piping stress analysis using caesar ii

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Pipe Stress Analysis Using Pipe Stress Analysis Using CAESAR IICAESAR II

Piping System Analysis

Why do we do it? When & Why Stress Analysis docWhy do we do it? When & Why Stress Analysis.doc

What do we do? How do we model the piping system?How do we document the work?

13-Feb-08 Introduction to CAESAR II and Pipe Stress Analysis

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Pitfalls of Piping Flexibility Analysis

Just about any set of numbers can runJust about any set of numbers can run through a piping program (GIGO)Elements used in piping programs have their limitationsA good analysis addresses these


limitations

3D Beam Element

A purely mathematical modelA purely mathematical modelAll behavior is described by end displacements using F=KxBasic parameters define stiffness and load (K and F, respectively)

Diameter wall thickness and length


Diameter, wall thickness, and lengthElastic modulus, Poisson’s ratioExpansion coefficient, density

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3D Beam Element

Behavior is dominated by bendingEfficient for most analyses


Sufficient for system analysis

3D Beam Element

What’s missing?gNo local effects (shell distortion)No second order effectsNo large rotationNo clashNo accounting for large shear load

Where wall deflection occurs before


Where wall deflection occurs before bendingAs in a short fat cantilever (vs. a long skinny cantilever)

Centerline supportNo shell/wall

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3D Beam Example

Si l il b diSimple cantilever bending:

δ

PL


IELP⋅⋅

⋅=3

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δ

)( KFx =

How Do We Represent Stress?

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Evaluating Stress at a Point

Local coordinate systemLocal coordinate systemLongitudinalHoopRadial

End loads and pressure


through a free body diagram

Stress Element

Longitudinal stressLongitudinal stressF/A, PD/4t, M/Z (max. on outside surface)

Hoop stressPD/2t

Radial stress0 (on outside surface)


0 (on outside surface)

Shear stressT/2Z, (V=0 on outside surface)

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From 3D to 2D

With no radial stress the cube can beWith no radial stress the cube can be reduced to a plane.


Equilibrium

Stress times unit area = forceStress times unit area forceAny new face must maintain equilibriumNew face will have a normal and shear stress component


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Mohr’s Circle

Calculation of these new face stresses areCalculation of these new face stresses are symbolized through Mohr’s circle


Named Stresses (Definitions)

Principal stress – normal stress on thePrincipal stress normal stress on the face where no shear stress existsMaximum shear stress – face upon which shear stress is maximum


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Mohr’s Circle Representation

Principal Stresses:S1, S2, S3

Maximum Shear Stress:


Maximum Shear Stress:τmax

so....

Any complex stress on an element can beAny complex stress on an element can be represented by the principal stresses (S1, S2, S3) and/or the maximum shearing stress (τmax)


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How Do We Measure Failure?

Modes of Pipe Failure

Burst – due to pressureBurst due to pressureCollapse – due to overloadCorrosion – a material considerationFatigue – cyclic loading


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Other Failure Concerns

Too much deflection (clash)Too much deflection (clash)Overloaded pump or flange (bearing/coupling failure or leak)



Maximum principal stress – S1 (Rankine).p p ( )Principal stress alone causes failure of the element.Wall thickness calculations due to pressure alone.

Maximum shearing stress – τmax (Tresca).Shear, not direct stress causes failure.Common stress calculation in piping.

M i di t ti ( Mi )


Maximum distortion energy – wd (von Mises).Total distortion of the element causes failure.Octahedral shearing stress (τGmax) is another measure of the energy used to distort the element. This is known as equivalent stress.

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These are just threeThese are just threeOthers include maximum strain and maximum total energy


Which Measure Do We Use?

Energy of distortion is the most accurate e gy o d sto t o s t e ost accu ateprediction of failure but maximum shearing stress is close and conservative.Piping codes often utilize their own mix (through the term “stress intensity”).CAESAR II can print either Tresca or von Mises


CAESAR II can print either Tresca or von Mises stress in the “132 column” stress report.Our (code) focus is maximum shearing stress.

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From Lab to Field

How Do We Compare F il ?Failures?

Material Characteristics

Lab produces stress-strain characteristicsLab produces stress strain characteristics for our alloy


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Material Characteristics

Direct (axial) load on a test specimen toDirect (axial) load on a test specimen to yield and ultimate failureGives E, Sy, Sult

These terms vary with temperature


Lab Failure

If failure occurs atIf failure occurs at yield, the appropriate stress is calculated using the yield loadSy = Py/a


And this is our limitτmax ≤ Sy/2

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Field Failure

If stress of interest (S1, τ , τoct) on theIf stress of interest (S1, τmax , τoct) on the field element is greater than the lab element, failure is predicted


Piping Code Simplification

Using the maximum shear calculation…Us g t e a u s ea ca cu at oτmax is the radius of Mohr’s circle.τmax = (S1-S3)/2.So, (S1-S3)/2≤ Sy/2.Or (S1-S3) ≤ Sy


Piping codes define (S1-S3) as stress intensity.Stress intensity must be below the material yield.

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More Simple?

Hoop stress (SH) is positive and below yield due p ( H) p yto wall thickness requirements (design by rule).Radial stress is zero, assume this is S3.Longitudinal stress (SL), assumed positive, must be checked only if it exceeds hoop stress, then S1=f(SL,τ) and (S1-S3)= f(SL,τ).

S ith h t t d ith ll


So, with hoop stress accounted with wall thickness, you need only evaluate longitudinal and shear stresses and compare the results with the material yield, Sy.

If SL is negative, then SL becomes S3 andIf SL is negative, then SL becomes S3 and SH is S1. This produces a greater stress intensity of (SH – SL). This is a concern for “restrained pipe” most commonly found in buried piping systems. O h l l d l


Otherwise, as long as longitudinal stress is below yield, the pipe material will not fail.

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Or So You Might Think…

Other Failures Do Occur

Through-the-wall cracks on componentsThrough the wall cracks on components subject to thermal strain

Not immediateLow cycle and high cycle fatigue

Rupture at elevated temperatures (creep)


Again, over time

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Effects of thermal strain were investigatedEffects of thermal strain were investigated and addressed by A.R.C. Markl et. al. in the late 40’s and into the 50’s.


Yield Is Not the Only Concern

Yield is a “primary” concern for force-Yield is a primary concern for forcebased loads which lead to collapse.But other, non-collapse loads exist.


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Non-collapse Loads?

Deadweight loads must satisfy equilibriumDeadweight loads must satisfy equilibrium (F in F=Kx is independent) or collapse.Displacement-based loads such as thermal strain can satisfy static equilibrium through deformation and even local structural yielding.


structural yielding.Here, x in F=Kx is independent but material yield will limit K and therefore F.

Are There Strain Limits?

Going cold to hot may produce yield inGoing cold to hot may produce yield in the hot state but there will also be a residual stress in the system when it returns to its cold condition


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But what if this residual cold stressBut what if this residual cold stress exceeds its cold yield limit?



Yield will occur at both ends of everyYield will occur at both ends of every thermal cycleThis is low cycle fatigueFailure will occur in only a few cycles(Try this with a paper clip.)


(Try this with a paper clip.)

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Shakedown and Its Limits

Initial yield is acceptable.Initial yield is acceptable.This is known as shakedown.But to avoid low cycle fatigue failure, the overall change in stress – installed to operating – must be less than the sum of


the hot yield stress and the cold yield stress…two times yield!

Shakedown and Its Limits

Yielding is acceptable; The pipe “shakesYielding is acceptable; The pipe shakes down” any additional strain.Expansion stress range ≤ (Syc+Syh).The code equations limit this stress to (1.25Sc+1.25Sh).


c h

The stress at any one state (hot or cold) cannot measure this fatigue stress range.

(One limit for S is based on Sy: S=2/3 Sy, so Sy=1.5S)

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But We’re Not Done…

Yet other systems have been in service,Yet other systems have been in service, cycling for many years, only to fail later in life.This is evidence of high cycle fatigue.


Material Fatigue

Polished bar test specimens will failPolished bar test specimens will fail through fatigue under a cyclic stressThe higher the stress amplitude, the fewer cycles to failure


Fig. 5-110.1, Design Fatigue Curves from ASME VIII-2 App. 5 –Mandatory Design Based on Fatigue Analysis

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Piping Material Fatigue

This is reflected in the allowable stress by theThis is reflected in the allowable stress by the cyclic reduction factor – f.

Expansion stress Se ≤ f(1 25S +1 25S )


Expansion stress Se ≤ f(1.25Sc+1.25Sh).To address ratcheting, the force-based stress (SL) will reduce this acceptable stress amplitude. Therefore, Se ≤ f(1.25Sc+1.25Sh-SL).

Some Components Fail “Sooner” Than Others

Failures occurred at pipe connections,Failures occurred at pipe connections, bends and intersections.Markl’s work examined the cause of these fatigue failures


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Bend Failure

Pipe bends ovalizePipe bends ovalize as they bendThis makes them more flexibleAnd makes them


fail “sooner” than a butt weld

Component Fatigue

Markl tested various piping componentsMarkl tested various piping components and plotted their stress and cycle count at failure.


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Stress Intensification

Rather than reduce the allowed stress forRather than reduce the allowed stress for the component in question, this SIF (or i) increases the calculated stress.Stress = Mi/Z.


el

bwS

Si =

In-Plane/Out-Plane

Process piping distinguished between in-Process piping distinguished between inplane bending and out-plane bendingIn-plane bending keeps the component in its original planeOut-plane bending pulls the component


out of its plane

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In-Plane/Out-Plane


Markl’s Work in Today’s Code

Markl extended his findings to severalMarkl extended his findings to several pipe components and joints.This work appears in Appendix D.Pay attention to the notes.


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B31.1 Appendix D


B31.3 Appendix D


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B31.3 SIF Example

B31.3 Sample SIF CalculationspWelding elbow or pipe bend Reinforced fabricated tee with pad or saddle

Input InputPipe OD : 10.75 10.75 10.75 10.75 Pipe OD : 10.75 10.75 10.75 10.75Pipe wall : 0.365 0.365 0.365 0.365 Pipe wall : 0.365 0.365 0.365 0.365

Bend radius : 15 10 30 50 Pad thickness : 0 0.25 0.365 0.5

Intermediate Calculations Intermediate CalculationsTbar = 0.365 0.365 0.365 0.365 Tbar = 0.365 0.365 0.365 0.365

R1 = 15 10 30 50 Tr = 0 0.25 0.365 0.5r2 = 5.193 5.193 5.193 5.193 r2 = 5.193 5.193 5.193 5.193


h = 0.203 0.135 0.406 0.677 h = 0.070 0.147 0.194 0.259

Stress Intensification Factors Stress Intensification Factorsout-of-plane = 2.171 2.845 1.368 1.000 out-of-plane = 5.284 3.234 2.688 2.215

in-plane = 2.605 3.414 1.641 1.167 in-plane = 4.213 2.676 2.266 1.911

B31.1 SIF Example

B31.1 Sample SIF CalculationspWelding elbow or pipe bend Reinforced fabricated tee with pad or saddle

Input InputPipe OD : 10.75 10.75 10.75 10.75 Pipe OD : 10.75 10.75 10.75 10.75Pipe wall : 0.365 0.365 0.365 0.365 Pipe wall : 0.365 0.365 0.365 0.365

Bend radius : 15 10 30 50 Branch OD : 4.5 4.5 4.5 4.5Branch wall : 0.237 0.237 0.237 0.237

Branch OD at tee : 5Pad thickness : 0 0.25 0.365 0.5

Intermediate Calculations Intermediate Calculationstn = 0.365 0.365 0.365 0.365 tn or tnh = 0.365 0.365 0.365 0.365R = 15 10 30 50 r or Rm = 5 193 5 193 5 193 5 193


R = 15 10 30 50 r or Rm = 5.193 5.193 5.193 5.193r = 5.193 5.193 5.193 5.193 tnb = 0.237 0.237 0.237 0.237

rm = 2.132 2.132 2.132 2.132rp = 2.250 2.500 2.250 2.250

h = 0.203 0.135 0.406 0.677 h = 0.070 0.147 0.194 0.259

Stress Intensification Factor Stress Intensification Factor2.605 3.414 1.641 1.167 Header : 5.284 3.234 2.688 2.215

Branch : 3.471 3.124 3.471 3.471

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To Summarize:

Unchanging loads (loads that do not vary with Unchanging loads (loads that do not vary with system distortion – weight, pressure, spring preloads, wind, relief thrust, etc.) must remain below the material yield limit.Strain-based loads (thermal growth of pipe, movement of supports) must remain below the


pp )material fatigue limitSeveral piping codes such as the transportation codes also limit operating stress

Piping Code Implementation

What Are the Code Stress E ti d Th i Li it ?Equations and Their Limits?

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A Review of the Basic Concerns

Force-based loads are limited by yieldForce based loads are limited by yieldBut also! Permanent or temporary?These are “primary” loads and they produce sustained and occasional stresses

Strain-based loads are limited by fatigue


These are “secondary” loads and they produce expansion stresses

Piping code equations:

Power PipingPower PipingB31.1, ASME III, B31.5, FBDR (, EN-13480?)Most stringent limitationsSample Equations

Sustained: Slp + (0.75i)Ma/Z < ShE i iM /Z f(1 25S 1 25Sh S t i d)


Expansion: iMc/Z < f(1.25Sc + 1.25Sh – Sustained)Sustained + Occasional:Slp + (0.75i)Ma/Z + (0.75i)Mb/Z < kSh

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Process PipingProcess PipingB31.3, ISO 15649Wider applicationsSample Equations

Let Sb = {sqrt[(iiMi)2+(ioMo)2]}/ZSustained: Slp + Fax/A + Sb < Sh


pExpansion: sqrt(Sb2 + 4St2) < f(1.25Sc + 1.25Sh – Sustained)Sustained + Occasional: Slp + (Fax/A + Sb)sus +(Fax/A+Sb)occ < kSh


Transportation PipingTransportation PipingB31.4, B31.8, TD/12, Z662, DNVBased of proof testing and yield limitsAddresses compressionSample Equations

Let Sb = {sqrt[(iiMi)2+(ioMo)2]}/Z


Let Sb {sqrt[(iiMi) +(ioMo) ]}/ZSustained: Slp + Sb < 0.75SyExpansion: sqrt(Sb2 + 4St2) < 0.72SyOperating: Sustained + Expansion < Sy

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FRP (GRP) PipeFRP (GRP) PipeBS 7159, UKOOA (ISO14692)Different materials different concernsEquations evaluate the interaction of hoop and axial stressB d d i i h h


Based on design strain rather than stress (but σ=εE)

CAESAR II – The Program

An Overview of th D i P dthe Design Procedure

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Pipe Stress Analysis

andand


Design by Analysis


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Design by Analysis

The design cycleThe design cycleCollect data (with assumptions)

Generate the model and load sets

Run the analysis

Check the assumptions


Diagnose any problems

Re-run with fixes

Document the analysis

The Design Cycle

ModelA system model, not a local model

AnalyzeIt’s just F = KX

EvaluateCheck the design limits


Check the design limits

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Is It a Good Model?

Focus on stiffness boundary conditions andFocus on stiffness, boundary conditions and

loads.

Consider the stiffness method assumptions

(remember, it’s only an approximation).


Run a simple “sensitivity study” when you’re

unsure.

A Sensitivity Study

Treat CAESAR II as a black box.Treat CAESAR II as a black box.Examine the effects of a single input modification.Determine the sensitivity of the results to that particular piece of data.


Examples: nozzle flexibility, friction, support location, restraint stiffness.

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Verifying Results

Equilibrium exists in static analyses.Equilibrium exists in static analyses.Resultant loads equal applied loads.Restraint loads for weight analysis sum to total deadweight.

You can verify coordinates of key i i


positions.Check the plotted deflections.

Design Limits

Pipe failure (stress)

Pipe Deflection

Equipment loads


Equipment loads

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Use a Sensitivity Study:

To improve the values

To improve your


p yconfidence

Which Is Better –

a complex modelor a simple model?


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Summary

Basic stresses reviewedBasic stresses reviewedFailure theories reviewedSIFs introducedLoad case (stress) type introducedExpansion case explained


Expansion case explainedCode equations summarized

Pipe Stress Analysis Using CAESAR II


piping stress analysis using caesar ii

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