Snap-Through Buckling of Framed Triangulated Domes

The elastic stability problems that develop when a concentrated load is applied to a frictionless joint of a framed triangulated dome were studied. They were found to be of two types: (1) bar stability problems; and (2) joint stability problems. The solutions to the first are given by the Euler critical load. The latter were investigated by developing a general expression for the axial deformation of any component member and by taking the vanishing of the first order variation of the total potential of the system as the criterion for equilibrium. The force-radial displacement relationship at the loaded joint was found to be nonlinear and the critical load was defined to be the maximum force the system can support before the loaded joint snaps-through. A general theory is proposed and two approaches to the solution, one iterative and the other involving a parabolic approximation, are presented. A method for checking the results from the snap-through problem against bar stability and against yielding, is also suggested.