring hanger (on the jacket). This mid-span node will divide the segment into two 9 ft lengths, which exceed the maximum spider spacing of 6 ft. Therefore, the eighteen foot span will be divided into four elements, each 4 ft 6 in. The nodes assigned are 1520,

7-74 Examples


1525 (for the hanger location), and 1530. The segment is finished off with the elbow mod-eled by nodes 1540 and 1550.

Segment D

This horizontal segment in the 2nd level is modeled using nodes 1560, 1570, and nodes 1575 and 1580 at the elbow. The nodes 1560 and 1570 are for spiders while 1575 is a hanger location.

Segment E

This horizontal segment contains the valve. Nodes for this segment are: 1590, 1600, 1610, and 1615. Note that node 1615 terminates the elbow and is also a hanger location. The ele-ment from 1590 to 1600 should be declared rigid with a weight of 452 lb. Note also that starting with the elbow 1610-1615, all of the elbows will be modeled as individual ele-ments. This will ease the coding of the jacket later on. The elbows in this part of the model will consist of two straight pieces of pipe, equal in length to the radius of the elbow.

Segment F

The third horizontal leg of the expansion loop, modeled using nodes 1620, 1630, 1640, and 1650.

Segment G

The last horizontal run of the 2nd level is modeled using nodes 1655, 1660, and 1670. Note that 1655 is a hanger location.

Segment H

The second vertical section of piping returns the system to ground level. The only addi-tional nodes required for this section are for the elbow, at 1130 and 1135. The node 1135 is a +Y location on the jacket.

Segment I

This is the last segment that terminates at the vessel nozzle. The nodes used to model this segment are: 1140, 1150, and 1155.

Step 3 - Input of Core Piping

During the input of the above sections, frequent use of the CAESAR II plot facility should be made. This will insure that the system is being modeled correctly and that any input errors are detected as soon as possible. The following figure shows a volume plot of the completed core piping, with node numbers and anchors.

Examples 7-75


Completed Core Piping

At this phase of the input, it would be prudent to save the input file and invoke the CAESAR II error checker. Running the error checker at this time is a wise idea, because we intend to use the core piping model to generate the jacket piping model. Any errors that exist in the core will be duplicated in the jacket, thus doubling our correction efforts.

The additional data required to finish the model (allowable stresses, temperatures, pres-sures, etc.) are contained in the CAESAR II input file which accompanies the software. This data is found in the file Jacket._a in the Examples subdirectory of the Caesar II instal-lation directory.

Step 4 - Input of Jacket, 1st Half

At this point there are several ways to obtain the jacket model. The first and obvious method is to continue with the spreadsheet input and simply build the jacket. The second method is to duplicate the core pipe input file, and then use the “include” feature to com-bine the two models. The third method is to use the “List” processor and duplicate the nec-essary elements from within the preprocessor. The later method is the one we will use for this example.

The modeling of the jacket will begin by invoking the List processor from the CAESAR II spreadsheet by choosing the Edit-List menu option. The various list options are available by choosing the appropriate tab at the bottom of the window. We want to choose the Elements tab, which is the default. The resulting list of the elements contains their associated delta coordinates. This screen is shown as follows:

7-76 Examples


Core Pipe Input Listing

For the first half of the jacket, we will duplicate the core piping. The duplicated region will start at the pump and terminate at the valve. The duplication can be accomplished by per-forming the following steps:

1. Click the mouse cursor to the row number for the element from 1105 to 1110.

2. Click the mouse cursor, while holding the shift-key down, to the row number for the element from 1580 to 1590, which is the element just before the valve. All rows between our two selections should now be highlighted.

3. Next, select Block - Duplicate to generate the duplicate dialog box. Click on the radio button for identical. Choose the radio button to place the duplicate block at end of input. Specify 1000 for the node increment.

4. After clicking OK to dismiss this Window and again to dismiss the Duplication Status Window, CAESAR II will duplicate the block and increment all of the node numbers by 1000. This will result in a section of pipe identical to the pipe from 1105 to 1590 with node numbers from 2105 to 2590.

Examples 7-77


Three changes must be made to the new section of pipe to obtain the jacket piping. First the diameter and wall thickness must be changed to 12 in., schedule 40. This is easily accomplished in the List Editor by finding the element from 2105 to 2110, and simply typ-ing over the current values. The following values should also be specified here: jacket temperature, jacket pressure, jacket insulation, and jacket fluid weight. The final modifica-tion requires changing all of the jacket bend radii from long to short. The best way to accomplish this change is to enter the Bend list by clicking on the Bend tab on the bottom of the list window. Then, starting at the bend at node 2120, change the radius from Long to 12.0 in. This change must be made to all of the following bends.

Once the above changes have been made, the 1st half of the jacket is finished. A volume plot of the system will now show the core piping overlaid by the jacket piping.

7-78 Examples


Note Even though the two models are correctly positioned with respect to each other, they are not connected. All we have done so far is duplicate several pipes. The fact that the graphics shows them positioned properly is merely coincidence. As far as CAESAR II is concerned, we have two discontiguous systems in the same input file. The graphics module plots discontiguous systems such that they all start from the same point, which is why the jacket and core line up properly in this case.

The next step is to correctly connect the jacket to the core, and apply any external restraints. The connection between the jacket and the core piping will model the spiders that align the two in the real system. These connections can be modeled in CAESAR II by using restraints with connecting nodes (CNodes).

Note A CNode associates degrees of freedom. Simply stated, if a CNode connects two nodes in the Y-direction, they will experience identical displacements in the Y-direction. Use CNodes to restrain two nodes to each other without restraining them to the "outside world."

The modeling of the connection between the jacket and the core will start at the pump. On the very first spreadsheet of the model, the restraint field should be entered. Then add a restraint at node 1105 with a CNode at 2105 of type "anchor." This will associate all six degrees of freedom between nodes 1105 and 2105.

On the same spreadsheet, add two restraints at node 1110. Both of these restraints have a CNode at 2110, one in the Y-direction, and one in the Z-direction. These two restraints model the spider between the core and the jacket.

Note The spider was not modeled using gaps. The actual clearance between the spider and the pipes is very small, and attempting to numerically model this clearance using restraints with gaps causes the job to be highly non-linear. Models with gaps at each spider will have convergence problems and in all probability never reach a solution.

The next spreadsheet from 1110 to 1120 defines the first elbow. A total of four restraints should be added to this spreadsheet: at 1115, put a CNode of 2115 with Y and Z-direction restraints, at 1120, put a CNode of 2120 with X and Z-direction restraints. Note that these restraints are perpendicular to the axis of the pipe. Also recall that at 2115 we have an external restraint, a +Y. This support should be added to the system on the spreadsheet containing the node 2115.

In similar fashion, the remaining spiders should be added to the model (see the example job “JACKET” found in the Examples directory to review these restraints). When node 1590 is reached, the CNode at 2590 is connected with an Anchor. The spring hangers at nodes 2525 and 2575 should also be added.

Aside from the two anchors at the pump and the valve, all of the spider connections between the jacket and the core are modeled using two perpendicular restraints, with con-necting nodes. How are the other four degrees of freedom restrained? What keeps this model from undergoing rigid body motion? These questions can be resolved by consider-ing two points. First, the jacket is continuous over the core from the pump to the valve. At both of these points we have connected all six degrees of freedom. Second, the transla-

Examples 7-79


tional restraints obviously prevent motion in the three translational directions. Addition-ally, these restraints also prevent rotation, because the jacket is continuous.

Note Whenever a model is constructed, you must insure that the model, or parts of the model, cannot undergo rigid body motion. Such a model produces a singular stiff-ness matrix, and the solution can not be attained. An example of such a poor model is a cantilever beam with a hinge at mid span.

At this point in the input session, the user should invoke the error checker (click on the single running man button). The input will be saved and any errors reported should be cor-rected at this time.

Step 5 - Input of Jacket, 2nd Half

The input of the 2nd half of the jacket is more complex than the 1st half, since the jacket only covers the straight runs of piping. For this reason, the jacket elements will be coded manually, as opposed to any form of duplication. Duplicating portions of the model would work, however the extra time involved in deleting the jacket from the elbows is greater than the time required to input only the straight sections. By modeling the jacket directly, the restraints for the spiders can be input as we encounter them.

To start the input session, enter Piping-Input and press [Control-End] to go to the last spreadsheet in the model. At this point, press the continue button and change the node numbers to 2600 and 2610, with a DX of 5 ft. Where is the element from 2600 to 2610? Return to the spreadsheet and temporarily change the diameter of 2600-2610 to 24 in., and try the volume plot. The element 2600-2610 has been positioned at the plot origin, because at this time the element is not connected to anything. Return to the spreadsheet and correct the diameter, back to 12-in. nominal.

To properly connect the jacket to the core, restraints must be added at 2600 and at 2610. At 2610 a CNode of 1610 will be added with restraints in the Y and Z-directions. At 2600, we need a CNode of 1600. Avoid the temptation to associate these two nodes (2600 and 1600) in the Y and Z-directions as this is incorrect and will produce an unstable model. The rea-son for this is because doing so would allow the jacket to move freely in the X-direction and to spin about the X-axis, hence we have a mechanism. Note that we did not have this problem in the first half of the model since the jacket was continuous over the elbows and the model was three dimensional in nature. We must ensure that in this half of the model the appropriate axial and torsional restraints are applied to the jacket. At node 2600, we will model an Anchor to 1600. (This is simpler than modeling separate X, Y, Z, and RX restraints.) This causes the 8-in.line to be physically connected to the 12-in.line in all 6 degrees of freedom.

The next jacket element covers the core from 1616, the end of the elbow, to 1640. The node 2615 is anchored to 1616 via a CNode.

The next two elements 2620-2630 and 2630-2640 are standard pipe element with a DZ of -4.333 ft. Each To- node is connected to the corresponding core node with a CNode asso-ciating the X and Y-directions.

The remaining three sections of jacket are modeled in exactly the same manner. The final step in the modeling is to add the spring hangers at nodes 2615 and 2655, and the +Y restraint at 2135. The completed model is shown below in the following figure.

7-80 Examples


Completed Jacketed Piping System

The completed input file can be found as part of the “examples” set, under the job name JACKET. Once the input task has been completed, the job must be error checked and then analyzed for the specified loading conditions. The resulting output should be checked to ensure that the system was modeled correctly. These checks should include the following:

• Verification of the weight of the core system, the jacket system, and the combined sys-tem. The “Sustained-Restraint” report can be used for this check. Be sure that the jacket pipe fluid density accounts for the volume lost due to the core. CAESAR II does not do this automatically, the user must reduce the density of the jacket fluid accordingly.

• Verify that the piping system does not develop large axial loads in either the core, the jacket, or equipment anchors. This can be caused by improperly over restraining the pipe in the axial direction, or the effects of thermal growth on dissimilar metals.

• Check the displacements at the elbows in the operating case and make sure that the core pipe does not tend to move through the jacket. It is important to note that CAESAR II does not perform interference checking.

• Check the displacements at the spiders, where the jacket and the core are connected. In the direction of the spiders the displacements should be the same for both the jacket and the core.

• If wind or wave loads are specified, they should be disabled on the core piping.

• The core pipe should probably have its insulation thickness set to zero.

Examples 7-81

Example 9: WRC 107 CAESAR II - Applications Guide

Example 9: WRC 107The example problem which follows goes through a comprehensive local stress analysis of a vessel/nozzle using WRC 107 and ASME Section VIII, Division 2 criteria.

In order to determine whether the WRC 107 Bulletin is appropriate for the computation of the local stress state in the vessel due to external loading, geometry guidelines should first be reviewed:

7-82 Examples

CAESAR II - Applications Guide Example 9: WRC 107

D = 120.0 in., T = 0.625 in., d = 12.75 in., t = 0.375 in.

d / D = 0.10625 < 0.33

Dm/ T = (D-T) /T = 191 > 50

In the present case, both conditions are satisfied. The actual preparation of the WRC 107 calculation input can now begin. One of the most important steps in the WRC 107 proce-dure is to identify the correlation between the CAESAR II global coordinates and the WRC 107 local axes. The CAESAR II program performs this conversion automatically. The user will, however, have to identify the vectors defining the vessel as well as the noz-zle centerline. The following figure is provided to illustrate the definition of the direction vectors of the vessel and the nozzle.

Converting Forces/Moments in CAESAR II Global Coordinates to WRC 107 Local Axes

Notice that in order to define a vessel direction vector, the user first needs to designate the output data points (A-D) as defined by the WRC 107 Bulletin. Note that the line between data points B and A defines the vessel centerline (except for nozzles on heads, where the vessel centerline will have to be defined along a direction which is perpendicular to that of the nozzle). Since, in the vessel/nozzle configuration shown, point A is assigned to the bottom of the nozzle, the vessel direction vector can be written as (0.0, -1.0, 0.0), while the nozzle direction vector is (1.0, 0.0, 0.0).

Note The nozzle direction vector is always defined as the vector pointing from the ves-sel nozzle connection to the centerline of vessel.

In the figure, the user may also notice that there are two nodes occupying the same space at the nozzle/vessel surface junction: nodes 55 and 56. An anchor at 55 with a connecting

Examples 7-83


node at 56 could be used to model the local vessel flexibility as “rigid.” (For those who are not familiar with this modeling approach, refer to Chapter 3 of the Technical Reference Manual for more details). The anchor could then be replaced with a WRC 297 local ves-sel flexibility model, and the job rerun to get a good idea of the range of loads and dis-placements that exist in the system around the vessel nozzle. In either case, the restraint loads (forces and moments) can be obtained from the CAESAR II restraint report. These loads reflect the action of the piping on the vessel. The restraint report of the rigid anchor model are shown as follows.

The total sustained axial load on the nozzle may not be reflected in the restraint report. A pressure thrust load will contribute an additional axial load to the nozzle. The pressure

7-84 Examples


thrust force always tends to push the nozzle away from the vessel. For example, with a pressure of 275 psi over the inside area of the 12-in. pipe, the total P load becomes:

P = -26 - P(A)

= -26 - 275p (122) / 4

= -31,128

The P load may be adjusted automatically for the input by CAESAR II’s WRC 107 mod-ule, if the user so requests.

The WRC 107 module is started by selecting Analysis-WRC-107 from the CAESAR II Main Menu. The program first prompts the user for the entries of geometric data describ-ing both the vessel and nozzle, followed by spreadsheets for loadings. The values of the geometric entries in this example are shown in the following printouts from the program.

Examples 7-85


The user may enter up to three sets of loadings representing Sustained (SUS), Expansion (EXP), and Occasional (OCC) load cases. The program automatically performs the stress calculation of each of the load cases consecutively. In the present case, we only have to be concerned about the sustained and thermal expansion cases. The loads are shown in the following two screens. The user can elect to leave any input cells blank if they are found not applicable. If a static analysis has been performed on the system to be analyzed with WRC-107 then the Caesar II can import the loads directly from the output file. This is accomplished using the Get Loads from Output File button on the bottom of the dialog for each load case. Caesar II will then read in the loads for the nozzle node number that was specified under the nozzle data tab.

7-86 Examples


To run the analysis the User selects the Analyze - WRC-107 from the menu. An Output tab will be generated, which the User clicks on to review the Output. After the input echo, the parameters extracted from the WRC 107 figures are printed to this report. This step is similar to collecting the data by hand. These non-dimensional values are combined with the nozzle loads to calculate the two normal and one shear stress. The stresses will be reported on the outer and inner vessel surfaces of the four points A, B, C & D located around the nozzle. The program provides the normal and shear stresses and translates them into stress intensities which can be used for comparisons against material allowables.

The output of the stress computations are shown as the following four tables. As the out-put shows, the largest expansion stress intensity (117475 psi) occurs at the outer surface of point B (Bu).

Examples 7-87


WRC 107 Stress Calculations Date = Mar 6, 1996 Page = 1 of 4Attachment/Shell ID = EXP14 Time = 2:02 pm

Vessel Stresses @ Nozzle Junction

Vessel Node: 60 DESCRIPTION:

Vessel Type: Cylindrical THIS IS INPUT TITLE PAGE FOR CAESAR II

Vessel Ori.: 0.00,-1.00, 0.00 APPLICATION GUIDE, EXAMPLE NO.14.

Nozzle Node: 55 WRC 107 STRESS CALCULATION AND ASME SEC.VIII

Nozzle Type: Round-hollow DIV.2 STRESS SUMMATIONS.

Nozzle Ori.: 1.00, 0.00, 0.00

Pressure : 275.0 lb./sq.in.

-------------------------------------------------------------------------

Dimensions | Nozzle Loads (SUSTAINED)

------------------------------------------------------------------

Vessel Mean Rad. Rm = 59.688 in.| Axial Force P = -31128. lb.

Vessel Thickness T = 0.625 in.| Circ. Sh. Force VC = 32. lb.

Noz. Outside Rad. ro = 6.375 in.| Long. Sh. Force VL = 1389. lb.

Nozzle Thickness t = 0.375 in.| Circ. Moment MC = 127. ft.lb.

| Long. Moment ML = 4235. ft.lb.

| Tors. Moment MT = 65. ft.lb.

Parameter(s) used in the Interpolation of Dimensionless Loads:

Gamma = 95.50

Dimensionless Loads for Cylindrical Shells

-----------------------------------------------------------------

Curves read for Beta Figure Value

-----------------------------------------------------------------

N(PHI) / ( P/Rm ) 0.093 4C 14.994

M(PHI) / ( P ) 0.093 2C1 0.059

N(PHI) / ( MC/(Rm**2 * Beta) ) 0.093 3A 3.449

M(PHI) / ( MC/(Rm * Beta) ) 0.093 1A 0.085

N(PHI) / ( ML/(Rm**2 * Beta) ) 0.093 3B 10.793

M(PHI) / ( ML/(Rm * Beta) ) 0.093 1B 0.035

N(x) / ( P/Rm ) 0.093 3C 12.082

M(x) / ( P ) 0.093 1C1 0.097

N(x) / ( MC/(Rm**2 * Beta) ) 0.093 4A 5.631

M(x) / ( MC/(Rm * Beta) ) 0.093 2A 0.045

N(x) / ( ML/(Rm**2 * Beta) ) 0.093 4B 3.511

7-88 Examples


M(x) / ( ML/(Rm * Beta) ) 0.093 2B 0.051

Stress Points C & D (March 1979)

N(PHI) / ( P/Rm ) 0.093 3C 12.082

M(PHI) / ( P ) 0.093 1C 0.094

M(PHI) / ( ML/(Rm * Beta) ) 0.093 1B1 0.035

N(x) / ( P/Rm ) 0.093 4C 14.994

M(x) / ( P ) 0.093 2C 0.060

M(x) / ( ML/(Rm * Beta) ) 0.093 2B1 0.052

WRC 107 Stress Calculations Date = Mar 6, 1996 Page = 2 of 4

Attachment/Shell ID = EXP14 Time = 2:02 pm


-----------------------------------------------------------------

| Stress values at

Type of | (lb./sq.in.)

-----------------------------------------------------------------

Stress Load| Au Al Bu Bl Cu Cl Du Dl

-----------------------------------------------------------------

Circ. Memb. P -Pl | 12510 12510 12510 12510 10081 10081 10081 10081

Circ. Bend. P -Q | 28242 -28242 28242 -28242 44865 -44865 44865 -44865

Circ. Memb. MC -Pl | 0 0 0 0 -25 -25 25 25

Circ. Bend. MC -Q | 0 0 0 0 -358 358 358 -358

Circ. Memb. ML -Pl | -2635 -2635 2635 2635 0 0 0 0

Circ. Bend. ML -Q | -4938 4938 4938 -4938 0 0 0 0

|

Total Circ. Stress | 33179 -13429 48325 -18035 54563 -34451 55329 -35117

-----------------------------------------------------------------

Long. Memb. P -Pl | 10081 10081 10081 10081 12510 12510 12510 12510

Long. Bend. P -Q | 46473 -46473 46473 -46473 28748 -28748 28748 -28748

Long. Memb. MC -Pl | 0 0 0 0 -41 -41 41 41

Long. Bend. MC -Q | 0 0 0 0 -190 190 190 -190

Long. Memb. ML -Pl | -857 -857 857 857 0 0 0 0

Long. Bend. ML -Q | -7325 7325 7325 -7325 0 0 0 0

|

Total Long. Stress | 48372 -29924 64736 -42860 41027 -16089 41489 -16387

-----------------------------------------------------------------

Shear VC -Pl | 2 2 -2 -2 0 0 0 0

Shear VL -Pl | 0 0 0 0 -110 -110 110 110

Shear MT -Pl | 4 4 4 4 4 4 4 4

Examples 7-89


|

Total Shear Stress | 6 6 2 2 -106 -106 114 114

-----------------------------------------------------------------

Stress Intensity | 48372 29924 64736 42860 54563 34451 55329 35117

-----------------------------------------------------------------

WRC 107 Stress Calculations Date = Mar 6,1996 Page = 3 of 4



Vessel Node: 60 DESCRIPTION:

Vessel Type: Cylindrical THIS IS INPUT TITLE PAGE FOR CAESAR II

Vessel Ori.: 0.00,-1.00, 0.00 APPLICATION GUIDE, EXAMPLE NO.14.

Nozzle Node: 55 WRC 107 STRESS CALCULATION AND ASME SEC.VIII

Nozzle Type: Round-hollow DIV.2 STRESS SUMMATIONS.

Nozzle Ori.: 1.00, 0.00, 0.00

-----------------------------------------------------------------

Dimensions | Nozzle Loads (EXPANSION)

-----------------------------------------------------------------

Vessel Mean Rad. Rm = 59.688 in.| Axial Force P = 8573. lb.

Vessel Thickness T = 0.625 in.| Circ. Sh. Force VC = -5866. lb.

Noz. Outside Rad. ro = 6.375 in.| Long. Sh. Force VL = -23715. lb.

Nozzle Thickness t = 0.375 in.| Circ. Moment MC = -5414. ft.lb.

| Long. Moment ML = -52583. ft.lb.

| Tors. Moment MT = -31659. ft.lb.

Parameter(s) used in the Interpolation of Dimensionless Loads:

Gamma = 95.50

Dimensionless Loads for Cylindrical Shells

-----------------------------------------------------------------

Curves read for Beta Figure Value

-----------------------------------------------------------------

N(PHI) / ( P/Rm ) 0.093 4C 14.994

M(PHI) / ( P ) 0.093 2C1 0.059

N(PHI) / ( MC/(Rm**2 * Beta) ) 0.093 3A 3.449

M(PHI) / ( MC/(Rm * Beta) ) 0.093 1A 0.085

N(PHI) / ( ML/(Rm**2 * Beta) ) 0.093 3B 10.793

M(PHI) / ( ML/(Rm * Beta) ) 0.093 1B 0.035

7-90 Examples


N(x) / ( P/Rm ) 0.093 3C 12.082

M(x) / ( P ) 0.093 1C1 0.097

N(x) / ( MC/(Rm**2 * Beta) ) 0.093 4A 5.631

M(x) / ( MC/(Rm * Beta) ) 0.093 2A 0.045

N(x) / ( ML/(Rm**2 * Beta) ) 0.093 4B 3.511

M(x) / ( ML/(Rm * Beta) ) 0.093 2B 0.051

Stress Points C & D (March 1979)

N(PHI) / ( P/Rm ) 0.093 3C 12.082

M(PHI) / ( P ) 0.093 1C 0.094

M(PHI) / ( ML/(Rm * Beta) ) 0.093 1B1 0.035

N(x) / ( P/Rm ) 0.093 4C 14.994

M(x) / ( P ) 0.093 2C 0.060

M(x) / ( ML/(Rm * Beta) ) 0.093 2B1 0.052

Examples 7-91


WRC 107 Stress Calculations Date = Mar 6,1996 Page = 4 of 4



-----------------------------------------------------------------

| Stress values at

Type of | (lb./sq.in.)

-----------------------------------------------------------------

Stress Load | Au Al Bu Bl Cu Cl Du Dl

-----------------------------------------------------------------

Circ. Memb. P -Q | -3445 -3445 -3445 -3445 -2776 -2776 -2776 -2776

Circ. Bend. P -Q | -7778 7778 -7778 7778 -12356 12356 -12356 12356

Circ. Memb. MC -Q | 0 0 0 0 1076 1076 -1076 -1076

Circ. Bend. MC -Q | 0 0 0 0 15282 -15282 -15282 15282

Circ. Memb. ML -Q | 32728 32728 -32728 -32728 0 0 0 0

Circ. Bend. ML -Q | 61318 -61318 -61318 61318 0 0 0 0

|

Total Circ. Stress | 82823 -24257-105269 32923 1226 -4626 -31490 23786

-----------------------------------------------------------------

Long. Memb. P -Q | -2776 -2776 -2776 -2776 -3445 -3445 -3445 -3445

Long. Bend. P -Q | -12799 12799 -12799 12799 -7917 7917 -7917 7917

Long. Memb. MC -Q | 0 0 0 0 1758 1758 -1758 -1758

Long. Bend. MC -Q | 0 0 0 0 8120 -8120 -8120 8120

Long. Memb. ML -Q | 10647 10647 -10647 -10647 0 0 0

Long. Bend. ML -Q | 90954 -90954 -90954 90954 0 0 0 0

|

Total Long. Stress | 86026 -70284-117176 90330 -1484 -1890 -21240 10834

-----------------------------------------------------------------

Shear VC -Q | -468 -468 468 468 0 0 0 0

Shear VL - Q | 0 0 0 0 1894 1894 -1894 -1894

Shear MT - Q | -2380 -2380 -2380 -2380 -2380 -2380 -2380 -2380

Total Shear Stress | -2848 -2848 -1912 -1912 -486 -486 -4274 -4274

-----------------------------------------------------------------

Stress Intensity | 87691 70459 117475 90393 2879 4709 33038 25069

-----------------------------------------------------------------

Once the stress intensities are computed, the user can elect to use the WRC 107 stress summation routine to compare the computed stress intensities against the stress allowables as required in Appendix 4 of ASME Section VIII, Division 2.

The WRC 107 stress summation routine can be activated by selecting the Analyze-Stress Summation menu option. The stress summation will be performed and the output will be appended to the existing report. A sample output is given below.

7-92 Examples


WRC 107 Stress Summations Date = Mar 6,1996 Page = 1 of 1


Vessel Stress Summation @ Nozzle Junction

-----------------------------------------------------------------

Type of | Stress values at

Stress Intensity | (lb./sq.in.)

-----------------------------------------------------------------

Location | Au Al Bu Bl Cu Cl Du Dl

-----------------------------------------------------------------

Circ. Pm (SUS) | 26125 26125 26125 26125 0 0 0 0

Circ. Pl (SUS) | 9875 9875 15145 15145 10056 10056 10106 10106

Circ. Q (SUS) | 23304 -23304 33180 -33180 44507 -44507 45223 -45223

Circ. Q (EXP) | 82823 -24257-105269 32923 1226 -4626 -31490 23786

-----------------------------------------------------------------

Long. Pm (SUS) | 0 0 0 0 12994 12994 12994 12994

Long. Pl (SUS) | 9224 9224 10938 10938 12469 12469 12551 12551

Long. Q (SUS) | 39148 -39148 53798 -53798 28558 -28558 28938 -28938

Long. Q (EXP) | 86026 -70284-117176 90330 -1484 -1890 -21240 10834

-----------------------------------------------------------------

Shear Pm (SUS) | 0 0 0 0 0 0 0 0

Shear Pl (SUS) | 2 2 -2 -2 -110 -110 110 110

Shear Q (SUS) | 4 4 4 4 4 4 4 4

Shear Q (EXP) | -2848 -2848 -1912 -1912 -486 -486 -4274 -4274

-----------------------------------------------------------------

S.I. Pm (SUS) | 26125 26125 26125 26125 12994 12994 12994 12994

-----------------------------------------------------------------

S.I. Pm+Pl (SUS) | 36000 36000 41270 41270 25463 25463 25545 25545

-----------------------------------------------------------------

S.I. Pm+Pl+Q (TOTAL)| 143059 100299 52607 47992 55893 39087 34819 20533

-----------------------------------------------------------------

-----------------------------------------------------------------

Type of | Max. S.I. S.I. Allowable | Result

Stress Intensity | (lb./sq.in.) |

-----------------------------------------------------------------

S.I. Pm (SUS) | 26125 20000 | Failed

S.I. Pm+Pl (SUS) | 41270 30000 | Failed

S.I. Pm+Pl+Q (TOTAL)| 143059 60000 | Failed

-----------------------------------------------------------------

Examples 7-93


Since the present nozzle loading will cause stress intensities that are not acceptable to the ASME Section VIII, Division 2 criteria, it will have to be corrected. One way of dealing with this type of situation is to adjust the nozzle loading form its source, while the other option might be to reinforce the nozzle connection on the vessel side either by increasing the vessel thickness or by adding a reinforcing pad. The same analysis procedure can be repeated until the final results become acceptable.

Note Once a reinforcing pad is selected, the program will automatically compute the stress at the edge of the pad as well.

7-94 Examples

CAESAR II - Applications Guide Example 10: NEMA SM23

Example 10: NEMA SM23

This section illustrates the use of the NEMA SM-23 computations of the CAESAR II Equipment module. Two examples are presented. The first example can be found in the NEMA SM-23 Standard, 7th edition as Example 8A, beginning on page 47. The second example illustrates the use of metric units and the correct implementation of paragraph 8.4.6.2.

Enter a NEMA SM23 problem by choosing the Analysis - NEMA SM23 option from the CAESAR II Main Menu.

NEMA Example PT69M

This example illustrates the computations for Dc and De, the use of metric units, and the correct computation of the total moment loads resolved about the discharge nozzle. The input is shown in the following figures.

Examples 7-95

Example 10: NEMA SM23 CAESAR II - Applications Guide

7-96 Examples


The results for this analysis and discussion follow.

Examples 7-97


7-98 Examples


Nozzle Results for PT69M

The first item of interest in this output report is the variation in the units systems used. The input values are reflected in the User set of units, in this case millimeters, newtons, and newton-meters. The computed values are reported in inches, pounds, and foot-pounds. This is necessary due to the equations used to determine code compliance. These equa-tions combine, directly, forces and moments, and then compare the sum to a dimension. In essence, pounds plus foot-pounds must be less than inches. The results can be interpreted correctly only if presented in English units.

For the exhaust nozzle, the input value of 254 millimeters converts to a 10-in. nominal pipe. Since this is larger than 8 in., De is equal to (16 + 10 ) divided by 3, or 8.667 in. This yields an allowable of 500 times 8.667 or 4333.

Then, the square root of the sum of the squares of the forces acting on the exhaust nozzle yields 7922 newtons, which converts to 1781 pounds. Similarly, the square root of the sum of the squares of the moments acting on the exhaust nozzle yields 3000 newton-meters, which converts to 2213 foot-pounds. Applying the 3F + M equation yields 7566. Since 7566 is larger than 4333, this nozzle fails the requirements of the SM-23 Standard.

The same computations must also be performed on the inlet nozzle. The output shown above shows that this nozzle also fails the requirements of the SM-23 Standard. Also shown for the inlet nozzle are the moments about the discharge nozzle caused by the inlet nozzle forces. Applying the standard right hand rule sign convention, a positive “Y” force offset a positive “Z” distance, causes a negative “X” moment. Similarly, a positive “Z” force offset a positive “Y” distance, causes a positive “X” moment. Therefore, the inlet nozzle forces cause an “MX” moment about the exhaust nozzle of: -(3296*.6) + (3999*0) which yields -1978 newton-meters. The “MY” and “MZ” moments caused by the suction nozzle forces about the exhaust nozzle can be computed in a similar fashion. These moments are needed to correctly comply with Section 8.4.6.2.

The above report is repeated for each extraction nozzle specified. This particular example did not contain extraction nozzles, so these reports are not produced. Following the indi-

Examples 7-99


vidual nozzle reports is the summation of forces and moments about the exhaust nozzle. This report is shown in the figure below.

Nozzle Load Summation Report

This report shows the force summations in the three global directions as well as the result-ant force, computed by the SRSS method discussed above. These forces are shown in the user’s set of units on the left, followed by the forces in pounds. The next column shows the allowable for each force, as a function of Dc, which is defined above.

Following the force summation is the moment summation. This summary reports the total moment about the three global directions and the resultant moment, computed by the SRSS method. It is important to note that the total moment is the sum of the individual moments plus the contribution from the forces multiplied by their distanced from the dis-charge nozzle. Consider for example the MX moment of 721 newton-meters. This value was obtained from: 1200 + 1499 + -1978.

The final line of this report combines the resultant force and resultant moment and com-pares the result to its allowable.

7-100 Examples

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System Overview CAESAR II - Applications Guide

System Overview

This tutorial presents the flexibility and stress analysis of a piping system using CAESAR II. This process includes the creation and entry of the pipe stress model, the analysis and evaluation of the results, and a re-design of the system. The system chosen for this purpose, though small, exercises common modeling situations, as illustrated in the following figure. As noted on the drawing, this system moves crude tower bottoms from the bottoms pump to a steam stripper unit which is utilized in a refining process. The end suction, top discharge pump has a 10-in. suction nozzle and an 8-in. discharge nozzle. The 8-in. line runs through a check valve with a 6-in. bypass, up to a spring hanger support and over a hard support before entering the vertical vessel.

The Tutor Piping System Layout

The boundaries of this system are the pump discharge nozzle and the vessel nozzle. Other acceptable choices could have been the pump support (or base) point and the vessel foun-dation. The pump nozzle is a satisfactory boundary because the movement of that point (as the pump heats up in operation) is rather certain and easily calculated from the thermal strain between the pump nozzle and the base point. The vessel nozzle is an adequate boundary because of the known thermal growth of the vessel and the greater stiffness of the vessel with respect to the 8-in. pipe. An opposite approach may be taken by running the model all the way to an immovable point - the vessel foundation.

The check valve sits right on top of the welding tee for the 6-in. bypass piping. The 6-in. line runs through a gate valve before re-entering the 8-in. line through a second welding

8-2 Tutorial A

CAESAR II - Applications Guide System Overview

tee above the check valve. The total weight and length of this valving is unknown at this time, therefore the valve lengths and weights were pulled in from the CAESAR II GENERIC data base. Note that the spring hanger above this valving will be quite sensitive to the weights used here. The difference between the actual installed valve weights and modeled weights should be used to adjust the spring pre-load. It is best to make sure that the hot load on the spring is toward the center of the manufacturers recommended spring working range to allow errors in load estimation. If there is any appreciable change in these weights perhaps the system should be re-analyzed.

The hanger is included at the top of the vertical run to carry the deadweight and absorb its thermal growth. The hanger is attached to the elbow and in line with the vertical pipe at the “near” end of the elbow. (Near is a term associated with the path used to define the elbow. Here, by coding up the vertical leg and then the horizontal leg, the weld point on the vertical run of the elbow is the near end and the horizontal run weld point is the far end.) The other end of the hanger is attached to some available structure above this point. Because of the vertical thermal growth of the hanger attachment point a simple rod hanger is not acceptable here. The analysis will be set to force CAESAR II to select a variable or constant support hanger at this point. The program will probably select a variable, spring support and for that reason the Grinnell table is specified for its selection.

The horizontal piping rests on an unspecified support at the far end of the next elbow. This support, modeled as a rigid, nonlinear restraint acting on the pipe centerline, allows the piping to grow upward but prevents downward motion. In some cases a more accurate model for supporting structures may be required, in which case the structural steel may be included in the model and analysis.

Preparing the Drawing

The following figure shows the worked up drawing used to construct the model. Immedi-ately apparent are the node numbers. These labels are assigned where anywhere we have a change in geometry (pipe diameter, wall thickness, change in direction), a change in mate-rials, operating conditions (temperature or pressure), or the application of boundary condi-tions (restraints, point loads, displacements, etc.). Additional node numbers should be assigned at any other location for which output is desired. For this tutorial the progression is by 5’s starting with node 5 at the pump nozzle. These nodes are the basis through which the piping stress isometric is tabulated for the analysis. The bypass piping also has the 5’s progression but they are incremented by 600. In reviewing the results the 600 series will indicate 6-in. pipe.

Tutorial A 8-3


Tutor Example with Node Numbers and Other Technical Information

Note how in the plot the elbows are shown squared with the node assigned to the intersec-tion. The elbows will be defined so that output is available for the near, mid, and far points of the bend (at 0, 45, and 90 degrees). The hanger will be sized at the first elbow’s near point (node 28).

Other information required for the model is collected on this drawing before the program is started. Most of the data should be readily available but some research may be required. Items such as pump nozzle deflections and valve data details can slow down the input ses-sion if not noted on the drawing. The next figure shows the dimensions for this system.

input

8-4 Tutorial A


Tutor Example with Dimensions

Generating CAESAR II Input

Click on the CAESAR II icon to start the program, CAESAR II will confirm the External Software Lock (ESL) connection. Next, Go to File-New menu selection and enter a new filename of Tutor in the resulting dialog. Be sure to note the data directory path that you will create and store the file in. You may want to use the Browse button to choose another directory for storage of your CAESAR II data files.

New Job Name Specification Dialog

Tutorial A 8-5


Before beginning the input session it will be useful for this tutorial to set the numeric increment between nodes. In previous discussion it was stated that node numbers would use an increment of 5 for this model. The default nodal increment is 10 so this must be changed. From the Main Menu select Tools-Configure Setup and the window shown below will appear. Next choose the Geometry Directives tab. Select the number 5 from the drop list in the Auto Node Number Increment item as shown in the following figure. Next click on the Exit w/ Save button to save this change and return to the Main Menu.

Changing the Auto Node Number Increment in Configuration Setup

The input session is started by selecting Input-Piping from the Main Menu. If the job is new, CAESAR II will present the list of input units that will be used. Otherwise, if a job by the name Tutor already exists on the machine, the first piping element spreadsheet will appear. If this is the case, exit out of this input by clicking on the x in the top-right of the window or by selecting File-Exit from the menu. Return to the Main Menu to repeat the above process to pick an unused jobname. The following window will be displayed if the file is new.

8-6 Tutorial A


This Review Current Units window is only provided if the file is new and did not previously exist in the data directory.

If the units file label (bottom left of the Review Current Units dialog) does not show English Units then click Cancel. Select Tools-Configure Setup, click on the Database Directives tab and select English in the units drop list there.

If the English units are shown, click OK to continue with the input. An empty piping ele-ment input spreadsheet will appear as shown in the following figure.

Tutorial A 8-7


Blank Input Spreadsheet

All the input spreadsheets for this tutorial are provided on the following pages. Individual spreadsheets may be repeated if more than one auxiliary field or command is used. Text will appear with the spreadsheets where explanations are required. Use the Tab key, the arrow keys, or the mouse to navigate the input spreadsheet. Also, liberally use the Plot command to review the work completed. If errors are made simply go back to the appro-priate spreadsheet [PgUp] and fix the entry.

CAESAR II automatically generates the From Node and To Node when you start a new spreadsheet. The cursor is initially positioned in the From Node cell. The From Node should read 5 (assuming the node increment is set to 5 in Configure/Setup -- if not, it can be reset using Edit-Insert), but if not, simply select the node number in the white input box and type a 5 over it. Now use either the Tab or Enter key or Down Arrow key to move to the next input (the To Node in this case). Enter a 10 in the To Node field if one is not already there. All the remaining data entered on this screen will now be associated with the first element from node 5 to node 10 or these two end points.

8-8 Tutorial A


Move down to the DY cell and enter the element length of 2 ft by entering 2-, the “-” indicates feet. Node 10 marks the centerline inter-section of the 8-in. main line with the 6-in. by-pass. In the next block enter the nominal pipe size of 8 in. Note that upon leaving this cell the actual OD replaces this nominal. Also with the standard wall thick-ness, the entered S is replaced by the actual wall thickness. The insu-lation thickness and corrosion allowance are entered next. Note that fractions are allowed in these cells as well.

Next enter the Operating Conditions of Temperature (600°F) and Pressure (30 psi). We omit the units in our entries of course as CAESAR II already has our units information. The completed first column of data is given in the figure to the left.

At the top of the second column of this first spreadsheet double click on the Displacements checkbox to activate the Displacements Auxil-

iary Data area to the right where we will enter our dis-placement information. For node 5 enter the Y and Z anchor displacements of 0.077 in. and 0.046 in. respec-tively. These two numbers are calculated as the thermal growth of the pump discharge nozzle from the base sup-port point. Note that the other four degrees of freedom must be entered as 0 - without the entry of zero (or any

other definition of these boundaries), node 5 would be free to move in these four directions. The figure below shows the displacements entered properly.

Displacement Boundary Condition at Node 5 of Tutor Model

Geometry and Operating Condi-tions for First Element of Tutor

Tutorial A 8-9


Next we enter the pipe material by clicking on the drop list to the right of the Material label and choose number 1 Low Carbon Steel. Material properties will now be read in automatically from CAESAR II's material database. Ambient Elastic Modulus, Poisson’s Ratio, and Pipe Density will be filled in. The material number will also be referenced to pick up the coefficient of expansion for the specified temperatures.

Now double click on the Allowable Stress check box to activate the Allowable Stress Aux-iliary data area to the right. The first 21 materials are Generic and do not have Allowable Stress values associated with them in the database. However the other materials in the list will also fill in the Allowable Stress values as found in the database. The cold and hot allowable stresses (Sc and Sh) as defined by the piping code are entered for the type of pip-ing material to be analyzed. Here the cold allowable stress of 20,000 psi (don’t use com-mas) and the hot allowable stress of 17,300 psi is automatically extracted from the database. Exponential format may be used in these fields to simplify data entry and reduce mistakes. Click on the drop list and select B31.3 if it is not already there by default (The default code is defined in the Configure/Setup). The material property and allowable stress entries are shown in the following figure.

Material Properties are brought in automati-cally from the included Material Database.

Allowable Stresses Extracted from Database

8-10 Tutorial A


Node 10 is the intersection of the 8-in. and 6-in. lines. This intersection is constructed using a 8x6 welding tee. Piping codes recognize the reduced strength of this pip-ing component by increasing the calculated stress at this point in the system. For CAESAR II to include this stress intensification factor in the stress calculation, the node must be identified as a welding tee. First double click on the SIFs and Tees check box to activate the SIFs and Tees Auxiliary data area. Specify node 10 as our intersection node and select Welding Tee from the Type drop list. CAESAR II will calculate the SIFs at this intersection according to the piping code selected (B31.3 in this case) so no more input is needed here.

With an insulation thickness specified, CAESAR II will assume a density for calcium silicate. For purposes of illustration this value is entered by hand as 11.5 lbf/ft3. The input is accepted as lbf/in3 (use the F1 function key to confirm) so the entered value is divided by 1728 in3/ft3 to make this conversion. To clarify: type in 11.5/1728 in the Insulation Density field and CAESAR II will con-vert it. Another conversion capability is shown with the Fluid Density cell - the commodity is specified as 80% the deadweight of water so we enter 0.8SG in the field and CAESAR II will convert it to the proper units.

Defining a Welding Tee at the Intersection Node 10

Density Specifications

Tutorial A 8-11


To move on to define the next piece of pipe, press ALT-C, select Edit-Continue, or click on the Continue button on the far right hand side of the Toolbar.

Note on this new spreadsheet that the To Node of the previous spreadsheet now appears as the From Node. Also, all the distributed data values (the information that carries on from one pipe to the next) remain on this new screen. The user only needs to add element length and any new boundary conditions or changes from the previous element. The distributed data need only be re-entered when they change value. Allowable Stress data carries for-ward even though the checkbox on subsequent spreadsheets is unchecked. Do not check this box unless you have a change in material, code, or temperature. Uniform Loads and Wind also carry forward without the checkbox being checked. None of the other check-boxes in the input carry forward.

This second element runs from the intersection point to the beginning of the check valve. This short run finishes out the welding tee and is bounded by nodes 10 and 15 as entered by CAESAR II. The length of this element is 7 in. in the Y direction so 7 is entered in the DY field. This data finishes the description of the second element. The entire Spreadsheet for this second element follows.

Second Element Spreadsheet for Tutor

The next element (15-20) is the flanged check valve. This CAESAR II element would include the flanged valve and the mating flanges as these piping components are much more stiff than the attached pipe. If the length and weight of this “rigid” element were

8-12 Tutorial A


known, this data could be entered directly by entering the length in the DY field, checking the Rigid box and then entering the Rigid Weight in the Auxiliary Data area. Here, for lack of better data and for convenience, the CAESAR II CADWorx valve/flange database will be accessed to generate this input automatically. This data is made available through the Model-Valve menu option or clicking the Valve/Flange Database button on the tool-bar. This command will bring up the window shown below. If the following window does not appear, refer to Chapter 2 of the CAESAR II Technical Reference Manual (Config-uration and Environment).

Valve/Flange Database Selection Window

To select the valve type and class use the mouse to highlight the Check Valve selection as shown above (instead of the default of Gate). A 150 psi class flanged check valve will be entered between nodes 15 and 20 when the OK button is clicked (or the Enter key is pressed). CAESAR II will make three entries on the input spreadsheet: The element length, the Rigid checkbox is activated, and the weight is input into the Rigid Auxiliary Data area. Here the rigid element runs 2 ft. 3.625 in. in the +Y direction and weighs 470 pounds. When FLG End Type is selected, this rigid element includes the added length and weight of the mating flanges.

The bypass piping rejoins the main line through a second welding tee sitting on top of the check valve. The run of pipe to the intersection of the main line and bypass centerlines is 7 in. (half of the total length of the 8 x 6 welding tee). The next figure shows the definition of this element 20 - 25 and the specification of the welding tee at 25.

Tutorial A 8-13


The next node entered is located at the intersection of the vertical pipe centerline and the horizontal pipe centerline above it. This “construction point” at node 30 is not actually a node on the piping system. Any additional input specified at 30 and all output for node 30 will be located at the far weld point of the elbow which connects the vertical and horizon-tal runs. The dimension of 10 ft. 2 in. runs from node 25 to node 30. The elbow is speci-fied by checking the Bend checkbox. The Bend specification automatically generates additional nodes around this elbow locating the near weld point and the bend midpoint (designated by the letter M). Node 28 is listed in the auxiliary data field at angle 0 and the elbow midpoint is listed as node 29. These added nodes will appear as output points and they may also be used to locate restraints. By default a long radius elbow (1.5 nominal pipe size) will be added at the change in pipe direction. The bend radius may be changed by the user.

Tee Specification on fourth element of Tutor

Bend Specification at end of element from 25 to 30 in Tutor

8-14 Tutorial A


The hanger to be sized at this elbow is placed at node 28 in line with the vertical run of pipe To enter the hanger sizing information, double-click the Hanger checkbox. The Hanger Auxiliary Data area like that shown in the next figure should be filled out as fol-lows: node 28 is entered as the Hanger Node. For this first pass through the analysis, the default settings will be used with no additional hanger design data specified. Press F1 on any of these input cells for a quick definition. Here, the hanger will be chosen from Table 1 – the Grinnell hanger catalog. Additionally, a short range spring will not be permitted at this point as the mid range spring will probably be cheaper.

Hanger Auxiliary Data Specification in Tutor

The piping system continues on to the elbow at node 35. Again, the distance entered as CAESAR II input is the distance between the intersections of the pipe centerlines; not the physical length of the straight piece of pipe between the elbows. Here, -12 ft in the X direction. This X run of pipe will finish off the elbow at 30 by creating a 90 degree turn. Double click the Bend checkbox to generate the long radius elbow at 35 with the two extra nodes. There is also a support at the far weld point of this bend. This far end of the bend is node 35 in the model so the restraint is specified at node 35. This support will not allow

Tutorial A 8-15


the pipe to move downward but it cannot prevent the pipe from moving upward. This non-linear restraint (a restraint whose stiffness, rather than remaining constant, is a function of load or displacement) is entered as a +Y type. The +Y indicated that the restraint supplies a positive Y (upward) load to the pipe; most users interpret the +Y as indicating the pipe is free to move in the +Y direction. With no stiffness entered with this restraint, CAESAR II will set this to a very stiff (rigid) restraint; meaning that under any practical load, the pipe will not “push” the restraint down. Note that up to four restraints may be specified in this auxiliary data field. Except for the anchor designation, a restraint is a vector. If there was a guide restraining lateral motion of node 35, an X restraint would also be defined here as the second restraint. Press the F1 function key for more information about these restraint parameters.

Bend Specification and Restraint Specification on element from 30 to 35 in Tutor

From the second elbow, the pipe runs in the Z direction for 18 ft where it terminates at the intersection with the vessel wall. As with the pump connection at node 5, node 40 is a sat-isfactory boundary for this model. The thermal growth of the vessel at this point is calcu-lated and entered as displacements of node 40.

8-16 Tutorial A


.

The model now returns to the 6-in. by-pass piping around the 8-in. check valve above the pump. The welding tee nodes of 10 and 25 will be completely defined as reducing tees when these 6-in. piping elements are modeled. The figure below shows the changes required to start the 6-in. line, which are explained here.

The input processor automatically shifts the previous To Node to the current From Node. Since the model is no longer continuing from node 40, the From Node must be changed here to 10 and the To Node is set to 605 as the 600 series of node numbers will indicate 6-in. pipe. The X length of -2 ft is measured from the 8-in. centerline to the centerline of the vertical 6-in. line. Diameter is entered as 6 and Wt/Sch is entered as S. An elbow is spec-ified at node 605 by double-clicking the Bend checkbox. Note that CAESAR II automati-cally generates a long radius elbow for this 6-in. line. This elbow is flanged on one end. This flange acts like a stiffening ring which reduces the bending flexibility of the elbow. This characteristic of flanged elbows is addressed by the piping codes through a modifica-tion of the flexibility factor and stress intensification for the elbow. To include this effect, select Single Flange from the Type drop list in the bend auxiliary data area. As simple by-pass piping, the inclusion of flange stiffening is probably insignificant and can be ignored.

Displacement Boundary Condition SimulatingVessel Thermal Growth at Node 40 in Tutor

Tutorial A 8-17


Bypass Inputs in Tutor

8-18 Tutorial A


The 6-in. piping continues up to node 610, which marks the beginning of the gate valve. The distance between the hori-zontal centerline (nodes 30 to 605) and the bottom of the valve is 9 in. in the Y direction. This 9-in. specification puts node 610 at the far end of the bend defined on the previous screen. The input locations of nodes 605 and 610 then are coincident which would produce a zero length element. CAESAR II inserts a length for this element 605-610 equal to 5% of the bend radius - here 0.45-in. This 5% default value, which can be changed in the CAESAR II configura-tion, prevents the generation of a zero length element.

The next element is the 6-in. 150 psi class, flanged gate valve run-ning from 610 to 615. Use the valve/flange data base (with the command Valve) for this rigid element. Select the 150 psi flanged gate valve (default) and click the OK button. CAESAR II will return from the data base with rigid Y run, 17.625 in. long, weighing 225 pounds. As with the 8-in. check valve, the deadweight and length of the attached flanges should be included in this analysis. (Use the NOFLG End Type if you do not want these included.)

Resulting CAESAR II Element Definition for the 150# Flanged Gate Valve

The element from 615 to 620 is the length required to bring the pipe up level with the intersection at node 25. This distance is easy to find by choosing the Distance command from the toolbar or from the menu with Edit - Distance. The Y-distance in this case between 615 and 25 is 15 in., so we input this distance as DY on the spreadsheet for 615 to 620. Also a bend must be specified here since the next element will connect the current element to the intersection at node 25.

150# Flanged Gate Valve selected from theCadWorx Valve/Flange Database.

Tutorial A 8-19


The Y value of the distance between nodes 615 and 25 gives us the dimension for the ele-ment from 615 to 620.

For the element running from 620 to 25 we know from the previous Distance command that it is 2 ft in the x-direction. But imagine for a moment that we did not have this infor-mation. In this case we can use the Close Loop command (Edit - Close Loop) and CAE-SAR II will calculate this dimension and enter it into the appropriate DX, DY, and DZ fields. First create the spreadsheet and type in 25 for the To Node. Then perform the Close Loop command. DX will now have a value of 2 ft.

Close Loop on element 620 to 25 will fill in the distances for DX, DY, and DZ fields.

Input Review

Two commands are available on any input screen to review the data – Plot and List. While the input may be checked by paging through each input screen, these commands are quite useful in confirming and/or editing the entire model. The use of these commands will be demonstrated in this section.

To enter the plot processor, click the Plot button or choose Plot from the menu. The cen-terline plot for the current piping system is shown with toolbar buttons and menu com-mands for performing various functions.

8-20 Tutorial A


A few notes about the commands may be useful here:

Use the arrow keys or insert and delete keys to rotate the plot. Pressing the Shift key down once will pan the plot when the arrow keys are used. The SHFT designation in the lower-right hand corner of the plot window indicates that model translation is enabled. Another useful method of panning the plot is accomplished by clicking the right mouse button on the display and selecting Pan from the pop-up menu. The model will then follow the mouse cursor within the display. Hit the escape key to terminate panning with this method. The plus sign (+) will zoom in and the minus sign (-) will zoom out. There are toolbar but-tons and menu items to alter the plan view and to display element and restraint information on the plot. Common entries are N to display nodes and V to show a two line volume plot. The user is encouraged to experiment with these different items to become familiar with them. To reset the plot to the default there is a toolbar button and a menu command.

Tutorial A 8-21


To print a copy of the display simply choose the File-Print menu item.

The next illustration shows a simple centerline plot with the node numbers indicated. By default, CAESAR II will not print a node number if it will over-write another number. This simple plot is very useful for confirming the general layout – bad connectivity and improper directions are quite obvious.

Node Numbers Displayed on the Plot in Tutor

8-22 Tutorial A


The next illustration displays a volume plot of the piping system. Note the differing out-side diameters for the 8-in. and 6-in. lines. The restraint at 35 and the hanger at 28 are also shown by pressing the appropriate toolbars.

Volume Plot Showing Spring Hanger and Support Locations in Tutor

Tutorial A 8-23


The illustration below shows a view down the Z axis with a zoom and pan to show the pipe valving. This volume plot shows the nodes, identifies the tees, and lists the thermal displacements imposed on node 5.

Volume Plot View Along Z-Axis Showing Nodes, Tees, and Displacements in Tutor

Again, when finished with the plot module, click on the x button in the upper right-hand corner (or select File-Exit) to exit back to the piping input spreadsheet.

8-24 Tutorial A


The List command (Edit-List) is used to review and edit different categories of data in the job. List is used here to quickly check the data and modify it if necessary. Clicking on the row number to the left of a line of data will highlight the entire row. Holding the Shift key down while clicking on a second row of data will highlight all rows in between these two. Different types of data sets are available by choosing the appropriate tab along the bottom of the spreadsheet. The Element list displayed as default is shown in the next figure. Use the scroll bar on the bottom to view more element data such as temperatures and pressures. Use the arrows on the bottom left of the window to scroll through the various report tabs.

Element Data in the List Editor

Ending the Input Session

If the input session is interrupted before all the data is collected (say, to go to lunch), be sure save the model input before exiting the input processor. To save the current input use the File-Save command from any element input spreadsheet. CAESAR II will interrupt the input session and prompt for this update 30 minutes after the last save. Input data may also be saved through the input exit processor which is accessed through the File- Quit command. The input processor can be re-entered later to continue the model creation.

Upon exiting and saving the input or running the Error Checker (Single Running Man but-ton) CAESAR II will first save binary data for this model under the filename Tutor._a. (All input files are composed of the jobname with the suffix “_a” added.) CAESAR II then checks the job for errors and list a variety of notes and warnings. This tutorial should generate 2 notes during the error checking. Both notices from the error check are notes to the user regarding the hanger in the model – one hanger must be sized by the program and certain analyses are required to perform this hanger sizing Toggle through these messages to arrive at the end of the error checker (by pressing the OK button). The analysis may pro-ceed with notes and warnings but fatal errors must be corrected before continuing. If no

Tutorial A 8-25


fatal errors are found, CAESAR II will continue on and build the intermediate (scratch) files for the static analysis. With the scratch files created, the input process is complete and control is returned to the CAESAR II Main Menu.

Performing the Static Analysis

Now that the piping model is correct and verified the static analysis of the system may be performed. The analysis is started by selecting Analysis - Statics from the Main Menu. The first step in the static analysis is to specify the load sets for analysis. For a new model, CAESAR II assists in this step by reviewing all load categories (e.g. Temperature, Pres-sure, Displacements, Forces, Weight, etc.) specified in the input and recommending a set of load cases based on the most standard stress analysis requirements. For the job Tutor the hanger must be sized before the standard structural and stress analyses are performed. This hanger sizing algorithm requires two analyses before the standard three cases are ana-lyzed. The five recommended analyses are shown below. (If this window does not appear, the job has the load cases set from a previous session. From the menu that appears in the following figure select the option that recommends the load cases.)

Load Case Editor with Two Hanger Design Cases and the Standard Three Load Cases for Tutor

The standard three cases could use a little explanation here. CAESAR II creates load sets to analyze the operating conditions of the piping system and the installed conditions of the piping system. The operating condition for this analysis consists of the deadweight of the pipe, its contents and insulation, the design temperature and pressure, and the pre-load on

8-26 Tutorial A


the just-selected hanger at node 28. The installed condition includes the deadweights and hanger pre-load. In addition to these structural analyses, certain stress conditions must be addressed. For the piping code used here, the sustained and expansion stresses must be calculated. Sustained stresses include deadweights, pre-loads and pressure. Sustained stresses can be taken from the installed condition analysis if the pressure loads are included. CAESAR II will include the pressure term in the installed case since pressure, in most cases, has no impact on the structural loads on the piping. With the installed case structural analysis also serving as the sustained case stress analysis, no additional load case must be added to calculate the sustained stresses. Expansion stresses reflect the change in system position from its installed position to its operating position. Because of system non-linearity this change in position cannot be determined by analyzing thermal loads alone. By default CAESAR II will construct a third load case to calculate the expan-sion stress (range). This case is not, strictly speaking, a third, complete analysis of the sys-tem but instead a product of the operating and installed structural analyses already performed. The difference in system displacements between these two cases is the dis-placement stress range from which the expansion stresses are calculated. The third class of stress in piping – occasional stresses (as opposed to expansion and sustained) – are not included in the recommended analyses and must be specified by the user. Likewise, FATigue stress cases are provided only when specifically required by the active piping code (TD/12, for example).

For most systems, the recommended load cases are exactly what the user wishes to ana-lyze. Here, Case #1 calculates the deadweight carried by the proposed spring at node 28. Case #2 also calculates only one number – the vertical travel of the proposed spring. All the load categories which compose the operating load case are used for this analysis - deadweight, displacements, thermal set 1, and pressure set 1. With these two numbers - the load carried by the hanger and the amount of travel it must accommodate - CAESAR II will enter the Grinnell catalog and select the appropriate spring. This spring and its proper pre-load are installed in the model for the remaining analyses.

Case #3 is the operating Hanger Load case. It is identical to case #2 but has the sized hanger pre-load included in the category (H). This analysis will produce the operating forces and moments on the supports and the deflections of all points in the system. Case #3 is a structural analysis case and not a B31.3 stress analysis case. The refining piping code does not recognize pipe stress in the operating condition as a test for system failure and does not establish a limit for this state of stress. Case #4 is both a structural and stress case. By eliminating the (assumed) thermal effects (D1+T1), the analysis is of the cold system. By including pressure (P1), this case also has the necessary components to be used to report the system’s sustained stresses. Case #5 (L3-L4) is an algebraic combination of two basic load cases. The displacements of case #4 are subtracted from the displacements of case #3 to produce these results. This case develops the displacement range of the sys-tem in its growth from the installed position to the operating position. This displacement range is used for the calculation of the system’s expansion stresses.

With the selection of the recommended load cases CAESAR II will proceed with the static analysis. The program continues with the data processing by building, sorting, and storing the equation (matrix) data for the system and the basic load cases. (This process may be terminated at any time by pressing the Cancel button.) Once this is done the CAESAR II Solution Module is entered briefly.

Tutorial A 8-27


CAESAR II will analyze the four basic loads (hanger design, operating, and installed) before leaving this screen. At this point the solution screen is replaced with messages con-cerning the post processing of this data. The displacement results of cases 3 and 4 are used with the element stiffness matrices to calculate the forces, moments, and stresses through-out the system. The difference between these two sets of displacements is used to establish the displacement range of the piping system as defined in load case #5. This new displace-ment set is similarly used to calculate forces, moments, and stresses. At the completion of this step, all the results are loaded into the binary data file TUTOR._P and the CAESAR II output processor window is displayed so that output for this job may be reviewed. The “._p” file can only be examined through the output processor. The analysis need not be rerun to review these results at a later time, instead, the option Output-Statics from the Main Menu may be used to bring up the output from the TUTOR._P file.

8-28 Tutorial A

CAESAR II - Applications Guide Reviewing the Static Results

Reviewing the Static Results

Whether entering the output processor directly from the static analysis or through the Main Menu, the program’s Output Window will appear.

Static Output Processor

Usually the first look at output is to verify that the piping model is responding as expected. Checking deflections and restraint loads in the operating and installed cases should quickly uncover any major problems with the system layout or input. If there are unusual results, the input should be re-examined for correctness. If the output verifies the model, the results can be used to collect pipe stresses, support and equipment loads, and any other useful data found in the output. This information is useful in documenting a good piping design or troubleshooting an inadequate one.

A good view of the operating displacements of this piping system is available through Dis-play Graphical Results button or through Options-Graphical Output. Be sure to select a load case (not a hanger case) prior to issuing the command. The image shown in the fol-lowing figure will appear on the screen.

Tutorial A 8-29

Reviewing the Static Results CAESAR II - Applications Guide

Output Plot for Tutor

As in other Caesar II windows both the Toolbar Buttons and Menu Items may be used to select display options. From the menu select Show-Displacement-Deflected Shape. The plot will show the centerline plot along with a normalized deflected shape of the system in the operating condition. This screen is shown in the next figure.

8-30 Tutorial A


Plot of Displaced Shape

When finished viewing the plotted output for the operating case, change the case to Sus-tained in the drop list on the left of the second toolbar. Select Show-Stress-Overstress and note that there are no over-stressed points exist in the system. Reset the plot and now select Show-Stress-Symbol-Code to display the code defined stresses throughout the sys-tem. The stress symbols will appear on the screen and locate the highest stress points in the system. Now select Show-Stress-Maximum to list the stress values on the plot; use the [Enter] key to list the stresses one at a time starting with the highest. The upper-left hand corner of the screen shows the node number for the stress value placed on the screen. Here, the highest (first) expansion stress listed is at node 10 (the first welding tee) with a value of 12816 psi. This information is displayed in the next figure. Return to the output processor menu by clicking the Standard Windows Exit button or File-Exit menu option.

Tutorial A 8-31


Output Plot with Maximum Stress Point Revealed

For a quick look at the selected hanger data select Hanger Table with Text from the Gen-eral Computed Results Column in the main Output Processor. The program reports the Grinnell Fig. B-268 Size 10 spring selected at node 28. This selection is based on the val-ues found in the first two analyses (both, of which, provide no load case reports in the out-put processor) – the expected hot load for the proposed support at node 28 and the thermal growth of node 28 (1220 lb. and 0.750 in., respectively). Return to the Output Menu and select only the operating load case and Displacements and Restraint Summary. The restraint loads at nodes 5 and 60 will be compared to the pump and vessel load limits. Return to the Output Menu and now select the installed case (turn off 3 and turn on 4) to examine the installed condition of the piping system. (Both the operating and installed cases could be reviewed together by having both 3 and 4 highlighted at the same time.) Now highlight the sustained and expansion cases (4 and 5) and Stresses. Each stress report will start with a summary stating that the code stresses are below their allowable stress. In the table that follows the summary, the stresses will be for each node in the system. These nodes will be listed in pairs with their associated element. Note the last column lists the ratio of actual stress to allowable stress in terms of percentage.

8-32 Tutorial A


These results can be dumped to the printer or to a file rather than sent to the screen. Before creating the report, a title line for the hardcopy may be generated through Options-Title Lines on the Output Menu. Enter the following two lines for the report header:

CAESAR II TUTORIALBOTTOMS PUMP TO STEAM STRIPPER

To send the output to the printer, simply select the File-Print option or click on the Print button. Start the report with the hanger table by selecting it an clicking Print. For the next selection turn off the hanger request (click on it while holding the control key down) and select the operating and sustained load cases and Displacements and Restraint Summary reports before entering clicking on Print again. Finally add the sustained and expansion stress reports by having only load cases 4, 5, and Stresses highlighted; again clicking the Print button to service this request. This completes a typical output report. Segments of the output reports are included at the end of this section.

Note that an input echo is available through the output processor. A complete input listing can start the printed report or output file created by this processor. When the output pro-cessor is terminated, it will also generate a table of contents for the report built in this ses-sion.

To archive the static analysis electronically, the report may be sent to a data file rather than to the printer. Simply use the above instructions substituting the Save button for the Print button. The first time you select the Save option it will prompt you for a filename. The resulting data file, Tutor.out, may be copied with the CAESAR II input and output files (Tutor._a and Tutor._p) to a floppy diskette. These files along with the configuration file Caesar.cfg and the Time Sequencing File (Tutor.otl) present a complete record of the anal-ysis and should be stored with the drawing and any listings.

Tutorial A 8-33


Static Analysis Output Listing

The following is a CAESAR II tutorial output report:

Hanger Report

Note - The output listed in the example includes significant output only.- Notes which discuss the results are included with each report.- The reports included in this output are Complete Hanger Report, Operating Case Displacement Report, Installed (Sustained) Case Displacement Report, Operating & Installed Restraint Summary, Sustained Stress Summary and Stress Report, and the Expansion Stress Summary and Stress Report. (Stresses in the operating con-dition are not used in B31.3 analyses)

The hot load of 1222 lbf. was calculated in the initial weight run (load case #1) with a rigid Y restraint installed at node 28. The load on the restraint was 1222 lbf.

A 1222 lbf. +Y load replaced the rigid Y restraint at 28 and then an operating case was analyzed (load case #2). Node 28 moved 0.750 in. in the +Y direction in this analysis.

CAESAR II entered the Grinnell hanger table with these two values and selected an appropriate mid-range spring. The size 10 spring has the hot load of 1222 lbf. in its work-ing range. This mid-range spring (short range springs were excluded) has a spring rate of 260 lbf./in. Assuming that node 28 moves 0.750 in. between the cold to hot position this increases the spring load by (.750)(260) or 195 lbf. The cold load on the size 10 spring is 1222+195 or 1417 lbf. This cold load is also within the working range of the size 10 spring so it is selected by CAESAR II.

8-34 Tutorial A


Operating Case Displacement Report

Note The deflections of nodes 5 and 40 - these were entered as input.

Note Node 28 again moves up 0.750 in. in the Y direction with the spring installed.

Tutorial A 8-35


Sustained Displacements

Note The zero position of nodes 5 and 40. When the imposed displacements are not included in the analysis, the node is fixed with zero movement in each of the defined directions.

8-36 Tutorial A


Restraint Summary for the Operating and Sustained Cases

This restraint report lists the piping forces and moments on the restraint; not the restraint loads on the piping. The loads at node 5 are the nozzle loads and can be used without sign change to check the API 610 allowable loads. Loads for node 40 may be used to check the vessel stresses due to the nozzle loads.

The loads at 28 shows the operating load and the actual installation load (with contents) for the selected spring. Note how the spring carries the designed load of 1222 pounds in the operation condition.

The +Y restraint at node 35 shows its nonlinear nature. In the cold condition, the restraint is active. As the piping moves to the hot position it disengages from the support. Refer back to the displacement reports to confirm that the Y displacement is 0.0 in the installed (sustained) condition and +Y in the operating condition.

Tutorial A 8-37


Sustained Case Stress Report - Summary Information

The summary shows that the sustained stresses throughout the system are below their allowable values.

The sustained stress closest to its allowable limit is at the vessel node, 40.

8-38 Tutorial A


Tutorial A 8-39


For the stress detail report previous: Note the application of the tee and bend stress intensi-fication factors. The tee at 25 has SIFs other than 1.00 for all three listings: 25 to 28, 20 to 25, and 25 to 620. Bend SIFs are applied only on the bend side of the node - compare node 28 on 25-28 and 28-29.

No stresses are listed for rigid elements as no valid moment of inertia is provided for these elements.

Expansion Case Stress Summary

The summary shows that the expansion stresses throughout the system are below their allowable values.

The expansion stress closest to its allowable limit occurs along the header at the node 10 tee.

8-40 Tutorial A


Tutorial A 8-41

Conclusions CAESAR II - Applications Guide

For the stress detail report previous: Compare the bend side of 30 with the straight side of 30; the SIF doubles the calculated stress. Also note the changing allowable stress. This is the result of applying an allowable stress which takes credit for “unused” stress in the sus-tained case.

ConclusionsThe review of piping stresses show that the piping has adequate wall thickness and support to keep within the sustained allowable stress and also enough flexibility to remain below the expansion allowable stress limit. A quick review of the system displacements do not reveal any interference problems from pipe expansion. Equipment loads must still be checked to ensure a safe and effective design. The pump loads at node 5 may be compared to the API (American Petroleum Institute) Standard 610 (Seventh Edition, February 1989) - Centrifugal Pumps for General Refinery Service. The nozzle loads, too, can be compared to allowed maximum limits. The nozzle loads can be translated into local stresses using Welding Research Council Bulletins 107 or 297 - Local Stresses in Cylindrical Shells Due to External Loadings on Nozzles (WRC 107) or its Supplement (WRC 297). These local stresses can then be compared to allowable stress values established in ASME Section VIII Division 2 Appendix 4 - Mandatory Design Based on Stress Analysis. Since the loads on these boundary conditions are related to the piping system layout, the piping system cannot be properly approved until these load limit are also verified. These verifications will be done in the following chapter.

8-42 Tutorial A

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Evaluating Pump Discharge Loads CAESAR II - Applications Guide

Evaluating Pump Discharge LoadsCollecting pump and load information is the first step in reviewing the pump loads. API 610 (8th Edition) examines pump loads at two levels—first the individual nozzle loads and then combined nozzle loads on the pump housing. The suction and discharge nozzles have a set of allowable load limits based on nozzle orientation and nozzle size; both the individual X, Y, and Z components and the resultant forces and moments are checked. Additionally, to assure maintenance of proper pump / motor alignment, all loads on the pump are resolved about a base point and also compared to their allowable values. The CAESAR II API 610 processor requires the suction and discharge size, position, and ori-entation and the loads on these nozzles. The load limits are provided by the processor. For this evaluation only the discharge nozzle loads have been calculated, therefore, only the discharge nozzle will be checked and neither the suction limits nor the resolution to the base point will be evaluated.

Even though all the loads are not known, the entire description of the pump will be col-lected for the API 610 processor in CAESAR II. The dimensioned isometric shown in the next figure defines the orientation of this pump with its end suction nozzle and top dis-charge nozzle. Both nozzles are dimensioned back to the base point—the intersection of the shaft axis and the support line for the pump. This pump’s drive shaft is along the X axis.

9-2 Tutorial B

CAESAR II - Applications Guide Evaluating Pump Discharge Loads

The discharge nozzle loads are found in the static analysis output that has just been run. Since the discharge nozzle served as a boundary condition for this analysis, the nozzle loads are conveniently listed in the restraint reports. These forces and moments on the restraint at node 5 are the piping loads acting on the discharge nozzle. No sign change is required. The operating loads and installation loads must both fall below the defined lim-its. Examination of the restraint summary for the operating and sustained (installed) cases reveals the operating loads as the controlling case. The terminal output showing these numbers is found in the following figure. The operating case loads will be used for the dis-charge nozzle analysis.

Tutorial B 9-3


The API 610 processor is entered through the CAESAR II Main Menu selection Analy-sis-API 610. At this point the Open File dialog box will be displayed as shown in the fol-lowing figure. Navigate to the appropriate directory and then either select an existing file to work on or in this case type in the name of your new file. This name does not have to match your jobname, but for this example we will choose the name Tutor.

9-4 Tutorial B


Upon clicking the Open button you will be prompted: "The file specified does not exist, do you want to create one?" Respond by clicking on the Yes button and the new file named Tutor.610 will be created. The API 610 Window will be displayed as shown in the next figure. Type in comments and notes related to the analysis here.

Tutorial B 9-5


Next select the Input Data tab and fill it out as described below. Arbitrary node numbers are assigned for the pump base point and for the pump suction nozzle (1 & 105 respec-tively). Use the data shown in the figure below to enter the remaining data. It is best to enter as much data as is currently available so that when remaining (suction) data is deter-mined, recollection of data will be minimal. The factors for the Table 2 load multipliers are left blank. CAESAR II will use the default values established in API 610. If the pump manufacturer defines pump load limits that are different from those defined in API 650, enter the modified limit here (This value must be between 1.0 and 2.0).

Define the pump shaft centerline direction, the nozzle types, node numbers, and nominal diameters under the Input Data tab.

9-6 Tutorial B


Next select the Suction Nozzle tab and enter the known data. The distance for the base point to the suction nozzle (not from the nozzle to the base point) and the nozzle loads. Since the nozzle loads are unknown at this time, no forces and moments are entered.

Tutorial B 9-7


Discharge nozzle data is next. The next figure shows the Discharge Nozzle tab with the Nozzle orientation. The nozzle orientation is taken from the piping isometric.

9-8 Tutorial B


Next, choose the Get Loads from Output button. From the popup dialog navigate to and choose the name of the output file that contains the restraint loads for this pump (in this case we select Tutor._P from the list).

The next dialog allows you to choose the appropriate load case for inclusion in the API-610 analysis. For this tutorial we will select the Operating case and click OK. Now the loads from the restraint report at node 5 are read in automatically. This is the end of the input for the API Standard 610 pump load evaluation.

Tutorial B 9-9


Select the Analyze menu item or the EQP toolbar to perform the API-610 equipment check. The results will become available under the Equipment Report tab.

With no suction nozzle data entered, the suction nozzle cannot be evaluated. But this report has some value in that the individual load component limits for the suction nozzle are listed. The discharge nozzle report is complete in its comparison of the operating loads on the nozzle and the defined limits. If the nozzle load components are less than the Table 2 limits, no additional checks must be made. If the nozzle load components are greater than the Table 2 values but less than two times the Table 2 values, the pump may still pass if other checks are within their allowable values. The CAESAR II report first compares these loads to the Table 2 limits. If the ratios in the report (see the following figure) are all less than 1.0 the pump is OK; if all the ratios are less that 2.0, the pump must pass addi-tional checks. The moments about the X and Z axes are greater than two times the API 610 standards therefore additional checks are not valid. The moment about the X axis is 10,175 ft-lbf and the (conditional) limit is 5200 ft-lbf1. The moment about the Z axis is 5866 ft-lbf and the limit is 2600 ft-lbf. The discharge nozzle loads must be reduced.

9-10 Tutorial B


If the discharge nozzle loads were less than two times the Table 2 values, checks shown in the next part of the report would be used to qualify the pump loads. Here, the resultant of the applied nozzle forces and moments on each nozzle are compared to their related Table 2 limits (Condition F.1.2.2). Both the suction and discharge loads are also resolved to the pump base point and again compared to a Table 2 limit (Condition F.1.2.3). For this analy-sis, these data have no significance as the components of the discharge loads are greater than two times the Table 2 values.

Once the output has been reviewed, the user may review the reports again or send the report to a file or to the system printer (File-Print). For this tutorial, the limits on the dis-charge nozzle will be noted for quick checks on future, re-design analysis. Once this pip-ing system is redesigned so that the discharge nozzle is not overloaded, the existing data in the equipment file TUTOR can be updated for the final pump verification report. This ends the rotating equipment tutorial.

Tutorial B 9-11

Creating a More Accurate Model CAESAR II - Applications Guide

Creating a More Accurate ModelThe operating moments (X and Z) on the pump nozzle are too large. The system appears to be modeled correctly so it must be modified to reduce these loads. To make the most effective change to the system, the cause(s) of these large loads must first be determined. Returning to the static output for the operating load case, there are two major clues as to the cause of these excessive loads:

1 Compare the operating loads on the pump to the installed loads on the pump — if they are vastly different, the thermal effects are the cause of the overload; if they are simi-lar, the sustained effects cause the high loads. In this case, only the operating loads are high, therefore this system has a thermal expansion problem. For a given amount of thermal growth, thermal forces and moments will be reduced by adding flexibility to the system (F = KX; for a given X - thermal growth between the end points - F or M can be reduced by reducing K). If the system would be overloading the pump due to sustained effects, the system pressure or deadweight is causing the problem. Systems with pressure problems usually include untied expansion joints; deadweight problems can be traced back to improper system support — either spring pre-loads or support locations.

2 Go back to the displaced shapes plot of the operating load case to examine the source of the high moments. Most engineers / analysts find it easier to understand system response to loads in terms of system displacements rather than internal forces and moments. The displacement plot is useful in identifying which runs of pipe are gener-ating the thermal strain and which runs of pipe are turning that thermal strain into the large forces and/or moments on the pump.

The next figure makes it clear that the large moment about the Z axis at the pump is caused by the thermal growth of “B” working against the stiffness of legs “A” and “C.” The large moment about the X axis is due to the thermal growth of “A” working against the stiffness of legs “B” and “C.” (The thermal growth of the vessel connection also may contribute to these high loads.)

9-12 Tutorial B

CAESAR II - Applications Guide Creating a More Accurate Model

How can these excessive loads be reduced? Or, more to the point, how can additional flex-ibility be added to the system so that these loads drop? Two possible solutions are the addition of an expansion loop to the piping and the installation of an expansion joint. Before either of these choices be made a much simpler and cheaper solution will be exam-ined—improving the model to incorporate the inherent flexibilities found in the vessel/nozzle intersection. Certainly the pump loads due to expansion would drop if the thermal growth of the three legs A, B & C could deflect the vessel nozzle. Such nozzle flexibilities are defined in Welding Research Council (WRC) Bulletin 297 - Local Stresses in Cylin-drical Shells Due to External Loadings on Nozzles—A Supplement to WRC Bulletin No. 107. WRC 297 supplies curves by which the OD’s and thicknesses of the vessel and noz-zle are used to define local nozzle flexibilities. These curves are limited to certain ratios of nozzle and vessel terms, such as the following:

d/D < 0.5d/t > 2020 < D/T > 2500d/T > 5

Where:

d = nozzle OD (= 8.625 in.)t = nozzle thickness (= 0.322 in.)D = vessel OD (= 60 in.)T = vessel thickness (= 7/16 in.)

In this system where the vessel is vertical and the nozzle is in the Z direction, flexibilities are defined at node 40 for translation in the Z direction and rotation about the X and Y axis. The other three degrees of freedom (the three local shear terms) remain rigid as in the original model where this nozzle was modeled as a rigid connection with its thermal

Tutorial B 9-13


deflections. Note that the vessel wall thickness is 3/16 in. but the nozzle has a 1/4 in. pad reinforcing the connection; this produces an effective vessel wall of 7/16 in.

So before any costly system modification is made, the model will be refined to incorporate these WRC 297 nozzle flexibilities. It is possible that a more thorough and accurate model of the system will show that re-design is not needed. To assist in this model update, CAESAR II provides a processor which will calculate and insert these flexibilities into the system. This change will constitute the second analysis of this layout.

Return to the input processor for the job Tutor. Go to the spreadsheet that contains the noz-zle node (40) and double click on the Nozzle checkbox. Enter the correct data in the Auxil-iary Data Area as illustrated in the following figure.

The nozzle pipe size is imported from the spreadsheet. If this nozzle connection had no associated thermal growth, the vessel node number need not be entered. Since this vessel has thermal growth, the vessel node number must be identified and the thermal displace-ments previously assigned to node 40 must be re-assigned to this new node number. Enter the vessel node number as node 6000. The calculated nozzle flexibilities will be applied between nodes 40 and 6000. The vessel dimensions are entered here in terms of OD, wall thickness, and reinforcing pad thickness. WRC 297 flexibilities are also sensitive to the proximity of stiffeners to the nozzle. Here, a tray in the vessel is closest to the nozzle and is 4 ft above the nozzle. On the other side of the nozzle, the bottom head tangent and skirt connection is 6 ft below. The vessel orientation, based on a direction vector, is entered next. Simply enter 1 in the Y direction to indicate a vertical vessel. This Z nozzle and Y

9-14 Tutorial B


vessel will define the orientation of the local stiffnesses assigned through WRC 297. This completes the definition of the nozzle. There will be no piping element defined between nodes 40 and 6000. Now the displacements provided at node 40 must be moved to node 6000. Simply click on displacements and change node 40 to 6000.

Displacement on Vessel Node

WRC 297 Input

Tutorial B 9-15


WRC 297 Calculations Completed at the End of Error Checking

With the nozzle specification and the node number change for the vessel deflections, the job is ready for analysis. Simply select start run to invoke the error checker. The error checker again produces the two notes regarding the hanger sizing. Additionally there is a warning generated regarding the specification of a vessel node number in the WRC 297 input when this node number is not included on any piping element. This warning mes-sage (75) is shown in the following figure. There is no trouble with this job since the dis-placements of the vessel node (node 6000) are defined.

The following figures review the nozzle flexibility calculations performed by the CAESAR II error processor.

9-16 Tutorial B


The previous figure lists the flexibilities extracted from WRC 297 — an axial stiffness of 318,640 lb./ in., a longitudinal bending stiffness of 290,366 in.lb./deg, and a circumferen-tial bending stiffness of 58,498 in.lb./deg. These three numbers are certainly much less than the magnitude of the default rigid stiffness which is 10E12. The local coordinate sys-tem is defined by the nozzle/vessel orientation. With the nozzle in the Z direction and the vessel in the Y direction, this new axial stiffness is in the global Z direction (the nozzle centerline), longitudinal bending is about the global X axis (bending into the vessel center-line or long axis), and circumferential bending is about the global Y axis (about the vessel centerline).

After the display of the WRC 297 calculations CAESAR II shows the error processor is completed by summarizing the type and number of messages. With no fatal errors encoun-tered, press the OK button to build the new set of execution files and return to the pro-gram’s Main Menu. The model is now ready for a second static analysis; select Analysis-Statics to proceed. There will again be five analyses - two for the hanger sizing followed by the operating case, the installed or sustained case, and the expansion case.

Once the analyses are completed, the Output Processor is presented for output review.

With only a minor change to the input, a rigorous, error-checking review of the results should not be necessary. Instead, check the sustained and expansion stresses to confirm they are still below their allowable limits, check the hanger selection, and then the operat-ing and sustained (installed) restraint summary will be displayed to check the loads on the pump nozzle node 5.

Tutorial B 9-17


9-18 Tutorial B


The highest sustained and expansion stresses are 986 psi and 14,096 psi, respectively; well below the allowable limits. The program selected a lighter spring for installation at node 28. Previously a size 10 spring was selected, now a size 9 is recommended. In the first analysis the spring carried 1222 lb. in the hot position, now it carries only 914 lb. The sys-tem should still weigh the same so why is the spring load smaller? The reduced longitudi-nal bending stiffness at the nozzle may explain this change. Finally, to further investigate the effect of the nozzle flexibilities, show the displaced position of the piping system in its operating condition.

Something can be said about each of these restraints. The pump discharge nozzle loads at node 5 reveal the impact of the change in flexibility at node 40. The operating moment about the Z axis shows the greatest change dropping to 748 ft.lb. from 5866 ft.lb. The shear force in the X direction has also been reduced by 50%. The axial force in the Y direction, however, has risen from 1562 lb. to 1815 lb. This higher pump load is tied directly to the hanger selection which was also affected by the WRC 297 nozzle flexibili-ties. The spring support at node 28 is shown next. While the previous analysis had the spring carrying 1222 lb. in the operating position, now it carries only 914 lb. This 300 lb. reduction in the spring load returns as an additional 300 lb. load on the pump nozzle. With the spring installed directly above the pump nozzle, simply increasing the load carried by

Tutorial B 9-19


the spring will reduce the load on the nozzle. If another analysis is required, the hanger sizing procedure will be adjusted so that more load is carried by the hanger so that the pump load drops. Looking at the +Y support at node 35 reveals why the hanger load has changed so much. In the first analysis, the support at node 35 was not active in the operat-ing case; the pipe rested on the support in its installed position but lifted off the support as it went into operation. The hanger sizing algorithm readjusted the spring load so that it would carry its portion of the system no longer resting at 35. In this second analysis, the restraint at 35 remains active in the operating position, therefore the hanger at 28 does not carry any additional load from 35. The added longitudinal bending flexibility at node 40 is what allows the pipe to rest at node 35. The support definition at node 40 shows the changes inherent in the WRC 297 nozzle flexibility calculations. Flexibilities are added in the axial and bending directions (Z, RX, and RY) while the shear terms remain rigid (X, Y and RZ). This added flexibility greatly reduces the bending moments about the X and Y axes at node 40. Again, these reduced loads are not a result of design modifications but modeling refinements. If the vessel nozzle connection meets the requirements of Welding Research Council Bulletin 297, there is much to gain in nozzle flexibility.

9-20 Tutorial B


One final report from this analysis shows the displacements of node 40. The imposed ther-mal growth of the nozzle were removed from node 40 and redefined at node 6000. This output would show the operating position of node 6000 as (0, 0.28, -0.10; 0, 0, 0) [defined as (X, Y, Z; RX, RY, RZ)]. Comparing these numbers with node 40 above, one can again see the impact of the nozzle flexibilities. The biggest difference is due to the circumferen-tial bending flexibility (RY) but the longitudinal bending flexibility (RX) plays a large role in the weight distribution of the system.

Do the new pump loads meet the allowable limits defined in API 610?

Tutorial B 9-21

Checking Nozzle Loads CAESAR II - Applications Guide

Checking Nozzle LoadsThe operating moments (X and Z) on the pump nozzle were too large in the initial model. A quick run through the API 610 processor will quickly evaluate the refined model. Now in the TUTOR input only the discharge loads need be changed so click on the Discharge Nozzle tab and then Get Loads from Output as before to obtain the new loads.

API 610 Discharge Nozzle Input

Accept the processor’s warnings and continue with the analysis. The API 610 report fol-lows.

9-22 Tutorial B

CAESAR II - Applications Guide Checking Nozzle Loads

Tutorial B 9-23

Checking Nozzle Loads CAESAR II - Applications Guide

Continued...

The situation is better but not good enough. The Z moment on the discharge nozzle is well below the limit. The X moment, however, remains more than twice the allowable load. Exceeding twice the allowable load would be fine if Condition F.1.2.2 is satisfied but it is not. Condition F.1.2.2 states that even though the individual load components may be more than twice their individual limit, the loads are satisfactory if the resolved forces divided by their resolved limits plus the resolved moments divided by their resolved limits is less than 2. The sum of the ratios for the discharge nozzle is 2.822 so the pump loads are still too high.

There is a quick “what if” check that may prove the pump loads may be brought within their allowable values. The discussion of the restraint loads mentioned that the vertical load on the discharge nozzle is directly controlled by the set load on the spring at node 28. This spring pre-load could be ideally set so that when the pump is in operation, there is no pump load in the Y direction. At this point the hanger carries 914 lb. in the operating posi-tion while the pump carries 1815 lb. If the spring load carried 2729 lb. it stands to reason that the load on the pump would be zero in Y. Would that satisfy Condition F.1.2.2? Rerun-ning the API 610 processor with the Y load set to zero will show the Condition F.1.2.2 reduced to 2.313 which still remains above the limit. Spring load adjustment is useful but system redesign is indicated.

9-24 Tutorial B

CAESAR II - Applications Guide System Redesign

System RedesignThe probable causes of the large X moment at node 5 were developed earlier. This exces-sive load is caused by the thermal expansion of the leg from node 35 to 40 (the “A” leg) working against the stiffness of the remainder of the system (legs “B” and “C”). Assuming the thermal strain of leg “A” is fixed, only the system stiffness may be changed to reduce the operating load at 5. This reduced stiffness may be realized by the addition of an expan-sion loop or the addition of an expansion joint. For this system an expansion loop is cho-sen.

Where should the expansion loop be added? As a rule of thumb, the best location for an expansion loop is determined by the orientation of the leg which produces the thermal strain causing the problem. Here leg “A” sets the orientation of the loop. The added piping to generate the expansion loop will lie perpendicular to leg “A” which runs in the Z direc-tion. This means that for this system pipe may be added in either the X or Y direction. This added pipe effectively increases the cantilever length which is displaced by leg “A”. By increasing cantilever length, stiffness is reduced and load(s) will drop. It will be sensible, therefore, to add a loop on the “A” run of pipe (35 - 40) by adding pipe in the X direction.

How long should the loop legs be? There are several conditions which would set the loop size: available support location, maximum distance between supports, cost of pipe, and space available to name a few. For this system an eight foot by 8-ft loop will be used. For systems that are not analyzed, the recommended maximum spacing between supports for 8-in. water-filled pipe is 19 ft (see ASME B31.1 121.5 or MSS SP-69). The 8-ft loop run will lengthen the 30 - 35 pipe from 12 ft to 20 ft, which is close to this recommended spac-ing.

Return now to the CAESAR II Main Menu and re-enter the input processor with TUTOR as the current jobname. When testing layout modifications which may not prove success-

Tutorial B 9-25

System Redesign CAESAR II - Applications Guide

ful, it is wise to create a new input set with the proposed changes and leave the original model intact. If the proposed changes do not produce the desired results, the original model is still available for the next attempt; the proposed changes need not be “de-con-structed” from the model. The easiest way to do this is to choose File-Save As from the menu and give the model a new name. The current model will now be the new one. Changes can be made to this new model and the original is intact with the original name. Let's call this new model Tutor2.

There are several ways to add the loop to Tutor2. For this tutorial try following these steps:

• Change the length of 30 - 35 from 12 ft to 20 ft

[PgDn] through the element input screens to display the element From 30 To 35. Move the cursor over the DX field and re-specify the twenty foot length by highlight-ing the current value and then entering -20-

• Move the +Y support from 35 to 33

The recommended maximum spacing between supports for this size pipe is 19 ft *. Leaving the support at 35 would place the support 21 feet from the hanger at 28 so the support is moved closer - to node 33. Move the cursor to the Restraints field. Once the cursor is in the restraints field the Auxiliary Data Area will display the current +Y restraint at node 35. Move the cursor over the 35 and enter 33.

• “Break” 30 - 35 by adding 32 at the midpoint

Node 32 is added as an output point to check mid-span sag. Still on element 30 35 select Model-Break to call up the Break command. Answer the questions so that node 32 is added to this line 10 ft from node 30 with no restraints at node 32. The dialog box for this line break is shown in the next figure.

* The maximum distance between supports as specified in ASME B31.1 and MSS SP-69 ensures avery low sustained stress in the line. Since CAESAR II calculates these sustained stresses, the out-put would confirm that much greater distances between supports are safe. The recommended spac-ing also limits the pipe sag between supports to 0.1 inch. The recommended spacing is conservativebut it serves as a useful guideline here.

9-26 Tutorial B


• Break 35 - 40 8 ft down the line by adding 135.

[PgDn] to the element 35 - 40. Break this element and add the new node 135, 8 ft (8-) from node 35.

• Insert an 8-ft element after 35 - 135.

While still on the (new) element 35 - 135 press I to invoke the Insert command. Select the After button to place this new element after the element 35 - 135. CAESAR II then displays a new input screen for the new element. Enter the To Node as 235, spec-ify the length in the DX field as 8 ft (8-) and double click the Bend checkbox to add the bend at node 235. [PgDn] to the next element (135 - 40) and change the From Node (135) to the new node 235. This change will “button up” the system to finish the entry of the new element. One final step is required for this element - the specification of the bend at node 135. [PgUp] two elements to display element 35 - 135 and double click the Bend checkbox.

• Add a support to the new run 135 - 235.

As mentioned earlier both ASME B31.1 and MSS SP-69 provide limits to spacing between supports. These guidelines were used to set the size of this expansion loop (maximum support spacing for 8-in. carbon steel water line is 19 ft). These guidelines also state that the maximum run of pipe where bends are included is 3/4 of the straight run limit. Here, that limit is about 15 ft. There are over 26 ft of pipe between 35 and 40 so a new support should be added. The support will be added about halfway between 35 and 40 - 13 ft from the nozzle at 40 or 3 ft back from 235. [PgDn] to the element 135 - 235 and issue the Break command. Define a single node 140, 5 ft (5-) from node 135. Enter 33 in the Get support condition from? field. This will cause CAESAR II to duplicate the +Y support entered at node 33 at this new node 140.

Tutorial B 9-27


One final modification is suggested for this analysis. A large vertical load remained on the pump nozzle after the hanger at node 28 was sized and installed by CAESAR II. The spring selected from the Grinnell hanger table should carry more of the deadweight of the pipe and valving. The sizing algorithm may be adjusted so that the pump nozzle carries no load when the program calculates the load to be carried by the spring. This change will greatly reduce the final nozzle load by sizing a larger spring at 28. To make this change, enter the Hanger input auxiliary data area. Type in a 5 in the Free Anchor at Node field; Then move down to Free Code field and select Y from the drop list. With this change, CAESAR II will disconnect the Y restraint at node 5 while it calculates the deadweight load carried by the proposed spring at 28.

To invoke the error checker select either File-Start Run - or select the Start Run toolbar. This data should now process without error. If any errors do occur, carefully read the error messages and return to the input processor to correct them. If everything looks correct, allow CAESAR II to create the execution files and return to the Main Menu.

The job is again ready for static analysis. Enter Analysis-Statics from the Main Menu and run Tutor2 with the same load cases that where created for Tutor. Do this by accepting the default setting on the Load Case Editor. The Output Processor will be presented once the analysis is complete.

As previously recommended, the sustained and expansion stresses are first checked to confirm that they remain below their allowable limits. The hanger selection and the oper-ating and sustained (installed) restraint summary will be displayed to examine the impact of this model modification on the pump nozzle loads at node 5. The highest sustained and expansion stresses are 1708 psi and 5415 psi, respectively; well below the allowable lim-its. The sustained stresses increased a small amount due to the longer spans between sup-ports while the expansion stresses show a significant reduction. The added system flexibility caused this reduction in expansion stress; a good indication that the nozzle loads

9-28 Tutorial B


have dropped as well. Now select the Hanger Table with Text from under the General Com-puted Results column. The program selected a heavier spring for installation at node 28. In the last analysis a size 9 spring was selected, now a size 12 is recommended. The spring now carries 2221 lb. in its hot position. This greater load is the result of the modification to the spring hanger selection criteria where the pump is “disconnected” when the spring’s hot load is calculated. Hopefully, the added load-carrying capability of the spring will reduce the vertical load on the pump nozzle. Be aware that the spring loads can be further manipulated if the nozzle load needs additional adjustment. Select Operating and Sus-tained load cases and Restraint Summary to display the restraint summary report. Finally, to quickly check the effect of the loop on the overall displacement, show the displaced shape of the piping system in its operating condition. The following figures show the vari-ous reports referred to above.

Tutorial B 9-29


9-30 Tutorial B


Tutorial B 9-31


The pump discharge nozzle loads at node 5 look much better; revealing the impact of the change in flexibility at node 40. The loop adds flexibility in the Z direction. The Z force on the pump fell from 750 lb. to 235 lb. The large operating moment about the X axis and the target of this re-design dropped from almost 10,000 lb. to 2753 lb. Another interesting effect of this added flexibility is the increase in the Z moment from -300 ft.lb. to +1541 ft.lb. The pump load in the Y direction exhibits the adjustment to the hanger selection. The hot load on the pump is -204 lb. and the cold load on the pump is +332 lb. The absolute magnitude of the pump load could not be much smaller. If necessary, the hanger load could be adjusted to bring the pump installation load to zero or the pump operating load to zero. The spring support at node 28 now shows a hot and cold load of 2221 lb. and 2558 lb., respectively. By releasing the anchor in the initial weight analysis the spring carries the riser load. This load was only 913 lb. in the previous analysis. The extra flexibility has also changed the support load at node 33. Previously the support load dropped as the pipe became hot; now the load increases as the pipe heats up. The vessel nozzle loads at node 40 shows a similar pattern of change as the pump nozzle. Most loads drop but there is one moment (here it’s X) that increases.

Are the nozzle loads OK?

The API 610 processor need not be used to confirm that the discharge nozzle loads are below their maximum allowed values. Refer back to either of the previous analyses to quickly locate the individual limits and compare them to the new operating loads on node 5:

9-32 Tutorial B


Direction API Limit Model Results

X (lb.) 1700 136.

Y (lb.) 2200 -204.

Z (lb.) 1400 -236.

RX (ft.lb.) 5200 -2709.

RY (ft.lb.) 3800 -1547.

RZ (ft.lb.) 2600 1543.

Since all six components of the discharge nozzle loads are below their limits, no additional checks (conditions F.1.2.2. & F.1.2.3.) need be made. The discharge nozzle is no longer overloaded. The final pump evaluation cannot be made until the suction nozzle loads are compared with their API 610 limits.

Tutorial B 9-33

Conclusion CAESAR II - Applications Guide

ConclusionThe pump discharge loads are now within their allowable limits. The vessel loads from the nozzle at node 40 should also be checked to ensure they are not too high. These loads can-not be compared to a fixed load limit as with the pump. Instead, these loads must be con-verted to local stresses on the vessel and these stresses compared to their limits as defined by ASME Section VIII, Division 2. As a very rough guide for evaluating local vessel stresses, one can check the code defined stress on the pipe connected to the vessel. If those stresses are below about 6000 psi, the vessel stresses should be OK. Looking at the operat-ing, sustained, and expansion stresses at node 40, the maximum stress is less than 2500 psi. The vessel loads seem fine. If the stresses are to be checked, the Welding Research Council Bulletin 107 (WRC 107) can be used to convert the applied forces and moments to the appropriate local stresses. CAESAR II provides a processor to convert these loads into WRC 107 stresses and a second processor to combine the different stress categories (general or local primary membrane stress intensity, primary membrane plus primary bending stress intensity, and primary plus secondary stress intensity) for comparison with their design limits.

Final reports should now be made to document this design change. As shown earlier in this tutorial, the input listing could be generated from the Input Processor or from the Out-put Processor. It would be wise to include the current status of the program’s default set-tings in this input echo. A hard copy of a few input plots would also help in defining this model and analysis. Structural and stress results from the Output Processor will substanti-ate the current design. Structural output includes the system displacements and restraint loads for both the operating and installed cases. The code-defined pipe stresses are gener-ated for the sustained and expansion cases. The hanger report should also be generated from the Output Menu. The data files for and from this analysis may also be archived with the hard copy reports. Copy the files Tutor2._a, Tutor2._J, and Tutor._P and Caesar.cfg to diskette to archive a copy of the CAESAR II input, load case definition, CAESAR II out-put, and program default settings. Also save the Tutor2.otl file to enable full access to these CAESAR II files without the need to re-run the analysis. Note that often upon release of a new version of CAESAR II that archived files will have to be converted to the new version and subsequently re-analyzed. This is primarily due to frequent format changes within CAESAR II as new features are added. To avoid this, limited-run users are encouraged to keep the old version of the software available to them and use newest version for new jobs. The other files generated for this analysis (Tutor._b, Tutor._n, etc.) can be deleted from the hard disk without losing any information. These “scratch files” are produced by the input processor for use in the analysis and can always be regenerated. The CAESAR II Main Menu selection File-Cleanup/Delete Files can be used to copy and delete the files generated by CAESAR II.

Any questions or comments about this tutorial may be directed to anyone in the COADE support staff. COADE may be reached in Houston, Texas at (281)890-4566. Our Fax num-ber is (281)890-3301. We can also be reach via E-mail at [email protected].

9-34 Tutorial B


Numerics180 degree return (fitting-to-fitting 90 deg.bends) A2 -6

AAcoustic waves A7 -29Analysis-statics A7 -50, A9 -28Analyzing water hammer loads A7 -28Anchors A3 -2Anchors with displacements A3 -3Anchors, flexible A3 -5Angle field A2 -2Angle to adjacent bend A2 -3Angular gimbal A5 -25Angular-only gimballed joint A5 -26Archive A8 -33Axial deflection A5 -4

BBall joints A6 -5Bellows angular stiffness A5 -14Bellows ID A5 -2Bellows with pressure thrust A5 -3Bellows, Simple A5 -2Bellows, Tied A5 -4, A5 -8Bend

Angle A2 -2, A2 -3Auxiliary input A2 -4Definition A2 -2Radius A2 -2

Bend Flexibility Factor A2 -14Bends A2 -1Bends, double A2 -4Bends, single-flanged A2 -4Bends, stiffened A2 -4Bilinear restraints A3 -47Bilinear supports A3 -47Bottom-out A4 -15Bottom-out spring A4 -23Break command A9 -26Button

Get loads from output file A7 -86

CCan design A4 -8

Can design, Multiple A4 -8Can design, Single A4 -4Closely spaced mitered bend A2 -8CNodes A3 -6, A3 -22, A3 -32Coade technical support contact informationA1 -2Cold spring A6 -8Combination cases A7 -30Computation Control tab A4 -2Concentric reducer modeling A6 -3Concentric reducers A6 -2Configuration/setup A7 -68Configure-setup—geometry A2 -3Connect geometry through CNodes A4 -12Connecting node displacements A4 -10Connecting nodes A4 -10, A7 -79Constant effort support design A4 -5Constant effort supports A4 -6Control stops, Lateral A5 -17Core piping A6 -6, A7 -75Core piping, Input A7 -75Cryogenic piping dynamics example A7 -36

DDeformation A6 -6Discharge nozzle A9 -8, A9 -22Discontiguous systems A7 -79Displacement

Report A7 -16, A7 -30Stress range A8 -27Vector A3 -4

Displacements, Non-zero A3 -3DLF spectrum A7 -12DLF spectrum files A7 -23Double-acting restraint (rotational) A3 -18Double-acting restraints A3 -17Double-acting restraints (translational) A3 -17Dual gimbal A5 -29Dummy leg on bends, Horizontal A3 -40Dummy leg, Vertical A3 -36Dynamic analysis A7 -58Dynamic analysis of independent supportearthquake excitation A7 -36Dynamic analysis of water hammer loads A7 -20

i


EEarthquake excitation, Independent support A7-36Eccentric reducer modeling A6 -4Eccentric reducers A6 -2Eigensolution A7 -4Elbows - different wall thickness A2 -13Elbows, pressure-balanced A5 -31EQP toolbar A9 -10Equipment report A9 -10Example

Dynamic analysis A7 -58Dynamic analysis (nureg9) A7 -58Dynamic analysis of independent support

earthquake excitation A7 -36Dynamic analysis of water hammer loads

A7 -20Dynamic analysis of water hammer loads

(hammer) A7 -20Harmonic analysis A7 -2Harmonic analysis (table) A7 -2Jacketed piping A7 -72Jacketed piping (jacket) A7 -72Natural frequency analysis A7 -2NEMA SM23 A7 -95Omega loop modeling A7 -66Omega loop modeling (omega) A7 -66Relief valve loads A7 -7Relief valve loads (relief) A7 -7Structural analysis A7 -47Structural analysis (frame) A7 -47WRC 107 A7 -82

Expansion joint rating A5 -4, A5 -10Expansion joints A5 -1, A5 -2, A5 -6, A5 -8,A5 -10Expansion load case A7 -86Expansion stresses A8 -27External software lock A8 -5

FFile-Cleanup/Delete Files A9 -34Flexible anchors A3 -5Flexible anchors with predefined displace-ments A3 -6Flexible nozzle (WRC bulletin 297) A3 -8Flexible nozzle w/ complete vessel model A3 -

12Flexible nozzle w/ predefined displacementsA3 -11Force sets A7 -12Forces/moments, Conversion to WRC 107 lo-cal axes A7 -83Free code option A4 -13Frequency cutoff A7 -4

GGas thrust load calculations A7 -9Generating input, Tutorial A8 -5Get loads from output

Button A9 -9, A9 -22Gimbal joint A5 -23Guides A3 -20

HHanger

Between two pipes A4 -12Data A4 -3Design A4 -2, A4 -11Design with anchors A4 -13Design with anchors in the vicinity A4 -13Design with support thermal movement A4

-11Design with user-specified operating load

A4 -14Sizing algorithm A8 -26Supported from vessel A4 -10

Hanger assembly, Trapeze A4 -8Hanger design, Simple A4 -3Hanger table with text A9 -29Hangers A4 -1Harmonic

Analysis A7 -2, A7 -4Force data A7 -5Loads A7 -2

Hinge joint, Slotted A5 -20, A5 -21Hinged joint A5 -18Hinges, plastic A3 -52

IIndependent support motion A7 -58Input

Constant effort supports A4 -6

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Data A9 -6Review A8 -20Session A8 -25Structural steel A7 -48

JJacket, Input A7 -76, A7 -80Jacketed pipe A6 -6Jacketed piping A7 -72Jacketed piping systems A7 -72

KK-factor A2 -14

LLateral deflection A5 -4Layout of nodes A7 -73Lift-off A4 -15Limit stops A3 -22Loads, Large A7 -72

MMass participation report A7 -14, A7 -30Methods for modeling dummy legs on bendsA3 -36Missing mass correction A7 -29Mitered bend, evenly spaced A2 -7Mitered bend, widely spaced A2 -10Mitered bends A2 -7Miters, closely spaced A2 -7Model-break A9 -26Modeling dummy legs on bends A3 -36Modeling plan A7 -73Modeling reducers A6 -2Modeling, Guidelines A9 -12Models, Complex A5 -4Models, Miscellaneous A6 -1Models, Simple A5 -4

NNear/Far Point Method A3 -36NEMA A7 -95Nodal degree of freedom A3 -3Node fields A2 -2Non-zero displacements A3 -3Nozzle load summation report A7 -100

Nozzle loads A9 -22Nozzle results for pt69m A7 -99Nozzle spreadsheet A3 -12NRC

Benchmark problems A7 -58Spectrum example A7 -58

NRC example NUREG9 A7 -58

OOccasional load case A7 -86Offset element method A3 -36Offset gimbal A5 -25Offset gimbal joint A5 -27Old spring A4 -9Old spring redesign A4 -9Omega loop A7 -66Omega loop modeling A7 -66On Curvature Method A3 -36Operating load, User-specified A4 -14Output-view animation A7 -4Overview A1 -2

PPipe and hanger support A4 -10Pipe nominal diameter A2 -2Pipe supported from vessel A4 -10Plastic hinges A3 -52Predefined displacements A3 -6Preparing the drawing A8 -3Pressure

Pulses A7 -21Thrust A5 -2Wave A7 -28

Pressure thrust, Bellows A5 -3Pressure-balanced tees and elbows A5 -31Pump discharge loads A9 -2

RReducers A6 -2Relief

Valve loads A7 -7Valves A7 -10

Relief valve example problem setup A7 -10Relief valve loading - output discussion A7 -14Report

Displacement A7 -16, A7 -30

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Equipment A9 -10Force A7 -30Mass Participation A7 -14, A7 -30Restraint A7 -30Stress A7 -30

Restrained weight run A4 -13Restraint

Report A7 -17, A8 -37Settlement A3 -28

Restraint and guide, Single-directional A3 -27Restraint between two pipes A3 -32Restraint between two pipes (use of CNodes)A3 -32Restraint between vessel and pipe models A3 -33Restraint, Single-dimensional A3 -26Restraint, Single-directional A3 -19Restraint, Skewed double-acting A3 -29Restraint, Skewed single-directional A3 -31Restraint/force/stress reports A7 -30Restraints A3 -1Restraints on a bend at 30 and 60 degrees A3 -35Restraints on a bend at 45 degrees A3 -34Restraints, Rotational directional A3 -25Results A7 -45Rigid

Body motion A7 -80Rotation rods (basic model), Large A3 -42Rotation rods (chain supports), Large A3 -44Rotation rods (constant effort hangers), LargeA3 -46Rotation rods (spring hangers), Large A3 -45Rotation rods (struts), Large A3 -47Rotation rods, large A3 -42Rotational directional restraints with gaps A3 -25

SSegments A7 -74, A7 -75Shock spectra A7 -58Simple "bottomed-out" spring A4 -23Simple bellows A5 -2Simple bellows with pressure thrust A5 -2Simple hanger design A4 -3Single and double flanged bends A2 -4

Single and double flanged bends or stiffenedbends A2 -4Single-directional restraint with predefined dis-placement A3 -26Single-directional restraints A3 -19Singular stiffness matrix A7 -80Skewed double-acting restraint A3 -29Skewed single-directional restraint A3 -31Slip Joint A5 -31Slip joint A5 -23Slotted hinge joint A5 -20, A5 -21Slotted hinge joint (comprehensive) A5 -21Slotted hinge joint (simple) A5 -20Snubbers, static A3 -51Speed of sound A7 -21Spring can characteristics A4 -16Spring can models A4 -15Spring can models with “bottom-out” and “lift-off” capability A4 -15Spring cans w/ friction, Modeling A4 -24Spring cans with friction A4 -24Spring hanger model with rods A4 -19Spring hanger model with rods, bottom-out,and lift-off A4 -19Spring hangers, Existing A4 -7Spring hangers, Existing (no design) A4 -7Spring Rate field A4 -9Spring, Bottomed-out A4 -23Static analysis A8 -26Static analysis output listing A8 -34Static results A8 -29Static snubbers A3 -51Stiffness characteristics A4 -15Stress report A7 -17Structural analysis A7 -47Structural input files A7 -39Structural preprocessor A7 -47Structural steel A7 -39Suction nozzle A9 -7Support A1 -2Support / user assistance A1 -2Sustained load case A7 -86Sustained stresses A8 -27System overview A8 -2System redesign A9 -25

iv


TTangent intersection point A7 -66Technical support A1 -2Tees, pressure-balanced A5 -31Thermal support movement A4 -11Tie bar A5 -4, A5 -15Tie rod model, Comprehensive A5 -17Tied bellows (simple vs. complex model) A5 -4Tied bellows expansion joint A5 -6, A5 -8Tied bellows expansion joint (complex model)A5 -8Tied bellows expansion joint (simple model)A5 -6Trapeze A4 -8Trapeze hanger assembly A4 -8Turbine trip A7 -20Tutorial A8 -1, A9 -1Tutorial, Generating input A8 -5

UUniversal expansion joints A5 -10Universal expansion joints (simple models) A5-10Universal joint (comprehensive tie rod model)A5 -16Universal joint with lateral control stops A5 -17

Universal joint with lateral control stops (com-prehensive tie rod model) A5 -17

VVertical dummy leg on bends A3 -36Vertical leg attachment angle A3 -39Vessel, Pipe and hanger supported from A4 -10

WWater hammer A7 -21Water hammer loading - output discussion A7-30Water hammer loads A7 -28Widely spaced mitered bend A2 -10Windows A3 -22WRC 107 A7 -82WRC 297 A3 -8

YYield force A3 -52

ZZero length expansion joint A5 -18, A5 -20, A5-25Zero weight A5 -20

v

COADE, Inc.

12777 Jones Rd., Suite 480

Houston, Texas 77070

Phone: (281)890-4566

Fax: (281)890-3301

E-mail: [email protected]

WWW: www.coade.com

C A E S A R I I

A p p l i c a t i o n s G u i d e

V E R S I O N 4.40

( L A S T R E V I S E D 5/2002 )

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