Beam structure to support two joists
Hello, this is my first time posting. I have a load bearing wall that I want to remove. The critical load it is carring is two sets of neighboring joists, a span of 32". Having concluding that I can't successfully replace or reinforce/splice these joists so their load can be carried by other walls, what I would like to do is replace this wall with a beam below the joists, about 4' long. The ends of that beam would be attached with hangers to 8' long members, running perpendicular to the beam. These 8' members are supported by posts/studs at each end (a total of four posts). Where the posts are located can easily be integrated into existing walls, so that I have a clear area where the bearing wall used to be.
Here's a sketch of the current situation, showing the framing: joists, brick wall and the supporting wall. The far ends of the joists are properly supported (not shown). All joists are full 2" thick by 7-1/2" tall. The light wood colored joists are the ones the need support. The black cylinder represents a toilet drain above -- presumably one of these joists was cut to allow for this drain, way back when.
And here's a sketch of what I'm proposing to do:
Questions that I have are:
1. what should be the dimension of the 4' long beam
2. what should be the dimension of the two 8' long carrying beams?
3. is there a better way to do this?