Regardless of what goal posts you shift the analogy is invalid. In building structures there's a concept called the square-cube effect.
Say for example we have an umbrella shaped shelter that is 10 ft & 10 ft deep with a flat concrete roof 1 ft thick and a single center column having an area of 1ft2.
Concrete is roughly 150 Lbs/ft3, the total load on the column is about 15 kips, and the compressive stress is 15 kips/ft2
Note: 1 kip = 1,000 lbs
Take the same structure and increase the size 3 fold, overall size increases to 30 ft in each dimension; The roof slab would increase in thickness to by 3 fold as well resulting in a slab with about 2700 ft3, and a weight of 405 kips. The area of the center column would increase to 9 ft2. The column stress would be 45 kips, which is three times that of the original smaller structure. In order to effect the same compressive stress , the column area would have to triple to 27 ft2 with column dimension increasing to 5.2 ft on each side.
In other words even using the same materials in you "analogy" would result in drastically different results. The problem is compounded just by using different materials... A 1 ft3 volume of concrete can be loaded with many times it's own weight, however a slab of concrete the size of a building may only support double it's own weight.