IBC 2308.8.2 states a rule of not notching more than 1/6 the depth of a wooden joist (emphasis added):
Framing details. Joists shall be supported laterally at the ends and at each support by solid blocking except where the ends of the joists are nailed to a header, band or rim joist or to an adjoining stud or by other means. Solid blocking shall not be less than 2 inches (51 mm) in thickness and the full depth of the joist. Notches on the ends of joists shall not exceed one-fourth the joist depth. Holes bored in joists shall not be within 2 inches (51 mm) of the top or bottom of the joist, and the diameter of any such hole shall not exceed one-third the depth of the joist. Notches in the top or bottom of joists shall not exceed one-sixth the depth and shall not be located in the middle third of the span.
Would it be acceptable to notch a joist more than 1/6th of the depth if adding a steel plate or sistered wood beam (going the full length) or some other method (short of putting a column in the middle)? I need to cut about 2.5" out of a 9.5"-deep beam to get an HVAC duct through.
The joist is between the basement and first floor. Above is, I believe, the living room.
The joist spans 10'.