I am assigning custom interior wall. Is there an easier way to assign the construction to the "Outside Boundary Condition Object" since it is the same wall type?

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If I'm understanding correctly, you are using a default construction for most of your interior wall constructions, but you some interior wall constructions that you want to hard assign a custom construction for. Looking at the screenshots below. Initially all of the constructions were inherited from construction sets so they showed up as "green".

I then dragged a custom construction to the wall in "Perimeter_ZN2" that happens to be adjacent to a wall in "Perimeter_ZN1". Notice how when I did that, the construction in "Perimeter_ZN1" changed it's construction but still shows as inherited. I think that is the behavior you are looking for so you don't have to assign the construction twice.

As a side note, if there is a logic to where you area adding custom construction you have some additional options.

1. If you want to apply a custom interior wall to all interior walls on a specific building story, you can custom construction set with only interior wall construction and assign it to a specific building story object.
2. If you have a specific space type like X-ray that you want to assign a custom wall construction to you can create a custom construction set as described in option 1 and assign it to a specific space type used in your model.
3. Lastly you can also assign a custom construction set to a specific space.

The approach described above is typically used for attics, and when modeling plenum zones or raised floors as their own thermal zones.