I drafted this myself in Blender. Dado joints are depicted, mortise/tenon joints and bolted joints are not. This is to-scale, planned with douglas fir 2x4s and jute webbing/coil spring/4 way tie construction/ and then tie on cushions. Dimensions are about 31" x 7.5' x 36".
I have never built a couch (or any furniture) before, but have been studying woodworking a lot, so I am looking mostly for tips on how I might improve this, or especially, if it's structurally weak in any way.
I would build the bottom grid where the cushions sit with mortise and tenon joints. Then attach it to the back legs and side legs using a dado. The two short legs shouldn't receive much lateral stress - You can probably get away with just a mortise and tenon joint there. If you change the orientation of the long horizontal boards, you could eliminate the middle legs all together (a 2x4 will only sag about 0.1 inches with 250 pounds directly in the middle). I put a 10 degree angle on the back, which is probably too much, but it gives you an idea.
If you attach the back to the base using a glued dado, it isn't going to rack at all.
I would say you don't have enough triangles.
The short front legs are the most obvious place, they will tend to be a weak spot. They only have one point of attachment and that is on the end, the weakest joint.
I would put triangle pieces on all four of the legs in the middle and attach to the cross piece under the seat.
There is also a chance of racking the whole thing from side to side (the long way). For that I would put a board (an other triangle) from the bottom of the feet on the outside (in the back) to the next upper corner.
I'd say you probably want some triangular braces under where the legs meet the lower (front to back) supports. They probably only need to be a couple of inches deep/tall, glued/pinned/screwed into the legs and underside of the supports.
It may not seem like they'd do much, but you should find they'll add a lot of rigidity. Anywhere you can add in triangular bracing without spoiling the look is going to help against the kind of lateral racking forces you're going to get when people stand up and sit down, and are moving around on the couch.
Your design needs a wee bit of work before it becomes a complete or workable design. Design is an iterative process of which you have made the first iteration. Two or three more cycles and you should be ready to begin construction. Some things that I think you should consider:
Others have addressed the fact that the long horizontals in the seat structure will deflect vertically; they will also be have large horizontal loads induced by the jute webbing.
Well constructed lap joints as well as mortise and tenons can be considered as rigid joints lessening or eliminating the need for triangular bracing (think Danish Modern furniture from the mid 20th century.)
In your next iteration make the 2x4's their correct size (1 1/5 x 3 1/2) and consider the orientation of your mortice and tenon joints. Also will they be blind or through tenons?
Although many woodworkers eschew mechanical fasteners, you might consider the concept of "screw and glue" making sure not to screw into end grain.
Even if the structure for the back remains vertical, you still need to consider the cushioning to be inclined. With your 36" depth for the seat, your cushioning should be 14" thick at its base. This suggests that the seat cushion is going to thicker and that the seat structure will have to be lowered considerably.
Good luck on your next iteration.
I really think you need an angle in the back leg. You're going to have your guests sitting pretty upright if you don't and it won't be very comfortable.
