Bench seat strength question
First, as this is my first post here, allow me to give a bit of background: I am a self-taught hobbyist woodworker - that is, everything I know I have learned from TV Woodworking shows, found on the internet, or figured out for myself. I have been doing woodworking as a hobby for about three years now, primarily just furniture for my own use. I would describe my skill level as intermediate - My designs all seem to work, and look good enough to get praise from family and friends (not that that means much), but I run into plenty of problems getting them together that I have to work around, and the finished product has any number of flaws. I have signed up for this message board in the hope that it will be a good resource for filling in the many gaps in my knowledge.
On to the specific question for this post. I am currently working on building a love seat for my brother. As per his request, the seat itself measures 24" deep by 42" wide. I realize this is quite deep for a standard seat, but he likes to sit indian style, and wanted something deep enough to support his feet comfortably. The seat bottom is a slatted design, with the slats being birch, 3/4" x 1 1/2", spaced approximately 1" apart. The slats are mortised into rails measuring 2 1/2" tall by 1 1/8" thick, which in turn are mortised into legs measuring 3" x 1 1/8"
My concern is that I have no idea how much weight such a design would theoretically be capable of holding. Obviously I would want it to support at least two adults comfortably. Are the 3/4" boards thick enough to do this, given their 2' span, or do I need to look at reinforcing the design somehow, perhaps with a thicker cross beam under the slats or the like? I am attaching a png of the design I am using. Thanks for any feedback.