In performing a detailed stress analysis of piping components or pipe support attachments (that is practically the relevant case of pipe support analysis), not only the induced stress origin (e.g. Sustained/Primary, Secondary/Expansion etc.) is to be considered, but also the stress types should be taken into account - meaning Membrane Type / General (Pm) or Local Membrane (Pl, Pb), Secondary Type (Q = meaning LOCAL BENDING due to discontinuity effects), Peak Type (F = due to local discontinuities with relevance for Fatigue Failure).

For Connected Equipment Nozzles and welded Pipe Support Attachments, it appears indeed that the relatively recent editions (e.g. post-2007) of ASME Codes (both VIII-2 and III-1 NB/NC) brought supplementary provisions that mainly require to include piping restrained thermal expansion loadings (and the assimilated ones with externally imposed movements) within PRIMARY Stress category.
This means an additional conservative requirement to include the external piping loads induced by restrained thermal expansion in the Primary Loads when Pm (General Membrane) and Pm+Pl/ Pm+Pb (Local Membrane) stresses are to be qualified.

However, to go further and to qualify the resultant Operating (P+W+T) stresses as B31 Sustained ones (e.g. against Material Basic Allowable Stress), either for a piping component (spool, elbow, intersection) or for a welded attachment (trunnion), definitely would mean an unrealistic approach.

B31 Codes do not include General Membrane (Pm), Local Membrane (Pm+Pl, Pm+Pb) and Secondary (Q) stress categories, as are defined by ASME VIII-2 and III-1 NB/NC Codes.
B31 Sustained Stresses are evaluated using Stress Indexes, which are established by limit load analysis and are not identical with Primary Stress Concentration Factors. Besides Sustained Stresses, the Displacement Stress Ranges (EXP) may be considered as Peak (e.g. Pm+Pl+Q+F) Stresses directly. B31 Codes do not include Secondary Stress (Pm+Pl+Q) concept.
The resultant stress limitation Pm+Pl+Q+F <= Sa, as provided by ASME VIII-2 Part 5, might be considered similar to B31 Displacement Stress Limitation SE <= SA = f*{1.25*(Sh+Sc) - SL}, which might be written as SE+SL <= f*1.25 * (Sh+Sc). In such case, ASME VIII-2 "Sa" would be similar to f*1.25*(Sh+Sc) stress limit and "SE+SL" overall effective stress might be seen as "Pm+Pl+Q+F" overall Peak stress. Of course, there are some inadvertances regarding B31 SIFs employment, which are 50% from the overall ASME VIII-2 Stress Concentration Factors, but this is another discussion...

The point is that when Stress Concentration Effects in Piping Systems are to be analyzed accurately (meaning pipe fittings - e.g. intersections, equipment nozzles or pipe support attachments), B31 Codes' equations and stress categories are not sufficient and therefore more refined concepts and methods are required - such those provided by ASME VIII-2 Part 5 or ASME III-1 NB-3200.

But such detailed assessments are required only for non-typical circumstances - such as Fitness for Service (FFS) assessments, for instance.
In my opinion, there is no need to consider B31 (31.3, 31.1) Codes as inappropriate or insufficiently safe/accurate any more. When piping layout is correctly designed and the system is well-balanced, B31 Codes equations ensures a safe and proper design.
Regarding Pipe Support design (e.g. welded attachments analysis), there are several specific design methods validated by common engineering practice: Kellogg Line Method, ASME III-1 Non-Mandatory Appendix Y-1000/2000/3000 (that are former ASME Nuclear Code Cases N-318,391,392), WRC-107 etc.

As final argument, I would bring into discussion the initial problem I found unacceptable in my previous comment:
<< For eg, for SS pipe, if we have temp drop of 100C between two anchors in straight length configuration, stress will be E*alpha*DT i.e. 2E6*0.018/1000*100 = 3600 kg/cm^2 .. which can cause primary failures in weld.>>

Sam still might disagree or dislike it, but...such design is WRONG, does not match the most elementary requirements of flexibility and safe design and is definitely AGAINST B31 Code Design Philosophy.
Please remember B31.3 Para. 319.2.3 statement:
<system....>>.

LOCAL YIELDING is definitely out of discussion when we deal with an uniform compression load that induces axial compression stress exceeding significantly material Yield Limit. In such case, piping fails by general material yielding (collapse) overall pipe section. Under such circumstances, we cannot check SE against SA any more, there is no basis for that any more!

When B31 Code mentions LOCAL YIELDING, the BENDING loadings are specifically regarded. This means to design the layout by including lateral offsets for thermal growth "compensation".

There is no excuse to restrain piping axial thermal growth by subsequent anchors on same straight pipe run (buried pipelines are excluded in this discussion). In case of axial vibration susceptibility, the layout should be changed by providing offets/loops that would allow intermediate stops, or to provide SNUBBERS (NOT Rigid Struts!) that would allow thermal expansion growth but would lock sudden chocks or vibratory movements.