Calculate bedframe strength

This is the bed frame that I have build now, the part in red is something I have created but did not dare to attach it yet.

I have used Spruce wood for everything, and the long side of the frame is attached to the short side via dowels and two large wood screws on each side.

Now my question is about the load on the frame that I created (see the arrow pointing to the rectangular shaped object).

My feeling says that I need to add extra support to that frame, and that I need to add extra support between the three components as well to create a stable frame.
However, to gain trust in my schema I would like to calculate some stresses, or deflections that the beams will undergo due to the static load and dynamic load of me and my partner.

I have found some equations to calculate some part of the load, but I dont think this will capture all the stresses. Can somebody point me in the right direction?

PS: Thanks for the tips and the comments guys, I hope the question is now better suited for this forum.