Pipe Stress Analysis Using CAESAR II
Piping System Analysis Why do we do it? What do we do? How do we model the piping system? How do we document the work? When & Why Stress Analysis Analysis.doc doc
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Introduction to CAESAR II and Pipe Stress Analysis
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Pitfalls of Piping Flexibility Analysis 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 limitations
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Introduction to CAESAR II and Pipe Stress Analysis
3D Beam Element 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, Diameter thickness and length Elastic modulus, Poisson’s ratio Expansion coefficient, density 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
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3D Beam Element Behavior is dominated by bending Efficient for most analyses Sufficient for system analysis
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Introduction to CAESAR II and Pipe Stress Analysis
3D Beam Element What’s missing? g No No No No No
local effects (shell distortion) second order effects large rotation clash accounting for large shear load Where wall deflection occurs before bending As in a short fat cantilever (vs. a long skinny cantilever)
Centerline support No shell/wall 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
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3D Beam Example Si l cantilever Simple il bending: b di
P
L
δ δ = P⋅
L3 3⋅ E ⋅ I
(x = F 13-Feb-08
K
)
Introduction to CAESAR II and Pipe Stress Analysis
How Do We Represent Stress?
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Evaluating Stress at a Point Local coordinate system Longitudinal Hoop Radial
End loads and pressure through a free body diagram 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Stress Element Longitudinal stress F/A, PD/4t, M/Z (max. on outside surface)
Hoop stress PD/2t
Radial stress 0 (on outside surface)
Shear stress T/2Z, (V=0 on outside surface)
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Introduction to CAESAR II and Pipe Stress Analysis
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From 3D to 2D With no radial stress the cube can be reduced to a plane.
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Introduction to CAESAR II and Pipe Stress Analysis
Equilibrium 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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Introduction to CAESAR II and Pipe Stress Analysis
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Mohr’s Circle Calculation of these new face stresses are symbolized through Mohr’s circle
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Introduction to CAESAR II and Pipe Stress Analysis
Named Stresses (Definitions) 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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Introduction to CAESAR II and Pipe Stress Analysis
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Mohr’s Circle Representation
Principal Stresses: S1, S2, S3 Maximum Shear Stress: τmax so.... 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Any 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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Introduction to CAESAR II and Pipe Stress Analysis
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How Do We Measure Failure?
Modes of Pipe Failure Burst – due to pressure Collapse – due to overload Corrosion – a material consideration Fatigue – cyclic loading
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Introduction to CAESAR II and Pipe Stress Analysis
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Other Failure Concerns Too much deflection (clash) Overloaded pump or flange (bearing/coupling failure or leak)
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Introduction to CAESAR II and Pipe Stress Analysis
How Do We Measure Failure? Maximum p principal p stress – S1 ((Rankine). ) 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 Maximum distortion di t ti energy – wd (von ( Mises). Mi )
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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Introduction to CAESAR II and Pipe Stress Analysis
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How Do We Measure Failure? These are just three Others include maximum strain and maximum total energy
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Introduction to CAESAR II and Pipe Stress Analysis
Which Measure Do We Use? Energy e gy o of d distortion sto t o iss tthe e most ost accu accurate 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 stress in the “132 column” stress report. Our (code) focus is maximum shearing stress.
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Introduction to CAESAR II and Pipe Stress Analysis
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From Lab to Field
How Do We Compare F il Failures? ?
Material Characteristics Lab produces stress-strain stress strain characteristics for our alloy
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Introduction to CAESAR II and Pipe Stress Analysis
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Material Characteristics Direct (axial) load on a test specimen to yield and ultimate failure Gives E, Sy, Sult These terms vary with temperature
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Introduction to CAESAR II and Pipe Stress Analysis
Lab Failure If failure occurs at yield, the appropriate stress is calculated using the yield load Sy = Py/a And this is our limit τmax ≤ Sy/2 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
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Field Failure If stress of interest (S1, τmax , τoct) on the field element is greater than the lab element, failure is predicted
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Introduction to CAESAR II and Pipe Stress Analysis
Piping Code Simplification Us g tthe Using e maximum a u sshear ea ca calculation… cu at o τmax 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. 13-Feb-08
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More Simple? Hoop p stress (S ( H) is positive p and below yyield due to 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 with So, ith h hoop stress t accounted t d with ith wallll thickness, you need only evaluate longitudinal and shear stresses and compare the results with the material yield, Sy. 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
If 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. Oh Otherwise, as long l as longitudinal l d l 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 subject to thermal strain Not immediate Low cycle and high cycle fatigue
Rupture at elevated temperatures (creep) Again, over time
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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.
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Introduction to CAESAR II and Pipe Stress Analysis
Yield Is Not the Only Concern Yield is a “primary” primary concern for forceforce based loads which lead to collapse. But other, non-collapse loads exist.
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Non-collapse Loads? 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. Here, x in F=Kx is independent but material yield will limit K and therefore F. 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Are There Strain Limits? 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 exceeds its cold yield limit?
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Introduction to CAESAR II and Pipe Stress Analysis
Are There Strain Limits? 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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Introduction to CAESAR II and Pipe Stress Analysis
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Shakedown and Its Limits 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! 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Shakedown and Its Limits Yielding is acceptable; The pipe “shakes shakes down” any additional strain. Expansion stress range ≤ (Syc+Syh). The code equations limit this stress to (1.25Sc+1.25Sh). 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) 13-Feb-08
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But We’re Not Done… Yet other systems have been in service, cycling for many years, only to fail later in life. This is evidence of high cycle fatigue.
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Introduction to CAESAR II and Pipe Stress Analysis
Material Fatigue 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 cyclic reduction factor – f.
Expansion stress Se ≤ f(1.25S f(1 25Sc+1.25S +1 25Sh). ) To address ratcheting, the force-based stress (SL) will reduce this acceptable stress amplitude. Therefore, Se ≤ f(1.25Sc+1.25Sh-SL). 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Some Components Fail “Sooner” Than Others Failures occurred at pipe connections, bends and intersections. Markl’s work examined the cause of these fatigue failures
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Introduction to CAESAR II and Pipe Stress Analysis
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Bend Failure Pipe bends ovalize as they bend This makes them more flexible And makes them fail “sooner” than a butt weld 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Component Fatigue 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 the component in question, this SIF (or i) increases the calculated stress. Stress = Mi/Z. i=
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S bw
S el
Introduction to CAESAR II and Pipe Stress Analysis
In-Plane/Out-Plane Process piping distinguished between in inplane 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
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Introduction to CAESAR II and Pipe Stress Analysis
Markl’s Work in Today’s Code 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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Introduction to CAESAR II and Pipe Stress Analysis
B31.3 Appendix D
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B31.3 SIF Example B31.3 Sample p SIF Calculations Welding elbow or pipe bend Input Pipe OD : Pipe wall : Bend radius :
10.75 0.365 10
10.75 0.365 30
10.75 0.365 50
Intermediate Calculations Tbar = 0.365 0.365 R1 = 15 10 r2 = 5.193 5.193
0.365 30 5.193
0.365 50 5.193
0.135
0.406
0.677
Stress Intensification Factors out-of-plane = 2.171 2.845 in-plane = 2.605 3.414
1.368 1.641
1.000 1.167
h=
10.75 0.365 15
Reinforced fabricated tee with pad or saddle
0.203
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Input Pipe OD : Pipe wall : Pad thickness :
10.75 0.365 0
10.75 0.365 0.25
10.75 0.365 0.365
10.75 0.365 0.5
0.365 0.25 5.193
0.365 0.365 5.193
0.365 0.5 5.193
0.147
0.194
0.259
Stress Intensification Factors out-of-plane = 5.284 3.234 in-plane = 4.213 2.676
2.688 2.266
2.215 1.911
Intermediate Calculations Tbar = 0.365 Tr = 0 r2 = 5.193 h=
0.070
Introduction to CAESAR II and Pipe Stress Analysis
B31.1 SIF Example B31.1 Sample p SIF Calculations Welding elbow or pipe bend
Reinforced fabricated tee with pad or saddle
Input Pipe OD : Pipe wall : Bend radius :
Input 10.75 0.365 15
10.75 0.365 10
Intermediate Calculations tn = 0.365 0.365 R= 15 10 r= 5.193 5.193
h=
0.203
0.135
Stress Intensification Factor 2.605 3.414
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10.75 0.365 30
10.75 0.365 50
0.365 30 5.193
0.365 50 5.193
0.406
0.677
1.641
1.167
Pipe OD : Pipe wall : Branch OD : Branch wall : Branch OD at tee : Pad thickness :
10.75 0.365 4.5 0.237
10.75 0.365 4.5 0.237
0
10.75 0.365 4.5 0.237 5 0.25
0.365
0.5
Intermediate Calculations tn or tnh = 0.365 r or Rm = 5 193 5.193 tnb = 0.237 rm = 2.132 rp = 2.250
0.365 5 193 5.193 0.237 2.132 2.500
0.365 5 193 5.193 0.237 2.132 2.250
0.365 5 193 5.193 0.237 2.132 2.250
0.147
0.194
0.259
3.234 3.124
2.688 3.471
2.215 3.471
h=
10.75 0.365 4.5 0.237
0.070
Stress Intensification Factor Header : 5.284 Branch : 3.471
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To Summarize: 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, pp ) must remain below the movement of supports) material fatigue limit Several piping codes such as the transportation codes also limit operating stress 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Piping Code Implementation
What Are the Code Stress E Equations ti and d Th Their i Li Limits? it ?
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A Review of the Basic Concerns Force-based 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
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Introduction to CAESAR II and Pipe Stress Analysis
Piping code equations: Power Piping B31.1, ASME III, B31.5, FBDR (, EN-13480?) Most stringent limitations Sample Equations Sustained: Slp + (0.75i)Ma/Z < Sh E Expansion: i iMc/Z iM /Z < f(1.25Sc f(1 25S + 1 1.25Sh 25Sh – Sustained) S t i d) Sustained + Occasional: Slp + (0.75i)Ma/Z + (0.75i)Mb/Z < kSh
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Piping code equations: Process Piping B31.3, ISO 15649 Wider applications Sample Equations Let Sb = {sqrt[(iiMi)2+(ioMo)2]}/Z p + Fax/A + Sb < Sh Sustained: Slp Expansion: sqrt(Sb2 + 4St2) < f(1.25Sc + 1.25Sh – Sustained) Sustained + Occasional: Slp + (Fax/A + Sb)sus +(Fax/A+Sb)occ < kSh 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Piping code equations: Transportation Piping B31.4, B31.8, TD/12, Z662, DNV Based of proof testing and yield limits Addresses compression Sample Equations Let Sb = {sqrt[(iiMi)2+(ioMo)2]}/Z Sustained: Slp + Sb < 0.75Sy Expansion: sqrt(Sb2 + 4St2) < 0.72Sy Operating: Sustained + Expansion < Sy 13-Feb-08
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Piping code equations: FRP (GRP) Pipe BS 7159, UKOOA (ISO14692) Different materials different concerns Equations evaluate the interaction of hoop and axial stress B d on d Based design i strain i rather h than h stress (but σ=εE)
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Introduction to CAESAR II and Pipe Stress Analysis
CAESAR II – The Program
An Overview of th D the Design i P Procedure d
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Pipe Stress Analysis and
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Introduction to CAESAR II and Pipe Stress Analysis
Design by Analysis
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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 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
The Design Cycle Model A system model, not a local model
Analyze It’s just F = KX
Evaluate Check the design limits
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Is It a Good Model? Focus on stiffness 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. 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
A Sensitivity Study 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. 13-Feb-08
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Verifying Results 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 positions. ii Check the plotted deflections. 13-Feb-08
Introduction to CAESAR II and Pipe Stress Analysis
Design Limits Pipe failure (stress) Pipe Deflection Equipment loads
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Use a Sensitivity Study: To improve the values To improve p your y confidence
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Introduction to CAESAR II and Pipe Stress Analysis
Which Is Better –
a complex model or a simple model?
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Summary Basic stresses reviewed Failure theories reviewed SIFs introduced Load case (stress) type introduced Expansion case explained Code equations summarized
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Introduction to CAESAR II and Pipe Stress Analysis
Pipe Stress Analysis Using CAESAR II
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