Peak Stress – What Is Piping

Stress Intensity Factor Meaning As per Code ASME Section III, Stress Intensity Factor or SIF is defined as the Fatigue Correlation Factors that compare the fatigue life of Piping Components (Tees, branch connections) to that of girth butt welds in straight pipe subjected to bending moments. This is also widely known as Stress Intensification Factor. Note that, Stress Intensity factors are often confused with stress concentration factors, stress coefficients, or other stress indices used in various mechanical design and fracture mechanics problems. Stress intensification factor in piping stress analysis provides the fatigue correlation of piping elbow and branch connections for evaluating moment loading. History of Stress Intensity Factor Markl Fatigue Curve for Straight Pipe (Fig. 1): Fig. 1: Markl Fatigue Curve for Butt Welded Steel pipe Markl stress intensity factor : iS = 245,000N-0.2 i =( CN-0.2)/S Where i=Stress intensity factorC=245,000 for carbon steel materialsN=Cycles to failureS=Nominal stress amplitude Markl Stress Intensity Factor is based on deflection control, fully reversed, cyclic bending fatigue tests. Stress Intensity Factor Equation As per Section III, for class 2 & 3 piping and B31.1 Calculated stress S = i*M / Z where M = (MX2 + MY2 + MZ2)1/2Z=Section Modulusi= Stress intensity factor This approach is conservative. Thermal expansion stress SE = (Sb2 + 4St2)1/2 where Sb=resultant bending stressSt=torsional stress = Mt/2Z The resultant bending stress is calculated by Sb= [((iiMi)2 + (ioMo)2) ½]/Z where ii = in-plane bending stress intensification factor (Refer Fig. 3)io= out-of-plane stress intensification factor (Refer Fig. 3)Mi = in-plane bending moment (Refer Fig. 2)Mo = out-of-plane bending moment (Refer Fig. 2) Fig. 2: Moments in Elbow and Branch Connections Fig. 3: Table D300 of ASME B 31.3 Eg: For 12” Std schedule long radius elbow. a)Elbow without flange R1 = 1.5(12) = 18”T = 0.375” (Std) Assume same thk for pipe & elbowr2 = ( OD-T)/2 = 6.1875”h = (TR1 )/(r2)2= 0.176 (From table D-300 of B31.3)ii = 0.9 / h2/3 = 2.86io = 0.75/ h2/3 = 2.4 b)If one end is flanged the correction factor C1 = h1/6 = 0.7486 ii = C1 ( 0.9 ) / h2/3 = 0.7486 x 2.86 = 2.14io = C1 ( 0.75)/ h2/3 = 0.7486 x 2.4 = 1.797 Pressure vs Stress Intensity Factor Effect of Pressure on Stress Intensity Factor: Fig. 4: Calculation showing effect of pressure on SIF Finite Element Methods for Stress Intensity Factor Calculation The various methods for calculating Stress Intensity Factor are Analytical Methods defined by Piping CodesFEM techniques The user can see that the basic SIF procedure is: Build the model.Apply a moment through the nominal attached pipe.Read the highest stress from the result plot.Divide by M/Z to get the SIF. The Fem Softwares widely used for calculating Sif are FE-pipeAnsys Stress Intensity Factor Calculations The basic definition of a stress intensity factor (SIF) is: SIF = (Actual Peak Stress in Part)/( Nominal Stress in Part) The nominal stress in the part for a piping component subject to bending loads is M/Z where “M” is the moment that the pipe exerts on the component, and Z is the section modulus of the matching pipe welded to the part being analyzed. Example Case: For example, when Stress Intensity Factors are needed for a large D/T “Wye” Fitting, there are usually four SIFs involved. one for the in-plane moment about the wye,one for the out-plane momentFor both the main header and branch sections. An example, demonstrating this calculation for a 32x0.375 wye fitting is shown in the example. Markl’s definition of the SIF is the ratio of the actual stress in the part due to a moment “M”, divided by the nominal stress in a girth (circumferential) butt weld due to a similar moment “M”. B31 Stress Intensity Factor (SIF) = Actual Stress in Part (due to M)/ Stress in Girth Butt Weld (due to M) Fig. 5: FEM model for Y type fitting. Two load cases for the model are setup automatically by FE/Pipe. They are Operating, andOccasional Various displacements and stresses from each load case are shown in Fig 6 and Fig 7. Fig. 6: Displaced shape in FEM analysis Fig. 7: Peak Stress results in FEM analysis Some more Resources that may be of your interest Piping Elbow or Bend SIF (Stress Intensification Factor) How to use ASME B31J-2017 and FEM for SIF and k-factors for Stress Analysis ASME B 31J & B 31J Essentials: Why these are useful in Piping Stress Analysis? Further Studies for Stress Intensity Factor https://cadeengineering.com/study-case/stress-intensity-factor-sif-for-special-geometries-in-piping-stress-analyisis/