I need some knowledge on a Direct3d11 crash i am getting.

I don't think so, there are other people experienced this problem (even with great gpus) before all over the steam community so its probably the game itself.
But can you try lowering your direct x version?

Perhaps so, here's your first start:
http://www.pcgameshardware.de/Bioshock-Infinite-PC-235561/Tests/Bioshock-Infinite-Test-Grafikkarte-Benchmark-1061764/2/
It's german but you can tell by the chart below the page

I don't believe so since you have the latest video card with extra features, it's just the mechanism in the game and your steam app conflicting to each other because they have different direct x versions. Have you tried those steps I showed you in the link?

good idea, you can do that before trying those steps in the steam link

Check inside, if you're able to operate computer, then it's fine. Play other games to do some testing.

I'm providing another solution here that's not really obvious, and I don't think most have figured out the deeper meaning of the TDR issue.

My error also said something like "the direct3d 11 device has been removed or has crashed", but looking closer this old Windows "display driver has stopped working and has been recovered" seemed to be the culprit - saw the balloon message once in a while.

Now, it seems common to blame everything from Steam to drivers to nvidia for this, but looking closer into the matter those TDR timeouts turned out to be more of a symptom than the cause. TDR was introduced by Windows to avoid those BSOD thingys. So don't kill the messenger, my good friends

I tried ALL of what's in this thread (except rolling back to pre-280.xx drivers), even increased the TDR levels to ridiculous heights in the registry. Nothing worked.

Here is what worked, though:

I realized - from something posted on the nvidia forums - that the cause could be some overclocking (OC) that caused the real instability. Only BioShock Infinite brought it out more readily ... Typical company white-washing, right? Luckily not

So I thought ... do I OC my stuff? Kinda forgot my BIOS settings, but wasn't that old Gforce 450 GTS GS not OC'ed from the factory? Indeed I found something.

My ASUS BIOS did have aggressive settings on both CPU and Memory, or CPU Level-Up as it's called in my BIOS. Lowering to normal speeds helped a little (added 1 minute or so before crashing).

When I finally UNDERclocked my graphics card everything fell into place. I went from a crash every minute or so (literally!) to BioShock Infinite NEVER crashing on me. Not a single crash since the underclocking of the too-aggressive factory settings on that Gainward card. Just so you know: this card was delivered with a factory OC on it, and back in the days it actually didn't crash that much with the games present.

On my rig and for my Nvidia card I could use the "Expert Tool" to underclock. In my case I chose not to believe the "Safe Mode Settings". They were far too high! For my (Gainward) NVidia GTS 450 GS these settings provide rock solid stability:

Core Clock setting 851 MHz
Memory Clock setting 1892 MHz
Shader Clock setting 1702 MHz

("Safe Mode" settings were:

Core Clock setting 930 MHz
Memory Clock setting 2000 MHz
Shader Clock setting 1860 MHz)

Now, just a word about those numbers. I have NOT toyed around with the settings to find any optimal ones. These just provided the needed stability and I could play through ALL of the game afterwards without a single crash.

I'll probably track down the normal GTS 450 clock speeds if I want to crank out a little more performance. So far I'm just happy the entire problem has gone away