I think Shen just needs to have his ratio's changed on a lot of his abilities. Ap bruiser itemization just doesn't really work for him, since he has no mana. He is supposed to stack health so that he can tank and to do more damage with his passive. However his other abilities all scale off ap which is really just an outdated remnant from when all abilities scaled with ap.
This is where I get the confusion on what I should build to do semi relevant damage while tanking.
- His passive scales off health, so to make that do more damage I want to buy health.
- To make his passive trigger faster I need attack speed to attack faster.
- I want to have his shield up to make his passive even more consistent, however without any ap the shield will rarely last long enough to get 2 let alone 1 aa off. So I need to build ap.
- My q scales with ap as well so building ap will allow me to have a damage source besides my passive, So I should build ap.
So let's look at what itemization falls into Shen's priorities:
Rod of Ages: This has the health and ability power that Shen needs! But wasted money on the mana, which makes this a worthless item for him.
Trinity force: With a bit of health, some attack speed and ability power this item tends to be Shen's only option for a damage item that compliments his kit. There is mana on this item which lowers it's efficiency for Shen, but he'll take what he can get.
Rylai's crystal scepter: This is a nice item for Shen giving him some health for his passive and to make him hit a bit harder. Some of the power budget is pushed into the passive, but with Shen's inability to really stick to his opponent this is a worthwhile buy. This won't make Shen too intimidating alone though, as the damage bump is fairly low.
Liandries: This item has health and ap for Shen... but other than that this item is not very efficient as Shen can't make much use of the passive. Unless the enemy team is all fairly tanky.
Those are the only items that really help Shen out in bumping his damage up overall for his kit. Honorable mentions to Sunfire Cape.
Now the new Randuin's looks AMAZING for Shen. Giving him a chunk of health, a slow AND an AS steroid to help him with his Passive. So maybe that's all he needs. Idk I wish his shield or q scaled off health so that he wouldn't be as awkward to build. But that's just me. I love Shen though, really cool and fun champ to play, he just feels outdated.