If my guitar had 9-42 in standard, will the tension be the same if I used 10-46 in Eb?

Or if I went from 9-42 in standard to 11-56 in drop c, will I have to make truss rod adjustments? I know I also have to adjust the action and intonation but what I'm mainly concerned about is the truss rod.
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#1 - No, It won't be. There will be small differences.

#2 - You might, depending on how much relief is in the neck right now. I don't think its likely that you will but its possible. Are you going to leave this guitar in Drop C with these strings or are you going to use this guitar for multiple tunings?
Always tin your strings.


Don't be afraid to be honest.
You can compromise with string sizes and tunings to keep from ajusting the truss rod but your never going to find the exact same amount of tention. You can get close and not have to worry about it bit it wont play as good as it can if you do ajust it. Hold down the 1st fret and one frett up from the body joint. When doing that the space from the Low E string from the middle fret should be about the thickness of your average thing pick. About .015 of and inch. I hope i explained that well and it helps.
No two string gauges will result in exactly the same tension when being tuned to different useful tunings. When changing gauges I would definitely check the nut for snagging, check the relief on the neck, and adjust the action if necessary/desired. I would never swap string gauges without doing so as you could be sacrificing performance, but if you swap them out and find no problems in the tuning you are using with your current set up leave it be.
9's in E to 11's in Drop C might need an adjustment of the truss rod.

9's in E to 10's in Eb will be pretty close in tension, but not the same.