LOWER BOUND LIMIT ANALYSIS OF PARABOLIC DOMES BASED ON SPHERICAL ANALYTICAL SOLUTION

The limit analysis of masonry structures is a topic of great interest and relevance, as these structures constitute a large part of the world's historical and cultural heritage. The authors proposed a formulation that allows evaluating the stability of curved structures like arches, vaults, and domes made of masonry and the calculation of the collapse multiplier of the applied loads. The approach has started from the analytical solution of the equilibrium of domes of revolution, obtaining the selfequilibrated stress by interpolating polynomials. Moreover, we calculated the actual elastic response of the structure by the finite element method. Finally, the used strategy superimposed the elastic stress to the self-equilibrated ones as the starting point of the optimization process. The procedure constitutes an effective way of assessing the structural safety and the limit load of structures; such an approach fulfills the requirements of the 'upper bound' theorem of the limit design. The proposed method can give a twofold response, namely the limit multiplier of prescribed load conditions and the safety assessment of a prescribed load level. The paper presented some examples of parabolical domes subjected to self-weight and variable loads; by applying the procedure, we calculated the load limits and the corresponding residual stress. Moreover, the thrust line at the incoming collapse is also derived.