 Elevation diagram referencing variables used it seismic analysis. Figure 3. Reference drawing of relevant variables for seismic analysis. Concrete dome seismic analysis Dome Diameter = 110’ Dome Height = 37’ Dome Thickness = 3" @ top and 8" @ bottom Reference: Billington 1985 Ed., p. 55 pz = p cos θ sin φ pφ = pθ = 0 Membrane Forces Nφ = −a p k1 cos θ Nφ θ = −a p k2 sin θ Nθ = −a p k3 cos θ Seismic Force Reference: UBC 1985 Edition V = Z S I C K (Formula for the total design lateral force) Z = 1.0 Zone IV (seismic zone factor) C × S  = 0.14 I = 1.5 (Importance factor = hospital) K = 2.0 (Unusual building such as a dome — very conservative) Analysis Therefore, V = 1.0 × 1.5 × 0.14 × 2.0 W = 0.420 W (Note, V = 0.14 W for normal shear wall building!) V = 0.420 × 100 = 42.0 psf (One square foot of shell 8” thick weighs 100 lbs.) The value of p = V = 42.0 psf. For demonstration purposes assume p = 60 psf. This represents earthquake forces in excess of the most severe code requirement by a factor of 1.4. Maximum stress due to Nθ is −64.8 psi; Nφ is −70.6 psi. Maximum bending moment is 909.3 lbs-ft/ft. For a vertical live load of 40 psf in addition to the dead load of the shell the following stresses and moment are obtained. Maximum stress due to Nφ = −82.5 psi; Nθ = −70.7 psi or 0.146.5 psi. The maximum bending moment is 1,588.0 lbs-ft/ft. The maximum allowable compressive force in the concrete is: fc = 1.33 × 0.45 × 4000 psi = −2.394 psi. This is many times greater than the −70.6 psi needed. The forces caused by a major earthquake are considerably less than normal provided for when a dome is designed for nominal vertical loads. Drawing by Dave South