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• A timber system is proposed for the seismic retrofit of URM buildings. • Analytical equations are derived for design against different failure modes. • Wall in-plane and out-of-plane responses, diaphragms and connections are addressed. • The proposed equations are applied to case-study buildings and structural members. • Good agreement between analytical calculations and experimental data is shown. An innovative timber retrofit was investigated at the EUCENTRE and at the University of Pavia, Italy, as part of a comprehensive research campaign on the seismic vulnerability of existing unreinforced masonry buildings subjected to induced seismicity in The Netherlands. The retrofit system consists of timber frames, connected to the masonry piers and to the floor diaphragms, and oriented-strand board sheathing nailed to the frames and to flexible timber diaphragms. Starting from the main critical aspects observed in experimental tests, the proposed solution was conceived to enhance the in-plane and out-of-plane capacities of masonry piers, improve the overall wall-to-diaphragm connections, increase the floor diaphragm stiffness and strength, and allow possible integration with energy efficiency upgrades. This paper, the first of a series of two, focuses on the conceptual bases of the seismic retrofit system and on the analytical equations that can be used for the design of its components. Moreover, a step-by-step design procedure is presented to guide the reader through the application of these equations. A companion paper [1] will discuss the validation of the analytical formulation with the experimental data from quasi-static cyclic and dynamic shake-table tests on building components and complete specimens. [ABSTRACT FROM AUTHOR]

• Continuum damage and brick-to-brick modeling techniques are compared. • A masonry wall strengthened with bed joint reinforced repointing is considered. • For un-strengthened case, all models provide accurate predictions of crack pattern. • For strengthened case, the simplified brick-to-brick model provides the best results. • Modelling of pre-damage should be considered with care. Bed joint reinforced repointing is a retrofitting technique for unreinforced masonry structures that is commonly applied in the Netherlands to repair settlement-induced damage. Using this technique, the bed joints of masonry walls are reinforced with steel rebars that are embedded in a high strength repair mortar. Due to the increase of induced seismic events in the northern part of the Netherlands, an experimental study was carried out at Delft University of Technology to investigate the performance of this retrofitting technique for combined settlement and seismic loading. This paper aims to simulate the experimental results, with a focus on the comparison of different finite element modelling approaches for studying both un-strengthened and strengthened full-scale tested walls. To that end, three different models are investigated – comprising both macro (continuum) and simplified and detailed micro (brick-to-brick) modelling approaches. The bricks and mortar joints are modelled as one homogenous continuum in the macro model, whereas in the two brick-to-brick models these structural components are modelled separately, with the detailed model including interface elements to simulate the brick–mortar bonds. Nonlinear pushover analyses are subsequently carried out using all three modelling approaches, for both monotonic and cyclic loading cases. Based on these analyses, the detailed brick-to-brick model was found unsuitable to simulate the strengthened wall because cracks in the model mainly occur in the form of opening of the brick–mortar bond interfaces, while smeared cracking in the plane stress elements of the mortar joints is very limited. Similarly, the continuum damage model was found to be inaccurate when pre-existing damage in the experiment needed to be taken into account. The continuum damage model also showed lower axial stresses in the rebars, compared with the simplified brick-to-brick model, as the former does not allow for the direct assignment of material properties for the high strength repair mortar in the strengthened joints. [ABSTRACT FROM AUTHOR]