It depends what the place is made of. Right now in my apartment, I am also on the 2nd floor. I have a 125 gallon, a 75 gallon, as well as a 90 gallon. I am about to put in another at 70 gallons. My building is made of concrete and I check every few weeks with a level to make sure nothing is sinking or bending. If your place is concrete, id say it SHOULD, and I stress SHOULD be safe, as long as the aquarium is long and not high, thus allowing the weight to spread over a long distance. If you do not have concrete, it is an absolute no-no. A friend of mine was in a 2nd floor building made of mostly wood, and after about 1 year of having his 125 gallon, the floor started to give beneath the tank. Eventually the floor just can't take it when its wood. There is not an exact guide on this, only recommendations. In the end however, whatever you decide on, make sure you purchase insurance. I have a million dollars insurance and it costs me around 150 dollars a year.
Hope this helps!
EDIT: For clarity