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How to consider Fatigue load case in AutoPIPE (method #2)?
sTR = Tresca stress.
Maximum of abs(s1 - s3), abs(s2- s3) & abs(s1 - s2)
Appendix 5 - Mandatory Design Based on Fatigue Analysis, Artical 5-1
5-110.3 Cyclic Loading Design Procedure.
Subparagraphs 5-110.3(a) and 5-110.3(b) apply to the determination of primary plus secondary stress intensity range (see 4-134) and peak stress intensity range (see 4-135).
(a) When Principal Stress Direction Does Not Change. For any case in which the directions of the principal stresses at the point being considered do not change during the cycle, the following steps shall be followed to determine the alternating stress intensity.
(1) Principal Stresses. Consider the values of the three principal stresses at the point versus time for the complete stress cycle. These are designated as s1, s2, and s3 for later identification.
(2) Stress Differences. Determine the stress differences
S12 = s1 - s2
S23 = s2 - s3
S31 = s3 - s1
versus time for the complete cycle. In what follows, the symbol Sij is used to represent any one of three stress differences.
(3) Stress Intensity Range. Determine the extremes of the range through which each stress difference Sij fluctuates, and find the absolute magnitude of this range for each Sij. Call the largest absolute magnitude of these values Srij.
(b) When Principal Stress Direction Changes. For any case in which the directions of the principal stresses at the point being considered do change during the stress cycle, it is necessary to use the following more general procedure.
(1) Consider the values of the six stress components st, sl, sr, tlt, tlr, and trt versus time for the complete stress cycle.
(2) Choose a point in time when the conditions are one of the extremes for the cycle (either maximum or minimum, algebraically) and identify the stress components at this time by the subscript i. In most cases it will be possible to choose at least one time during the cycle when the conditions are known to be extreme. In some cases it may be necessary to try different points in time to find the one which results in the largest value of alternating stress intensity.
(3) Subtract each of the six stress components sti, sli, etc., from the corresponding stress components st, sl, etc., at each point in time during the cycle and call the resulting components s¢t, s¢l, etc.
(4) At each point in time during the cycle, calculate the principal stresses s¢1, s¢2, and s¢3 derived from the six stress components s¢t, s¢l, etc. Note that the directions of the principal stresses may change during the cycle, but each principal stress retains its identity as it rotates.
(5) Determine the stress differences,
S²12 = s¢1 - s¢2
S²23 = s¢2 - s¢3
S²31 = s¢3 - s¢1
versus time for the complete cycle and find the largest absolute magnitude of any stress difference at any time. Call this value Srij.
(c) When evaluating the limits for the primary plus secondary stress intensity range, Srij is compared to the 3Sm limit (see 4-134).
(d) The alternating stress intensity Salt is one half the value of Srij.
(e) Design Fatigue Curves. Figures 5-110.1, 5-110.2.1, 5-110.2.2, 5-110.3, and 5-110.4 contain applicable design fatigue curves for some of the materials permitted by this Division [see AM-100(c)]. When more than one curve is presented for a given material, the applicability of each is identified. Where curves for various strength levels of a material are given, linear interpolation may be used for intermediate strength levels of these materials. As used herein, the
FIG. 5-110.1 DESIGN FATIGUE CURVES FOR CARBON, LOW ALLOY, SERIES 4XX, HIGH ALLOY STEELS AND HIGH TENSILE STEELS FOR TEMPERATURES NOT EXCEEDING 700°F
strength level is the specified minimum room temperature value. The design fatigue curves are defined over a cyclic range of 10 to 106 cycles, except that for nickel-chromium-molybdenum-iron alloy, a cyclic range of 10 to 108 cycles is provided in Fig. 5-110.4 and that for series 3XX high alloy steels, nickel-chromium-iron alloy, nickel-iron-chromium alloy, and nickel-copper alloy, the design fatigue curves are extended to 1011 cycles in Fig. 5-110.2.2. Criteria for the use of the latter curves are given in Fig. 5-110.2.2 and are also presented graphically by the flowchart given in Fig. 5-110.2.3.
TABLE 5-110.1 TABULATED VALUES OF Sa, ksi, FROM FIGURES INDICATED
(f) Use of Design Fatigue Curve. Multiply Salt [as determined in (a) or (b)] by the ratio of the modulus of elasticity given on the design fatigue curve to the value used in the analysis. Enter the applicable design fatigue curve at this value on the ordinate axis and find the corresponding number of cycles on the axis of abscissas. If the operational cycle being considered is the only one which produces significant fluctuating stresses, this is the allowable number of cycles.
(g) Cumulative Damage. If there are two or more types of stress cycle which produce significant stresses, their cumulative effect shall be evaluated as given below.
(1) Designate the specified number of times each type of stress cycle of types 1, 2, 3, etc., will be repeated during the life of the vessel as n1, n2, n3, etc., respectively. In determining n1, n2, n3, etc., consideration shall be given to the superposition of cycles of various origins which produce a total stress difference range greater than the stress difference ranges of the individual cycles. For example, if one type of stress cycle produces 1000 cycles of a stress difference variation from zero to +60,000 psi and another type of stress cycle produces 10,000 cycles of a stress difference variation from zero to -50,000 psi, the two types of cycle to be considered are defined by the following parameters:
Type 1 cycle:
n1 = 1000
S alt 1 = (60,000 + 50,000)/2 = 55,000 psi
Type 2 cycle:
n 2 = 9000
S alt 2 = (50,000 + 0)/2 = 25,000 psi
(2) For each type of stress cycle, determine the alternating stress intensity S alt by the procedures of (a) or (b) above. Call these quantities S alt 1, S alt 2, S alt 3, etc.
(3) For each value S alt 1, S alt 2, S alt 3, etc., use the applicable design fatigue curve to determine the maximum number of repetitions which would be allowable if this type of cycle were the only one acting. Call these values N 1, N 2, N 3, etc.
(4) For each type of stress cycle, calculate the usage factors U 1, U 2, U 3, etc., from
U 1 = n 1/N 1
U 2 = n 2/N 2
U 3 = n 3/N 3
(5) Calculate the cumulative usage factor U from
U = U 1 + U 2 + U 3 + ...
(6) The cumulative usage factor U shall not exceed 1.0.
Note, Pipe code stresses are not principal stresses as defined by Von-Mises or the Maximum Shear stress theory, they are a very specific combination of loads to determine stresses in different stress categories e.g. sustained, stress range, and occasional.
In this example, cannot be sure of the loading but below is summary of Fatigue or Peak stresses which can be calculated by AutoPIPE.
Fatigue (Peak stresses) are calculated as Max Tresca stress i.e. max S1, S2 or S1-S2. where S1 and S2 are principal stresses.
AutoPIPE can calculate the maximum shear stress intensity (instead of Von-Mises) which is Max Tresca stress divided by factor = 2 (also known as Alternating Stress Intensity) and represented by "Total Stress" in the General stress report or General piping code (calculated at every 15deg around the circumference of the pipe from zero location)
1. On General Model Options dialog, set the "Piping Code" = General and "SIF bases for General piping" = B31.3:
This provides allowable stresses (established by yield stress) to be calculated based on design factors (shown below) as applicable whereas no allowable stresses are available for General stress report
Total allowable factor
Hoop safety factor
Long. safety factor
Shear safety factor
For Fatigue analysis concerns, Total stress (i.e maximum shear stress intensity) are the most import values in the reported results.
With AutoPIPE, option to set User defined allowable stresses on the Code Comb tab of the Load Combinations dialog. Accomplished by disabling Auto Update check box for any load case and changing Total Allow stress for respective load cases from Automatic to "user value" (ex. 12345).
1. Since maximum shear stress intensity = Max Tresca stress/2, the calculated allowable Peak stress should be multiplied by 0.5.
2. Set "Total Stress(Oct/Max) = M, on Results Model Options dialog
3. Define appropriate load combinations e.g.static GR, GR+P1+T1, GR+P1+T1+E1 or dynamic cases M1, R1, H1 etc
"Fatigue" - AutoPIPE load case