I'm finishing a kitchen remodel and have to install a downdraft vent. The best place to install the vent to the outside is through the basement. Naturally the best place to cut the 6-inch hole through the floor lands directly on top of a floor joist 2x10. The house is 15 years old. The floor joists are 16 inch on center. There is a steel beam running perpendicular to the floor joist & through the center of the house (2-floor cape cod).

Is it structurally sound to cut the floor joist and box around it to the joists on either side of the cut joist? I'm thinking something like the picture in the link below (scroll down to bottom of page for last drawing).

http://www.rd.com/familyhandyman/content/18251/

If this is OK is there a better way to do it?

thanks..