I use Shen in an very Aggressive manner, and have played him lots and now it works.
I have two different builds with him. One Hard tank, that is how I almost awlays use him.
But if we have already have one Hard tank, and maybe one support champ. I pick one a bit more offensive build.

BUILD 1
Shen is one of few champs that I think synergize well with warmogs. With his Feint, he get quite hard to get down, and top of that his passive makes warmogs very viable, and with it, u get some kills early one if your opponent isnt careful. Sunfire cape, ecxept is synergize well with your taunt, makes your passive more lethal. After that, just plain survival items have been chosen, as often, your Vorpal Blade, passive and Sunfire is enough to help
damage. It can be quite painful to chase Shen, if he has low health late game, as he heals upp lots of health and have some skills that can easily trap the chaser.

BUILD 2
Is a bit more offensive build with some surviveabilty. I have just tested it some times, and cant garantee success yet, but have been quite fun when, my feint ends and the hexdrinker start and finnaly my opponent thinks im dead for sure and my Veil restart....and then feint again =). I would very much had Force of nature instead of Banshee, but i dont think it synergize as well. Thought about if u have problem cathing people, Hexdrinker can be replaed with Rylais, as it syergizing some with Shen.

BUILD 3
Some say AP Shen is Awesome. Moste say it is ****. I have never seens one, or played.
This is my contribution. The Sunfire cape I thinks is nice choice on him anyways (on paper) as it help surviveabilty, damage, Passive and farming. Rylais is given, Health, AP and Vorpal blade slow. Rabadons,a must. I think I prefers zhonyas over abyssal, because it can get u time to CD your skills, and the armour to use with taunt seems a must. Lich bane on the other hand. Maybe, maybe not. Could work. I took it instead of abyssal as it gives Some MR, and AP and maybe can be used nicely with his passive. Taunt, Hit (passive, Autoattack, Lichbane, Sunfire) And the vorpal blade.

Maybe Shoes, Rabadons, 3 rylais and Lichbane would be better for that. His passive gets buffed some then.

BUILD 4
I did what I said above, and statwise i didnt get so much better. Some more ap, and health but lose a lot else.

Ofc U can do an AP shen with mejai and all out ap, and come out nearly 600 ap, but i want him able to take some punshes, and it feels like I want to synergize Lichbane with him. Must Try it soon.