When is it important to evaluate a change in the direction of a load on a piping component? How do analysts perform such an evaluation? These questions are intended to address both changes due to operation, and due to constructed modifications to the piping.

For example: An existing A106 carbon steel B31 piping system having a hundred or so full temperature cycles (FTCs) from ambient to 750 Deg. F is modified by adding a branch connection via a hot tap.

A B16.9 welding tee in the existing system experienced in-plane bending during the FTCs that resulted in stresses greater than Sy.

The addition of the proposed branch line will result in out-of-plane bending during a projected remaining life of another hundred or so FTCs, also with stresses greater than Sy.

If the owner directs the designer to follow the requirements of the B31 Code for the design of system modifications, is a cumulative life evaluation in accordance with BPVC Sec. VIII, Div. 2, Appendix 5 necessary, or is a B31 analysis sufficient for the evaluation of the tee (and other piping components)?

I think that if the secondary stresses were below Sy, then a B31 analysis is sufficient. With secondary stresses in the plastic region (due to shakedown) I’m not understanding the effect of stress on a component when developed from loads from one direction, later receiving stresses from loads in a new direction. It appears to me that Appendix 5 addresses this situation in 5-110.3(g) where it requires the evaluation of “…two or more types of stress cycle(s)…”

The Markl tests evaluated bending in-plane in one test, and then out-of-plane in a separate test. However, bending between planes, or the cumulative effect of bending in-plane and then bending out-of-plane on the same fitting were not evaluated (that I have found).

The B31 Codes evaluate the secondary stresses as individual load cases, not the cumulative effect of various load cases on a node or component. If Appendix 5 considers it important to evaluate the cumulative effect of different types of stress cycles, why doesn’t the B31 Code require the evaluation the cumulative effect also?

My thoughts .....
I think many analysts simply things a bit here to make things workable. If the torsional loadings are low, we ignore local temperature stresses, and we consider only 2D beam elements [ie Caesar], it is reasonable to assume that the principle stresses will not change direction. Hoop stress will [by definition] always be in the same direction, as will radial stress, which we simplify to a constant value for a thin shell. The longitudinal stress, in the third mutually perpendicular direction will always act in the same direction along the pipe. The magnitude may change as the pipe recieves loads both 'in-plane'and 'out of plane' [so to speak] so the location of the maximum fibre stress may move around the circumference, but the direction will always remain the same. If torsion stresses are high, then things change as that may cause the 'hoop' stress to rotate to perpendicular to the combined longitudinal bending / torsoinal stress, but for many systems the torsion stresses are low compared to longitudinal bending so it can be neglected.
By only considering beam elements we really make a statement that we 'don't know or care' about the finer points of what is going on in a particular fitting. We trust the code directions on SIFs to take care of that.
The justification is that App 5-110.3(a) talks about principle stress directions at the point being considered. It does not give a definition of what 'point' means in this context. It may mean a small element or it may mean the node of a beam element. Both are points being considered.
The engineering judgement comes in knowing when the beam approach is lacking and something more powerfull should be employed.
Am I correct in MY understanding here?

B31.3 addresses the combination of various fatigue components in para. 302.3.5. I don't see it used too much.

You calculate the expansion stress range for each load; identify the largest stress range; and for each node, adjust the number of cycles to include the effects of the lesser stress ranges. See Eqn. (1d).

Since you are comparing and combining stress, the moment directions do not come into play. Maybe they should, but they don't here.

Perhaps the following gets at my question better. Consider the following load cases:

L1 = W+T1+P1
L2 = W+T2+P2
L3 = W+P1
L4 = W+P2
L5 = L1-L3
L6 = L2-L4
L7 = L1-L2

For B31 analysis, why is it sufficient to consider fatigue stresses individually in load case L5, L6, and L7? Why is it not important to consider the combined effect: (expansion stress & number of cycles for L5) + (expansion stress & number of load cycles for L6) + (expansion stress & number of load cycles for L7)? The latter paralleling the approach for calculating the cumulative usage presented in BPVC VIII, Div. 2, Appendix 5.

I think the para. 302.3.5, Eqn. (1d) approach pointed out by Dave would get at my question. However, it seems that where a large number of load cases exist, it would be practically unmanageable to identify the highest stress locations in one load case in order to establish the maximum computed displacement stress range, and then to that add the stress ratios multiplied by the associated stress cycles for all the other load cases.

Captain Kenny, I found your description of the combination of the principal stresses for a particular point in the model helpful in the way you said it. I can, however, envision conditions where the principal longitudinal stress may be opposite in sign for certain load case combinations. So, I don't understand why it does not seem that the code considers the cumulative effect of such conditions.

Ken
If the principle longitudinal stress changes sign, does that nessecarily mean it has changed 'direction'. Could you not consider the direction to be the same, but with a negative magnitude? that would be my interpretation.
Good old code semantics!

I think the opinion 'round here is that 302.3.5 eq(1d) is a simplified response to the fatigue issue, but usefull never the less. There is of course the question of what stress range allowable to apply f to: the 'conservative' or 'liberal' version. I don't know of other codes where the fatigue life is based on the minimum level of stress experienced by the component during it's life [i.e. the SUS stress].
If we consider a very well supported branch at ambient subject to vibration in the horiziontal plane, such that S=Sc=Sh, and SL=0 then:
Sa [conservative] = 1.25Sc +0.25Sh = 1.5S
Sa [liberal] = 1.25(Sc+Sh)-Sl = 2.5S
If SE = S [to make it simple] then we have as limits

for the conservative stress range allowable
f = S/1.5S = 0.667 => 5.5E4 cycles

for the liberal stress range allowable
f = S/2.5S = 0.4 => 8E5 cycles


That is a 14.5 times increase in predicted fatigue life! Both ASME VII Div 2 App 5 and PD5500 App C only offer one fatigue curve. PD5500 goes even further, by stating fatigue strength is absolutely independant of material yield strength for all steels and aluminium alloys [when adjusted for E]. So if we were to change our notional branch to a material with a higher B31.3 allowable [say from 20ksi to 30ksi, a ratio of 1:1.5], and keep everthing else, including SL & SE, the same, then B31.3 would predict an even better fatigue life:

for the conservative stress range allowable
f = S/[1.5*1.5]S = 0.444 => 8E5 cycles

for the liberal stress range allowable
f = S/[2.5*1.5]S = 0.2667 => 7E6 cycles
That is a 14.5 to 130 times increase in predicted fatigue life against our original prediction by changing the allowable stress range used and the material. This is inconsistant with other codes to say the least.
Hmmmmmm?

Hi, there!

Although several points of this interesting subject may be found among previous Caesar II topic posts, I've taken the liberty to expose briefly my personal opinions below.

So:

1) Piping stress analysis is generally performed in acordance with piping design codes (ASME B31 - 1, 3, 4, 8 etc.). The stress calculation is performed based on material LINEAR-ELASTIC behaviour assumption.

Although B31.3 - 2004 Edition has recently introduced the "Operating Stress" concept (see Appendix P - "Alternative Rules for Evaluating Stress Range"), the common engineering practice for pipe stress analysis is different from pressure vessel analysis and is based on pipe stress discrimination between
a) Sustained Stresses
b) Expansion Stresses
c) Occasional Stresses.

Each stress category should be identified and treated separately, comparing the maximum actual values with the corresponding allowable limits - ASME B31 codes provide all the necessary details and requirements.

Cyclic loading of piping is associated with expansion stresses. Basically, the Maximum Allowable Stress Range depends on the strength characteristics of the material (i.e. cold and hot allowable stresses - Sc and Sh, which depend on material tensile stress and yield limits), on the one hand, and on the number of loading-unloading cycles (N), on the other hand - see for details ASME B31.3, par. 302.3.5(d) (mentioned also by Mr. Diehl above).


2) The piping loading cases exemplified by Ken above represent a "classical" situation:

"L1" and "L2" cases describe the system loading induced by two different operating regimes - (p1, T1) and (p2, T2) parameter sets;
"L3" and "L4" cases represent the Sustained (SUS) loading cases;
"L5" and "L6" cases represent the thermal expansion loading cases;
"L7" case describe the cyclic loading between (p1, T1) and (p2, T2) regimes and allows the "operating stress range" assessment, in accordance with B31.3-2004, Appendix P, par. P302.3.5.

"L5" and "L6" cases analysis has to be performed in accordance with par. 319.4.4 and 302.3.5(d) of B31.3 Code. Assuming the loading-unloading cycle numbers are known, the Allowable Stress Range for each case may be established - see par. 302.3.5 (d) (the usual approach is to assume the reference cycle number of 7000, that yields an unitary Stress Range Reduction Factor f = 1.00).
In my opinion, for "L5" and "L6" thermal expansion cases, the Allowable Stress Range could be assessed either conservatively by 302.3.5 (1a), or by 302.3.5 (1b) formula of B31.3 Code (i.e. "liberal stress" approach considered).

"L7" expansion/cyclic loading case has to be treated in accordance with P302.3.5 procedure.
The effective stress range SE has to be assessed by (P17b) formula, taking into account ALL the individual loadings and the corresponding stress components: bending, torsion and axial load.
The Allowable Stress Range has to be established this time by (P1a) formula - S0A = 1.25 * f * (Sc + Sh).

As Mr. Diehl mentioned above, all the cyclic loading regimes may be simultaneously considered using eq. 302.3.5 (1d) or P302.3.5 (P1d).


3) A more accurate fatigue analysis may be performed following ASME Sect. VIII - Div. 2 - Appendix 5 (Article 5-1) provisions.

Basically, this analysis procedure has been implemented within Caesar II software - see Caesar II Technical Reference manual, Chapter 6 (Technical Discussions), paragraph entitled "Fatigue Analysis using Caesar II", page 6-53 ... 6.69 (for V.5.00 documentation).
ASME fatigue analysis approach is based on stress range intensity assessment (for each node of the model) that is performed taking into account ALL the individual stress components and applying Tresca strength criterion. The Cumulative Usage Factor is finally evaluated in order to take into account ALL the cycle types that describe the loading-unloading history. I believe this is a clear response to Ken's doubts regarding the cumulative effect of stress cycles.

In fact, Caesar II is able to perform fatigue analysis not only in accordance with ASME Sect. VIII Div. 2 (or ASME Sect. III, Subsection NB) principles, but also according to IGE TD 12 British Code. All the basic guidelines are presented in Caesar II Technical Reference manual.

For certain special cases (as are the High Pressure Piping - see Chapter IX of B31.3 Code), ASME B31.3 code requires explicitly the Fatigue Analysis procedure in accordance with ASME Sect. VIII - Div. 2 - Appendix 5 provisions (see par. K304.8).


4) For each pipe fitting component (including here pipe branches - tees, olets etc.), the expansion stress range (SE) is evaluated taking into account the Stress Intensification Factor (SIF), which amplifies the nominal value of the individual (in-plane or out-plane) bending stress component in order to quantify the actual "peak" stress component value of the fitting under discussion.

The resultant stress (i.e. equivalent normal stress) is obtained employing superposition principle for combined loading. So, the resultant bending stress and the torsion stress are combined in accordance with Tresca strength criterion - see eq. 319.4.4 (17) of B31.3 Code.

Piping stress values corresponding to thermal expansion may exceed the material yield limit. However, these high quantities do not represent actual stress values, but rather stress ranges which have to be compared against material Allowable Stress Ranges. Due to shakedown phenomenon, the actual stress levels cannot exceed material yield limit (well, a small exceeding may occur, due to material hardening, but this is another subject...).


5) Finally, an opinion to the ultimate post of Cpt. Kenny.

ASME Section VIII Div.2 operates with different stress categories than B31 Piping Code does.
According to ASME VIII Div. 2 Code, the fatigue analysis takes into account ALL the individual loadings defined by a cyclic history: Pressure, working fluid weight, thermal expansion, thermal gradient etc.
Therefore, in my opinion, as an equivalent fatigue analysis of the piping systems, ASME B31.3 - 2004 Ed. Appendix P provisions should be followed as MINIMUM requirements.
A detailed fatigue analysis can be performed only in accordance with ASME Sect. VIII Div.2 App. 5 requirements.


Best regards,