If I have two temperature conditions in my pipe (T1=-140°C and T2=50°C). Must I calculate the expansion stresses by making T1-T2 or just T1 and T2 in two different case ?
Ok but the allowable stress in expansion is 295 MPa and the yield strength is 175 MPa. The maximum calculated stress in pipe at -140°C is 240 MPa > 175 MPa.
That means that the pipe is deformed in the plastic range (But the stresses are allowable according to the code) and consequently the stress level decrease.
So at -140°C, there is less stresses in pipe that 240 MPa (Calculated) but when I heat it at 50°C I will have the stresses for the displacement max between -140 and 50.
This is for this reason that I think that the maximum stress in the pipe is given for the difference between -140 to 50°C and not only for -140°C.
Hemmmm... Is it clear ? Are you OK with this reflection ?
I agree with your observation that the max stress (from thermal changes at least!) comes from the total heatup: from -140 C conditions (through a brittle fracture region!) up to room temperature (shutdown and startup conditions) then past that region to 50 deg C (operating cycle).
50 C isn't all that hot, but the lower end of your op cycle is pretty significant.
B31.3 wants the "extreme expansion stress range", with RANGE being a key word here.
The easiest way to get this is, as you said initially, T1-T2, assuming that is indeed a possibility for the system. If you just evaluate T1-ambient and T2-ambient, you may not have covered the "extreme".
What is the material of the system under discussion?
"allowable stress in expansion is 295 MPa"
There is no such thing as an "allowable stress in expansion". The B31 Codes address stresses due to thermal expansion displacement strains with the concept of allowable stress RANGE.
I think you are confused about the B31 Codes concept of Allowable Stress RANGE as a comparison for the calculated stress RANGE. The B31 Codes address the stresses due to thermal expansion/contraction displacement strains quite differently that the stresses due to sustained weight and pressure.
Read B31.3 paragraph 319.3.1(a). The stress RANGE is calculated as the algebraic difference between the value at MAXIMUM metal temperature and that at MINIMUM metal temperature for the cycle under analysis. You must calculate the full thermal displacement stress RANGE and compare that to the Code maximum allowable displacement stress RANGE (see B31.3 paragraph 302.3.5(d)). That is to say (in the case that you cite), the calculated full displacement stress RANGE is the SUM of the displacement stress that results from the thermal excursion from the installed temperature (say 21 degrees C) down to -140 degrees C ADDED TO the displacement stress that results from the thermal excursion from the installed temperature (say 21 degrees C) up to 50 degrees C. Each of these is a "zero to peak" stress and the RANGE (the sum of the two) is a "peak to peak stress RANGE". According to B31.3 paragraph 319.3.1(a), the value of this sum (the "peak to peak stress RANGE") must be less than the value of the Code maximum allowable displacement stress RANGE s calculated in accordance with B31.3 paragraph 302.3.5(d).
The equation from see B31.3 paragraph 302.3.5(d) is of the form:
Sa f * ((1.25 * Sc) + (0.25 * Sh)
Sa is the calculated maximum allowable stress RANGE
Sc is the cold allowable stress at temperature from App. A
Sh is the hot allowable stress at temperature from App. A
So, where does this equation for maximum allowable stress RANGE come from?
The stress RANGE concept was introduced into the B31 Pressure Piping Code in the early 1950's. The concept underlying this rule is very well described in the famous book by S.W. Spielvogle (Piping Stress Calculations Simplified, Fifth Edition, 1955). When you read Spielvogle's explanation please understand that in the original form in which this concept was introduced into the Code allowed Sc and Sh to be either 1/4 of the tensile strength of the material or 5/8 of the yield strength of the material (whichever is smaller). In the modern B31.3 the Code allows Sc and Sh to be either 1/3 of the tensile strength of the material or 2/3 of the yield strength of the material (whichever is smaller).
Spielvogle explains that the B31 rules intend for the piping engineer (analyst) to be able to use the entire range of stress from the material yield point at the operating (hot) temperature to the material yield point at the ambient (or coldest) temperature (less a factor of safety). Since Sh (neglecting the possibility of creep) is set at 2/3 Sy for both the hot and cold conditions, we can calculate the hot yield stress as Sh*1.5 and we can calculate the cold yield stress as Sc*1.5. Taken together the total allowable stress range for the combined SUSTAINED loadings of weight (bending), longitudinal pressure (tension) AND thermal expansion (displacement) would be (1.5*Sc) + (1.5*Sh), or 1.5(Sc + Sh). This range of allowable stress has been reduced slightly to allow for the vagaries of material and for other “real world” inaccuracies. The Code philosophy would then permit the total allowable stress range (after the factor of safety is applied) for all the combined loading described above to be 1.25(Sc + Sh) (if ,in this discussion, we neglect the stress range reduction factor ,”f”, for simplicity). However the Code uses 1.0Sh for the sustained loadings of weight and longitudinal pressure (so we then must subtract this from the maximum allowable stress range for thermal displacement alone) and this leaves 1.25*Sc + 0.25*Sh for the allowable thermal expansion (displacement) stress range alone.
Because the Code intends for the entire strength of the material (from hot yield to cold yield) to be used for the total loading (except for the “adjustment” made for vagaries), it follows that the rule in the Code paragraphs cited above allows the analyst to put the unused (difference between calculated sustained longitudinal stresses and the allowable 1.0*Sh) portion to use in increasing the allowable thermal expansion (displacement) stress range (this is sometimes referred to as the "liberal allowable stress RANGE) . You will recognize that the “excess” sustained case allowable stress will vary across the system being analyzed and that the variation will directly reflect how well supported the system is (bending stresses will have the greater effect). This variation in “excess” sustained case allowable stress from node to node in the model will (when the “liberal” option is used) result in the allowable stress range, Sa, being different at every node when the Code compliance report is viewed.
The concept of allowable stress RANGE addresses the piping at its coldest and at its hottest so the maximum allowable stress RANGE can only be compared to the calculated stress RANGE (peak to peak) from the RANGE from its coldest to its hottest. However, there should be really very few of these full RANGE temperature excursions in the life of the system - perhaps only one. All the other RANGES of temperature excursions (e.g., ambient to operating and operating to ambient) will be "partial cycles" and the Code describes the method of addressing these in B31.3 paragraph 302.3.5(d), equation (1d). Remember we are addressing many cycles as this is a fatigue based approach. This method of addressing thermal displacement stress RANGE (peak to peak) differs significantly from the way "sustained" stresses are addressed. The stresses due to sustained weight and pressure (Sustained Stresses) are zero to peak.
Again, the Code allows the "peak to peak" stress to be nearly as high as 1.25(Sc + Sh), but no higher. If you just look at the zero to peak stress of only one of the two constituents that one constituent still "usually" cannot exceed 0.66 of the yield strength of the material at temperature (I hedge there because under occasional loadings we can take it up to 0.80 of the yield strength). So, if the "half" of the "peak to peak" thermal displacement stress (as you say from ambient to -140 degrees C) exceeds the yield strength of the material you have a problem. We know that when we apply these concepts to cycling piping systems (especially to hot pipes) there may be a little plastic deformation in the first few cycles and then the system will "shake down" to purely elastic behavior. As long as we do not see continuous plastic deformations (yielding of the material) in opposite directions at the hottest condition and the coldest condition of each cycle (racheting) the system will "relax" into a sustaining level of stress ("completely shaken down") where subsequent temperature excursions will not result in additional plastic deformation at either temperature extreme throughout its cycle life. So if you calculate that the ambient to -140 degrees C temperature excursion will exceed 100 percent of the yield strength of the material you had better find a design solution to that problem.
After all that it occurs to me that I did not point out that the temperature range to be considered is from -140 degrees C to +50 degrees C which is a RANGE of 190 degrees C. But for stress calculations you would have to change the default "ambient" (or "installed") to +50 and T1 would be defined as -120. That would assure that the value of Sh used in the stress calculation would be correct for the "high" temperature 50 degrees C (no "step down" in Sh for a temperature higher than the actual 50 degrees C). Most software will automatically use the 21 degrees C modulus of elasticity required by the Code for stress calculations.
Or of course you could as you suggest and make two runs: Case 1 T1 = -140°C and Case 2 T2 = 50°C (default ambient temperature in each case would be 21 degrees C). Then take the calculated stresses from each run and add them manually to arrive at the calculated stress RANGE. The you could compare that to the Code maximum allowable stress RANGE.
Very informed and useful handling of the subject, John.
I can't follow you, however, when, at the end of your first post, you say that exceeding the yield strength at one of the two extremes of a thermal cycle would be a problem: this is exactly the contrary of what you state speaking about ratcheting and shake down.
Recalling that the limits you discuss are applicable to elastically calculated stresses (so that, by definition, they have little to do with actual stresses), there is nothing requiring to limit the peak thermal stress in a piping (or a vessel BTW), the only limit being, as you state, on the range (peak to peak) of the thermal stress (or of the total stress, as in ASME VIII Div.2).
This is explained with the classical example of the simplest situation where shake down occurs: a straight heated bar (may be a straight piece of pipe) fully constrained against expansion (and contraction). If you heat it up till it goes beyond yield by, say, a factor of 1.5 (of course based on elastic stresses), upon cooling down the bar will go into tension because of the plastic deformation incurred, and the remaining tensile stress will be 50% of yield; at the next cycle then, the stress will only reach yield and no ratcheting will occur. The structure has shaken down in only one cycle.
If I incorrectly understood your position, will you please clarify your point?
Upon rereading I see your point – what I wrote there is not what I wanted (intended) to write. I was reflecting upon how many words I had already used to get to that point and in my haste to quickly sum-up I got sloppy while trying to address the OP’s second posting. I got the primary stresses (sustained loadings) tangled up with the secondary stresses (thermal loadings) as I wrote. I certainly appreciate your mention of that.
As I did not know the material at issue, I was doing a little mindless back-calculating using the numbers that the OP provided (in the Imperial units in which I think, with approximate conversions). The OP says that the temperature RANGE is 190 degrees C. Assuming ambient to be 21 degrees C, the ambient to -140 degree temperature excursion is 85 percent of the temperature range and the ambient to 50 degree C temperature excursion is only 15 percent of the temperature range. This implies that (applying linear elastic beam bending stress theory) if the “calculated stress” due to the 21 degree C to -140 degrees C temperature excursion is (as stated) 240 MPa (zero to peak) then the “calculated stress” due to the 21 degree C to 50 degrees C temperature excursion would be about 42 MPa (zero to peak). That would make the total calculated stress range about 282 MPa (peak to peak) which is less than the (calculated by the OP) allowable stress range of 295 MPa (about 96 percent of the allowable stress range, peak to peak). Not much margin there.
So yes, (second OP posting) the first few full cycles would result in significant plastic deformation and the resulting residual stresses and as the system warmed through 21 degrees C and up to 50 degrees C there would likely also be additional plastic deformations (and material hardening due to working) as that temperature is reached. Plastic deformations will result in residual stresses “in the opposite direction” that will be beneficial in facilitating the system shake-down (in systems that will shake down).
What I should have said is that CONTINUOUSLY exceeding the yield strength of the material at one or both of the temperature extremes (if shake-down does not occur) would eventually result in ratcheting failure. The potential problems that I alluded to in my original posting were not a consideration of the thermal stress range alone (and I should have said that). It is an unusual piping system that develops its higher thermal strains at a time when the material ductility is at its lowest. What I should have said is that I get a little nervous when the piping system is operating with the secondary stresses that high (96 percent of Sa) because that might act in concert with other loadings in ways not normally considered. If the piping system life-time thermal cycles are to exceed 7000, the Code reduces the allowable stress range to 0.80 Sa. Also, it does not leave much room for “Occasional Variations” in temperature and pressure. There might also be some issues at valves and flanged connections due to the thermal strains. This might be offset if the system is well supported as the so-called “liberal allowable stress range” will be increased (see Spielvogle).
Prex also mentions the point that (unlike the ASME Section III piping Codes) we really do not calculate true elastic stresses in the B31 Code stress calculation methodology. Using the B31 Stress Intensification Factors means we calculate an “equivalent stress” that we compare to B31 allowable stresses and stress ranges. Furthermore, when we go beyond the yield strength of the material the calculated elastic stresses pale to insignificance. The plastic stresses are not calculated but B31 Code equations which are by design a “simplified approach”.
Again, thank to Prex for the feedback and correction.
