It helps some, but you don't provide enough information as to the application (low temperature service conditions) and weld joint detail. ASTM A 588 is considered a high stregnth low alloy steel that is supplied in Grade A or Grade B. From my reference material, it looks like a 70 Ksi min UTS (ultimate tensile strength) and 50 Ksi YS (yield strength) for both Grades.
The ASTM A 572 is high stregnth low alloy (HSLA) steel and also comes in various Grades based on yield strength. What you reported as 50 Ksi would fall under a Grade 50, with a min UTS of 65 Ksi.
Ok. If you need to perform a post weld heat treatment(PWHT) be aware that it may result in degraded toughness properties in the heat affected zone of the A 588 and A 572 base materials adjacent to the weld region (this would apply only to low temperature service).
What is the thickness of the rolled beam and weld joint configuration or detail? My suggestion is to use the SMAW process with an E 7018 H4 electrode for welding these materials. Watch you heat input and follow AWS D1.1 recommendations for suggested preheat.