CAESARII Assorted Topics

CAESAR II (Assorted) Topics COADE, Inc. (3/2005) page: 1

CAESAR II (Assorted) Topics

3D Graphics Intentions 2 ANSI versus ASME Flanges 3 ASME NC / ND 4 Bourdon Pressure 5 Static Snubber Analysis 8 Convergence Issues 9 Friction Convergence Issues 10 Friction Stiffness 11 Expansion Load Case 12 Harmonic Load Simulation 14 Sturm Sequence Failure 15 Tee Types 16 Von Mises Theory 18 WRC107 Details 19


3D Graphics Intentions

Following the release of CAESAR II Version 4.10 in January of 1999, we received many complaints (from users and dealers) that the CAESAR II graphics were: old, ugly, and lacking capability. At this time, we also wanted to have additional graphics capabilities which were beyond the technology built into the basic graphics engine we were using (which had been developed in-house in 1987). So we evaluated a number of 3rd party graphics tools and libraries. We selected the HOOPS library as the tool to base all future graphics development on.

With the release of CAESAR II Version 4.20 in February of 2000, we introduced the 3D HOOPS graphics. At this time, these new graphics were not complete, and did not provide all of the capabilities that the old standard graphics did. However, throughout the life of Versions 4.20 and 4.30, the 3D HOOPS graphics were constantly improved. From this point on, no work has been done with regards to the old standard graphics. All graphics development is targeting the 3D HOOPS graphics. With the release of CAESAR II Version 4.40 in May of 2002, users were informed that the 3D HOOPS graphics (in the piping input module) were almost complete, and to start using them - this was the future. The intent here was to solicit comments and suggestions on these new graphics, so we could improve them further.

With the release of CAESAR II Version 4.50 in November of 2003, the 3D HOOPS graphics are superior to the old standard graphics, and include additional capabilities not available before. Also with the release of Version 4.50, the old standard graphics have been disabled to ensure that everyone has the same capabilities.

For those users who never reviewed the 3D HOOPS graphics before (during their 5 year development), and are surprised by the graphics in Version 4.50, we can offer the following resources (from the COADE website) to get you up to speed in using these graphics:

From "Technical Articles\CAESAR II": - Usage Tips Vol 1,

http://www.coade.com/product_info.asp?varfile=caesar/c2_420_tipsa.asp&varflag=CAESARII&varflagmaster=CAESARII- Usage Tips Vol 2,

http://www.coade.com/product_info.asp?varfile=caesar/c2_430_tipsa.asp&varflag=CAESARII&varflagmaster=CAESARII- Usage Tips Vol 3,

http://www.coade.com/product_info.asp?varfile=caesar/c2_440_tipsa.asp&varflag=CAESARII&varflagmaster=CAESARII

From "Animated Tutorials: - 3D Graphics Usage,

http://www.coade.com/viewlets/c2/c2_3dgraphics/c2_3dgraphics_viewlet_swf.html- Reducer Modeling,

http://www.coade.com/viewlets/c2/c2_reducers/c2_reducers_viewlet_swf.html

The 3D HOOPS engine provides many more capabilities than our own Standard Graphics engine. It may take a few hours to make the transition, but the transition must be made. The 3D HOOPS engine is where all future development will be targeted.


ANSI versus ASME Flanges

As you may now realize many ANSI Standard flanges do not pass the rigors of ASME Appendix 2 stress analysis. These flanges have been in use longer than the rules have been around that perform the analytical stress evaluation.

These ANSI flanges have been allowed for use by ASME. If your flange rating is met per ANSI the flange is deemed to be OK regardless of what App. 2 predicts. Appropriate consideration of external forces and moments is also expected.

The cause of the problem is typically the gasket. The stiffer the gasket, the higher the seating stresses. If you had the luxury of using a softer gasket, this issue would probably have not arisen.

The CAESAR II Flange Module address two concerns, which are unrelated to each other. The first is the stress in the flange. This procedure is as per ASME Section VIII Division 1 Appendix 2. This is a "code" calculation. If the stress report states the flange is overstressed, then it is overstressed according to the equations in this appendix. Note, many "standard flanges" can be overstressed depending on the loads you put on them. As to "whether or not this is a concern" is the engineering decision the end user must make. (Usually, you don't want to be overstressed.) The second concern is leakage. The CAESAR II Flange Module provides three different indicators for the "leakage potential" of the flange in question, under the specified loads. a) The B16.5 MAWP rating (equivalent pressure model): Personally I feel this on is worthless. B16.5 provides MAWP based on the elastic modulus of the flange material. It ignores bolting and gasket particulars. There is no connection between the MAWP of the flange material/body and whether or not the flange will leak. Unfortunately, this assumption is made by many, so we included the MAWP in this report. b) The ASME Section VIII Division 1 Rigidity Factor: This is a "code equation". This single equation is an "indicator" of leakage potential. c) The CAESAR II FE Leakage Model: This is a procedure invented here at COADE, because at the time (1991), there was nothing better available to address leakage potential. The article introducing this methodology can be found in the October 1991 issue of COADE's Mechanical Engineering News. This issue is on the website (http://www.coade.com/) if you don't have a hard copy.


ASME NC / ND

CAESAR II does not perform the “alternative” methods described in NC-3654.2(b) and NC-3655(b). What it does do is:

Equation (8) is implemented for load cases designated as (SUS).

Equation (9) is implemented for load cases designated as (OCC). The allowable stress is determined depending upon the value currently set in the “Occasional Load Factor” in the “SIFs and Stresses” tab. If you have the value 0 (default) or 20 (20% increase over SUS values) you will get the lesser of 1.2*1.5Sh = 1.8Sh or 1.5Sy, which corresponds to Service Level A/B. If you have the value 50 (50% increase over SUS values) you will get the lesser of 1.5*1.5Sh = 2.25Sh or 1.8Sy, which corresponds to Service Level C. If you have the value 100 (100% increase over SUS values) you will get the lesser of 2.0*1.5Sh = 3.0Sh or 2.0Sy, which corresponds to Service Level D.

Either equation 10 or 11 is implemented for load cases labeled as (EXP), depending upon whether “Liberal Stress Allowable” is deactivated or activated, respectively, in the Special Execution Options. In the latter case, equation 11 is slightly rearranged, as so:

Ste = iMc/Z <= (Sa + Sh) – PDo/4tn – 0.75i(Ma/Z)

Equation 10a is not implemented.

Equation 11a is not implemented.

The following equations are not implemented for Service Level D in CAESAR II:

B2*( Do/2I)Mw<0.5 Sm;

B1(PdDo/2t)+B2(Do/2I)Me<3 Sm

C2Mam*Do/2I <S1

Fam/Am < S2

Since CAESAR II does not perform the “alternative” method, there is no need to change the B2 stress indices for Level D.

CAESAR II does not perform support calculations, therefore it does not consider ASME NF


Bourdon Pressure

Currently, there are no codes, equations, or technical papers that mention the Bourdon effect. We have hunted in vain for such a thing for years without success. Therefore we have a phenomenon that "everybody" knows how to use, how and when to apply, etc. but that nobody will put their name to. The reason, we believe, is because the traditional Bourdon implementation that everybody uses does not match up with reality.

Bourdon has little to do with the pressure translation of ovalized cross-sections into circular cross-sections - that is the pressure stiffening effect that most codes use to modify bend SIFs and flexibility factors. Bourdon is an attempt to take into account the strain that the piping undergoes when subjected to pressure. This strain is due to two components - the axial strain due to the pressure end cap effect (roughly PD/4tE) and then the Poisson effect (axial shrinkage due to radial and hoop expansion under pressure).

Virtually all pipe stress programs implement the Bourdon effect in the manner first developed for the MEC-21 pipe stress program, circa 1960. This method applies pressure elongation as a uniform strain to the entire piping system, in a way similar to thermal expansion (some codes, such as BS 7159, actually instruct the user to convert pressure strain to "equivalent temperature"). The actual pressure strain calculation is done as:

e = P(Ri * Ri) / (Ro * Ro - Ri * Ri) / E - V P(Ri) / (Ro - Ri) / E , or, slightly more exact,

but virtually identical for "thin" wall pipe:

e = [P(Ri * Ri) / (Ro * Ro - Ri * Ri) / E] (1 - 2 V)

Where:

e = uniform pressure strain P = pressure Ri = internal radius Ro = outer radius E = modulus of elasticity V = Poisson's ratio

In the Bourdon method, this strain is then applied throughout the piping system, in the same manner as a thermal strain would be. The upshot of this is (think piping systems loaded with thermal strain):

1) On an unrestrained system (i.e., a cantilever), this leads to no stress, non-zero displacements, and no anchor loads.

2) On a restrained system (straight pipe anchored at both open ends), this leads to compressive stresses and compressive forces on the restraints and zero displacements.

3) On a restrained system (straight pipe with intermediate anchors), this leads to compressive stresses, zero anchor loads, and zero displacements.

In real life, the situation would be:

1) On an unrestrained system (i.e., a cantilever), there would be tensile stress equal due to the end cap effect, non-zero displacements, and an anchor load (pressure thrust load).


2) On a restrained system (straight pipe anchored at both open ends), there would be tensile stresses equal to the Poisson's effect (due to hoop stress), tensile loads on the restraints, and zero displacements.

3) On a restrained system (straight pipe with intermediate anchors), there would be tensile stresses equal to the Poisson's effect (due to hoop stress), zero loads on the intermediate restraints, and zero displacements.

(Note that real life piping systems are much more complicated than any of these three scenarios.)

For all load cases containing pressure (whether Bourdon is activated or not), CAESAR II (and probably most other pipe stress programs) then adds the constant value P(Ri * Ri) / (Ro * Ro) to the stress due to other loads (since this is required by most piping codes).

So looking at the implications of different scenarios:

1) On an unrestrained system (i.e., a cantilever), with no Bourdon activated, this leads to a stress of P(Ri * Ri) / (Ro * Ro), no displacements, and no anchor loads. Technically this is correct for stress, incorrect for displacements, and incorrect for anchor loads.

2) On an unrestrained system (i.e., a cantilever), with Bourdon activated, this leads to a stress of P(Ri * Ri) / (Ro * Ro), displacements equal to length * P(Ri * Ri) (1 - 2V) / (Ro * Ro - Ri * Ri) / E, and no anchor loads. Technically this is correct for stress, correct for displacements, and incorrect for anchor loads.

3) On a restrained system (straight pipe anchored at both ends), with no Bourdon activated, this leads to a stress of P(Ri * Ri) / (Ro * Ro), no displacements, and no anchor loads. Technically this is incorrect (but conservative, as intended by most codes) for stress (the stress should probably actually be tension equal to only the Poisson term: -V P(Ri) / (Ro - Ri), correct for displacements, and incorrect for anchor loads.

4) On a restrained system (straight pipe anchored at both ends), with Bourdon activated, this leads to a stress equal to the end cap tension, less the Bourdon compression, or just the Poisson effect: V P(Ri) / (Ro - Ri), no displacements, and compressive anchor loads. So this would be correct for the stress, correct for displacements, and incorrect for anchor loads.

5) On a restrained system (straight pipe with intermediate anchors), with no Bourdon activated, this leads to a stress of P(Ri * Ri) / (Ro * Ro), no displacements, and no anchor loads. Technically this is incorrect (but conservative, as intended by most codes) for stress (the stress should probably actually be tension equal to only the Poisson term: -V P(Ri) / (Ro - Ri), correct for displacements, and correct for anchor loads.

6) On a restrained system (straight pipe anchored at both ends), with Bourdon activated, this leads to a stress equal to the end cap tension, less the Bourdon compression, or just the Poisson effect: V P(Ri) / (Ro - Ri), no displacements, and compressive anchor loads. So this would be correct for the stress, correct for displacements, and incorrect for anchor loads.

In our opinion, the correct answer is to model pressure elongation as two distinct effects:

(1) a primary (force driven) load equal to the pressure end cap thrust load, modeled at every elbow, valve seat, or other thrust surface; and


(2) a secondary (displacement driven) uniform strain equal to the Poisson's effect of the hoop stress.

This sort of model would make each of the above layouts (as well as all in between) work out correctly. The problem would be that this would buck a forty-year old trend, and probably would not be easily implemented by most pipe stress software available today, without modification. A secondary by-product is that this sort of analysis would not provide the sort of conservatism that is currently allocated to longitudinal pressure stress by most codes.


Static Snubber Analysis

Because CAESAR II can not perform "load stepping", static analysis with snubbers requires a manual "up front" analysis to determine thermal movements. Here is the procedure. 1) Analyze a "hot operating" case, without your occasional loads. 2) Take the displacements from this analysis at the snubbers, and put them back into the input. At the location where the snubbers are defined, define a CNODE and put these displacements on the CNODE. 3) For your "real" analysis, apply these displacements to all load cases. Because they are on the "far side" of the snubber, they won't affect anything unless the load case is called "OCC", which activates the snubber stiffness. So, - when you run your standard OPE case (W+T1+P1+D1), the snubber node will displace as before. There will be no restraint because the load case is OPE, not OCC. - when you run the operating + occasional case (W+T1+P1+D1+WIND1), the snubber node will displace along with its CNODE. There will be a difference in these two displacements due to the WIND1 load and the snubber stiffness, because the case is now set as "OCC".


Convergence Issues

I can't give a specific reason as to why a specific change might allow a job to converge. In a nut-shell, here is what is going on:

1) The system parameters are used to define the global stiffness matrix [K] and load vector {f}. This defines the system of equations [K]{x} = {f}.

2) In a system with non-linear boundary conditions, each load case must undergo an iteration process. In this process, the above system of equations is solved for {x}. Then, at each non-linear boundary condition, the status is checked. If the boundary condition changed (a +Y lifted off, a gap opened or closed, etc), then that DOF in the stiffness matrix [K] is altered. When all changes to [K] have been made, the next iteration for that load case begins. This process is repeated until all boundary conditions are within the convergence tolerances.

3) The only convergence tolerances users can control are for friction and large rotation rods. Items like +Y supports, gaps, and soil restraints are either on-off, or yielded-nonyielded.

4) CAESAR II doesn't have an iteration limit. If the job doesn't converge, we don't give an answer. We feel no answer is better than a wrong answer.

If during the solution, you click the [F2] key, CAESAR II will give you a list of the restraints that are not converged at that time. Changing characteristics of any of these restraints may allow the job to converge. Details of what this report contains can be found below.

For jobs with friction, please read the section on friction in the Technical Reference Manual (or the next section). Additionally, the magnitude of the "coefficient of friction" can be changed globally for all restraints using the "load case options" tab of the static load case editor.

I can not say how any one specific boundary condition change will affect the system of equations in [K], and the subsequent matrix decomposition. When you encounter this behavior, all you can do is play with the system, using the list of non-converged restraints as a guide.

Interpreting the information from the [F2] key:

Old State - New State: This indicates the status of two successive iterations. The old state is iteration "x", while the new state is iteration "x+1".

Open - Closed: This indicates the status of a directional or gapped restraint. Open means the pipe is not on the restraint, while closed means the pipe is contacting the restraint.

Direction X, Y, Z: These values define the direction cosine of the restraint.

Sliding - Not Sliding: For jobs with friction this indicates whether or not the load was sufficient to cause sliding. Details on this can be found in the "friction discussion" in the Technical Reference Manual.

Error: This value indicates the percent change in the normal force between iterations. A value of 0.5 indicates that the normal force changed by 50%, which means the friction force changed by 50%.


Friction Convergence Issues

Adding friction to a job makes the job highly non-linear. There is a discussion on the solution to the "friction problem" in the CAESAR II Technical Reference Manual, P6-16. In general, the steps to achieving convergence in a "friction problem" are: 1) Determine what load case isn't converging and make sure it is realistic. By this, I mean don't setup a load case with only a single load component such as WIN1. Why? Well, wind will never act alone, and for code compliance, you should really obtain the effects of wind by subtracting two operating cases, one with wind and one without - then combine with sustained. 2) Once you have determined that the load cases are ok, for the case that isn't converging, use the [F2] key to see exactly which restraints aren't converging and why. Wait until the solution starts cycling before you do this. The report will show which restraints aren't converged, and the difference between the last two iterations. 3) While you can use the [F3] key to adjust the friction settings during the solution, I don't like doing this because it makes the solution hard to repeat, especially after 6 months or a year. I prefer to change the friction parameters in the configuration file, and then archive this file with the job. 4) Here are my recommendations, based on the [F2] report:

• If the report shows "sliding - not sliding", the best thing to do is reduce the "friction stiffness". The lower you make this value, the easier it is for the job to converge, but you are making the system very loose, in other words introducing some error into the solution.

• If the report shows "err=xxx", the value "xxx" is the percent change in the normal force on the friction restraint. To help convergence, you need to increase this value. Obviously you don't want to go too high here, what ever you're comfortable with.

• If the report shows "angle=xxx", the value "xxx" is the angle variation between iterations. Again you would increase this value to help convergence. Again you don't want to go too high here.

• If the report shows "open - closed", this is not a friction issue. This is something like the pipe bouncing on a +Y or against a gap. Try changing the gap size or moving the restraint.

Here is a link to an excellent table of friction factors. Caution is urged in the use of these values, as they change over time. Note the warning at the top of the table with regards to the effects of oxide films.

http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm#coef


Friction Stiffness

CAESAR II models friction by inserting artificial restraints orthogonal to each of your real restraints. It sets the stiffness of these artificial restraints to the value that you have in your Configuration file. What stiffness is correct? That is hard to say. The lower the stiffness, the "softer" the distribution of the friction over multiple supports. For an example, lay a board across a mattress, extending out over the side, then push down on the part that extends over the side. The mattress gets pushed down, and resists the force on the board with a triangular force distributed over a particular length (a force over a distributed length is the equivalent of distribution over a number of restraints in the CAESAR II model). When the stiffness is higher, the analogy is laying the board across a table and pushing down on the part that extends beyond the table. Now the board pivots around the edge of the table, and the force is totally resisted at one point. Which of these models is correct? It depends; how do you think your friction is reacting? The former tends to converge more easily (since changes to the system load equate to smaller changes to individual restraints, as opposed to the latter, where restraint responses may be multiples of system loads), but the latter minimizes displacement at the frictional restraint, if you do not want sliding. In effect, friction has a large number of possible solutions (for example, the frictional response changes during the time history of the load application). The best we can hope for is a solution that is approximately in the vicinity of the most predominant (in other words, the magnitude/duration combination that tends to dominate) friction load that we expect. So are your nozzle loads "correct"? Yes (if you consider "in the vicinity of" as correct), no (since there are probably an infinite number of other solutions that it will see as well), and maybe. What would I suggest? In general, use some relatively high stiffness (either 175120 or 87560 are OK); if you get a job that doesn't converge, then decrease the stiffness for that model until it does. I would not really recommend changing the friction stiffness to get numbers that make the loads low enough to pass, unless you have some real understanding as to how your system friction is going to react.


Expansion Load Case

This is the classic misunderstanding of what the code defines as the expansion case. The code states that the expansion stresses are to be computed from the "extreme displacement stress range". These are all very important words. Consider their meaning ... EXTREME: In this sense it means the most, or the largest. RANGE: Typically a difference. What difference? The difference between the extremes. What extremes? DISPLACEMENT: This defines what extremes to take the difference of. STRESS: What we are eventually after. Putting everything back together, we are told to compute stresses from the extreme displacement range. How can we do this? Consider the equation being solved; [K] {x} = {f}. In this equation, we know [K] and {f}, and we are solving for {x}, the displacement vector. In CAESAR II, when we setup an expansion case, we define it as "L1 - L2", where the "1" and "2" refer to the displacement vector ({x}) of load cases 1 and 2 respectively. (Obviously the load case numbers are subject to change on a job by job basis.) What do you get when you take "L1 - L2"? Well {x1} - {x2} yields {x'}, a pseudo displacement vector. {x'} is not a real set of displacements that you can go out and measure with a ruler, rather it is the difference between two positions of the pipe. Once we have {x'}, we can use the same routines used in the OPE or SUS cases to compute element forces, and finally element stresses. However, these element forces are also pseudo forces, i.e the difference in forces between two positions of the pipe. Similarly, the stresses computed are not real stresses, but stress differences. This is exactly what the code wants, the stress difference, which was computed from a displacement range. As to whether or not this stress difference is the extreme, well that depends on the job. Consider the users question again; "Is L1-l2 the same as a load case with just T1?". My answer to this is maybe. If you have a linear system (from a boundary condition point of view), then the answer is yes. You will get exactly the same results. However, if the system is non-linear (i.e. you have +Ys, or gaps, or friction), then the answer is no. You will get different results - how different depends on the job. The reason for this can be found by examining the equation [K] {x} = {f} for the two different methods. For this discussion, rearrange the equation to {x} = {f} / [K], where we know we don't really divide by [K], we multiply by its inverse.

CAESAR II

OPE: {xope} = {fope} / [Kope] = {W + T1 + P1} / [Kope] SUS: {xsus} = {fsus} / [Ksus] = {W + P1} / [Ksus} EXP: {xexp} = {xope} - {xsus} = {W + T1 + P1} / [Kope] - {W + P1} / [Ksus}

This user wants to simplify the above equation as follows: EXP: {xexp} = {W + T1 + P1} / [K] - {W + P1} / [K} Canceling like terms (the ones in red) yields: {xexp} = {T1} / [K]


The assumption here is that [Kope] is the same as [Ksus]. This assumption is only true for linear systems. For non-linear systems, the stiffness matrix is unique for each load case and the above cancellation of loading terms is incorrect. You get the wrong stress results for the expansion case if you do it this way.

Another proof that the "L1-L2" method is the correct way to go is to consider a job with two operating temperatures, one above ambient and one below ambient. Say T1 = +300, and T2 = -50. CAESAR II would setup load cases as follows: (1) W + T1 + P1 (OPE) (2) W + T2 + P1 (OPE) (3) W + P1 (SUS) (4) L1 - l3 (EXP) (5) L2 - L3 (EXP) These cases, while correct, don't address the "extreme" term of the code requirements. This is because CAESAR II isn't looking at what the load components represent. To satisfy the requirements of the code, the user must define an additional load case: (6) L1 - L2 (EXP) This load case will be the "extreme", that will typically govern the EXP stress criteria. You can't do this at all using the "T1" only method. To summarize, we take the difference between two load cases to determine a displacement range. From this range we compute a force range and then a stress range. The code requires the extreme displacement stress range. The user only has to worry about whether or not the "extreme" case has been addressed.


Harmonic Load Simulation

To solve a harmonic acoustic or pulsation problem, you need to simulate the loading, and adjust it to match your measured response. Load simulation for this sort of problem is a trial and error procedure, as follows:

1. Pick a unit load, 1000 lbs for instance. 2. Apply this node axially in one of your pipe segments, perhaps start with the longest one. 3. Excite the system with this load at the frequency of the (measured) system response. 4. If the overall general system response from CAESAR II doesn't match the field response

of the real system, move the load to a different segment. 5. Repeat step 4 until the CAESAR II response matches (in form) the field response. 6. Finally, scale the unit load up or down as necessary so that the displacements match 7. Now that the loading has been simulated, you are in a position to evaluate the response

to see if it is a problem, and if so, alter the system to avoid responding to the (simulated) load.

Note, this procedure assumes your response is dominated by a single (natural frequency) mode, and that you can simulate the loading with a single force. The biggest problem with most dynamic analysis is determining the dynamic loading. Using the dynamic response as the loading is incorrect since you will not be in a position to resolve any issues with the system.


Sturm Sequence Failure

The "sturm sequence failure" does not mean there is anything wrong with your job, rather that there is at least one more mode close to where you stopped extracting frequencies

Take as an example a system where you set the input up to extract all frequencies below 95 hz. The extraction routine will stop as soon as a frequency is found that exceeds 95 - for this discussion, assume this is 100hz. How do you know there isn't another frequency very close to this 100hz that may affect your results? You don't unless you rerun, changing the frequency cut-off. However, a better way is to implement the Sturm Sequence Check, which determines how many frequencies exist between 0 Hz and some other value (not what they are, just how many). So we take your last frequency (100 hz in this case) and add 5%, which in this case yields 105 hz. We then use the Sturm Sequence Check to determine how many frequencies exist between 0 and 105 hz. If the count is the same as the number of frequencies just extracted (between 0 and 100hz), then we report that the check passed. If we get a higher count, we report that the check failed.

There are some models that will always fail. For example, consider a cantilever running in the "X" direction. For every mode in the "Y", there is a corresponding identical mode in the "Z". Regardless of what your cut-off frequency is, the extraction will stop at the first mode of any given pair. The Sturm Sequence Check, by adding 5%, will always find (at least) the 1st mode of the pair, and therefore report a failure.


Tee Types

The CAESAR II fittings correspond to the following:

1 - Reinforced tee (designation from Appendix D of B31.3: Reinforced fabricated tee with pad or saddle): Hole cut in the header pipe, branch pipe stubbed against it and welded, then a pad or saddle welded around the connection to provide reinforcement.

2 - Unreinforced tee (designation from Appendix D of B31.3: Unreinforced fabricated tee): Hole cut in the header pipe, branch pipe stubbed against it and welded, with no pad or other reinforcement.

3 - Welding tee (designation from Appendix D of B31.3: Welding tee per ASME B16.9 with... (specific dimensional requirements)): A single piece component, forged or cast, that meet the dimensional requirements of B16.9. This fitting tends to have very smooth contours that provide the best stress distribution.

4 - Sweepolet (designation from Appendix D of B31.3: Welded-in contour insert with... (specific dimensional requirements)): A fitting available from Bonney Forge (or their imitators), installed by cutting a large hole in the header and then setting the sweepolet into the hole such that it makes a smooth contour with the header, similar to that of the B16.9 welding tee.

5 - Weldolet (designation from Appendix D of B31.3: Branch welded-on fitting (integrally reinforced)): A fitting available from Bonney Forge (or their imitators), installed by cutting a smaller hole in the header and then setting the weldolet onto the header, over the hole. The weldolet has a big block of steel on it that provides reinforcement for the connection.

6 - Extruded Welding tee (designation from Appendix D of B31.3: Extruded welding tee with... (specific dimensional requirements)): A single piece component, made from a straight piece of pipe, with the branch opening extruded. The crotch radii must meet the specified dimensional requirements.

7 - Butt weld (designation from Appendix D of B31.3: Butt welded joint): This is not a tee, but simply a butt-welded connection between two pieces of pipe or fittings. Some codes specify non-1.0 SIFs for butt welds.

8, 9 - Socket (designation from Appendix D of B31.3: Fillet welded joint, or socket weld flange or fitting): These are not tees, but simply fillet(socket)-welded connections between two pieces of pipe or fittings. Some codes differentiate between as-welded ("unfinished") and Ground-smooth fillet welds.

10 - Taper (designation from Appendix D of B31.3: none): This is not a tee, but a butt-welded connection between two pieces of pipe or fittings, where the two welded components are of different thickness and one is tapered down to match the other. This type of connection is recognized by a number of codes, such as B31.1.

11 - Threaded (designation from Appendix D of B31.3: Threaded pipe joint or threaded flange): This is not a tee, but simply a threaded connection between two pieces of pipe or fittings.

12 - Double welded (designation from Appendix D of B31.3: Double welded slip-on flange): This is not a tee, but simply the welded connection between a slip on flange and the pipe.


13 - Lap joint (designation from Appendix D of B31.3: Lap joint flange (with ASME B16.9 lap joint stub)): This is not a tee, but a lap joint flange.

14, 15, 16 - BF Sweepolet, BF Latrolet, BF Ins Wld (designation from Appendix D of B31.3: none): Selection of these types uses Bonney Forge's published recommendations for SIFs for their sweepolets, latrolets, and weldolets, respectively, overriding the code requirements thereof. We don't recommend using these types.

17 - Full encirclement tee (designation from Appendix D of B31.3: none): This type of tee is only recognized by the IGE/TD/12 code, other codes treat it as a reinforced fabricated tee. The reinforcing pad goes completely around the header.


Von Mises Theory

"Octahedral Shear Stress" is defined as 1/3 sqrt[(S1-S2)(S1-S2) + (S2-S3)(S2-S3) + (S3-S1)(S3-S1)]. Von Mises is referenced in the name of the theory (the "Octahedral - Von Mises Theory").

This is because the two theories are identical, with the only difference between the two being the constant used. For example, if a failure theory states that failure occurs when X exceeds Y, this same theory would be the basis for stating that failure occurs when 2X exceeds 2Y (see Maximum Shear Stress vs. Stress Intensity criteria).

As per such references as "Advanced Strength and Applied Stress Analysis" (Richard Budynas, 1977) and "Design of Piping Systems" (M. W. Kellogg, 1956) octahedral shear stress is defined as 1/3 sqrt[(S1-S2)(S1-S2) + (S2-S3)(S2-S3) + (S3-S1)(S3-S1)], so failure would occur in a uniaxial test specimen when the octahedral shear stress exceeds sqrt(2) * SY / 3. This isn't a very convenient failure point, so von Mises adjusted the constant on both sides of the equation (calculated stress and allowable stress) to look more like the maximum shear stress theory:

Von Mises stress = [1/(2 sqrt(2))] sqrt[(S1-S2)(S1-S2) + (S2-S3)(S2-S3) + (S3-S1)(S3-S1)], with failure occurring when von Mises stress exceeds SY / 2.

We have also seen the constant adjusted further to 1/sqrt(2), in which case the requirement conveniently looks more like that for stress intensity:

Von Mises stress = [1/sqrt(2)] sqrt[(S1-S2)(S1-S2) + (S2-S3)(S2-S3) + (S3-S1)(S3-S1)], with failure occurring when von Mises stress exceeds SY.

When it comes down to it, it really doesn't matter wha

t the constant is, as long as the same constant is used on each side of the equation.

(By the way, when CAESAR II prints octahedral shear stress, we print the "pure" equation, with a constant of 1/3.)


WRC 107 Details

Users should first determine whether an elastic approach or a fatigue analysis is required, using the guidelines given in section AD-160 of the ASME VIII Div 2 Code. If an elastic analysis is only required then following points should be kept in mind using the WRC 107 module,

• Set up different type of load cases (Sustained, Expansion and Occasional). • Include Pressure Thrust if needed. • Do not include Pressure Stress Indices. • Do not include stress concentration factors Kn and Kb. (This is done by omitting the fillet

radius between the vessel and nozzle). See below for more detail explanation of Kn and Kb factors.

• Use stress summation to get the comparisons of actual stress to the allowable stress. Refer below for detail discussion on stress summation.

If a fatigue analysis is required then elastic analysis will still be required. Furthermore there will be additional checks for fatigue stress. For doing fatigue analysis Peak stress intensities are required to be calculated or estimated. When the requirements of section ASME VIII Div 2 AD-560.1 to AD-560.6 are met then Pressure Stress Indices can be used to compute the peak stress intensities, see the detailed discussion on Pressure Stress Indices below.

First set up the range pair and load cycles (e.g. - Cold to operating, pressure fluctuations) for the fatigue loading.

• Now evaluate each load range using the WRC 107 module one by one. Entering each cycle load as a sustained load and leave the other types of loads as blank.

• Include Pressure Thrust if needed. • Include stress concentration factors Kn and Kb, by entering the fillet radius between the

vessel and nozzle. See below for more detail explanation of Kn and Kb factors. • There are 2 ways to combine the stresses due to external loads and the ones due to

internal pressure:

1. Calculate the pressure stress by hand (using AD-560.7 to manually apply Pressure Stress Indices) and combine with stresses due to external loads. Do not indicate the program to automatically include Pressure Stress Indices and do not perform stress summations.

Or

2. Automatically include the Pressure Stress Indices and perform stress summations. Use the results for Stress Intensity (Pm + Pl + Q) and ignore the results for first two equations (Pm and Pm+Pl) and also ignore the comparison to the allowable stresses.

The total stress intensity (Pm + Pl + Q) conservatively combines the effect of external loads intensified by Kn and Kb SCFs and internal pressure intensified by Pressure Stress Indices. This is the Peak Stress intensity needed for performing Fatigue Analysis. Now use this total stress intensity value with ASME Section VIII Div 2, Appendix 4 and 5 rules and the fatigue curves to compute cumulative usage.

Stress Summation:


The ASME Section VIII Division 2 code provides for a fairly elaborate procedure to analyze the local stresses in vessels and nozzles (Appendix 4-1 "Mandatory Design Based on Stress Analysis"). This approach is used to compute the overall stress intensities on the vessel/nozzle intersection. Local stresses due to sustained, occasional and occasional loads are combined with pressure stresses into code defined stress components and compared with their respective allowable stress values. Hence the name Stress Summation is used to identify the method. When only an elastic analysis is required (determined using AD-160) then fatigue loadings can be ignored. So, all the stress summation results can used.

The stress summation included in CAESAR does not compare fatigue stresses to their allowables. If fatigue analysis is required then only a part of the output should be used. The user can use the overall Stress Intensity (Pm + Pl + Q) values and refer to ASME Section VIII Div 2 Appendix 4 and 5 to compute cumulative usage.

Pressure Stress Indices:

The section AD-560 "Alternative Rules for Nozzle Design" can be used instead of Article 4-6 ("Stresses in openings for fatigue analysis") for calculating the peak stress intensities, needed for performing a fatigue analysis. This alternative method which is implemented in CAESAR II can be used when all the conditions of AD-560.1 through AD-560.6 are met. With this method a base stress value is multiplied by certain factors to get stress at different locations in the shell. These factors are known as Pressure Stress Indices and are given in the Table AD-560.7. Pressure Stress Indices, sometimes referred as Pressure Stress Concentration factors, are only applied to internal pressure stress.

This option should only be checked when users wants to perform a fatigue analysis.

Stress Concentration Factors Kn and Kb:

For external loads, the highest peak stress are usually localized in fillets and transitions. The tension and bending stresses are modified using the Stress Concentration Factors Kn and Kb respectively. The program uses the fillet radius between the Vessel and the Nozzle to estimate the Kn and Kb values using WRC-107 Appendix B equations (3) and (4). This option should only be checked when users wants to perform a fatigue analysis.

Stress Intensity at a point:

Twice the maximum shear stress at that point.


Index

ASME NC ................................................. 4 ASME ND ................................................. 4 Bourdon Pressure ..................................... 5 Convergence Issues.............................9, 11 Expansion Load Case ..............................13 Flanges ..................................................... 3 frequencies ..............................................16 friction ....................................................... 9 Friction .....................................................11 Friction Stiffness.......................................12 Graphics ................................................... 2 Harmonic Load Simulation........................15 HOOPS..................................................... 2 iteration limit.............................................. 9 leakage ..................................................... 3

modal analysis .........................................16 non-linear boundary condition ....................9 non-linear systems...................................14 octahedral shear stress ............................19 pressure stiffening......................................5 Pressure Thrust .......................................20 pulsation ..................................................15 Snubber .....................................................8 stiffness ...................................................12 stress range .............................................13 Sturm Sequence Failure...........................16 Tee Types................................................17 tolerances ..................................................9 Von Mises Theory ....................................19 WRC 107 Details .....................................20

CAESARII Assorted Topics

Documents

Transcript of CAESARII Assorted Topics