The yield and tensile strength of the Code materials are subject to the thickness of pipe, heat treatment, welding, and others, and the Code allowable stress is subject to the yield/tensile strength ,as well as material itself.
Generally the yield/tensile strength of ticker pipe/plate is lower than thinner ones. Hence, piping stress engineer should be careful of the selection of proper allowable stress per the ASME B31.3. The pipes listed below will have different allowable values for each thinner and thicker pipe in the oil&gas and petrochemical projects typically.

-321 grade austenitic stainless pipe for high temp./press. hydrocarbon service
-P91 low alloy pipe for high temp./press. power/steam piping

Also the allowable stress for bolting material(bolt & nuts) are subject to the bolt diameter similarly.