75577376 Point Pipe Stress Analysis by Computer CAESAR II

PIPE STRESS ANALYSIS USING A

COMPUTER MODEL OF THE PIPING SYSTEM

USING COMPUTER TO RUN A PIPE STRESS ANALYSIS

Mathematical model

of piping system built

using Caesar II

software.

BUILDING A MODEL WITH CAESAR II

Engineers nowadays do not have to worry about solving higher degree, or differential equations to perform complicated calculations, because they can create complete models of the system they are trying to design and analyse and let the software perform the analysis for them. However as the saying goes, “garbage in; garbage out” the engineer still has to possess good engineering judgment to know what to expect from a computer analysis and how to interpret the output.

Although there are various softwares available to do pipe stress analyses, Caesar II is one that is well known and frequently used for the oil and gas engineering analyses.

USING CAESAR II FOR PIPE ANALYSIS CAESAR II is most often used for the mechanical design of new piping systems.

Hot piping systems present a unique problem to the mechanical engineer—these

irregular structures experience great thermal strain that must be absorbed by the

piping, supports, and attached equipment. These “structures” must be stiff enough to

support their own weight and also flexible enough to accept thermal growth. These

loads, displacements, and stresses can be estimated through analysis of the piping

model in CAESAR II. To aid in this design by analysis, CAESAR II incorporates

many of the limitations placed on these systems and their attached equipment.

These limits are typically specified by engineering bodies (such as the ASME B31

committees, ASME Section VIII, and the Welding Research Council) or by

manufacturers of piping-related equipment (API, NEMA, or Expansion Joint

Manufacturers‟ Association - EJMA).

CAESAR II is not limited to thermal analysis of piping systems. CAESAR II also

has the capability of modeling and analyzing the full range of static and dynamic loads,

which may be imposed on the system. Therefore, CAESAR II is not only a tool for

new design but it is also valuable in troubleshooting or re-designing existing systems.

Here, one can determine the cause of failure or evaluate the severity of un-anticipated

operating conditions such as fluid/piping interaction or mechanical vibration caused by

rotating equipment.

CONFIGURING CAESAR II

Each time CAESAR II starts, the configuration file caesar.cfg is read from

the current data directory. If this file is not found in the current data directory,

eventually a fatal error will be generated and CAESAR II will terminate.

To generate the caesar.cfg file select Tools/Configure/Setup (or the

Configure button from the toolbar) from the CAESAR II Main Menu.

Once finished users must click Exit w/Save at the bottom of the

Configure/Setup window to create a new configuration file or to save

changes to the existing configuration file. The configuration program

produces the Computation Control window.

Important: The caesar.cfg file may vary from machine to machine and many of

the setup directives modify the analysis. The units' file, if modified by the user,

would also need to be identical if the same results are to be produced.

See the next slide for an image of the Computational Control panel.

CAESAR II – COMPUTATIONAL CONTROL

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Use Pressure Stiffening on Bends- if used it will be the maximum of all psi

Missing Mass ZPA- defaults to the last “extracted” mode

Bend Axial Shape- if ignored the bend will be stiffer

Rod Tolerance (degrees)- The default of CAESAR II is 1.0 degree

Rod Increment (Degrees)- for difficult-to-converge problems, use 0.1

Alpha Tolerance- the default value is 0.05

Ambient Temperature- use the ambient temperature

Friction Stiffness- default value is 1.0E6 lb./in (non-sliding)

Friction Normal Force Variation- default value is 0.15, (15%)

Friction Angle Variation- the default is 15 degrees

Friction Slide Multiplier- should never be adjusted by the user

Coefficient of Friction (Mu)- user defined (0 = no friction)

WRC-107 Version / WRC-107 Interpolation Method- the default is to use the

last value in the particular WRC table

In-core Numerical Check- user enabled

Decomposition Singularity Tolerance- the default value is 1.0 E10.

Minimum Wall Mill Tolerance (%)- default value is 12.5, (12.5%)

Bourdon Pressure- user choice except for FRP pipe; always considered

Include / Ignore Spring Hanger Stiffness- user enabled

Hanger Default Restraint Stiffness- default value is (1.0 E12 lb/in)

Default Translational Restraint Stiffness- default value is (1.0 E12 lb/in)

Default Rotational Restraint Stiffness- default value is (1.0 E12 in-lb/deg)

CAESAR II – STRESS INTENSIFICATION FACTORS

(SIFS)

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Default Code

The piping code the user designs to most often should go here. This code

will be used as the default if no code is specified in the problem input. The

default piping code is B31.3, the chemical plant and petroleum refinery

code. Valid entries are B31.1, B31.3, B31.4, B31.4 Chapter IX, B31.5,

B31.8, B31.8 Chapter VIII, B31.11, ASME-NC(Class 2), ASME-ND(Class

3), NAVY505, Z662, Z662 Chapter 11, BS806, SWEDISH1, SWEDISH2,

B31.1-1967, STOOMWEZEN, RCCM-C, RCCM-D, CODETI, Norwegian,

FDBR, BS-7159, UKOOA, IGE/TD/12, DNV, EN-13480, and GPTC/192.

Occasional Load Factor

B31.3 states, “The sum of the longitudinal stresses due to pressure,

weight, and other sustained loadings (S1) and of the stresses produced by

occasional loads such as wind or earthquake may be as much as 1.33

times the allowable stress given in Appendix A…” The default for B31.3

applications is 33%. If this is too high for the material and temperature

specified then a smaller occasional load factor could be input.

Yield Stress Criterion:

Von Mises Theory or the

Maximum Shear Theory

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B31.3 Sustained SIF Multiplier - the default is 1.0

B31.3 Welding and Contour Tees Meet B16.9- the default setting for this

directive is “NO”, which causes the program to use a flexibility characteristic

of 3.1*T/r, as per the A01 addendum.

Allow User's SIF at Bend- the default is off

Use WRC 329- this activates the WRC329 guidelines for all intersections

Use Schneider- activates the Schneider reduced intersection assumptions

All Cases Corroded- if enabled, uses the corroded section modulus

Liberal Expansion Stress Allowable- user choice to make it default

Press. Variation in Expansion Case- user controlled

Base Hoop Stress On ( ID/OD/Mean/Lamés )- The default is to use the ID

of the pipe. If enabled, hoop stress value has the following options:

ID—Hoop stress is computed according to Pd/2t where “d” is the internal

diameter of the pipe.

OD—Hoop stress is computed according to Pd/2t where “d” is the outer

diameter of the pipe.

Mean—Hoop stress is computed according to Pd/2t where “d” is the average

or mean diameter of the pipe.

Lamés—Hoop stress is computed according to Lamés equation, = P ( Ri2 +

Ri2 * Ro2 / R2 ) / ( Ro2 - Ri2 ) and varies through the wall as a function of R

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Use PD/4t- The more comprehensive calculation, i.e. the Default, is

recommended

Add F/A in Stresses- setting this to „Default‟ causes CAESAR II to use

whatever the currently active piping code recommends.

Add Torsion in SL Stress- setting to „Yes‟ will include the torsion term in

those codes that don‟t include it already by default

Reduced Intersection- options are B31.1(Pre 1980), B31.1(Post 1980),

WRC329, ASME SEC III, and Schneider

Class 1 Branch Flexibility- Activates the Class 1 flexibility calculations

B31.1 Reduced Z Fix- if used in conjunction with B31.1, it makes the

correction to the reduced branch stress calculation that existed in the 1980

through 1989 versions of B31.1

No RFT/WLT in Reduced Fitting SIFs- If enabled will use distinct in-plane

and out-of-plane SIFs

Implement B31.3 Appendix P- implements the alternate rules in B31.3

Appendix P.

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Bends:

Stiffened Bends

90-degree

Bends

Mitered Bends

Elbows

Expansion Joints Simple Bellows with

Pressure Thrust

Tied Bellows

Universal Joints

Hinged Joints

Slip Joints

Gimbal Joints

Ball Joints

Restraints: Anchors

Guides

Limit Stops

Windows

Double-Acting

Restraints

Hangers:

Single Can

Liftoff Spring Can

Bottom-out Spring Can

Constant Effort Hangers

Hanger w/ Sliding

Movement Capability Miscellaneous

Reducers

Jacketed Pipe

MODELLING PIPE BENDS

Bends 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 element direction is defined from the first node to the second node.)

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 midpoint (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 weld line of the bend, and adjacent to the straight element leaving the

bend.

Nodes defined in the Angle and Node fields are placed at the given angle on

the bend curvature. The angle starts with zero degrees at the near-point on

the bend and goes to degrees at the far-point of the bend.

MODELLING PIPE BENDS (CONT’D.)

Nodes on the bend curvature cannot be placed closer together than

specified by the Minimum 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.

Entering the letter M as the angle designates the bend midpoints.

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.

MODELLING PIPE BENDS (CONT’D.)

MODELLING PIPE SINGLE AND DOUBLE-FLANGED

BENDS Single and double flanged bend specifications only affect the stress

intensification and flexibility of the bend. There is no automatic rigid

element (or change in weight) generated for the end of the bend.

Single and double-flanged bends are indicated by entering 1 or 2

(respectively) for the 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 does not 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 component that significantly stiffens the pipe cross section is

found within two diameters of either bend end.

MODELLING PIPE

SINGLE AND

DOUBLE-

FLANGED BENDS

MODELLING PIPE 180º RETURN 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) the bend.

The user is recommended to put nodes at the

mid point of each bend comprising the 180

degree return. (See the example on this page)

MODELLING PIPE CLOSELY-SPACED MITER BENDS

Evenly 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(Ɵ) ]

Where:

Req - equivalent miter bend radius

S - spacing of the miter cuts along the centerline

Ɵ - code defined half-angle between adjacent miter cuts: Ɵ = α / 2N

And 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 equation:

B = S [ 1 - ro / Req ]

Where:

ro - outside radius of pipe cross-section

Miter bends are closely spaced if:

S < r [ 1 + tan (Ɵ) ]

Where:

S - miter spacing

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

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

ASME B31.1 has the additional requirements that:

B > 6 tn

Ɵ ≤ 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 below.

The mitered bend shown 2 slides above has 4 cuts through 90 degrees and

a spacing of 15.913 inches.

Req = S / [ 2 tan (Ɵ) ]

Ɵ = α / 2N = 90 / [2(4)] = 11.25 deg.

Req = 15.913 / [2 tan (11.25 deg.)] = 40

MODELLING PIPE WIDELY-SPACED MITERED BENDS

Mitered bends are widely spaced if:

S ≥ r * [1 + tan (Ɵ)]

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

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

Ɵ - one-half angle between adjacent miter cuts.

B31.1 has the additional requirement that:

Ɵ ≤ 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 (Ɵ)] / 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.

MODELLING PIPE WIDELY-SPACED MITER BENDS

Pipe O. D. = 10.375 in

Pipe Thk. = 0.500 in

Bend Angle = 90 degrees

Cuts = 2

Req = 45 in

Calculate the Δ 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.

Note: The straight pipe section coming into and going out of the bend

must be ≥ Req sin (Ɵ).

MODELLING ELBOWS WITH DIFFERENT WALL

THICKNESSES

When the fitting thickness in the bend auxiliary field is entered, 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 node 10 (in the next slide) has a thickness larger than the

matching pipe wall. The matching pipe has a thickness of 0.5

MODELLING ELBOWS WITH DIFFERENT WALL

THICKNESSES (CONT’D.)

RESTRAINTS

Anchors; Connecting nodes can be used with anchors to rigidly fix one

point in the piping system to any other point in the piping system.

Double-acting restraints; Double-acting restraints are those that act in

both directions along the line of action. Most commonly used restraints are

double-acting. A CNode is the connecting node.

Single-directional restraints; Friction and gaps may be specified with

single-directional restraints. A CNode is the connecting node.

Guides; Guides are double-acting restraints with or without a specified gap.

Connecting Nodes (CNodes) can be used with guides.

Limit Stop; Limit stops are single- or double-acting restraint whose line of

action is along the axis of the pipe. These can have gaps too. A gap is a

length, and is always positive.

Windows; Equal leg windows are modeled using two double-acting

restraints with gaps orthogonal to the pipe axis. Unequal leg windows are

modeled using four single-acting restraints with gaps orthogonal to the pipe

axis.

RESTRAINTS (CONT’D.)

Vertical / Horizontal Dummy Legs; Dummy legs and/or any other elements

attached to the bend curvature should be coded to the bend tangent

intersection point. For each dummy leg/bend model a warning message is

generated during error checking in CAESAR II.

Large Rotation rods; Large rotation rods are used to model relatively short

rods, where large orthogonal movement of the pipe causes shortening of the

restraint along the original line of action. These can be entered in any

direction. Large rotation is generally considered to become significant when

the angle of swing becomes greater than 5 degrees.

Static Snubbers; Translational restraints that provide resistance to

displacement in static analysis of occasional loads only. Static snubbers may

be directional, (i.e. may be preceded by a plus or minus sign).

Plastic Hinges; 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.

Sway Brace assemblies; The sway brace is composed of a single

compression spring enclosed between two movable plates. Manufacturers

typically recommend a specific size sway brace for a given pipe nominal

diameter.

SPRING HANGERS

The hanger design algorithm will not design hangers that are completely

predefined. 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 positive.

The basic parameters input into CAESAR II describe the wave height and

period, and the current velocity. The most difficult to obtain, and also the most

important parameters, are:

the drag, Cd

inertia, Cm and

lift coefficients, Cl

Based on the recommendations of API RP2A and DNV (Det Norske Veritas),

values for Cd range from 0.6 to 1.2, values for Cm range from 1.5 to 2.0. Values

for Cl show a wide range of scatter, but the approximate mean value is 0.7. The

inertia coefficient Cm is equal to one plus the added mass coefficient Ca. This

added mass value accounts for the mass of the fluid assumed to be entrained

with the piping element.

In actuality, these coefficients are a function of the fluid particle velocity, which

varies over the water column. In general practice, two dimensionless

parameters are computed which are used to obtain the Cd, Cm, and Cl values

from published charts.

NOTES ON CAESAR II HYDRODYNAMIC LOADING

This is a critical item for leakage determination and for computing

stresses in the flange.

The ASME code bases its stress calculations on a pre-specified, fixed equation

for the bolt stress. The resulting value is however often not related to the actual

tightening stress that appears in the flange when the bolts are tightened. For

this reason, the initial bolt stress input field that appears in the first section of

data input, Bolt Initial Tightening Stress, is used only for the flexibility/leakage

determination. The value for the bolt tightening stress used in the ASME flange

stress calculations is as defined by the ASME code:

Bolt Load = Hydrostatic End Force + Force for Leak-tight Joint

If the Bolt Initial Tightening Stress field is left blank, CAESAR II uses the value:

45000 / √(dbolt)

where 45,000 psi is a constant and d is the nominal diameter of the bolt

(correction is made for metric units).

NOTES ON BOLT TIGHTENING STRESS

This is a rule of thumb tightening stress, that will typically be applied by field

personnel tightening the bolts. This computed value is printed in the output from

the flange program.

It is interesting to compare this value to the bolt stress printed in the ASME

stress report (also in the output). It is not unusual for the “rule-of-thumb”

tightening stress to be larger than the ASME required stress. When the ASME

required stress is entered into the Bolt Initial Tightening Stress data field, a

comparison of the leakage safety factors can be made and the sensitivity of the

joint to the tightening torque can be ascertained. Users are strongly encouraged

to “play” with these numbers to get a feel for the relationship

between all of the factors involved.

NOTES ON BOLT TIGHTENING STRESS (CONT’D.)

MODELLING EXPANSION JOINTS

To define an expansion joint, activate the Expansion Joint check box (see

"Expansion Joints" on page 3-21 of the Caesar II manual) on the pipe

element spreadsheet.

The expansion joint will have a non-zero length if at least one of the

element‟s spreadsheet Delta fields is non-blank and non-zero. This will

usually result in a more accurate stiffness model in what is typically a very

sensitive area of the piping system.

Four stiffnesses define the expansion joint:

Axial Stiffness

Transverse Stiffness

Bending Stiffness

Torsional Stiffness

These stiffnesses are defined as shown in the figure shown in the next slide:

MODELLING EXPANSION JOINTS (CONT’D.)

Axial Stiffness Transverse Stiffness

Bending Stiffness Torsional Stiffness


The equation for estimating bellows‟ torsional stiffness is:

Where,

π = 3.14159

Re = Expansion joint effective radius

t = Bellows thickness

E = Elastic Modulus

ν = Poisson’s Ratio

L = Flexible bellows length

CAESAR II will calculate pressure thrust on the expansion joint if the

bellows effective I.D. is given in the expansion joint auxiliary screen.

The mathematical model for pressure thrust applies a force equal to

the pressure times the effective area of the bellows at either end of

the expansion joint. The force will tend to open the bellows if the

pressure is positive, and close the bellows if the pressure is negative.


According to EJMA (Expansion Joint Manufacturers Association), the

maximum permitted amount of axial movement per corrugation is

defined as erated where,

ex + ey + eq < erated

The terms in the above equation are defined as:

ex = The axial displacement per corrugation resulting from imposed

axial movements.

ey = The axial displacement per corrugation resulting from imposed

lateral deflections.

eq = The axial displacement per corrugation resulting from imposed

angular rotation, i.e. bending.

erated = The maximum permitted amount of axial movement per

corrugation. This value should be obtained from the Expansion Joint

Manufacturer‟s catalog.


The EJMA states:

“Also, [as an expansion joint is rotated or deflected laterally] it should

be noted that one side of the bellows attains a larger projected area

than the opposite side. Under the action of the applied pressure,

unbalanced forces are set up which tend to distort the expansion joint

further. In order to control the effects of these two factors a second

limit is established by the manufacturer upon the amount of angular

rotation and/or lateral deflection which may be imposed upon the

expansion joint. This limit may be less than the rated movement.

Therefore, in the selection of an expansion joint, care must be

exercised to avoid exceeding either of these manufacturer‟s limits.”


CAESAR II computes the terms defined in the erated equation

and the movement of the joint ends relative to each other. These

relative movements are reported in both the local joint coordinate

system and the global coordinate system.

The expansion joint rating module can be entered by selecting Main

Menu Analysis - Expansion Joint Rating option.

MODELLING PIPE SPRINGS Spring Design Requirements

The smallest single spring that satisfies all design requirements is

selected as the designed spring.

The spring design requirements are:

Both the hot and the cold loads must be within the spring allowed working

range.

If the user specified an allowed load variation then the absolute value of the

product of the travel and the spring rate divided by the hot load must be

less than the specified variation.

If the user specified some minimum available clearance then the spring

selected must fit in this space.

If a single spring cannot be found that satisfies the design requirements,

CAESAR II will try to find two identical springs that do satisfy the

requirements.

If satisfactory springs cannot be found, CAESAR II recommends a

constant effort support for the location.

MODELLING PIPE SPRINGS (CONT’D.)

Setting Up the Spring Load Cases

The load cases that must exist for hanger design, as described above,

are:

Restrained Weight

Operating

Installed Weight ...if the user requested actual hanger installed loads.

After the hanger algorithm has run the load cases it needs to size the

hangers. The newly selected springs are inserted into the piping system

and included in the analysis of all remaining load cases.

The spring rate becomes part of the global stiffness matrix, and is

therefore added into all subsequent load cases.

MODELLING PIPE BRANCH FLEXIBILITIES

When the Class 1 branch flexibilities are used, intersection

models in the analysis will become stiffer when the reduced

geometry requirements do not apply, and will become more

flexible when the reduced geometry requirements do apply.

Stiffer intersections typically carry more load, and thus have

higher stresses (lowering the stress in other parts of the system

that have been “unloaded”).

More flexible intersections typically carry less load, and thus

have lower stresses, (causing higher stresses in other parts of

the system that have “picked up” the extra load).


When the reduced branch rules apply, the following equations are used for

the local stiffnesses:

TRANSLATIONAL:

AXIAL = RIGID

CIRCUMFERENTIAL =

RIGID

LONGITUDINAL = RIGID

ROTATIONAL:

AXIAL = RIGID

CIRCUMFERENTIAL =

(kx)d/EI

LONGITUDINAL = (kz)d/EI where:

RIGID = 1.0 E12 lb./in. or 1.0 E12 in.lb./deg.

d = Branch diameter

E = Young’s Modulus

I = Cross Section Moment of Inertia

D = Header diameter

T = Header thickness

Tb = Branch fitting thickness

kx = 0.1(D/T)1.5[(T/t)(d/D)]0.5(Tb/T)

kz = 0.2(D/T)[(T/t)(d/D)]0.5(Tb/T)


The Significance of the unbraced/unsupported span length

“The significance of “k” depends upon the specifics of the piping system.

Qualitatively, if “k” is small compared to the length of the piping system,

including the effect of elbows and their k-factors, then the inclusion of “k” for

branch connections will have only minor effects on the calculated moments.

Conversely, if “k” is large compared to the piping system length, then the

inclusion of “k” for branch connections will have major effects. The largest

effect will be to greatly reduce the magnitude of the calculated moments

acting on the branch connection. To illustrate the potential significance of

“k’s” for branch connections, we use the equation [above] to calculate “k”

for a branch connection with D=30 in., d=12.75 in. T=t=0.375 in.:

k = 0.1(80)1.5(0.425)0.5 * (1.0) = 46.6

This compares to the more typical rigid-joint interpretation that k=1, rather

than k=46.6 !”

The following input parameters are required to get a leakage report. These

parameters include:

Flange Inside Diameter

Flange Thickness

Bolt Circle Diameter

Number Of Bolts

Bolt Diameter

Effective Gasket Diameter

Uncompressed Gasket Thickness

Effective Gasket Width

Leak Pressure Ratio

Effective Gasket Modulus

Externally Applied Moment

Externally Applied Force

Pressure

MODELLING PIPE FLANGES

Leak Pressure Ratio

This value is taken directly from Table 2-5.1 in the ASME Section VIII code.

This table is reproduced in the help screens of the software. This value is

more commonly recognized as “m”, and is termed the “Gasket Factor” in the

ASME code. This is a very important number for leakage determination, as it

represents the ratio of the pressure required to prevent leakage over the line

pressure.

Effective Gasket Modulus

Typical values are between 300,000 and 400,000 psi (20,684.27 and

27,579.03 bar) for spiral wound gaskets. The higher the modulus the greater

the tendency for the program to predict leakage. Errors on the high side

when estimating this value will lead to a more conservative design.

MODELLING PIPE FLANGES (CONT’D.)

Flange Rating This is an optional input, but results in some very interesting output. As mentioned

above, it has been a widely used practice in the industry to use the ANSI B16.5 and

API 605 temperature/pressure rating tables as a gauge for leakage. Because these

rating tables are based on allowable stresses, and were not intended for leakage

prediction, the leakage predictions that resulted were a function of the allowable

stress for the flange material, and not the flexibility, i.e. modulus of elasticity of the

flange. To give the user a “feel” for this old practice, the minimum and maximum

rating table values from ANSI and API were stored and are used to print minimum

and maximum leakage safety factors that would be predicted from this method.

Example output that the user will get upon entering the flange rating is shown as

follows:

EQUIVALENT PRESSURE MODEL ————————-

Equivalent Pressure (lb./sq.in.) 1639.85

ANSI/API Min Equivalent Pressure Allowed 1080.00

ANSI/API Max Equivalent Pressure Allowed 1815.00

This output shows that leakage, according to this older method, occurred if a carbon

steel flange was used, and leakage did not occur if an alloy flange was used. (Of

course both flanges would have essentially the same “flexibility” tendency to leak.)

MODELLING PIPE FLANGES (CONT’D.)

The B31G criteria provides a methodology whereby corroded pipelines can be

evaluated to determine when specific pipe segments must be replaced. The

original B31G document incorporates a healthy dose of conservatism and as a

result, additional work has been performed to modify the original criteria. This

additional work can be found in project report PR-3805, by Battelle, Inc. The

details of the original B31G criteria as well as the modified methods are

discussed in detail in this report.

CAESAR II determines the following values according to the original B31G

criteria and four modified methods.

These values are:

The hoop stress to cause failure

The maximum allowed operating pressure

The maximum allowed flaw length

MODELLING THE REMAINING STRENGTH OF CORRODED

PIPES

The four modified methods vary in the manner in which the corroded area is

estimated.

These methods are:

.85dL—The corroded area is approximated as 0.85 times the maximum pit

depth times the flaw length.

Exact—The corroded area is determined numerically using the trapezoid

method.

Equivalent—The corroded area is determined by multiplying the average pit

depth by the flaw length. Additionally, an equivalent flaw length (flaw length *

average pit depth / maximum pit depth) is used in the computation of the

Folias factor.

Effective—This method also uses a numerical trapezoid summation,

however, various sub lengths of the total flaw length are used to arrive at a

worst case condition.

Note that if the sub length which produces the worst case coincides with the

total length, the Exact and Effective methods yield the same result.

MODELLING THE REMAINING STRENGTH OF CORRODED

PIPES (CONT’D.)

ANALYSIS OPTIONS IN CAESAR II

• Statics—Performs Static analysis of pipe and/or structure. This is available

after error checking the input file.

• Dynamics—Performs Dynamic analysis of pipe and/or structure. This is also

available after error checking the input file.

• SIFs—Displays scratch pads used to calculate stress intensification factors at

intersections and bends.

• WRC 107/297—Calculates stresses in vessels due to attached piping.

• Flanges—Performs flange stress and leakage calculations.

• B31.G—Estimates pipeline remaining life.

• Expansion Joint Rating—Evaluates expansion joints using EJMA equations.

• AISC—Performs AISC code check on structural steel elements.

• NEMA SM23—Evaluates piping loads on steam turbine nozzles.

• API 610—Evaluates piping loads on centrifugal pumps.

• API 617—Evaluates piping loads on compressors.

• API 661—Evaluates piping loads on air-cooled heat exchangers.

• HEI Standard—Evaluates piping loads on feedwater heaters.

• API 560—Evaluates piping loads on fired heaters.

ERROR CHECKING IN CAESAR II

Static analysis cannot be performed until the error checking portion of the piping

pre-processor has been successfully completed. Only after error checking is

completed are the required analysis data files created. Similarly, any subsequent

changes made to the model input are not reflected in the analysis unless error

checking is rerun after those changes have been made. CAESAR II does not allow

an analysis to take place if the input has been changed and not successfully error

checked.

Error Checking can only be done from the input spreadsheet, and is

initiated by executing the Error Check or Batch Run commands from the

toolbar or menu. Error Check saves the input and starts the error checking

procedure.

Batch Run causes the program to check the input data, analyze the system,

and present the results without any user interaction. The assumptions

are that the loading cases to be analyzed do not need to change

Users may sort messages in the Message Grid by type, message number or

element/node number by double-clicking the corresponding column header.

Users can also print messages displayed in the Message Grid.

ERROR CHECKING IN CAESAR II

A fatal error would be if no length were

defined for a piping element, for example.

ERROR CHECKING IN CAESAR II (CONT’D.)

The software will give the user feedback when things are not right in the model.

Three types of messages are possible with Caesar II:

Fatal Error Message - Errors are flagged when there is a problem with

the model due to which analysis cannot continue.

Warning Message - Warnings are flagged whenever there is a problem

with a model, which can be overcome using some assumptions.

Note Message - The third category of alert is the informational note.

These messages simply inform the user of some noteworthy fact

related to the model. An example of a note may be a message

informing the user of the number of hangers to be designed by the

software.

BUILDING STATIC LOAD CASES IN CAESAR II

The first step in the analysis of an error-checked piping model is the specification

of the static load cases.

After entering the static load case editor, a screen appears which lists all of the

available loads that are defined in the input, the available stress types, and the

current load cases offered for analysis. If the job is entering static analysis for the

first time, CAESAR II presents a list of recommended load cases. If the job has

been run previously, the loads shown are those saved during the last session.

The load case input screen is shown on the next slide.

BU

ILD

ING

STA

TIC

LO

AD

CA

SE

S

(CO

NT’D

.)

The user can define up to ninety-nine load

cases. Load cases may be edited by clicking

on a line in the Load List area.

BUILDING STATIC LOAD CASES IN CAESAR II

The following commands are available to define load cases:

.

Edit-Insert - Inserts a blank load case following the currently selected line in

the load list. If no line is selected, the load case is added at the end of the list.

Load cases are selected by clicking on the number to the left of the load

case.

Edit-Delete - Deletes the currently selected load case.

File Analysis - Accepts the load cases and runs the job.

Recommend - Allows the user to replace the current load cases with the

CAESAR II recommended load cases.

Load Cycles - Hides or displays the Load Cycles field in the Load Case list.

Entries in these fields are only valid for load cases defined with the fatigue

stress type.

ENTERING ENVIRONMENTAL DATA PARAMETERS

The following environmental parameters can be added to the model:

.

Wind Data:

Up to four different wind load cases may be specified for any one job.

The only wind load information that is specified in the piping input is the

shape factor. It is this shape factor input that causes load cases WIN1, WIN2,

WIN3, and WIN4 to be listed as an available load to be analyzed. More wind

data is required, however, before an analysis can be made.

There are three different methods that can be used to generate wind loads on

piping systems:

ASCE #7 Standard Edition, 1995

User entry of a pressure vs. elevation table

User entry of a velocity vs. elevation table

The appropriate method is selected by placing a value of 1.0 in one of the

first three boxes.

ENTERING ENVIRONMENTAL DATA PARAMETERS (CONT’D.)

Hydrodynamic Parameters:

Up to four different hydrodynamic load cases may be specified for any one

job.

Several hydrodynamic coefficients are defined on the element

spreadsheet. The inclusion of hydrodynamic coefficients causes the loads

WAV1, WAV2, WAV3, and WAV4 to be available in the load case editor.

In the load case editor, four different wave load profiles can be specified.

Current data and wave data may be specified and included together or

either of them may be omitted so as to exclude the data from the analysis.

CAESAR II supports three current models and six wave models.

List Input Format

RUNNING THE STATIC ANALYSIS

The static analysis performed by CAESAR II follows the regular finite element

solution routine. Element stiffnesses are combined to form a global system

stiffness matrix. Each basic load case defines a set of loads for the ends of all

the elements. These elemental load sets are combined into system load

vectors. Using the relationship of force equals stiffness times displacement

(F=K∙X), the unknown system deflections and rotations can be calculated. The

known deflections however, may change during the analysis as hanger sizing,

nonlinear supports, and friction all affect both the stiffness matrix and load

vectors. The root solution from this equation, the system-wide deflections and

rotations, is used with the elements‟ stiffness to determine the global (X,Y,Z)

forces and moments at the end of each element. These forces and moments

are translated into a local coordinate system for the element from which the

code-defined stresses are calculated. Forces and moments on anchors,

restraints, and fixed displacement points are summed to balance all global

forces and moments entering the node. Algebraic combinations of the basic load

cases pick up this process where appropriate - at the displacement, force &

moment, or stress level.

Once the setup for the solution is complete the calculation of the displacements

and rotations is repeated for each of the basic load cases.

STRUCTURAL STEEL CHECKS (AISC) Allowable Stress Increase Factor The Allowable Stress Increase Factor is a multiplication factor applied to the

computed values of the axial and bending allowable stresses. Typically this

value is 1.0. However, in extreme events the AISC code permits the allowable

stresses to be increased by a factor.

Normally a 1/3 increase is applied to the computed allowables, making the

Allowable Stress Increase Factor = 1.33. Examples of extreme events are

earthquakes and 100 year storms. For more details see the AISC code,

section 1.5.6.

Young’s Modulus The slope of the linear portion of the stress-strain diagram. For structural steel

this value is

usually 29,000,000 psi (199,948 MPa).

Material Yield Strength The specified minimum yield stress of the steel being used.

STRUCTURAL STEEL CHECKS (AISC) (CONT’D.)

Stress Reduction Factors Cmy and Cmz

Cmy and Cmz are interaction formula coefficients for the strong and weak axis of

the elements (in-plane and out-of-plane).

0.85 for compression members in frames subject to joint translation

(sidesway).

For restrained compression members in frames braced against sidesway and

not subject to transverse loading between supports in the plane of bending:

0.6 - 0.4(M1/M2); but not less than 0.4

where (M1/M2) is the ratio of the smaller to larger moments at the ends, of

that portion of the member un-braced in the plane of bending under

consideration.

For compression members in frames braced against joint translation in the

plane of loading and subject to transverse loading between supports, the

value of Cmy may be determined by rational analysis. However, in lieu of such

analysis, the following values are suggested per the AISC code:

a. 0.85 for members whose ends are restrained against rotation in the

plane of bending

b. 1.0 for members whose ends are unrestrained against rotation in the

plane of bending

STRUCTURAL STEEL CHECKS (AISC) (CONT’D.)

Bending Coefficient

The bending coefficient Cb shall be taken as 1.0 in computing the value

of Fby and Fbz for use in Formula 1.6-1a. Cb shall also be unity when the

bending moment at any point in an un-braced length is larger than the

moment at either end of the same length. Otherwise, Cb shall be

Cb = 1.75 + 1.05(M1/M2) + 0.3(M1/M2)2 but not more than 2.3 where

(M1/M2) is the ratio of the smaller to larger moments at the ends.

Form Factor Qa

The form factor is an allowable axial stress reduction factor equal to the

effective area divided by the actual area. (Consult the latest edition of the

AISC code for the current computation methods for the effective area.)

Allow Sidesway

The ability of a frame or structure to experience sidesway (joint

translation) affects the computation of several of the coefficients used in

the unity check equations. Additionally, for frames braced against

sidesway, moments at each end of the member are required.

Normally sidesway is allowed (i.e., the box is checked).

RUNNING THE STATIC ANALYSIS (CONT’D.)

RUNNING THE STATIC ANALYSIS (CONT’D.)

The stress categories:

SUStained,

EXPansion,

OCCasional,

OPErating, and

FATigue

These are specified at the end of the load case definition.

STA

TIC

OU

TP

UT P

RO

CE

SS

OR

STATIC ANALYSIS OUTPUT

User defined retained output data

Report Options:

Displacements

Restraints

Restraint summary

Global element forces

Local element forces

Stresses

Stress summary

Code compliance report

Cumulative usage report

The next slide shows the on-screen static output processor.

STR

ES

S I

NTE

NS

IFIC

ATIO

N F

AC

TO

RS

OU

TP

UT

DYNAMIC ANALYSIS OF PIPING SYSTEMS

Four types of dynamic analysis are possible:

Natural Frequency calculations

Harmonic analysis

Response Spectrum analysis

Earthquake

[Valve] Relief loads

Water Hammer/Slug Flow

Time History analysis

DYNAMIC ANALYSIS OF PIPING SYSTEMS Caesar II‟s dynamic analysis capabilities include:

Natural Frequency calculations - Natural frequency information can indicate the

tendency of a piping system to respond to dynamic loads. A system‟s modal natural

frequencies typically should not be too close to equipment operating frequencies and, as a

general rule, higher natural frequencies usually cause less trouble than low natural

frequencies.

Harmonic analysis - These are „forcing frequencies‟ that include fluid pulsation in

reciprocating pump lines or vibration due to rotating equipment. These loads are modeled

as concentrated forces or displacements at one or more points in the system. To provide

the proper phase relationship between multiple loads a phase angle can also be

associated with these forces or displacements.

Response Spectrum analysis - The response spectrum method allows an impulse

type transient event to be characterized by a response vs. frequency spectra. Each mode

of vibration of the piping system is related to one response on the spectrum. These modal

responses are summed together to produce the total system response. And

Time History analysis - This is one of the most accurate methods, in that it uses

numeric integration of the dynamic equation of motion to simulate the system response

throughout the load duration. requires more resources (memory, calculation speed and

time) than other methods. spectrum method might be a viable substitute if it offers

sufficient accuracy.

PREPARATION OF MODEL FOR DYNAMIC ANALYSIS

The dynamic analysis techniques employed by many softwares like

Caesar II require strict linearity in the piping and structural systems.

Dynamic responses associated with nonlinear effects are not

addressed.

An example of a nonlinear effect is “slapping”, such as when a pipe

lifts off the rack at one moment and impacts the rack the next. For

the dynamic model the pipe must be either held down or allowed to

move freely. The nonlinear restraints used in the static analysis must

be set to be active or inactive for the dynamic analysis.

A second “nonlinear” effect is friction. Friction effects must also be

“linearized” for use in dynamic analysis. For example, if the normal

force on the restraint from the static analysis is 350 lb., the friction

coefficient (mu) is 0.3, and the user defined Stiffness Factor for

Friction is 50.0, then springs having a stiffness of 350 * 0.3 * 50.0 =

5250 lb/in are inserted into the dynamic model in the two directions

perpendicular to the friction restraint’s line of action.

PREPARATION OF MODEL FOR DYNAMIC ANALYSIS (CONT’D.)

Developing dynamic input for CAESAR II comprises four basic steps:

1) Specifying the load(s)

2) Modifying the mass and stiffness model

3) Setting the parameters that control the analysis

4) Starting and error checking the analysis

To enter the dynamics input, the proper job name must be current prior

to selecting the Analysis-Dynamics file options of the Main Menu.

CODE – STRESS EQUATIONS

below are the “code stress” equations for the actual and allowable stresses used

by CAESAR II. For the listed codes, the left hand side of the equation defines the

actual stress and the right hand side defines the allowable stress. The CAESAR

II load case label is also listed after the equation.

US Code Stresses Stress Cat.

CODE – STRESS EQUATIONS (CONT’D.)









International Code Stresses Stress Cat.



CODE – STRESS

EQUATIONS (CONT’D.)

BS 7159 (cont‟d.)




AVAILABLE MATERIALS (CAESAR II)

MATERIAL NAME

ELASTIC MODULUS

(lb/in2) POISSON’S

RATIO

DENSITY

(lb/in3) TEMPERATURE RANGE (F)

Low Carbon Steel 29.5 E6 0.2920 0.28993 -325 1400

High Carbon Steel 29.3 E6 0.2890 0.28009 -325 1400

Carbon Moly Steel 29.2 E6 0.2890 0.28935 -325 1400

Low Chrome Moly Steel 29.7 E6 0.2890 0.28935 -325 1400

Med Chrome Moly Steel 30.9 E6 0.2890 0.28935 -325 1400

Austenitic Stainless 28.3 E6 0.2920 0.28930 -325 1400

Straight Chromium 29.2 E6 0.3050 0.28010 -325 1400

Type 310 Stainless 28.3 E6 0.3050 0.28990 -325 1400

Wrought Iron 29.5 E6 0.3000 0.28070 -325 1400

Grey Cast Iron 13.4 E6 0.2110 0.25580 70 1000

Monel 67% Ni/30% Cu 26.0 E6 0.3150 0.31870 -325 1400

K-Monel 26.0 E6 0.3150 0.30610 -325 1400

Copper Nickel 22.0 E6 0.3300 0.33850 -325 1400

Aluminum 10.2 E6 0.3300 0.10130 -325 600

Copper 99.8% Cu 16.0 E6 0.3550 0.32270 70 400

Commercial Brass 17.0 E6 0.3310 0.30610 -325 1200

Leaded Tin Bronze 1 14.0 E6 0.3300 0.31890 -325 1200

CODES AND

STANDARDS

AVAILABLE IN

CAESAR II FOR

CODE-CHECKING A

PIPE MODEL

PIPING CODE PUBLICATION DATE REVISION DATE

ANSI B31.1 2004 16-Aug-04

ANSI B31.3 2004 29-Apr-05

ANSI B31.4 2002 4-Oct-02

ANSI B31.4 Chapter IX 2002 4-Oct-02

ANSI B31.5 2001 30-May-05

ANSI B31.8 2003 6-Feb-04

ANSI B31.8 Chapter VIII 2003 6-Feb-04

ANSI B31.11 2002 30-May-03

ASME SECT III CLASS 2 2004 1-Jul-05

ASME SECT III CLASS 3 2004 1-Jul-05

U.S. NAVY 505 1984 N/A

CANADIAN Z662 (9/95) N/A

CANADIAN Z662 Ch 11 (9/95) N/A

BS 806, ISSUE 1 Sept. 1993 N/A

SWEDISH METHOD 1 2ND EDITION STOCKHOLM, 1979 N/A

SWEDISH METHOD 2 2ND EDITION STOCKHOLM 1979 N/A

ANSI B31.1 1967 N/A

STOOMWEZEN 1989 N/A

RCC-M C 1988 N/A

RCC-M D 1988 N/A

CODETI 2001 Jun-04

NORWEGIAN 1999 N/A

FDBR 1995 N/A

BS7159 1989 N/A

UKOOA 1994 N/A

IGE/TD/12 2003 N/A

DnV 1996 N/A

EN-13480 (3/2002) N/A

GPTC/192 1998 N/A

REFERENCES

1. COADE, “Version 5.00 CAESAR II

Applications Guide” Caesar II Pipe

Analysis software, www.coade.com (E-

mail at [email protected])

2. British Standard, BS 806, Pipe Bends

3. Water Resources Council (WRC)

Specification 329

4. Caesar II enhancements and reference

topics,

http://www.intergraph.com/products/ppm/

caesarii/enhancements.aspx

5. American Institute of Steel Construction

(AISC), “Steel Construction Manual”, 13th

edition.

END OF PRESENTATION

75577376 Point Pipe Stress Analysis by Computer CAESAR II

Documents

evenly spaced miters

closely spaced miters

thumb tightening stress

structural steel checks

widely spaced miters

load case editor

reduced geometry requirements

bolt tightening stress