I find myself doing only 23k-26k as a prot warrior in raids, significantly behind other tanks i see. Are prot warriors just generally low dps?
Looking at logs for the higher end guilds, i see warriors doing 50k+ and i have no idea why.
In that one for example... your Shield Slam damage is really, really low. In part it's because you don't keep Shield Block up, but it looks too that you don't use it on CD. Revenge seems too low too, and devastate too high. Fix that, get some more hit/exp and you are mostly done. Grab Dragon Roar and use it on CD, you had shockwave and used it 3 times.
PD: There are too many Heroic Strikes in there too. If you are going to spend rage on damage, better do it on Execute. I don't think HS it's worth it.
You should be able to burst up to 70k dps in raids and sustain somewhere between 40-50k in ilvl 470 gear. From looking at the logs and your armory, you are not playing your prot war correctly.
While yes, on some fights it is imperative that you sustain above 35k+ dps. Your job is to actively mitigate as much damage as possible. I can tell from your reforging, gemming and logs that you are not. I can guarantee you that my 470 ilvl war is far easier to heal then your 476 and doing 20k more dps. This should not be the case.
Shield Slam and Revenge should constantly be on CD. You should never Devastate over SS/Rev. It is a dps decrease. Sblock uptime should vary based on the encounter. On some bosses you're actually losing mitigation by keeping a high uptime on Sblock instead of Sbar. You put out 62 heroic strikes and four shield barriers. Four!? If used correctly this is a 100k+ damage soak . Not using it is almost equivalent to a DK not using death strike. Learn it, live it, love it. This isn't Cata anymore.
Reforge ALL items to have either hit or expertise on them until you hit 7.5% on both. Ideally all of your items have mastery on them. Your mastery is very low. I am at 35% with less gear. Why do you have two stamina gems? What is your logic behind this? Why do you reforge some items but not others? Your parry needs to be roughly 2.5x higher than your dodge. Every item needs to be reforged to a stat that benefits you.
No living steel belt buckle on your belt? If you expect to main tank anything, then you need to be prepared to spend money on items you will ultimately replace maybe next week or the next day.
Why are you glyphed for gag order!? Is your guild struggling that much on caster trash that you need a 3s silence over the mobility/dmg boost you get with death from above?
I think your low dps is indicative of an overall misunderstanding of your class. You have the right gear to really crush this tier of content right now, you just need to do a little research and reading to figure out how to.
Here are some great resources that have some contradictory information. You may find it confusing when two sites tell you two different things but I think its great. It allows you to critically analyze the benefits of both sides and decide what works best for you.