Buckling Analysis of Concrete Spherical Shells

In some simple two-dimensional structures it is sufficient to determine only the lowest value of the load at which buckling commences. However, in the case of shells, it may be also necessary to investigate the postbuckling behavior because it has an important bearing on the magnitude of the failure load. The importance of the postbuckling behavior, which the small deflection theory of buckling is not capable of predicting, was discovered as a consequence of attempts to correlate experimental results with analytical predictions. Poor correlation between the results of theory and experiment exists when both principal membrane forces are compressive, as in the case of cylindrical shells under axial compressive load; cylindrical shells under distributed load normal to the surface, which causes bending; and domes under inward radial pressure. If both the principal membrane forces are compressive, they tend to increase with deformation of the shell. After the initial buckling, the shell can only transmit loads smaller than the initial buckling load. This is particularly true for concrete shells because of creep and deviation of the actual shape of the shell from the assumed theoretical surface. Good correlation exists when one of the principal membrane forces is tensile. If one of these forces is tensile, it tends to return the shell back to its original position, thus enabling it to carry loads greater than the initial buckling load. In general, the value of the buckling load depends on shell geometry, type of restraint at boundary, material properties of shell, the location of reinforcing steel, and the type of load.