Self-Supporting Dome

If you use beams to build a circular roof each beam under pressure is prone to failure. One solution is to connect the beams with hooped beams to distirbute the load to neighbouring beams creating a more stable roof,

However when span increases the beams begin to act like a net and center beginsto sag. If you make the beams thicker to be more resistant to bending and more stable roof but lowers interior height

If you arch the roof upwards it redirects the load along the beam towards the side, allowing smaller and efficient beams to be used.

This creates a spatial grid shell, a big spatial grid can still collapse if pressure is concentrated in one spot so build two layers of grid shells to work together sharing the load and reinforcing eachother.