The rebar on the beam is in interesting contraption. It is using the rebar as a tension spring, not as a structural member.
When a beam sags 3", the bottom edge elongates by about 1/8" (the top edge compresses a little bit less than that). So the purpose of the rebar would be to prevent that elongation, and hence prevent sag.
A quick calculation shows that it takes roughly 3000 lbs of tensile force to elongate a 1/2" round x 19 foot bar 1/8 of an inch.
I'm not exactly sure what this means... I can't quite figure how the vertical force of gravity correlates with the horizontal tension force on the rebar. Does anyone know if there are leverage ratios to take into account?
If not, then the rebar is kind of useless. A 2x12 by itself (typical Conifer tree like pine or douglas fir, 1100ksi modulus of elasticity), requires 15000 lbs of force to sag 3". Much more than it what it takes to stretch that wimpy piece of rebar.