Giovanni,
good point.
Problem is, that 'St 37' is no more available being referred to as 'St 37'.
DIN 17100 was the German Standard containing 'St 37' as a 'Steel for general structural purposes'.
It was replaced by the European Standard EN 10025 already in 1994.
The product range however was valid for bars, wire rod, flat products (strip, plate, wide flats) seamless and welded, square and rectangular hollow sections, forgings and semi-finished products (reference:
http://www.e-pipe.co.kr/DIN/17100.htm).
The question would be which 'equivalent' is meant by 'equivalent'.
I have used to use the 'compositional' equivalent as this is the one what's being used for estimating the 'weldability'.
In Germany we are going to limit the Carbon content for 'weldable' steels without using any further precautions (e. g. preheating) at 0.22 wt%.
'S 235 JRG2' (according EN 10025) has limited, i.e. maximum C-contents of 0.17 wt% (except t > 40 mm having a max. C content of 0.20 wt%) and Phosphorus and Sulfur contents of 0.035 wt% each.
In particular the C-content was the reason for me to set ASTM A 283 M as the 'equivalent' for an 'St 37' or even 'S 235 JR'.
This is - to the best of my knowledge - from the analytical side for an ASTM A 283 M-98 Grade B the 'most equivalent' composition in particular with regard to the Carbon content.
Carbon however, is higher with the 'A 36' as well as its P- and S-contents.
Also the Copper content is different between both steel grades.
Nevertheless I would fully agree with you as you say that 'A 36' has a more equivalent yield strength compared to the 'S 235 JR' (St 37).
'A 36' has a minimum yield strength of 36 ksi (~250 MPa) while 'S 235' has 235 MPa (~34 ksi). On the other hand however, 'A 36' has a tensile strength of 400 MPa - 550 MPa (~ 58... ~80 ksi). These values are above the 'S 235' (St 37) having tensile strengths of 360 - 510 MPa (~52... ~73 ksi).
These values are admittedly lower with the ASTM A 283 M. Nonetheless, it is listed in Germany to be the equivalent for an 'S 235 JR' plate.
Anyhow, as well-known you are the most experienced and appreciated expert in this field. As you mean that 'A 36' would be more 'equivalent' I would recommend to 'miggun' to follow your recommendation.
Thank you and regards,
Stephan