The chest, triceps, and shoulder should be trained together in a split routine to help eliminate the risk of over training. Exercises such as the bench press, targets primarily the chest, but will also recruit the triceps and anterior aspect of the shoulders, which is why it is important to train them on the same day rather than on different days in a traditional split.
Bench Press (5X5) or (5,3,1,3,5)
The bench press is one of the most effective exercises at developing upper body strength. This exercise should be performed in the lower repetition range to help develop strength that can be transferred into all other exercises.
The Incline Bench Press (3X10)
The incline bench press is an effective exercise at developing the upper pectoral muscles, while improving strength through the triceps and shoulders as well.
Perform dips on the parallel bars while leaning slightly forward to effectively target the chest. Dips are one of my favorite exercises as you can really feel the tension through the entire muscle as well as in the triceps. Dips are also useful at targeting the deltoid muscles.
Flat Bench Dumbbell Flies (3X12)
Finish off the chest routine with a fly to isolate the chest muscles.
Overhead Barbell Press (3X10)
This exercise is great for developing strength through the shoulders as well as the triceps.
For this part of the workout I will alternate performing a shoulder isolating movement with a triceps alternating movement wth no rest in between. This type of routine is useful to keep the heart rate up while also allowing enough rest time between sets of an exercise.
Bar Upright Rows/ Cable Triceps Extensions (3X10)
Perform one set of barbell upright rows for 10 repetitions and immediately move to the cable triceps push down for 10 repetitions. Repeat this for three sets
Dumbbell Lateral Raise/ Lying Triceps Extensions (3X10)
Perform 10 repetitions of one arm dumbbell lateral raises (10 per side), then immediately lie down on a flat bench and perform dumbbell triceps extensions. Repeat this process for 3 sets
Dumbbell Front Raise/ One-Arm Overhead Extensions (3X10)
Perform 10 repetitions of dumbbell front raises for 10 repetitions, immediately followed by one arm overhead triceps extensions. Repeat this for 3 sets.
This workout should provide you with strength gains, muscle gains, as well as cardiovascular system training with the superset. For the shoulder and triceps section of the workout I will often substitute the exercises out for different ones from week to week to keep the workout fresh and exciting.