Shear to elastic modulus ratio in unreinforced masonry

In the seismic design of unreinforced masonry walls, the elastic modulus E and shear modulus G are essential parameters for the calculation of the in-plane wall stiffness. Current codes provide empirical estimates of the elastic modulus and furthermore a ratio of shear to elastic modulus G/E. This ratio, however, is not based on scientific evidence and consensus concerning the value and influencing parameters is lacking. This article develops a closed-form formulation for the G/E ratio of masonry walls with running bond pattern. The formulation is derived by using an analytical homogenization tech-nique already employed in the literature and modified here to consider the finite thick-ness of the wall. The resulting formulation is based on the geometry of the units, the thickness of the joints and the elastic moduli of units and joints. The resulting analytical expression for the G/E ratio is used to assess the influence of various parameters and validated by comparing it to finite element simulations.