Limitations of Appendix P:

A conservative formulation of the allowable expansion stress range for many codes in CAESAR II is calculated from:

SA = f (1.25 Sc + .25 Sh)…………………………………Without Liberal

When the user requests that the "Liberal Allowable" be used, the difference between Sh and Sl, provided Sh > Sl, will be added to the term inside the parenthesis, i.e.

SA = f [1.25 Sc + .25 Sh + (Sh - Sl)]……………………………With Liberal

Longitudinal Stresses SL: The sum of the longitudinal stresses, SL, in any component in a piping system, due to sustained loads such as pressure and weight, shall not exceed the product ShW;

f: stress range factor

Sc: basic allowable stress at minimum metal temperature expected during the displacement cycle under analysis

Sh: basic allowable stress at maximum metal temperature expected during the displacement cycle under analysis

The liberal expression will only be employed when there is at least one sustained stress case in the load set. If there is more than one sustained stress case in a single problem, then the largest of Sl, considering all of the sustained cases, for any single element end will be chosen to subtract from Sh. Because the sustained stress varies from one pipe to another, the allowable expansion stress will also vary.

Appendix P

Allowable Operating Stress Limit: The greater of the maximum operating stress and maximum operating stress range in a piping system shall not exceed the allowable operating stress limit, SoA

The operating stress is the calculated stress at any operating condition, including pressure, weight and other sustained loads, and displacement. Occasional loads are not required to be included.

The operating stress range is the range of stress between any two operating conditions, including the ranges between operating conditions and a sustained case with the piping at ambient temperature.

SoA = 1.25 f (Sc + Sh)…………………………………………Appendix P

Conclusion: Based on above explanation Appendix P is not applicable for Expansion stresses.

If we select the Appendix P (in configuration setup) while doing stresses analysis we have to take care below points:

1. Allowable stresses are applicable for only operating (OPE) cases.

2. For Expansion (EXP) Cases these allowables are not applicable.

3. For complying Expansion (EXP) Cases better we have to check the piping system without selecting Appendix P (in configuration setup)


If any Augmentations welcome.


Thanks & Regards

Sathya Prakash Reddy

Engineer-Piping

No.

In Appendix P you compare the largest of operating stress range or operating stress (state) to that allowed limit.

The expansion stress range is an operating stress range.

The use of Appendix P requires that you confirm both the expansion stress range(s) and the operating stress state(s) remain below their respective limits.

Mr Dave,

Here what I am trying to say is Appendix P gives the same allowable for OPErating Cases and EXPansion cases.

(As per my knowledge piping system have defferent allowable for different cases.)

Clarify this.

Thanks & Regards
Sathya Prakash Reddy
Engineer-Piping

I don't like to use Appendix P simply because I don't believe that there is something known as operating stress. The failure mechanisms are like this:

1) Plastic collapse; due to high bending moment ( plastic hinge at across section)under high load or bursting due to high pressure.

2) Ratchetting: This is a complex phenomenon. This is what is known as cycle dependent creep. From basic theory of fatigue we know the effect of mean stress or mean strain on fatigue. In this phenomenon, due to high level of plasticity, mean strain increases in every cycle ( the opposite effect also sometime hapens when mean stress and not strain reduced in every cycle due to plastic action)and the filure can be due to platic collapse or fatigue.The 2yp range is based on Melan's shakedown theorem and is based on elastic perfectly plastic materials only.

3) Fatigue:

a) stress controlled : this is due to low level of stress ( less than yield point) and high no. of cycles.This is a localized phenomenon.

b) Strain controlled: this is due to high level of strain and lower no. of cycles.Mark's tests were strain controlled.

Fatigue in presence of mean stress is similar but not same as ratchetting.

4) Buckle: Also known as bifurcation buckling where the direction of displacement is orthogonal to applied load, making the effective ( material+geometric ) stiffess=0. This method overpredicts for perfect structure and under predicts the collapse load for imperfect structures.

Based on the above, under which failure category would you place operating stress? It is certainly not plastic collpase ( the code alowable does not indicate that either). Is it then fatigue or ratchetting ( both requires range of loadand cyclicing).The only possibility can be , it is a simplistic representation of checking for fatigue failure using monotonic analysis ( twice yield method of the new 2007 edition of SECTION VIII DIV 2). This is valid for simple cases ( papers by Mroz, Dowling and Kalnins provide the necessary mathematics) but use of cyclic stresss strain curve instead of monotonic is needed. Also the full range of loading is required .Hence in my opinion, this check does not address any proper failure mechanism and hence the expansion stress range check ( this is actually a fatigue check but the code uses one equation to check fatigue and ratchetting to keep this simple)is what should be used.

Please provide me some materials on this subject.

Thanks & Regards
Sathya Prakash Reddy
Engineer-Piping

Yes, B31.3 Appendix P provides the same allowable limit for expansion stress range and operating stress. These two independent evaluations replace the single, base Code, evaluation of expansion stress range with its "more coomplicated" allowable limit. More complicated in that it includes longitudinal stress due to sustained loads.

Sathya,

The following three books can be referenced:

1) Design methods for power plant structures by David Burgreen.

2) Mechanical behavior of materials (3rd Edition) by Norman Dowling.( this book is a must read to properly understand fatigue)

3) Theory of plasticity by Chakrabarty ( you will find proof of Melan's theorem in this book )

Papers:



1)On the description of Anisotropic workhardening by MROZ.Z , Journal of the mechanics and Physics of solids Vol 15 May 1967 pp-163-175

2) Boundary value problems in Cyclic plasticity by MROZ. Z Second International conference on structural mechanics in reactor technology , W.Berlin Germany,Vol 6B , Part L, PaperL7/6

Hope this helps.

Mr Anindya,

Thankyou for your information.

Thanks & Regards
Sathya Prakash Reddy
Engineer-Piping

Mr Sathyam,

Did you get an proper conclusion?

I have same problem.
In App. P of ASME B 31.3, there is same allowable limit for OPE case and EXP case (including range case).

I hope that you share advanced conclusion if you woud get it.


Thanks

My humble opinion

The appendix P wants to say this:


CASE 1 (OPE) W+T1+P1
CASE 2 (OPE) W+T2+P1
CASE 3 (SUS) W+P1
CASE 4 (EXP) L4=L1-L3
CASE 5 (EXP) L5=L2-L3
CASE 6 (EXP) L6=L1-L2
CASE 7 (OPE) L7=L6+L3

Where T1
Regards,

If not, which is possible, the following may occur.

Assume a simple system such the attached one. Simple 8" sch STD pipe, 20ft on Z direction, 8 ft X direction, achored both ends.

Without Appendix P activated:
-------------------------------------------------
LOAD CASE DEFINITION KEY

CASE 3 (SUS) W+P1
CASE 4 (EXP) L4=L1-L3
CASE 5 (EXP) L5=L2-L3
CASE 6 (EXP) L6=L1-L2


Piping Code: B31.3 = B31.3 -2006, May 31, 2007


CODE STRESS CHECK PASSED : LOADCASE 3 (SUS) W+P1

Highest Stresses: (lb./sq.in.) LOADCASE 3 (SUS) W+P1
CodeStress Ratio (%): 53.9 @Node 30
Code Stress: 10190.9 Allowable: 18900.0

CODE STRESS CHECK FAILED : LOADCASE 4 (EXP) L4=L1-L3
Highest Stresses: (lb./sq.in.) LOADCASE 4 (EXP) L4=L1-L3
CodeStress Ratio (%): 103.6 @Node 30
Code Stress: 39802.1 Allowable: 38434.1


CODE STRESS CHECK PASSED : LOADCASE 5 (EXP) L5=L2-L3

Highest Stresses: (lb./sq.in.) LOADCASE 5 (EXP) L5=L2-L3
CodeStress Ratio (%): 10.4 @Node 30
Code Stress: 4154.1 Allowable: 39809.1


CODE STRESS CHECK FAILED : LOADCASE 6 (EXP) L6=L1-L2Highest Stresses: (lb./sq.in.) LOADCASE 6 (EXP) L6=L1-L2
CodeStress Ratio (%): 114.4 @Node 30
Code Stress: 43956.2 Allowable: 38434.1
-----------------------------------------------------------

With Appendix P activated:

------------------------------------------

LOAD CASE DEFINITION KEY

CASE 1 (OPE) W+T1+P1
CASE 2 (OPE) W+T2+P1
CASE 3 (SUS) W+P1
CASE 4 (EXP) L4=L1-L3
CASE 5 (EXP) L5=L2-L3
CASE 6 (EXP) L6=L1-L2


Piping Code: B31.3 = B31.3 -2006, May 31, 2007


CODE STRESS CHECK PASSED : LOADCASE 1 (OPE) W+T1+P1

Highest Stresses: (lb./sq.in.) LOADCASE 1 (OPE) W+T1+P1
OPE Stress Ratio (%): 83.7 @Node 30
OPE Stress: 40692.2 Allowable: 48625.0


CODE STRESS CHECK PASSED : LOADCASE 2 (OPE) W+T2+P1

Highest Stresses: (lb./sq.in.) LOADCASE 2 (OPE) W+T2+P1
OPE Stress Ratio (%): 12.7 @Node 30
OPE Stress: 6361.6 Allowable: 50000.0


CODE STRESS CHECK PASSED : LOADCASE 3 (SUS) W+P1

Highest Stresses: (lb./sq.in.) LOADCASE 3 (SUS) W+P1
CodeStress Ratio (%): 53.9 @Node 30
Code Stress: 10190.9 Allowable: 18900.0


CODE STRESS CHECK PASSED : LOADCASE 4 (EXP) L4=L1-L3

Highest Stresses: (lb./sq.in.) LOADCASE 4 (EXP) L4=L1-L3
CodeStress Ratio (%): 82.2 @Node 30
Code Stress: 39961.6 Allowable: 48625.0


CODE STRESS CHECK PASSED : LOADCASE 5 (EXP) L5=L2-L3

Highest Stresses: (lb./sq.in.) LOADCASE 5 (EXP) L5=L2-L3
CodeStress Ratio (%): 8.3 @Node 30
Code Stress: 4171.2 Allowable: 50000.0


CODE STRESS CHECK PASSED : LOADCASE 6 (EXP) L6=L1-L2

Highest Stresses: (lb./sq.in.) LOADCASE 6 (EXP) L6=L1-L2
CodeStress Ratio (%): 90.8 @Node 30
Code Stress: 44132.8 Allowable: 48625.0

--------------------------------------------------------


Interesting, isn't it?

danb,

In case of with Appendix P activated,

If case 1 (OPE:T1) and case 2 (OPE:T2) shown code stress check "FAILED" but case EXP shown code stress check "PASS", we need to re-analyse our design or ignore those result??

Regards,

You need to re-analyse your design

Best regards,

I'd like to remember that even if you choose to use appendix P you still need to check your SUS case.

ok, we will check.

Regards,

Interesting changes in the 2010 edition of B31.3

Regards,