I happened to stumble on this question posted here by someone a long time ago, regarding how to calculate the βw for UNEQUAL LEG angles in major principal axis bending. The βw values are tabulated in the AISC Steel Manual Commentary for some common angles. But for those who wants to know how to calculate it from scratch for any angle size, plz take a look at these slides posted at slideshare.com
Regards!
Regards!