My computer shuts off for no reason

I built this computer a few months ago and when i play Bf4 it will just shut off. i upgraded my power supply to 600 watts and my gpu and cpu aren't over heating

computer specs

Amd athlon x4 740

R7 260x 

EVGA 600b

Mis motherboard ( too lazy to put exact)

corsair vengence 8gb

fractal design arc midi 

Any sugestions on what is going wrong would be great

Ok, several questions now:

Does it bluescreen? How do you know its not overheating? Did you check cpu temp limit in bios? When does the pc shut off (intense action, no action, does it take roughly the same amount of time before it shuts off)?

Another thing I would as of you is to do OCCT tests and post the results.

(you could also run memtest during the night or work/uni/school hours)

oh, and try updating gpu drivers.

i have monitored the cpu and gpu temps and the highest they ever got was 50c

the screen goes black all noise stops, the fans keep running and then the computer restarts

all drivers are up to date

Are you plugging it straight into the wall plug? It could be your power bar/protector. 

Have you tried running burn-in type tests to see if it crashes with those? Run Prime95 to see if the CPU is the issue. Run Furmark to see if it is your GPU. If both work fine for a decent time period (longer than it would usually take to crash), then your issue is elsewhere.

What make/model is the PSU you have put in? Wattage isn't the most important thing - what is its efficiency and how are the amps distributed over the rails, particularly 12v rail/s?