Expansion Allowable Stress SA

Hello,

I have some questions regarding SA- expansion allowable stress.

1. The code (B31.1) provides two formulas Eq.1A and Eq.1B to calculate SA. Sometime the results from these two formulas are quite different, normally which one should be used for expansion (or displacement) stress reange verification?

2. Some people say that Eq.1A is for expansion (or displacement) stress range calculation and Eq.1B is for operating loads (expansion loads + sustained loads) calculation, Is that right? or the old codes were required this way?

Carter

1) Both are correct. The paragraph between equations 1A and 1B indicates S_A may be calculated either way.

2. No. To the best of my knowledge, the B31 codes have always taken the simplified approach in use today.

The relevant code requirements are S_E <= S_A & S_L <= S_h.

But you could rewrite the first design equation with S_A = Eq 1A and S_A_liberal = Eq 1B.

S_E <= S_A_liberal
S_E <= S_A + (S_H - S_L)
S_E + S_L <= S_A + S_H

But you still have to make sure S_L <= S_H. Having a low displacement stress range doesn't give you any more margin against gravity (or pressure).

If you take Eq 1B:

Sa = f( 1.25Sc + 1.25Sh - Sl )

and rearrange it, you have this:

Sa = f( 1.25Sc + 0.25Sh + [Sh - Sl] )

The first part of this equation (in red) matches Eq 1A. The second part of this equation (in blue) can be considered as the "unused allowable left over from the Primary (sustained) case".

In c2, we refer to Eq 1B as the "liberal allowable", since this equation will give you a higher allowable stress than Eq 1A. To put numbers to these equations, assume both Sc and Sh are 20000, then Eq 1B can range from:

Sa_max = 1.25*20000 + 1.25*20000 = 50000 (when Sl approaches zero)

to

Sa_min = 1.25*20000 + 0.25*20000 = 30000 (when Sl approaches Sh)

Note that Sa_min is Eq 1A.

Thank you for your detail explanations.

So using Eq. 1B as expansion allowable stress envelops these two equations.

Carter