A simple micro-mechanical model for the homogenised limit analysis of in-plane loaded masonry is proposed. Assuming brickwork under plane stress condition and adopting a polynomial expansion for the 2D stress field, a linear optimisation problem is derived on the elementary cell in order to recover the homogenised failure surface of the brickwork. Different models of higher accuracy are obtained by increasing the degree of the polynomial approximation. Several cases of technical interest are treated in detail, varying both the geometrical characteristics of the cell and the mechanical properties of the components. The model is validated through comparisons with experimental data and kinematic approaches; the comparison with experimental data has the aim to reproduce in a qualitative way the shape of the failure surface, since 3D effects and brittle behaviour of bricks can not be taken into consideration with the model proposed. In an accompanying paper, the homogenised failure surfaces here obtained are implemented in a finite element limit analysis code and relevant structural examples are treated both with a lower and an upper bound approach

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This paper addresses the usage of a simplified homogenization technique for the analysis of masonry subjected to out-of-plane loading. The anisotropic failure surface, based on the definition of a polynomial representation of the stress tensor components in a finite number of sub-domains, is combined with finite element triangular elements employed for the upper and lower bound limit analyses. Several comparisons between the proposed model and experimental data available in the literature are presented, for wallettes subjected to bending at different orientations and for different panels loaded out-of-plane. The limit analysis results allow to identify the distribution of internal forces at critical sections and to obtain the collapse modes, as well as the failure loads. Excellent results are found in all cases, indicating that the proposed simple tool is adequate for the safety assessment of out-of-plane loaded masonry panels. The combined usage of upper and lower bound approaches, and their respective simplifications, allow to define a narrow interval for the real collapse load.

A simple micro-mechanical model for the homogenised limit analysis of in-plane loaded masonry is proposed. Assuming brickwork under plane stress condition and adopting a polynomial expansion for the 2D stress field, a linear optimisation problem is derived on the elementary cell in order to recover the homogenised failure surface of the brickwork. Different models of higher accuracy are obtained by increasing the degree of the polynomial approximation. Several cases of technical interest are treated in detail, varying both the geometrical characteristics of the cell and the mechanical properties of the components. The model is validated through comparisons with experimental data and kinematic approaches; the comparison with experimental data has the aim to reproduce in a qualitative way the shape of the failure surface, since 3D effects and brittle behaviour of bricks can not be taken into consideration with the model proposed.In an accompanying paper, the homogenised failure surfaces here obtained are implemented in a finite element limit analysis code and relevant structural examples are treated both with a lower and an upper bound approach.