loading

Step 4: The build..

I used the Kreg Pocket Hole Jig for all my joints
Assemble the glue up the seat
Measure and cut all members except for back member (will measure this on in place later)
Since this is a symmetrical chair I clamped and cut 2 members at one time (this ensure very consistent and accurate cuts)
Join all members except for back, clamp back in position and mark cut.
Final assembly..
Sand
Stain another day :)
 
That is a creative design on the chair and i like the statics free body diagram you did, but there is one inherent problem with the design of your chair - leaning back. When someone leans back in the chair, all of the dead load on the chair is transferred to the diagonal rear leg. This will create bending stress in this leg that the small cross sectional area will not likely be able to handle over a long period of time- especially poplar. In addition, the use of the pocket hole in this area also further weakens the wood at this intersection.

I would recommend increasing the cross sectional area of this leg to resist bending stress that will result from leaning back. Also, after cutting the angle in the leg, temporarily attach the down-leg to the diagonal leg with a splice and drill a hole through the diagonal leg into the down leg from underneath (in the same plane as the down leg to increase the area in shear in the dowel), and drive a wooden dowel and glue to support that joint. I hope this helps a little for the longevity of your chair.