I don't have the figures, but I did those calcs when building my crane. If I recall correctly, two 2x10s over a 12' span gave me more than 1.5 times the load support than I needed. I added in the upper 2x6 cross braces to shorten the span and boost the load carrying capacity of the beam. The cross braces also stiffened up structure and eliminated any lateral movement.
Obviously, finding clean, knot-free 2x10s for the beam is important. I also made sure I bolted the two 2x10s together at a couple points to make sure the whole thing functioned as on strong, semi-laminate.
I supposed you could, if you wanted, assemble the whole thing with screws, but I was more comfortable with carriage bolts for the important joints (e.g., beam to vertical supports). Carriage bolts are also pretty easy to remove when you want to take the thing down.