Assessment the stability of masonry walls by the transfer-matrix method

• Numerical procedure has been proposed for the assessment of the stability of masonry walls.
• The stability theory has been formulated using the relative form description.
• Algorithms were proposed to solve the equilibrium equation of the problem.
• The convergence has been studied for the cases of material and stability failures.
• The developed method provides a powerful tool to solve a wide range of problems.

Masonry walls are very sensitive to flexural effects due to low tensile strength which, in turn, greatly influences the load bearing capacity under compression. The main source of flexural effects may results from the eccentric loading at the ends of the wall or from any lateral loading like the wind action, the earth pressure, or the second order effect of the applied actions. Several analytical solutions were proposed in literature to solve the differential equation of the problem, but those solutions were limited to special conditions. In the current contribution, a general formulation for the non-linear stability problem has been formulated numerically based on the transfer-matrix method. Despite the method is out of professional use today and don’t possess the potential and flexibility of the finite elements but for the current addressed problem, it is still the most efficient.A relative form description has been introduced to formulate the stability theory of masonry walls. This description has been used to minimize the dimensions of matrixes in the transfer-matrix method and to produce the equations in a compact form. The algorithms of the method have been derived for general boundary and loading conditions with a user-defined non-linear material model. Algorithms and solution procedures have been explained and implemented into a computer code. The convergence of the iterative solution has been studied with clear definition for the cases at which the stability or material failures occur. The results of the developed solution procedure have been validated by comparing them with the existing solutions and the experimental results. The developed solution procedure provides a powerful tool to solve a wide range of problems related to stability of masonry walls and to check the existing empirical methods.