Funicular analysis of symmetric arches with finite friction accounting for stereotomy

In this contribution the funicular analysis of symmetric masonry arches is performed by accounting for stereotomy, as well as for the presence of Coulomb’s friction at the interfaces between the voussoirs. The classical thrust network analysis approach is then enhanced by removing the hypothesis that the friction coefficient is infinite. The procedure presented here handles networks with any topology, fixed plane projection and loads applied at the nodes, whose equilibrium conditions are managed by exploiting the force density method. At each joint, a set of local constraints is enforced to restrain the shear-to-normal component ratio of the force between two adjacent voussoirs. The minimization/maximization of the horizontal thrusts, formulated in terms of applicate of the restrained nodes, is achieved by solving the corresponding multi-constrained minimization/maximization problem through sequential convex programming. The results obtained via this funicular method are validated by means of a graphical procedure based on the lower bound theorem of limit analysis, known as Durand-Claye method, by considering a masonry arch with nonconventional stereotomy.