My question is does CEASER-II uses calculated Principal stresses, based on the Tresca theory, in determining the B31.3 code limit for longitudinal stresses due to sustained load? Since Principal stresses is a combination of the longitudinal stress, hoop stress and torsional shear stress and this (S1-S3) must not exceed the material yield based on the Tresca theory. Is it that B31.3 is not interested in the principal stress. Is it that the moment calculate the Longitudinal stresses due to sustained load and make sure it is less than the Basic allowable stress due to yield at the max metal temperature, then the piping will not fail for single point load. So what is the significance of principal stresses in this instance?

Hello Mucour

Q. My question is does CEASER-II uses calculated Principal stresses, based on the Tresca theory, in determining the B31.3 code limit for longitudinal stresses due to sustained load?

A. Caesar II follows the ASME B31 Codes for Pressure Piping and it includes the specific equations that these Codes provide for calculating stresses. That being the case, the better question is “Do the ASME B31 Codes use the Tresca failure criteria for combining calculated principal stresses?”. And the answer to that is yes.

Note that the circumferential stress (also known as “hoop stress”) due to internal (to the pipe) pressure, is addressed in accordance with the B31 Codes by calculating the required minimum allowable pipe wall thickness (e.g., B31.1, Paragraph 104). This circumferential stress is not required by the Codes to be calculated. The Codes state that the criterion for limits on internal pressure stress are satisfied (as far as circumferential stresses are concerned) when the wall thickness of the piping component, including any reinforcement, meets the minimum wall thickness requirements. Caesar II checks the user specified pipe wall thickness in accordance with the Code minimum wall thickness requirement and if the specified wall thickness is inadequate, a warning is printed.

Q. Since Principal stresses is a combination of the longitudinal stress, hoop stress and torsional shear stress and this (S1-S3) must not exceed the material yield based on the Tresca theory. Is it that B31.3 is not interested in the principal stress.

A. In May of 2005, a Code Case (B31 Case 178 – “Providing an Equation for Longitudinal Stress for Sustained Loads in ASME B31.3 Construction”) was issued that addresses the B31.3 evaluation of “sustained longitudinal stresses” (i.e., principal stresses). Obviously then, ASME B31.3 “is interested in” (i.e., adequately addresses) principal stresses.

The ASME B31 Codes do not use 100 percent of the material yield stress for a comparison (limit) for any calculated stress. The sustained (principal) stresses due to weight and internal pressure are limited to Sh at the material temperature (Sh at temperature is provided in Appendices “A” of the Codes). The values for Sh provided by the Code include the consideration of the fact that circumferential stresses are not included in the calculation of “sustained stresses”.

Q. Is it that the moment calculate the Longitudinal stresses due to sustained load and make sure it is less than the Basic allowable stress due to yield at the max metal temperature, then the piping will not fail for single point load. So what is the significance of principal stresses

A. Principal stresses are of primary importance in that they are “non-self limiting stresses”. These principal stresses will not diminish as the piping system deflects under the loadings of pressure and weight. In B31.1 the equation for the calculation of the (“additive”) sustained stresses includes two terms. One term addresses the longitudinal stresses due to internal pressure and the other term addresses the longitudinal stresses due to the resultant of the bending moments and the torsional moment. The absolute values of the stresses calculated by each term are added and the sum is the (unsigned) total sustained stress. The total sustained stress is compared to Sh – the maximum allowable stress at temperature. Again, this allowable stress (Sh) is a fraction of the material yield stress. The B31.3 equation for sustained stresses (from Code Case 178) is slightly different but it accomplishes the same thing.

Note that shear stresses are not often the primary concern in piping systems. However when shear stress IS the limiting factor the ASME B31 Codes provide adequate limits for its evaluation (e.g., B31.1 Paragraph 102.3.1 (B)).

All the above is my opinion and not that of ASME International or any ASME Code Committee.

Regards, John.

Hello John,

I am grateful for the detailed explanation. The question was a result of comparing text book explanation to code requirements. But you actually hits it on the head.

Many Regards

John

Regarding longitudinal stresses due to internal pressure... am I correct to assume its due to the unbalanced pressure forces in the piping system

Regards

Hello sri_idea,

The longitudinal stresses due to pressure (P * Do) / (4 * t) are tensile stresses in the longitudinal direction caused by the impingement of the pressure loads upon the piping at the changes in direction at opposing ends of the pipe section at issue. This is a sustained static loading stress. As long as the pipe wall is uninterrupted in the section at issue, the forces are opposite and equal and equilibrium is maintained (the opposing forces "cancel" each other). If there were a bellows element in the section of pipe (that did not have “tie-bars”), the opposing forces would act to pull the bellow element apart from end to end. In this case, the bellows element would have to be protected from the pressure forces.

Regards, John

hello John breen,

I m slightly confused by ur reply.

“Do the ASME B31 Codes use the Tresca failure criteria for combining calculated principal stresses?”. And the answer to that is yes.

I m of the opinion that B31.1 code use the Rankine (max. principal stress) failure criteria.

Please let me know if B31 codes highlight this point in any of its paras.

Hello RSP,

Yes, I agree. Regrettably, I wrote a confusing (confused) answer. It is important in such discussions to define terms and keep them straight. So, in the interest of brevity I would refer Mucour to the discussion of principal stresses (normal to principal planes), principal planes, shear stresses, unit cubes and combinations of triaxial and shear stresses that is to be found in "Design of Welded Structures" by Blodgett (the Lincoln Arc Welding Foundation). Another excellent reference is Chapter 8 of the book "Steam" by the Babcock and Wilcox Company. These references graphically show applications of the various failure theories in context with how we generally would use them for stress analysis.

The B31 Codes provide protection for various modes of failure. Therefore, various failure theories are used. Primarily, the equations for combining stresses that we are most familiar with use the maximum principal stress failure theory which states that if ANY one of the three principal stresses exceed the yield strength of the material a failure will occur. This theory is the easiest to apply and when used with an appropriate factor of safety it provides a good level of design margin. So, we have an equation (or set of equations) that combine(s) the stresses resulting from bending and torsional moments to determine the greatest principal stress(es).

The exception is found in the B31.3 high pressure chapter where the equation for calculating minimum wall thickness is a Hubert - Von Mises – Hencky derivation. There is a footnote that identifies this methodology in B31.3 but that is the only case that I know of where we have actually identified the evaluation methodology.

Shear is not commonly the limiting or controlling factor in the analysis of stress in piping. The Code provides protection in the cited paragraph such that when shear is the controlling factor the limit is predictable. When the maximum shear stress exceeds one half of the material yield strength at temperature failure is predicted. This sets the limit for shear stress. This is an application of the Tresca theory of failure.

The point that I was trying in haste to make (kids, don't try this at home) was that various theories of failure are used by the B31 Codes to address various modes of failure. While the Tresca and von Mises failure theories are more accurate for predicting failure of ductile material they were judged to be too cumbersome to apply for general application in the B31 Codes. In more rigorous analyses (e.g., in design by analysis applications in nuclear class 1) the Codes do use Tresca maximum shear theory to evaluate combined stresses.

I hope that is somewhat less confusing.

Regards, John.