[Rick TYler]

It would be better to describe the piece you want and then ask how to make it. Attaching a 4x4 end-to-end with a 2x4 is almost certainly the wrong answer to the question. If -- for example -- you really wanted a 12-foot-long arm with a 4-foot 4x4 section and an 8-foot 2x4 section, I would suggest that you make the arm up from a 12-foot 2x4 with a 4-foot section of 1x4 laminated onto each side of the butt of the arm using yellow glue and a some #8 2-1/2" screws to hold things together while the glue cures. Then, you won't be compromising on the strongest part of a wood laminate structure, which is its long fibers running longitudinally. Given the nature of a treb, I would strongly consider getting the nicest possible board for your arm. A clear piece of southern yellow pine or CVG Douglas fir would be good. Avoid anything with big growth rings or lots of knots.

Have you considered using an arm that is thinner and deeper? You could make a really nice, stiff arm out of some 3/4" plywood strips 8-inches wide and laminated with carpenter's glue. Stiffness increases hugely (the 4th power?) with thickness, and the deeper (higher) your arm, the stiffer it is.

Can you post a sketch?