Hello... 7) Can you post a Picture of the "electrical label" on your PS please?
8) How long have you Owned/used the PS?
9) What are the other components you are currently using with this PS? CPU/GPU/MB/drives
The GTX780Ti has the ability to take down a many Power Supplies for sure... it's up to your Graphics settings... with Great Power takes Great Responsibility... Some people brag about reducing a Component to a early death, ( I've had a few chiefton PS's that spit out sparks ) and Some people can live on the edge of components limits (Auto racing, Over clockers)... As others have stated here, You could be operating in a Danger Zone.
Basically Temperature kills a component, this can be from Over current, Over voltage, materials, workmanship or just a higher ambient air temperature... My experience is, if the Power Supply fails you JUST repair it OR replace it, And I have not had multi-component failure or explosion experience when theses events happen. I have worked for two world class manufacturers and have installed, built and maintained High/Low voltage, High/Low Current, Custom, OEM Power Supplies of varying types and purposes, in high ambient, Dirty, and Fast production processes.
Your PS WILL die someday, for what ever reason, BUT understanding the LIMITs and proper maintenance of them can prolong the life of them for years.
Another option is to DownClock the card, SO as too put a Firmware Speed (bump)/Power block on it... this could also be done with the APP/OS software... if you feel your want to create a personal "safety margin" when using the card with the PS.
Is having a GTX780 TI worth the experience in life to YOU? or are you going to let that PS in your case hold that experience back in your memories?
... do you feel lucky kid... Well do ya? ~Dirty Harry