I am sorry, how is this supposed to help. I google ASME section II and found nothing useful. Am I missing something? If anyone knows the values or can give a good resource I would really appreciate it.
I am sorry if I am not specific enough, I unfortunately dont know much about this kind of thing. Anyways, all I really know is that we have 1" OD steel tubing with 1/8" wall thickness and I was told that it is ASTM A513-07.
Whoever told you that you can find material properties from that spec is mistaken. The spec covers multiple alloys and governs the geometric manufacturing properties of tubes more specifically "Standard Specification for Electric-Resistance-Welded Carbon and Alloy Steel Mechanical Tubing."
There is a table in the back of the spec that covers approximately 15 alloys having varying properties. You need to find out the exact alloy used to make the tube you have. I have attached a snippet of the total table that gives the varying alloy requirements. Hopefully since it is only a single page there won't be any issues with copyright stuff.
I might try looking in the MMPDS or MIL-HDBK-5J to see if the specific alloy you're looking for is in there. Both publications are a strong resource for a limited number of steel, alumuinum, magnesium, and titanium alloys.