Broken pivot stud on Hinge

This looks like the arm of a casement window hinge. If this breaks or comes off, I'm afraid the entire hinge needs to be replaced. See if the 36-048 matches with what you have. 

I'm actually still pretty confident the 36-048 is what you need, though without seeing the base bar or track in the window sill that these two connect to I can't confirm the exact size. We see some variations in the size of these two connecting bars with a hinge set; what matters most is the size of the bar that connects to the window sill, which for the 36-048 is 10". Sometimes this can be a bit smaller, at 8", but we still typically recommend the 36-048; so long as both hinges in the window are replaced, it should work. Please see if you can find that base bar or track to compare. The only other possibility that immediately comes to mind is the 36-049 14" Hinge.