Need more info. Is the tank parallel or perpendicular to the joists? How far apart are the joists? Size of joists? You want to set the tank evenly over the joists. I have heard that some people set their stands on 3/4 inch plywood to even out the weight, but I am not sure if that helps much. I decided to put my 240 gallon in the garage because of the weight.
240 X 8.6 = 2064 lbs
live rock = 370 lbs
tank/stand = 200 lbs
about 2600 lbs. That's more than a ton of weight so I thought that the concrete floor was the safest option. Most homes should be able to handle the weight of a 120, but do some research before you set it up. Tell us about the joists.
Jay