I'm installing a range hood over my island after a kitchen remodel and I ran into an issue. If I try to run the ducting alongside the joists in the ceiling I run into a beam which looks to be supporting the sunroom which extends beyond the kitchen. I've included a picture of the kitchen layout below with an annotation showing the location and direction of the beam and an illustration of the direction of the joists (not to scale). To be clear there is a second floor above this one so I can't just go out the roof.
The beam and joists are 14" deep. I am concerned about drilling a 6" hole in the beam and perhaps a second one which is behind it. Is that acceptable? The range hood I have will not accommodate any reduction in diameter. The beam appears to be solid wood and a picture is shown below (looking down the hole in the ceiling along the joists.
An alternative route is for me to go a shorter distance through the joists and out the side of the house. The joists are engineered wood TJI 230 14". Now according to the manufacturer, I can drill a 6" hole through the web no problem since I am far enough from the ends and there are no other substantial holes in the ones I've looked at so far. My only concern here is that contrary to what I am reading from the manufacturer, everyone seems to be telling me that I shouldn't make a hole any greater than 1/3rd the depth of the joist, and that if I do that I need to re-enforce the hole. But I don't see this mentioned anywhere in the manufacturer's guidelines. By all indications it is perfectly acceptable to make a 6" hole in the joists.
Can anyone provide me feedback: am I okay going through the beam? Alternatively, can I go through the i-joists without re-enforcement? Does the 1/3rd rule not apply to engineered i-joists like this?