I would like to calculate the size of three I-beams with a span of 6
feet for a three story residential house.
The ceiling in need of support is the floor of the second story that has been dug out in the apartment below.
I would like to keep the height of the beams to a minimum by using heavier beams if possible.

All three beams will be carrying the load of the second story floor.

The sizes of the basement area where the three I- Beams need to go are:

Length 224.0157 in
Width 163.3858 in

The total size of the second story floor is:

Length 454.3307 in
Width 345.2756 in

The size of the third story floor is:

Length 395.2756 in
Width 314.9606 in