If a dome is a hemisphere (geodesic or otherwise), then extra load produces an outward stress at the opening, leading to a crack at the bottom. If a dome is close to a sphere, then extra load produces an inward stress at the opening, leading to a crash at the bottom. There may be a point where an outward force and an inward force cancel out, showing only a downward force by the gravity of the dome. Maybe domes like the former Expo '67 U.S. Pavilion and the Epcot Centre have this "Golden Dome Shape".
angle of dome = pi radian (180 degrees)
bottom opening = diameter (regular dome)
outward stress > inward stress
angle of dome < SA radian (SA*pi/180 degrees)
bottom opening << diameter (baseball dome)
outward stress > inward stress
angle of dome = SA radian (SA*pi/180 degrees) "Sunatori Angle"
bottom opening < diameter (Golden Dome Shape)
outward stress = inward stress
angle of dome > SA radian (SA*pi/180 degrees)
bottom opening << diameter
outward stress < inward stress
U.S. Patent 3 203 144 is limited to geodesic domes only (Special Theory of Domes). I am wondering how the exact angle of dome to achieve
outward stress = inward stress
could be calculated, assuming a cut hollow sphere with a uniform distribution of mass along the surface. Such "Sunatori Angle" would be considered a part of a more universal solution, i.e., The General Theory of Domes.
