Following your routine, you are working a standard split-training program. This is the training of a single body part/area eg legs, shoulders etc. on a single day, allowing a week for recovery and retraining the body part the week after. This type of program can be very robust and has been the mainstay of resistance training routines for decades.
I would recommend a good book to reassure you, The encyclopedia of Modern Bodybuilding by none other than Arnold Schwarzenegger. Its a classic yes, but it has a lot of information on basic split training, and then as you progress, it has different routines and advanced training methods. You say you are starting out - so I seriously recommend this resource. Its not about making you like Arnie, but it will give you a solid understanding of the basics and how to progressively change and improve your training.
To pick up on a point, you say:
I work in kind of a circuit fashion for 40-60 min each day(until I'm totally exhausted)
Now, there are different types of exhaustion. Roughly speaking muscle, tendon or cardio exhaustion, and you reach these all by very different mechanisms, and this has an impact on how you train, how you recover, and how you grow. For example - you may be doing very high reps (20's) with a light to moderate weight and having short rest periods. This will lead you towards cardio exhaustion with the weights, but not necessarily muscular exhaustion, or even hypertrophy, which is what you want to be able to hit with your training if you want to grow muscle. This is commonly assumed to be achieved by using 50-75% of your 1RM weight, with 8-12 reps per set.
I'm going to avoid giving more advanced information here as there are too many variables to consider e.g. how often can you train?, what are your ultimate goals?, how do you eat? etc.
That said, I think you can reorganise your training to be more effective. Personally I would do this (also doubling abs work):
- legs/abs
- Chest
- Shoulders
- Arms/abs
- Back
- Compound day/Olympic day/Functional day (your choice)
Comp = big movements, more than one muscle group
Olympic = Olympic lifts
Functional = Sport specific
Then for the next step, when you are 6 months in and strong - look at doing double split training, i.e. body part trained twice per week:
- Legs/abs
- Chest and Arms
- Back and Shoulders
- Legs/abs
- Chest and Arms
- Back and Shoulders
There are many other techniques that are more advanced, e.g. super-setting, antagonistic training, forced reps etc. etc. but they are all for another day. Seriously, don't run before you can walk or you will get injured and not be able to train at all.
Use Arnie's book as I say. A great place to start for information, and good luck with your training.