Liberal Allowable Stress Range

Perhaps it would be of some benefit to review the meaning of the term “Liberal allowable stress range”.

First of all, this is not a term that is used by the ASME B31 Pressure Piping Codes.

Caesar II (C2) uses the term as a sort of “short-hand” for referring to the increase in thermal (displacement) allowable stress range that is allowed in B31.1 [paragraph 102.3.2(D)] and B31.3 [paragraph 302.3.5(d)].

In these paragraphs, the B31 Codes allow the positive difference between the calculated combined longitudinal stresses (due to weight, bending and longitudinal pressure) and the maximum allowable stress, Sh, to be added to the term “0.25 Sh” (the second term) in the equation for calculating the maximum allowable stress range, SA.

The B31 Codes say that it “MAY” be added into the “0.25Sh” term, thereby making it optional. If the analyst elects to ignore the additional allowable stress range the decision (all other things being equal) would be judged conservative. If the analyst elect to employ this additional allowable stress range, the resulting allowable stress range is sometimes termed “liberal”. It is, of course, all semantics.

The Code allows the additional allowable stress range for a very good reason.

The concept underlying this rule is very well described in the famous book by S.W. Spielvogle (Piping Stress Calculations Simplified, Fifth Edition, 1955). Spielvogle explains that the B31 rules intend for the 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 (cold) 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 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).

But the Code uses 1.0Sh for the sustained loadings of weight and longitudinal pressure and this leaves 1.25*Sc + 0.25*Sh for the allowable thermal expansion (displacement) stress range (but you wondered where that came from). Because the Code intends for the entire strength of the material (from hot yield to cold yield) to be used (except for the “adjustment” made for vagaries), it follows that the rule in the 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.

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.

So, one might ask, why would an analyst opt to not use the “liberal” allowable stress range for comparison to calculated expansion (displacement) stress range?

This is an engineering judgement. For example, if the sustained stresses were calculated as 80 or 90 percent of Sh and the system were operated in the material’s creep range, the designer might want to take the conservative decision to not use the “liberal” allowable stress range when evaluating thermal (displacement) stress ranges. Another example might be offered as a case when the system is in severe cyclic service (see B31.3 paragraph 300.2 for the definition) and the designer is looking for a longer fatigue life.

Going the “conservative” route might also appeal to the designer (or owner) if the system would be operating within the pressure/temperature variations described in paragraph 302.2.4 in B31.3 or paragraph 102.2.4 in B31.1. If we have some degree of uncertainty, we employ an additional measure of conservatism. As the saying goes, “when in doubt, build it stout”.

Thank you for bringing up the topic for discussion. Good luck with your projects.

Of course, all the above is just my opinion and does not reflect the opinion of ASME or any Code Committee.

[This message has been edited by John Breen. Edited September 28, 2000]

- From COADE Caesar II Blog "Discussion Forum"