Masonry structural modelling needs of a completely different methodology from the ones adopted for ductile structures. In fact, the concepts of strength, stiffness and elastic stability, fundamental for the latter structures, play a marginal role in masonry mechanics. In this respect, Heyman's theory, gives a modern turn to the old methods of masonry design, adopting a set of very simple and clear mechanical hypotheses. In these papers, the basic ingredients of a new method based on unilateral equilibrium and rigid block kinematics, which may allow the implementation of Heyman's model for masonry on a computer, is introduced. In particular a simple method based on energy minimisation, with the possibility of combining the effects of loads and settlements on real masonry structures, is developed.

In this paper an homogenization procedure of a Vierendeel girders with elastic joints is shown. The method is based on the Stephen transfer matrix analysis and employs as substitute continuum a polar Timoshenko beam. The polar character of the equivalent beam arises quite naturally from the analysis of the pure bending eigenvector components of the girder force transfer matrix. Through the girder unit cell, two bending moments are transmitted: one is generated by the couple of axial forces acting\ud on each nodal section of the beam, the other is produced by the moments applied at the nodes of every ones by the adjacent cells and is modelled as the resultant of the micro-polar moments. Transfer force eigenvector analysis reveals that the unit cell bends maintaining the webs undeformed, a property that allows evaluating both the bending stiffnesses and the equivalent material micro-polar scale parameter by means of straightforward equations. The accuracy of the proposed method is verified by comparing the predictions of the homogenized model with literature data and with the results of the analysis of a series of girders carried out by the finite element method

Rocking of freestanding objects: theoretical and experimental comparisons