Piping stress Analysis using CAESAR II

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Pipe Stress Analysis Using

CAESAR II

Piping System Analysis

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

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Pitfalls of

Piping Flexibility Analysis

Just about any set of numbers can run Just about any set of numbers can run through a piping program (GIGO)

Elements used in piping programs have their limitations

A good analysis addresses these

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

limitations

3D Beam Element

A purely mathematical model A purely mathematical model All behavior is described by end displacements using F=Kx

Basic parameters define stiffness and load (K and F, respectively)

Diameter wall thickness and length Diameter, wall thickness, and length Elastic modulus, Poisson’s ratio Expansion coefficient, density

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3D Beam Element

Behavior is dominated by bending

Efficient for most analyses

Sufficient for system analysis

3D Beam Element

What’s missing?g

No local effects (shell distortion) No second order effects

No large rotation No clash

No accounting for large shear load

Where wall deflection occurs before Where wall deflection occurs before bending

As in a short fat cantilever (vs. a long skinny cantilever)

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3D Beam Example

Si l il b di Simple cantilever bending:

δ P L

I E L P ⋅ ⋅ ⋅ = 3 3 δ ) ( K F x=

How Do We Represent

Stress?

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Evaluating Stress at a Point

Local coordinate system Local coordinate system

Longitudinal Hoop

Radial

End loads and pressure

through a free body diagram

Stress Element

Longitudinal stress

F/A, PD/4t, M/Z (max. on outside surface)

Hoop stress

PD/2t

Radial stress

0 (on outside surface) 0 (on outside surface)

Shear stress

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From 3D to 2D

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

Equilibrium

Stress times unit area = force Stress times unit area force

Any new face must maintain equilibrium New face will have a normal and shear stress component

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Mohr’s Circle

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

Named Stresses (Definitions)

Principal stress – normal stress on the Principal stress normal stress on the face where no shear stress exists

Maximum 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:

τ_max

so....

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

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How Do We Measure

Failure?

Modes of Pipe Failure

Burst – due to pressure Burst due to pressure Collapse – due to overload

Corrosion – a material consideration Fatigue – 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)

How Do We Measure Failure?

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 – τ_max (Tresca).

Shear, not direct stress causes failure. Common stress calculation in piping.

M i di t ti ( Mi )

Maximum distortion energy – w_d (von Mises).

Total distortion of the element causes failure.

Octahedral shearing stress (τG_max) is another measure

of the energy used to distort the element. This is known as equivalent stress.

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How Do We Measure Failure?

These are just three These are just three

Others 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 ate prediction 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.

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From Lab to Field

How Do We Compare

F il ?

Failures?

Material Characteristics

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

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Material Characteristics

Direct (axial) load on a test specimen to Direct (axial) load on a test specimen to yield and ultimate failure

Gives E, S_y, S_ult

These terms vary with temperature

Lab Failure

If failure occurs at If failure occurs at yield, the appropriate stress is calculated using the yield load S_y= P_y/a

And this is our limit τ_max≤ S_y/2

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Field Failure

If stress of interest (S1, τ , τ_oct) on the If stress of interest (S1, τ_max , τ_oct) 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 o

τ_maxis the radius of Mohr’s circle.

τ_max = (S1-S3)/2.

So, (S1-S3)/2≤ S_y/2.

Or (S1-S3) ≤ S_y

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

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More Simple?

Hoop stress (Sp ( _H_H) is positive and below yield due ) p y

to wall thickness requirements (design by rule). Radial stress is zero, assume this is S3.

Longitudinal stress (S_L), assumed positive, must

be checked only if it exceeds hoop stress, then

S1=f(S_L,τ) and (S1-S3)= f(S_L,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, S_y.

If S_L is negative, then S_L becomes S3 and If S_L is negative, then S_L becomes S3 and S_H is S1. This produces a greater stress intensity of (S_H – S_L). 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 components Through the wall cracks on components subject to thermal strain

Not immediate

Low cycle and high cycle fatigue

Rupture at elevated temperatures (creep)

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Effects of thermal strain were investigated Effects 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 force based loads which lead to collapse. But other, non-collapse loads exist.

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Non-collapse Loads?

Deadweight loads must satisfy equilibrium Deadweight 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 in Going 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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Are There Strain Limits?

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

Are There Strain Limits?

Yield will occur at both ends of every Yield will occur at both ends of every thermal cycle

This is low cycle fatigue

Failure will occur in only a few cycles (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 “shakes Yielding is acceptable; The pipe shakes down” any additional strain.

Expansion stress range ≤ (S_yc+S_yh). The code equations limit this stress to (1.25S_c_c+1.25S_h_h).

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

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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 fail Polished bar test specimens will fail through fatigue under a cyclic stress The 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 the This is reflected in the allowable stress by the cyclic reduction factor – f.

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

Expansion stress Se ≤ f(1.25S_c+1.25S_h).

To address ratcheting, the force-based stress

(S_L) will reduce this acceptable stress amplitude.

Therefore, Se ≤ f(1.25S_c+1.25S_h-S_L).

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 ovalize Pipe bends ovalize as they bend

This makes them more flexible

And makes them

fail “sooner” than a butt weld

Component Fatigue

Markl tested various piping components Markl 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 for Rather than reduce the allowed stress for the component in question, this SIF (or i) increases the calculated stress.

Stress = Mi/Z.

el bw S S i =

In-Plane/Out-Plane

Process piping distinguished between in-Process piping distinguished between in plane bending and out-plane bending

In-plane bending keeps the component in its original plane

Out-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 several Markl 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

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B31.3 SIF Example

B31.3 Sample SIF Calculationsp

Welding elbow or pipe bend Reinforced fabricated tee with pad or saddle Input Input

Pipe OD : 10.75 10.75 10.75 10.75 Pipe OD : 10.75 10.75 10.75 10.75 Pipe 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 Calculations

Tbar = 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 0.5 r2 = 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 Factors

out-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 Calculationsp

Welding elbow or pipe bend Reinforced fabricated tee with pad or saddle

Input Input

Pipe OD : 10.75 10.75 10.75 10.75 Pipe OD : 10.75 10.75 10.75 10.75 Pipe 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 4.5 Branch wall : 0.237 0.237 0.237 0.237 Branch OD at tee : 5

Pad thickness : 0 0.25 0.365 0.5

Intermediate Calculations Intermediate Calculations

tn = 0.365 0.365 0.365 0.365 tn or tnh = 0.365 0.365 0.365 0.365 R = 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 5.193 r = 5.193 5.193 5.193 5.193 tnb = 0.237 0.237 0.237 0.237 rm = 2.132 2.132 2.132 2.132 rp = 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

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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 limit

Several 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 ?

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A Review of the Basic

Concerns

Force-based loads are limited by yield Force based loads are limited by yield

But 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 Piping Power Piping

B31.1, ASME III, B31.5, FBDR (, EN-13480?) Most stringent limitations

Sample Equations

Sustained: Slp + (0.75i)Ma/Z < Sh

E i iM /Z f(1 25S 1 25Sh S t i d) Expansion: iMc/Z < f(1.25Sc + 1.25Sh – Sustained) Sustained + Occasional:

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Piping code equations:

Process Piping Process Piping B31.3, ISO 15649 Wider applications Sample Equations

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

Sustained: Slp + Fax/A + Sb < Sh

p Expansion:

sqrt(Sb2_{+ 4St}2_{) < f(1.25Sc + 1.25Sh – Sustained)}

Sustained + Occasional:

Slp + (Fax/A + Sb)_sus +(Fax/A+Sb)_occ < kSh

Piping code equations:

Transportation Piping Transportation Piping

B31.4, B31.8, TD/12, Z662, DNV Based of proof testing and yield limits Addresses compression

Sample Equations

Let Sb = {sqrt[(i_iM_i)2_+(i

oMo)2]}/Z

Let Sb {sqrt[(i_iM_i) +(i_oM_o) ]}/Z Sustained: Slp + Sb < 0.75Sy

Expansion: sqrt(Sb2 _{+ 4St}2_{) < 0.72Sy}

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Piping code equations:

FRP (GRP) Pipe FRP (GRP) Pipe

BS 7159, UKOOA (ISO14692)

Different materials different concerns

Equations evaluate the interaction of hoop and axial stress

B 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 d

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Pipe Stress Analysis

and

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Design by Analysis

The design cycle

Collect 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

Model

A system model, not a local model

Analyze

It’s just F = KX

Evaluate

Check the design limits Check the design limits

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Is It a Good Model?

Focus on stiffness boundary conditions and Focus 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 y

confidence

Which Is Better –

a c

o

m

p

l

e

x

model

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Summary

Basic stresses reviewed Basic stresses reviewed Failure theories reviewed SIFs introduced

Load case (stress) type introduced Expansion case explained

Expansion case explained Code equations summarized