Published in: J. Elasticity, 106 (2012), 165–188 Equilibrium problems and limit analysis of masonry beams Massimiliano Lucchesi, # Miroslav ˇ Silhav´ y ## & Nicola Zani # Abstract. We consider no-tension beams with the constitutiveequation from [11, 14]. After stating some results about the solution to the boundary value problem, the limit analysis for this kind of bodies is outlined, based on energetic considerations. The static and kinematic theorems of limit analysis [1] are examined from this point of view [8]. It is seen that the kinematic theorem does not always hold but can be proved under some hypotheses that are frequently met in applications. Keywords: Beams, collapse, limit analysis, minimum energy AMS Subject Classifications: 74H20, 74H25, 74H40 Contents 1 Introduction  1 2 Beams  3 3 The stored energy of a no-tension beam  8 4 Affine loads and limit analysis  13 5 Examples  18 References  23 1 Introduction The study of the statics of masonry buildings firstly needs a constitutive equation which can model the main characteristics of this material, especially its differing responses under tension and compression. To this aim the so-called masonry-like or no-tension model has been proposed which assumes the material to be linear elastic in compression and incapable to sustain traction. More precisely, it is assumed that the stress tensor is negative semidefinite and that the strain tensor is the sum of two parts: the former depends linearly on the stress, the latter is orthogonal to the stress and positive semidefinite [3]. Because of the constrain on the stress the existence of the solution to the equilibrium problem requires the loads to satisfy some compatibility conditions; moreover the uniqueness of the solution is guaranteed for the stress but not for the strain and displacements. With appropriate numerical techniques this constitutive model has proven to be quite well-suited to studying the static # Dipartimento di Costruzioni, Piazza Brunelleschi 6, Universit` a di Firenze, 50121 Firenze, Italy, massimiliano.lucchesi@unifi.it, nicola.zani@unifi.it ## Institute of Mathematics the AV ˇ CR, ˇ Zitn´ a 25, 115 67 Prague 1, Czech Republic, silhavy@math.cas.cz