Fundamentals of Statics

Basics of Statics of masonry solids and structures are the subject of the chapter. Masonry behavior is strongly influenced by the dramatically lower strength in tension than in compression. Masonry structures can thus suffer cracks generating displacement fields, called mechanisms, which develop without any internal opposition of the material. Collapse can occur without any material failure. The Heyman masonry model, the idealized rigid in compression no tension material, is fruitfully assumed as basis of the approach followed in the chapter. The extension of this model to the masonry continuum is then developed. Strains and detachments occurring in a no tension masonry solid can thus obtain a suitable mathematical formulation together with the admissible equilibrium. A proper virtual work equation, that considers the boundary of the body including the crack surfaces, as a condition only on the loads, both necessary and sufficient to the existence of the masonry equilibrium, can be formulated. This last condition governs the collapse strength of masonry structures. The notion of the minimum thrust, from both static and kinematical approaches, is then introduced, widening the field of application of the Limit Analysis also to the study of the actual stress states. In this context, it follows that weight and geometry represent the essential elements in the strength of masonry structures. Further, it will be also proven that, if a structure under its own weight is stable, the k times magnified copy of the same structure will also be stable. This result, thoroughly discussed in the chapter, matches the so called theory of Proportions that has constantly ruled the Design in the history of Architecture. A critical analysis of the recent failure of the cathedral of Noto, in Sicily (Italy), useful to a better understanding of the above discussed mechanical concepts, ends the chapter.