In order to understand the behaviour of such constructions and in correctly interpreting the symptoms of possible disease, masonry structures are often modeled by means of the assumption of the so-called no tension (NT) material, which is a simple and complete phenomenological model for interpreting the behaviour of solids made by non-cohesive compact materials.

A reliable extension to NT structures of basic theoretical approaches for elastic structures and limit analysis approaches has been performed and discussed. Nevertheless, the non-linearity of the behaviour of the basic material and of the overall behaviour of the masonry construction, require a deeper insight into the question, since only an unsatisfactory knowledge of structural safety may be obtained by deterministic approaches, which despite the no-tension is a highly robust approach, in that only a few mechanical parameters need to be sought, no more than the elastic compliance coefficients in compression. When surveying existing masonry arches, the major sources of uncertainty can be identified in the load pattern and in the geometry of the arcade (middle line, thickness, etc.).

In the paper a probabilistic procedure for safety assessment of such structures is outlined. Kinematic and static theorems of stochastic limit analysis proved by Augusti and Baratta [1,2] are readapted to work with no-tension structures. It is demonstrated in the paper that the kinematic theorem, while yielding a lower (unsafe) bound on the collapse probability, can be applied in a straightforward way. On the other side, the static theorem, yielding an upper (safe) bound on the collapse probability, follows a path leading to a bilateral threshold crossing problem [3], that can be dealt with and solved by classical methods, after the stochastic differential equation ruling the stress funicular line of the applied load is solved. This solution is attained by expressing the statistical characters (expectation and autocorrelation functions) of the random stress line, from which all other statistics one needs to estimate the threshold crossing rates can be drawn.

1

G. Augusti, A. Baratta, "Limit Analysis of Structures with Stochastic Strength Variations", Journ. Struct. Mech., 1(1), 43-62, 1972. doi:10.1080/03601217208905332

2

G. Augusti, A. Baratta, "Theory Of Probability and Limit Analysis of Structures under Multiparameter Loading", Proc. Int. Symp. Problems of Plasticity, Warsaw, 347-364, 1972.

3

G. Augusti, A. Baratta, F. Casciati, "Probabilistic Methods in Structural Engineering", Chapman & Hall, London, 1984.

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