Connecting floor drain to sump pump

Hi guys, After sandy, my insurance company dropped me and the new one I found wants me to put in a sump pump. I'm going to install it in the utility room which has a door to the outside then 3 steps up to grade. In the stair well is a drain that goes nowhere. I want to put a drain in the stairwell, run the pipe into the utility room, put another floor drain in, then pipe to the pit. Is it a bad idea to put a trap near the stairwell drain? I figured it would keep any bugs from getting in the house. Or should I put the trap inside the door to prevent freezing? was gonna use 4" pipe throughout. There will be 2 pumps in the pit, 1 primary and 1 battery backup. Any help would be appreciated... Thanks - John

If its just a line running to a sump pump pit you dont need any traps at all.

I was only considering a trap to try and keep bugs from coming in through the outside drain to the inside drain. Maybe a Check Valve instead?

bug won't be a problem