Hey, I'm new to the forum but have an architecture degree so I hope at the very least to give you some basic insight.
The image attached shows several points you can concentrate on. The main property of wood that you don't have in stone for example is its pulling force, meaning that if stationed length-wise horizontally, the force applied to it from above can move along its fibres. When stationed vertically though, wood has a quite decent push force, meaning it can hold good wait from above.
As any construction beam, the longer ahorizontal beam is with no support from below, the taller it needs to be. So one tip would be to cut away from the sides of the beams put on the roof so they'd be as tall and light as possible. Refer to an H beam in steel construction - the weight of the beam is minimized while its strength is maximized by putting most material at the extreme ends(I think that I beam would be a better name for it since the extreme ends are situated above and below, and not on the sides)
You can see on my sketch some arrows, those are meant to indicate the direction of the force. In order to have an integral structure, make sure that each force from above coming from the weight of the structure, will have a clear path downwards, and will have the correct counterforce. In this case I've annotated the main diagonal beams - make sure they have a counterforce at the base(burrying the beams to a decent depth might do the trick though pay attention to rot!) and with the triangles formed between the diagonal, vertical and horizontal beams, make them fixed onto eachother.
A final detail I would pay attention to is the rectangle on the north and south facing(nonexistant) walls - any substantial horizontal force will knock your structure down sideways like a house of cards, since there is no element or fixed joints to support your beams. I sugest either creating fixed triangle joints at the top of the vertical beams connecting to the horizontal beams, or creating an x on one side of the structure like i've shown on the sketch.
Good luck!