AP Shen is a build that is severely underestimated, and does not see much play. His shield and Ult scale off of AP, so even without considering the damage boosts, the AP adds great tankiness for you and whomever you chose to Ult to. This build is meant to have above average damage while still maintaining the tank status. Depending on your lane opponent, there is always some room for movement.

Liandry's Torment and RCS give good synergy and damage together, and they also give a decent amount of health. This helps make his passive stronger, as it scales off of bonus health. If the situation is right, e.g. A Zed on the enemy team, getting a Zhonya's and Merc Treads would be a optimal idea, rather than Tabi and Abyssal Scepter. Void staff and Deathcap are self explanatory. Starting Doran's Shield gives you more health, which makes CS with your passive easier. Ever since the buff to tank junglers, it is a very good idea to get Liandrys Torment as soon as possible (if they have a tank jungler), as the damage penetration will have much more utility than straight AP, as your ratios are not ridiculous. With the ridiculous power in the Cinderhulk jungle enchantment, it is not a bad idea to take smite and go skirmishers.

Go AP Quints, Magic Pen Marks, Magic Resist glyphs, and Armor Seals. This gives you extra damage, but still great survivability. The main idea with this build is to turn a tank into a massive damage dealer, but his innate survivability with the Seals and Glyphs will make you very hard to kill. Move Speed Quints are also a decent option.

Get 9/21/0 on the AP side of the Offense tree. It is just the most logical option. Sticking to the logic above, it gives great survivability and gives some essential offensive stats, like CDR and a 5% AP Boost.

Flash is almost always essential, so that is an obvious pick. Normally a top laner would take Teleport, and that is an option, but Shen already has a "Teleport" in his Ultimate, so taking ignite is a great option for extra kill power. With Cinderhulk's ridiculous power, it is not a bad idea to take smite top for both cinderhulk and extra dueling potential (Skirmisher's)

Shen is immortal when built as a tank, so when built offensively, such as this build, he does damage while still not dying. His Q gives him great sustain in lane, and his passive is great for CS. Unfortunately, until you get LT and the Crystal Scepter, you won't be dealing any massive damage.

Make sure to be constantly watching the map to see if anyone could use a quick Ultimate for a 2v1, or to turn a gank into a 2v2. Shen is a champion whose most useful asset comes from map awareness, so if you do not look to see if there is an Ultimate opportunity, you will be somewhat isolated from your team. In the recent patch, Shen's ultimate' cooldown was reduced. This allows you to use it much less sparingly, and if you use in the wrong situation, it is more forgiving.

I believe that this is a great build that is severely underestimated. All of Shen's skills scale off of AP and Bonus Health, of which there is much in this build. The ridiculous amount of shield strength that he has in his W and his Ultimate is crazy, and can save you and a teammate. Thanks for reading!
Sincerely,
DLFresh