Buckling of Shallow Spherical Concrete Domes under Gravity and Earthquake Loads

Buckling analysis of spherical concrete domes constructed over prestressed concrete tanks subjected to gravity and earthquake load combinations is complex due to the sensitivity of spherical dome buckling to geometric imperfection, the effect of creep and shrinkage on amplifying the deflection of the dome (increasing the radius of curvature of the deformed dome and reducing the buckling resistance), and the geometric and material nonlinearity of the concrete dome. Study of imperfections has shown that imperfections that increase the average radius of curvature in an area the size of an elastic buckle have the highest impact in reducing buckling strength; thus, the problem of buckling of the concrete dome is reducible to the snap-through buckling of a shallow cap equal in size to an elastic buckle of the dome. In this paper, the buckling of a shallow cap subjected to gravity and seismic load combinations is determined using nonlinear geometry, material nonlinearity of concrete (accounting for softening and cracking in tension and microcracking and crushing in compression), and time-dependent creep and shrinkage of concrete. The analysis is performed in three steps: in the first step, the cap is analyzed for gravity loads; in the second step, the cap is analyzed for the effects of creep and shrinkage strains; and in the third step, the earthquake load is applied until the snap-through buckling occurs. The analysis was carried out on a set of domes designed for gravity load combinations alone. These domes cover the extremes of size and rise of the domes that are currently constructed over prestressed concrete tanks. The results show that the majority of existing domes that are not in high-seismicity zones and are designed for gravity load combinations have capacity for earthquake loading. The results are also of value in the design of new domes for load combinations that include earthquake loading.