TABLE A-1 ASME B31.3

Have a look at paragraph 302.3.2(d) Bases for Design Stress - Other Materials

(d) Other Materials. Basic allowable stress values at
temperature for materials other than bolting materials,
cast iron, and malleable iron shall not exceed the lowest
of the following:
(1) the lower of one-third of ST and one-third of
tensile strength at temperature
(2) except as provided in (3) below, the lower of
two-thirds of SY and two-thirds of yield strength at
temperature
(3) for austenitic stainless steels and nickel alloys
having similar stress–strain behavior, the lower of twothirds
of SY and 90% of yield strength at temperature
[see (e) below]
(4) 100% of the average stress for a creep rate of
0.01% per 1 000 h
(5) 67% of the average stress for rupture at the end
of 100 000 h
(6) 80% of the minimum stress for rupture at the
end of 100 000 h
(7) for structural grade materials, the basic allowable
stress shall be 0.92 times the lowest value determined
in paras. 302.3.2(d)(1) through (6)
In the application of these criteria, the yield strength
at room temperature is considered to be SYRY and the
tensile strength at room temperature is considered to be
1.1STRT.

For ASME B31.3, there are ready made Table A-1 which indicates directly the allowable tensile strength S of the specified pipe material at its design pressure.

See the example here for application of ASME B31.1.

And see the CR4 Threads:

• Pipe minimum allowable thickness, In service pipe thickness limits

• Schedule of pipe.

• Maximum Wall Thickness for Seamless Pipe

• Significance of "-Mill Tolerance" in the Piping Stress Analysis

• Pipe Wall Thickness.

• PIPE WALL THICKNESS CACULATION

• High Pressure Steam Pipe

• In service pipe thickness limits

Use the allowable stresses for basic designs. Anything above allowable stress needs to be evaluated on a case by case basis by engineering.

I had a design that would clearly fail under allowable stresses from ASME Section II so we chose to remain under yield strength. This was because our design was a temporary design for secondary pressure containment. If the gage in the design noticed pressure then the unit shuts down to replace our structure. Allowable tends to use safety factors to compensate for unknown stresses that may be induced.