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 in piping flexibility analysis 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 K 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.
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.
To produce the piping related SIF from a finite element program requires the following considerations:
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.
See PRG(Paulin Research Group) web and other papers liste below as references:
A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes.
http://www.cbi.com/images/uploads/technical_articles/A_Finite_Element-based_Investigation.pdf
A FINITE ELEMENT BASED STUDY ON STRESS INTENSIFICATION FACTORS (SIF) FOR REINFORCED FABRICATED TEES
http://www.cbi.com/images/uploads/technical_articles/140_Bhattacharya.pdf
WRC 429
3D STRESS CRITERIA GUIDELINES FOR APPLICATION
WRC 474
MASTER S-N CURVE METHOD FOR FATIGUE EVALUATION OF WELDED COMPONENTS
WRC 523
THE MASTER S-N CURVE METHOD AN IMPLEMENTATION FOR FATIGUE EVALUATION OF WELDED COMPONENTS IN THE ASME B&PV CODE, SECTION VIII, DIVISION 2 AND API 579-1/ASME FFS-1
http://www.forengineers.org/cgi-bin/wrcbulletin/bulletin.pl?action=list_all
Also you should take care of boundary conditions at end of run pipe and the length of pipe from branch point so as not constraint deflections of run and branch.
The recommendation is the multiplier of cylindrical characteristic length of (RT)^0.5 and 3-5D as minimum.
Widera discusses boundary condition effects in WRC 497. We default to all degrees of freedom fixed except radial on one end and free on the other (the free end is a little counterintuitive but it matches the test configuration originally used by the Markl team at Tubeturns). If you are using CAESAR II, you should be able to run automated SIF calculation based on FEA. I do not think Autopipe has automated SIF calculation based on FEA for unlisted components.
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.