Irv,
If your beam was precast concrete, there is a well-developed series of notched beam design procedures. The one you describe we call a dapped beam design. We reinforce with “hanger” steel that is vertical just behind the notch to make sure the entire depth of the beam participates in shear resistance as soon as it can; a horizontal rebar extends out of the extended end just above the notch to counter the moment developed in the extended end; and there is horizontal and vertical steel developed in the extended end in case the shear there exceeds the concrete capacity, as you mention for the described condition.
HTH,
Jim Getaz
Precast Concrete Engineer