Figure 1. The elevation profile of wind forces affecting a concrete dome.
Concrete dome wind analysis
Commercial dome building 30 feet high in exposure C — the most severe exposure in open, flat terrain. Using wind design pressure from UBC 1985 Edition, section 2311.d, of 70 MPH.
- p = Ce Cq Qs I
- I = 1.0 (commercial building)
- Qs = 13 psf (pressure from wind)
- Ce = 1.3 (building height 30-feet, exposure C)
- Cq = 1.3 (method 2)
Therefore, p = 1.3 × 1.3 × 1.3 psf × 1.0 = 22 psf
Assume same building from Example 1 and same exposure but with a wind speed of 300 MPH. (Reference: Fine, Mark, Handbook of Concrete Engineering; Nan Nostrand Reinhold, 1974.)
- p = ½ Cs Ca Cg P Vh2 (H/h)2/φ
Assume everything is constant except the wind speed.
- P = C Vh2 = 22 psf for V = 70 MPH (example 1)
- Therefore, C = 22 / 702 = 0.00449
- Then, p = 0.00449 Vh2 for V = 300 MPH; p = 404 psf
The maximum concrete stress in a dome 100 feet in diameter by 30 feet high with p = 400 psf is 1,098 psi compression. From the “Concrete dome seismic analysis” example (below) we see the allowable stress is significantly higher at 2,394 psi.