Still trying to get my head around your schedule! But I'd suggest maybe doing your first session straight after your first shift at work (hopefully before you go to bed and before working nights starts to affect you too much, then do your next session on your second day off (2 days later), and then your third session 2 days after that again if you aren't too knackered! (Basically a 1 on-2 off split).
Because time and energy is obviously a concern I would advise (and not just because I do it!) a HIT style session. The longer you're in the gym, the harder it's gonna be to get through it.
I'd make your 2 hardest sessions the first 2 seeing as your third session will be when you've worked 2 nights on the trot.
Maybe: Session 1 - Legs & Back
Session 2 - Chest and shoulders
Session 3 - Arms and abs
This way hopefully you'll have done the harder sessions before the week takes it's toll on you.
Aim for 3 -4 exercises for the bigger muscles (i.e. the first 2 sessions) and then 2 -3 for your 3rd session.
2 working sets for each exercise and aim for 6 - 8 reps.
To be honest, a lot of it will depend on how you feel on the day. I'm working a lot myself a the mo so have to adjust my schedule by bringin a session forward a day or pushing it back a day depending on how I feel.
As for cardio - personally my cardio is the mile run back from dropping my little girl at school, and it may be convenient for you to do something like that in your daily routine rather than have to devote a session to it when it could be spent hitting the weights.
On top of this make sure you get as much sleep as poss ( on all days when you train when you're working nights, I personally would rather train before going to bed rather than when I wake up but that may be up to you!) and keep up taking in the right amount of calories/protein/carbs, etc.
Don't know if this is what you were looking for but good luck anyway!
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