Is that like a 1"x1" square BEAM that is 9" long? I guess my coordinate system is confused by something that is wider than it is long.
Typically, you are looking for a thickness that is greater than 10% of the shorter aspect dimension before using solid elements, but this one is probably close enough considering the overall dimensions.
The real thought process is primarily how the structure will flex and probably how it is supported. If it is simply supported so that the end rotation is significant, you may want to try it with shells because brick elements are rotational rigid. If it is fixed on the ends, brick elements are likely more reasonable.
Since this is a fairly simple structure, I would get out a hand calculation and run a test. Build a model with bricks and one with shells. Simply support an end, or some other support scenario that Roark's has. Run both models, refine the mesh, run them again and see which one comes closer to the hand calculation.
What software are you using and how is your beam supported?