Dome vs. Flat Roof 2D — Snow/Wind Load Capacity Comparison

This 2D side-view cross-section places a flat roof beam and a masonry dome under the identical span and load, the same physics as the paired 3D voussoir model reduced to the cross-section an engineer would sketch on paper. Raising the snow or wind load grows the flat roof's bending moment and forces its beam depth up as the square root of that moment, visibly sagging and reddening at the tension face; the dome instead carries the same load as pure compression thrust flowing down its curve to the walls, needing only a thin shell because masonry resists compression far better than tension. A rise/span slider shows how a taller dome shortens the thrust's lever arm and shrinks the required shell thickness even further, while the live readouts and stress chart make the resulting material-efficiency gap between bending and compression load paths explicit.