Hello all,

This question came up while I was doing some research, I found that there were stress concentration factors (SCF), stress intensification factors (SIF) and stress intensity factors (KI), this last one refers to the stresses on a tip of a crack then:

wich is the difference between the SCF and the SIF?

I hope someone can help me with this

Thanks and Regards

I just got lazy and went googling:

From: http://www.epri.com/OrderableitemDesc.asp?product_id=000000000001012078&searchdate=06/29/2005

SIFs are often confused with stress concentration factors, stress indices, stress coefficients, factors used for evaluating crack propagation, and other multipliers that are used in various aspects of piping design and analysis. SIFs are actually fatigue correlation factors that compare the fatigue life of piping components (for example, tees and branch connections) to that of girth butt welds in straight pipe subjected to bending moments. The SIF is really a ratio of the number of cycles to failure for the component being tested as compared to the number of cycles to failure for a straight pipe with a girth butt weld. SIF's are about 1/2 the magnitude of ASME Section III Code Stress indices.

ASME Section III Code uses factors such as CAESAR II and K2 indices to account for fatigue effects produced by reversing loads. For piping systems designed to Class 1 requirements of ASME Section III, stress indices are used to evaluate specific stress limits. Stress indices also are used when analysis is performed to determine fatigue usage factor.

Also, see:

http://courses.washington.edu/me354a/chap6.pdf

Also found this:

STRESS - The instantaneous load applied to a material divided by the cross sectional area before any deformation. This is termed engineering stress. True stress is the instantaneous load applied divided by the instantaneous cross sectional area.

STRESS CONCENTRATION FACTOR - A multiplying factor for applied stress that allows for the presence of a structural discontinuity such as a notch or hole; Kt equals the ratio of the greatest stress in the region of the discontinuity to the nominal stress for the entire section. Also called theoretical stress concentration.

STRESS RAISERS - Flaws or structural discontinuities that cause local intensification of stress and from which cracks may propagate.

STRESS-INTENSITY FACTOR - A scaling factor used in fracture mechanics to denote the stress intensity at the tip of a crack of known size and shape.

Also found this on Wikipedia:

A stress concentration is a phenomenon encounterered in engineering where an object experiences a local increase in the intensity of a stress field due to discontinuity.

The examples of shapes that cause these concentrations are: cracks, sharp corners, holes and narrowing of the object. High local stresses can cause the object to fail more easily than its overall size suggests. A task for the engineer is to design the shape of the object to reduce stress concentrations.

A counter-intuitive method of reducing one of the worst types of stress concentration, a crack, is to drill a large hole at the end of the crack. The drilled hole, with its relatively large diameter, causes less stress concentration than the sharp end of a crack.

Classic cases of metal failures provoked by stress concentrations include metal fatigue in the windows of the De Havilland Comet aircraft and brittle fractures at the corners of hatches in Liberty ships in cold and stressful conditions in winter storms in the Atlantic Ocean.

A stress concentration factor is the ratio of the highest stress to a reference stress calculable from simple theory. These factors can be found in typical engineering reference materials to predict the stress in structures that could otherwise not be analyzed using strength of materials approaches.

Thank you very much Mr. Breen you have been very helpfull, but from these explanation another question came up.

According to these, the SIFs are related to the fatigue effects in pipe accesories due to their geometry.

The FEA methods used to determinate the SIFs on complexes geometries, like the one used in the software FE/PIPE, computes SIF´s by the ratio of (PL+PB+Q+F) and a nominal stress.

The primary membrane stress (PL), primary bending stress (PB), secundary stress (Q) and Peak stress (F), acording to ASME Sec. VIII Div. 2, are not related to fatigue effects.

Then the "SIFs" calculated by FEA methods seems more like stress concentration factors.

Are the SIFs calculated by FEA reliable?, I´m missing somethig?

Thanks and Regards

I haven't read all of the above, but a couple quick points.

John, you didn't state the definition quite correctly. Rather than being the ratio of cycles to failure, it is the ratio of nominal stress in the components, for the same number of cycles to failure.

Nominal stress is the nominal stress in the matching pipe, a M/Z calc where Z is the section modulus of matching pipe.

So, first, if you do an FEA on a component, you need to know what the matching pipe is to get a ratio to get the SIF. The second consideration is that due to the fact that the ratio in the codes is relative to girth welded straight pipe, there is another factor of two. So, for example, if you did an FEA of an elbow, you would have to divide the highest stress calculated (primary plus secondary plus peak in Div 2 terms) by two, and then divide that result by what the stress would be for the same moment in matching straight pipe.

This is very commonly misunderstood and very commonly done wrong, including in published papers.

See AR Markls original papers for more additional detail. And an excellent post by Dr. Becht!

Dr. Becht/John C Luf,

To the extent I know, computation of SIF as done in a FE code is somewhat like this:

If our structural finite element model is very fine in the areas of discontinuity, we can get the peak stress at that location (we may have to plot or extrapolate or extend), based on a unit load or moment application. The peak stress (which includes the stress concentration, considered as the product of class 1 indices K2.CAESAR II ) divided by the nominal stress away from the discontinuity = K2.CAESAR II . Stress Intensification factor from FEA results = (K2.CAESAR II )/2= 1/2( Peak stress/ Nominal stress).

Kindly advise if that is the way.

Regards

Ok except it is not nominal stress away from the discontinuity. It is the nominal stress in straight pipe. Remember that in the flexibility analysis, you have M/Z where Z is for the straight pipe (branch connections are an exception to this, as an equivalent section modulus is used)and the stress in the component is calculated as iM/Z. So, to get the correct i, you divide the calculated peak stress by M/Z for straight pipe, and then the additional factor of two.

.......and it is important not to confuse ASME Section III, class 1, "type" stresses with B31 "type" stresses. Note that the Section III multipliers are nearly twice those of B31.

As John Luf pointed out it is useful to go back and touch base with the original ARC Markl papers on occasion (e.g., ASME Paper 53-A-51, "Piping-Flexibility Analysis" by A.R.C. Markl). The Tube Turns team did not really measure stresses; they back calculated them (they had a known displacement, a known "lever arm" and a known number of cycles to the "failure"). Our colleague, Ron Haupt, has a nice summary here:

http://www.sstusa.com/00julsep.htm#sep00

and here:

http://www.ppea.net/Articles/Comments%20on%20allowable%20stresses%20_Jun-04_.pdf

And John Luf's illustrated paper can be found here (and other places):

http://www.coade.com/newsletters/jun00.pdf

There are some interesting things to study in the Markl papers. The data for the several types of tested piping components were plotted on S/N plots and the data was "statistically smoothed" such that it resulted in a curve that was the best fit of the data. There is a fair amount of "off-the curve scatter" on those plots. Pipe elbows were rather straight forward but branch connections required some creative rationalization (the team decided that branch connections were to a degree analogous to bends/elbows). It is also interesting to see that although testing shows a direct connection between SIF's and component flexibility, the Codes use a flexibility factor of 1.0 at branch connections (a little conservatism is not a bad thing). Ev Rodabaugh (who was on the Markl team) has subsequently developed WRC Bulletin 329 "Accuracy of Stress Intensification Factors for Branch Connections" which is also a "must read". Another "must read" from WRC is WRC Bulletin 392, "Standardized Method for Developing Stress Intensification Factors for Piping Components” by Ev Rodabaugh and Glynn Woods. There also have been many (maybe 8 - 10) ASME papers on the subject presented at ASME PVP Conferences through the years.

Of course if developing Stress Intensification Factors by the FEA method, you are calculating stresses and to get the SIF you must do the stress ratio comparison as describe (in many fewer words) above by Chuck.


Regards, John.

I asked Tony Paulin to comment. He has not review the current corrspondence. Here is his response:

To produce the piping related SIF from a finite element program requires the
following:

1) Compute the peak stress from the finite element analysis. Be careful thinking that increased meshes give peak stresses. Increased meshes around as welded geometries (effective notches) result in solution singularities and cannot be used. (See WRC 429 "3D Stress Criteria Guidelines for Application" and WRC 474 Master S-N Curve Method for Fatigue Evaluation of Welded Components" for FEA guidelines and recommendations.)

2) Be sure to use the restraint and loading definitions that are associated with a typical Markl-type fatigue test. See ASME B31J-2006 "Standard Method for the Determination of Stress Intensification Factors (i-Factors) for Piping Components by Test" (not sure if this has been released yet.) A good discussion can also be found in Nureg CR/3243 for SIF's, fatigue, tests, and the ASME Code rules.

3) Find the nominal stresses (M/Z), PD/2t, F/A, for the matching pipe and the corresponding load as discussed below by Dr. Becht.

4) Divide the range of peak stresses by the nominal stress caused by the same range of loads and then divide by 2, not letting the value become less than 1.0. The SIF thus derived can be used in a B31, beam-type analysis of a piping system. For reduced intersections, the user must also be sure that an effective section modulus is not used automatically by the pipe stress program with the user's defined SIF, otherwise the SIF must be further modified before use.

5) Many people use the actual loadings from a pipe stress program and perform a stress analysis per ASME Section VIII Division 2, Appendix 4 and 5 in accordance with B31.3 304.7.2 for "unlisted components". The actual combinations of loads are used since this is often simpler than generating SIF's. The singularity precautions mentioned above should still be observed when computing any peak stresses. The Master Curve methods removes this concern however.

I'm not sure these comments help, but they accurately address the issue as I understand it.

Hello
Is a copy of A.R.C Markl's paper available on the web ?

This link (http://www.klgsystel.com/product-services/cad-cae/pdf/newsletter/KNOWLEDGEJAN04.pdf) isn't working.

Any help is welcome.

TIA

regards

NO. The paper is not directly available.

Most of the people who post here have a copy of the paper but there is no way to share it with you. The paper is copywrited by ASME.

You could search this forum and you would find that we know where it was published but the actual ASME paper is long out-of-print. Maybe you can find the Tube Turns Company publication titled "Piping Design" at a used book web site. I won't repeat here what you can find by searching this forum.

Regards, John.

Thank you all for your response. As i see it, for a FEA the SIF is 1/2 the SCF.
In fact the User´s Manual of Ceasar II 4.5 in page 12-7 (Stress Concentration and Intensification) show the equation:
(m)(i)=(CAESAR II)(k2)
where:
CAESAR II is the ASME NB secondary stress index
K2 is the ASME NB peak stress index
i the stress intensification factor
m a multiplier ussualy 1.7 or 2.

This factor looks ambiguous to me, can anybody explain me where this factor came from?

Thanks in advance

Calculated stress using C2K2 is compared to design curves based on polished bar fatigue data. The B31 stress calculated using i is compared to a design curve based on girth welded pipe fatigue data. There is approximately a factor of two difference in those two fatigue curves.

Hi Chuck,

Thanks for the correction (above). I should have looked at the verbiage closer before I did the cut-and-paste.

Regards, John.

Hi friends,

Can anybody tell me the exact difference between flexibility factor, correction factor and reduction factor.

I read these three factors in a paragraph of 'Lummus Engineering Design Guide'....I qoute this paragraph as follows...

===========================================

In paragrah 4.2.1 the manner in which a bend develops its flexibility by a flattening of the cross section was described. since a flange by virtue of its heavy construction exerts a severe restraint to the flattening of cross section
it follows that the attachment of a flange to an elbow or mitre reduces the flexibility factor and by the same token reduces the stress intensification factor; a flange at both ends of an elbow reduces these factors further still.
The B31.3 code provides a chart for obtaining the appropriate correction factor to be applied. This can be as low as 0.25 in the case of large diameter thin wall pipes.

This correction factor C1 has value C1 = h^(1/6) when one end is flanged and CI = h^(1/3) when both ends are flanged. Note that this is a reduction factor.

===========================================

So, can anybody expalin me exact difference between the factors described in above pargraph..

Thanks

There is an extensive body of work on this subject and most can easily be found if you searched this forum. It is apparent that due to the cross section of an elbow flattening during bending [ovalising], that a bend is more flexible than a piece of pipe [same OD, wall thk etc] of the same centerline length. The flexibility factor tells you how much more flexilble the bend is when compared to that notional piece of pipe. ie the bigger the flexibility factor, the more flexible the bend is.
Since adding very stiff fittings to the end of the bend, such as flanges, will reduce the ovalising present in the bend, thus making the bend less flexible. The "correction factors" are used to simplify the calculation of this additional stiffness. Since the 'flanged' bend is stiffer than the unflanged bend, the calculated flexibity factor needs to be reduced [less flexible]. They are "reduction factors" as they are used to reduce the flexibility factor.
Ultimately these all correspond to how the structure behaves under loading and also lead directly to stress intensification factors.
Please have a look at your copy of B31.3 [if you have one]. It's all in there. Alternatively I believe the original work was done by Markl if you can get a copy of that. Some newer codes also publish these factors for reducers for all sorts of geometry beyound the usual branch fittings and elbows commonly seen.
This is really basic stuff, but since nobody was ever born a complete stress engineer, perhaps if you are starting off in the field a few words explaining that at the beginning of your posts will give a better response. There has certainly been an increase in 'basic' questions being asked here recently. Everyone is willing to help students. No-one wants to help 'chancers'.

Hello Bajwa,

Well, context is everything in this question. In the context of the Lummus document that you are citing:

"In paragraph 4.2.1 the manner in which a bend develops its flexibility by a flattening of the cross section was described."

This alludes to the Flexibility Factor. Elbows and bends are more flexible under loading than a similar piece of straight pipe. When we are performing structural analyses of piping systems, we must address the additional flexibility of elbows and bends. Simply stated, the Flexibility Factor for an elbow is the ratio of the bending flexibility of an elbow segment to the bending flexibility of a straight pipe. Dave Diehl wrote about this in the October, 2002 issue of COADE Mechanical Engineering News. Please download the issue (pdf format) at:

http://www.coade.com/newsletters/oct02.pdf

and read it over several times.

The "Correction Factor" comes from B31.3, Appendix D, Chart B (also read note (5) in B31.3, Appendix D). While an elbow or bend is more flexible than a straight piece of pipe, some of that additional flexibility is diminished if a flange is attached at the weld line and even more of that additional flexibility is diminished if two flanges are attached, one at each weld line. The Correction Factor is used when one or two flanges are attached to the elbow (bend). The "correction factor" is a coefficient that is applied to the "flexibility factor" to REDUCE it, thereby addressing the "stiffening" effect of the flanges.

So, when you read in the Lummus document that:

"This correction factor C1 has value C1 = h^(1/6) when one end is flanged and CI = h^(1/3) when both ends are flanged. Note that this is a reduction factor."

....in that context, the "Correction Factor" actually is a "Reduction Factor" in that it reduces (adjusts) the calculated "Flexibility Factor" to address the installation of flanges (which makes the elbow or bend "stiffer").

Regards, John.

Hi friends,

All thanks for your help...now i have my questions regarding these factors in context with caesar II...

1) The flexibility factor and SIF are already defined in caesar ii for carbon steel pipes. what about pipes of other materials; for example GRP.

2) If i weld dummy leg to the bend extrados, the stiffness is changed due to this attachment. Do caesar ii automatically caters this chnage in stiffness or i have to change value of k by myself.

3) If the flanges are attached to the end of elbows ar both sides; the flexibility factor must be changed. Do caesar ii automatically caters this or again i need to chnage flexibility factor manually by myself.

Thanks

Hello again Bajwa,

I am sure our moderators will answer your CAESAR II specific questions later in the day (at this hour they are just waking).

However, these are questions that have been asked many times in this discussion forum - please learn to use the search function at the top of this page (find the "post a poll" button and just below it in the middle is the "search" hypertext). When you use the search function you can read all the wisdom of the many people who contribute to this forum. Also, you should go to the COADE "Mechanical Engineering News" site and download and read all the past issues as they present a wealth of practical piping engineering.

Also, I would ask you to look at my posting here:

http://www.coade.com/cgi-local/ultimatebb.cgi?ubb=get_topic;f=1;t=001336

as you might find some more useful references for filling in the "background" of piping stress analysis. Thank you.

Regards, John.

:rolleyes: :rolleyes: :rolleyes: :rolleyes: :rolleyes: :rolleyes: :rolleyes:

Bajwa... read the applicable code you are working to and read the online manuals that come with CAESAR II these steps will eliminate asking questions like you have do you homework.

Bajwa,

In answer to your questions above:

1) That depends on which piping code you're using. If you activate one of the FRP codes (BS-7159 or UKOOA), then the answer is "yes". If you run any other code, the answer is "no".

2) No, CAESAR II will not adjust the bend flexibility when you add a dummy leg.

3) CAESAR II will adjust both the flexibility and the SIF based on whether you attach 1 or 2 flanges to the bend.

Sir John Breen,

about your post dated July 11,

how does the "correction factor" is a "reduction factor" actually?


confused,

Bajwa,

Expanding on Richard Ay's comment:

3) CAESAR II will adjust both the flexibility and the SIF based on whether you attach 1 or 2 flanges to the bend.

CII will not automatically adjust the bend properties. You MUST choose either TYPE 1 or TYPE 2 on the BEND/elbow card located below the bend radius entry.

Dusting off my big spoon,

Hello Dark,

When you are developing an analysis model with Caesar II, and you tell CAESAR II that a component is a bend (elbow) by checking "bend" on the spreadsheet, CAESAR II will use the equations prescribed by B31 to calculate the appropriate flexibility factor for a bend of the geometry you have described. If that bend (elbow) happens to have a flange welded onto one end of it or flanges welded onto both ends of it (at the weld lines) the flanges will effectively stiffen the elbow - it will not be as flexible as a bend (elbow) that has NO flanges welded to it. If you have flanges, the flexibility factor calculated by the B31 equations will be too great - the flexibility will be overstated.

For this reason, the B31 Codes provide correction factors to be applied to the calculated flexibility factor to "adjust" it such that it properly represents the flexibility of the bend (elbow) AFTER the flange (or flanges) are welded to the bend (elbow). You (or Caesar II) must multiply the flexibility factor that was originally calculated using the B31 equation by the B31 correction factor because the flexibility factor would be too great for a bend (elbow) with a flange (flanges). The correction factor will be a number with a value of less than one. Consequently, when you multiply the flexibility factor by the correction factor the result will be an "adjusted" flexibility factor that is less than the flexibility factor that was originally calculated. Multiplying the flexibility factor by the correction factor will have effectively REDUCED the magnitude of the flexibility factor (to make it appropriate for a bend (elbow) that has a flange (or flanges)). In this sense, the correction factor (having reduced the magnitude of the flexibility factor) could be called a "reduction factor". It is important to note that the use of the term "reduction factor" comes from the cited Lummus document and did not come from the B31 Codes. The term "reduction factor" when discussing flexibility factors IS NOT A B31 CODE TERM. To clarify the issue, simply ignore the Lummus reference to a "reduction factor" as it is really irrelevant. The apparent intention of including the term "reduction factor" in the Lummus Guide seems to be simply to emphasize to the reader that the correction factor REDUCES the magnitude of the flexibility factor.

The term "allowable stress range reduction factor" is used by the B31.1 Code, but this is an entirely diffenent discussion than is presented above.

Regards, John.

Sir John Breen,

Thank you very much!

Hi Richard,

Just want to confirm again:

If currrent version of CAESAR II [v5.10 build-080512 dated-May 12, 2008] do automatically adjust the bend flexibility when you add a dummy leg?

Kind Regards

No adjustment is made - CAESAR II has no clue you put a dummy leg on the bend. The only adjustment made is if you indicate the the bend has flanges.